[cvxopt] 01/64: Imported Upstream version 0.8.2
Andreas Tille
tille at debian.org
Wed Jul 20 11:23:43 UTC 2016
This is an automated email from the git hooks/post-receive script.
tille pushed a commit to branch master
in repository cvxopt.
commit 75f86c3472baa31abfb0890093cd034ada980106
Author: Andreas Tille <tille at debian.org>
Date: Wed Jul 20 08:26:47 2016 +0200
Imported Upstream version 0.8.2
---
INSTALL | 74 +
LICENSE | 319 +
doc/Makefile | 14 +
doc/README | 2 +
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doc/cvxopt/s-blas3.html | 435 ++
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doc/cvxopt/s-cholmod.html | 514 ++
doc/cvxopt/s-conventions.html | 470 ++
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examples/book/chap4/rls.pic | 1125 ++++
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examples/book/chap8/linsep.pic | 225 +
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examples/doc/README | 1 +
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examples/doc/covsel | 90 +
examples/doc/covsel.pic | 5261 +++++++++++++++
examples/doc/l1 | 127 +
examples/doc/mcsdp | 121 +
examples/doc/normappr | 34 +
examples/filterdemo/README | 12 +
examples/filterdemo/filterdemo_cli | 136 +
examples/filterdemo/filterdemo_gui | 213 +
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src/C/SuiteSparse/AMD/Source/amd.f | 1214 ++++
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src/C/SuiteSparse/AMD/Source/amd_aat.c | 185 +
src/C/SuiteSparse/AMD/Source/amd_control.c | 62 +
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src/C/SuiteSparse/AMD/Source/amd_info.c | 119 +
src/C/SuiteSparse/AMD/Source/amd_order.c | 200 +
src/C/SuiteSparse/AMD/Source/amd_post_tree.c | 121 +
src/C/SuiteSparse/AMD/Source/amd_postorder.c | 207 +
src/C/SuiteSparse/AMD/Source/amd_preprocess.c | 119 +
src/C/SuiteSparse/AMD/Source/amd_valid.c | 92 +
src/C/SuiteSparse/AMD/Source/amdbar.f | 1206 ++++
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src/C/SuiteSparse/CHOLMOD/Check/cholmod_read.c | 1319 ++++
src/C/SuiteSparse/CHOLMOD/Check/cholmod_write.c | 742 +++
src/C/SuiteSparse/CHOLMOD/Check/lesser.txt | 504 ++
src/C/SuiteSparse/CHOLMOD/Cholesky/License.txt | 24 +
src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_amd.c | 212 +
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src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_etree.c | 227 +
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src/C/SuiteSparse/CHOLMOD/Core/cholmod_memory.c | 565 ++
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src/C/SuiteSparse/CHOLMOD/Core/cholmod_transpose.c | 1139 ++++
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src/C/SuiteSparse/CHOLMOD/Include/cholmod.h | 122 +
src/C/SuiteSparse/CHOLMOD/Include/cholmod_blas.h | 451 ++
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src/C/SuiteSparse/CHOLMOD/Include/cholmod_core.h | 2257 +++++++
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src/C/SuiteSparse/CHOLMOD/Include/cholmod_io64.h | 46 +
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src/C/SuiteSparse/CHOLMOD/Include/cholmod_modify.h | 304 +
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src/C/SuiteSparse/CHOLMOD/Lib/Makefile | 473 ++
src/C/SuiteSparse/CHOLMOD/Makefile | 59 +
src/C/SuiteSparse/CHOLMOD/README.txt | 76 +
src/C/SuiteSparse/CHOLMOD/Supernodal/License.txt | 25 +
.../CHOLMOD/Supernodal/cholmod_super_numeric.c | 295 +
.../CHOLMOD/Supernodal/cholmod_super_solve.c | 221 +
.../CHOLMOD/Supernodal/cholmod_super_symbolic.c | 794 +++
src/C/SuiteSparse/CHOLMOD/Supernodal/gpl.txt | 340 +
.../CHOLMOD/Supernodal/t_cholmod_super_numeric.c | 741 +++
.../CHOLMOD/Supernodal/t_cholmod_super_solve.c | 430 ++
src/C/SuiteSparse/COLAMD/ChangeLog | 123 +
src/C/SuiteSparse/COLAMD/Contents.m | 18 +
src/C/SuiteSparse/COLAMD/Makefile | 51 +
src/C/SuiteSparse/COLAMD/README.txt | 108 +
src/C/SuiteSparse/COLAMD/colamd.c | 3611 +++++++++++
src/C/SuiteSparse/COLAMD/colamd.h | 254 +
src/C/SuiteSparse/COLAMD/colamd2.m | 103 +
src/C/SuiteSparse/COLAMD/colamd_demo.m | 178 +
src/C/SuiteSparse/COLAMD/colamd_example.c | 181 +
src/C/SuiteSparse/COLAMD/colamd_example.out | 50 +
src/C/SuiteSparse/COLAMD/colamd_global.c | 24 +
src/C/SuiteSparse/COLAMD/colamd_l_example.c | 185 +
src/C/SuiteSparse/COLAMD/colamd_l_example.out | 50 +
src/C/SuiteSparse/COLAMD/colamd_make.m | 18 +
src/C/SuiteSparse/COLAMD/colamd_test.m | 507 ++
src/C/SuiteSparse/COLAMD/colamdmex.c | 219 +
src/C/SuiteSparse/COLAMD/colamdtestmex.c | 576 ++
src/C/SuiteSparse/COLAMD/lesser.txt | 504 ++
src/C/SuiteSparse/COLAMD/luflops.m | 35 +
src/C/SuiteSparse/COLAMD/symamd2.m | 103 +
src/C/SuiteSparse/COLAMD/symamdmex.c | 200 +
src/C/SuiteSparse/COLAMD/symamdtestmex.c | 542 ++
src/C/SuiteSparse/Contents.m | 134 +
src/C/SuiteSparse/Makefile | 93 +
src/C/SuiteSparse/README.txt | 120 +
src/C/SuiteSparse/README_cvxopt | 28 +
src/C/SuiteSparse/UFconfig/README.txt | 25 +
src/C/SuiteSparse/UFconfig/UFconfig.h | 115 +
src/C/SuiteSparse/UFconfig/UFconfig.mk | 298 +
src/C/SuiteSparse/UFconfig/xerbla/Makefile | 31 +
src/C/SuiteSparse/UFconfig/xerbla/xerbla.c | 12 +
src/C/SuiteSparse/UFconfig/xerbla/xerbla.f | 46 +
src/C/SuiteSparse/UFconfig/xerbla/xerbla.h | 2 +
src/C/SuiteSparse/UMFPACK/Doc/ChangeLog | 452 ++
src/C/SuiteSparse/UMFPACK/Doc/License | 38 +
src/C/SuiteSparse/UMFPACK/Doc/Makefile | 59 +
src/C/SuiteSparse/UMFPACK/Doc/QuickStart.pdf | Bin 0 -> 133992 bytes
src/C/SuiteSparse/UMFPACK/Doc/QuickStart.tex | 1020 +++
src/C/SuiteSparse/UMFPACK/Doc/UserGuide.bib | 322 +
src/C/SuiteSparse/UMFPACK/Doc/UserGuide.pdf | Bin 0 -> 399999 bytes
src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed1 | 33 +
src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed2 | 3 +
src/C/SuiteSparse/UMFPACK/Doc/UserGuide.stex | 2695 ++++++++
src/C/SuiteSparse/UMFPACK/Doc/lesser.txt | 504 ++
src/C/SuiteSparse/UMFPACK/Include/umfpack.h | 438 ++
.../UMFPACK/Include/umfpack_col_to_triplet.h | 110 +
.../SuiteSparse/UMFPACK/Include/umfpack_defaults.h | 69 +
.../UMFPACK/Include/umfpack_free_numeric.h | 67 +
.../UMFPACK/Include/umfpack_free_symbolic.h | 67 +
.../UMFPACK/Include/umfpack_get_determinant.h | 196 +
.../SuiteSparse/UMFPACK/Include/umfpack_get_lunz.h | 137 +
.../UMFPACK/Include/umfpack_get_numeric.h | 254 +
.../UMFPACK/Include/umfpack_get_symbolic.h | 339 +
src/C/SuiteSparse/UMFPACK/Include/umfpack_global.h | 22 +
.../UMFPACK/Include/umfpack_load_numeric.h | 95 +
.../UMFPACK/Include/umfpack_load_symbolic.h | 95 +
.../SuiteSparse/UMFPACK/Include/umfpack_numeric.h | 543 ++
.../UMFPACK/Include/umfpack_qsymbolic.h | 150 +
.../UMFPACK/Include/umfpack_report_control.h | 76 +
.../UMFPACK/Include/umfpack_report_info.h | 86 +
.../UMFPACK/Include/umfpack_report_matrix.h | 203 +
.../UMFPACK/Include/umfpack_report_numeric.h | 112 +
.../UMFPACK/Include/umfpack_report_perm.h | 112 +
.../UMFPACK/Include/umfpack_report_status.h | 90 +
.../UMFPACK/Include/umfpack_report_symbolic.h | 111 +
.../UMFPACK/Include/umfpack_report_triplet.h | 153 +
.../UMFPACK/Include/umfpack_report_vector.h | 133 +
.../UMFPACK/Include/umfpack_save_numeric.h | 90 +
.../UMFPACK/Include/umfpack_save_symbolic.h | 90 +
src/C/SuiteSparse/UMFPACK/Include/umfpack_scale.h | 112 +
src/C/SuiteSparse/UMFPACK/Include/umfpack_solve.h | 301 +
.../SuiteSparse/UMFPACK/Include/umfpack_symbolic.h | 536 ++
src/C/SuiteSparse/UMFPACK/Include/umfpack_tictoc.h | 60 +
src/C/SuiteSparse/UMFPACK/Include/umfpack_timer.h | 39 +
.../UMFPACK/Include/umfpack_transpose.h | 216 +
.../UMFPACK/Include/umfpack_triplet_to_col.h | 263 +
src/C/SuiteSparse/UMFPACK/Include/umfpack_wsolve.h | 172 +
src/C/SuiteSparse/UMFPACK/Lib/libumfpack.def | 105 +
src/C/SuiteSparse/UMFPACK/Makefile | 74 +
src/C/SuiteSparse/UMFPACK/README.txt | 409 ++
src/C/SuiteSparse/UMFPACK/Source/GNUmakefile | 257 +
src/C/SuiteSparse/UMFPACK/Source/Makefile | 482 ++
src/C/SuiteSparse/UMFPACK/Source/cholmod_blas.h | 451 ++
src/C/SuiteSparse/UMFPACK/Source/umf_2by2.c | 859 +++
src/C/SuiteSparse/UMFPACK/Source/umf_2by2.h | 36 +
src/C/SuiteSparse/UMFPACK/Source/umf_analyze.c | 704 ++
src/C/SuiteSparse/UMFPACK/Source/umf_analyze.h | 23 +
src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.c | 43 +
src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.h | 14 +
src/C/SuiteSparse/UMFPACK/Source/umf_assemble.c | 1215 ++++
src/C/SuiteSparse/UMFPACK/Source/umf_assemble.h | 17 +
.../SuiteSparse/UMFPACK/Source/umf_blas3_update.c | 175 +
.../SuiteSparse/UMFPACK/Source/umf_blas3_update.h | 10 +
.../SuiteSparse/UMFPACK/Source/umf_build_tuples.c | 159 +
.../SuiteSparse/UMFPACK/Source/umf_build_tuples.h | 11 +
src/C/SuiteSparse/UMFPACK/Source/umf_colamd.c | 3139 +++++++++
src/C/SuiteSparse/UMFPACK/Source/umf_colamd.h | 255 +
src/C/SuiteSparse/UMFPACK/Source/umf_config.h | 324 +
.../UMFPACK/Source/umf_create_element.c | 592 ++
.../UMFPACK/Source/umf_create_element.h | 12 +
src/C/SuiteSparse/UMFPACK/Source/umf_dump.c | 1209 ++++
src/C/SuiteSparse/UMFPACK/Source/umf_dump.h | 191 +
.../SuiteSparse/UMFPACK/Source/umf_extend_front.c | 392 ++
.../SuiteSparse/UMFPACK/Source/umf_extend_front.h | 11 +
src/C/SuiteSparse/UMFPACK/Source/umf_free.c | 45 +
src/C/SuiteSparse/UMFPACK/Source/umf_free.h | 10 +
src/C/SuiteSparse/UMFPACK/Source/umf_fsize.c | 69 +
src/C/SuiteSparse/UMFPACK/Source/umf_fsize.h | 15 +
.../UMFPACK/Source/umf_garbage_collection.c | 695 ++
.../UMFPACK/Source/umf_garbage_collection.h | 14 +
src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.c | 222 +
src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.h | 15 +
src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.c | 293 +
src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.h | 14 +
src/C/SuiteSparse/UMFPACK/Source/umf_init_front.c | 267 +
src/C/SuiteSparse/UMFPACK/Source/umf_init_front.h | 11 +
src/C/SuiteSparse/UMFPACK/Source/umf_internal.h | 734 +++
.../UMFPACK/Source/umf_is_permutation.c | 55 +
.../UMFPACK/Source/umf_is_permutation.h | 13 +
src/C/SuiteSparse/UMFPACK/Source/umf_kernel.c | 299 +
src/C/SuiteSparse/UMFPACK/Source/umf_kernel.h | 18 +
src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.c | 1056 +++
src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.h | 18 +
.../SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c | 466 ++
.../SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.h | 12 +
.../SuiteSparse/UMFPACK/Source/umf_local_search.c | 1952 ++++++
.../SuiteSparse/UMFPACK/Source/umf_local_search.h | 12 +
src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.c | 151 +
src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.h | 12 +
src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.c | 225 +
src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.h | 19 +
src/C/SuiteSparse/UMFPACK/Source/umf_malloc.c | 91 +
src/C/SuiteSparse/UMFPACK/Source/umf_malloc.h | 25 +
.../UMFPACK/Source/umf_mem_alloc_element.c | 82 +
.../UMFPACK/Source/umf_mem_alloc_element.h | 17 +
.../UMFPACK/Source/umf_mem_alloc_head_block.c | 54 +
.../UMFPACK/Source/umf_mem_alloc_head_block.h | 11 +
.../UMFPACK/Source/umf_mem_alloc_tail_block.c | 133 +
.../UMFPACK/Source/umf_mem_alloc_tail_block.h | 11 +
.../UMFPACK/Source/umf_mem_free_tail_block.c | 142 +
.../UMFPACK/Source/umf_mem_free_tail_block.h | 11 +
.../UMFPACK/Source/umf_mem_init_memoryspace.c | 64 +
.../UMFPACK/Source/umf_mem_init_memoryspace.h | 10 +
.../SuiteSparse/UMFPACK/Source/umf_multicompile.c | 58 +
src/C/SuiteSparse/UMFPACK/Source/umf_realloc.c | 75 +
src/C/SuiteSparse/UMFPACK/Source/umf_realloc.h | 12 +
src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.c | 85 +
src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.h | 14 +
.../SuiteSparse/UMFPACK/Source/umf_report_vector.c | 110 +
.../SuiteSparse/UMFPACK/Source/umf_report_vector.h | 15 +
src/C/SuiteSparse/UMFPACK/Source/umf_row_search.c | 837 +++
src/C/SuiteSparse/UMFPACK/Source/umf_row_search.h | 32 +
src/C/SuiteSparse/UMFPACK/Source/umf_scale.c | 81 +
src/C/SuiteSparse/UMFPACK/Source/umf_scale.h | 12 +
.../SuiteSparse/UMFPACK/Source/umf_scale_column.c | 433 ++
.../SuiteSparse/UMFPACK/Source/umf_scale_column.h | 11 +
src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.c | 133 +
src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.h | 24 +
src/C/SuiteSparse/UMFPACK/Source/umf_singletons.c | 915 +++
src/C/SuiteSparse/UMFPACK/Source/umf_singletons.h | 31 +
src/C/SuiteSparse/UMFPACK/Source/umf_solve.c | 1395 ++++
src/C/SuiteSparse/UMFPACK/Source/umf_solve.h | 25 +
src/C/SuiteSparse/UMFPACK/Source/umf_start_front.c | 283 +
src/C/SuiteSparse/UMFPACK/Source/umf_start_front.h | 13 +
src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.c | 1056 +++
src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.h | 17 +
.../UMFPACK/Source/umf_symbolic_usage.c | 45 +
.../UMFPACK/Source/umf_symbolic_usage.h | 15 +
src/C/SuiteSparse/UMFPACK/Source/umf_transpose.c | 400 ++
src/C/SuiteSparse/UMFPACK/Source/umf_transpose.h | 27 +
src/C/SuiteSparse/UMFPACK/Source/umf_triplet.c | 428 ++
src/C/SuiteSparse/UMFPACK/Source/umf_triplet.h | 85 +
.../SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c | 135 +
.../SuiteSparse/UMFPACK/Source/umf_tuple_lengths.h | 12 +
src/C/SuiteSparse/UMFPACK/Source/umf_usolve.c | 226 +
src/C/SuiteSparse/UMFPACK/Source/umf_usolve.h | 12 +
src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.c | 331 +
src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.h | 20 +
.../SuiteSparse/UMFPACK/Source/umf_valid_numeric.c | 46 +
.../SuiteSparse/UMFPACK/Source/umf_valid_numeric.h | 10 +
.../UMFPACK/Source/umf_valid_symbolic.c | 47 +
.../UMFPACK/Source/umf_valid_symbolic.h | 10 +
src/C/SuiteSparse/UMFPACK/Source/umf_version.h | 874 +++
.../UMFPACK/Source/umfpack_col_to_triplet.c | 72 +
.../SuiteSparse/UMFPACK/Source/umfpack_defaults.c | 114 +
.../UMFPACK/Source/umfpack_free_numeric.c | 57 +
.../UMFPACK/Source/umfpack_free_symbolic.c | 56 +
.../UMFPACK/Source/umfpack_get_determinant.c | 308 +
.../SuiteSparse/UMFPACK/Source/umfpack_get_lunz.c | 55 +
.../UMFPACK/Source/umfpack_get_numeric.c | 1057 +++
.../UMFPACK/Source/umfpack_get_symbolic.c | 191 +
src/C/SuiteSparse/UMFPACK/Source/umfpack_global.c | 130 +
.../UMFPACK/Source/umfpack_load_numeric.c | 161 +
.../UMFPACK/Source/umfpack_load_symbolic.c | 165 +
src/C/SuiteSparse/UMFPACK/Source/umfpack_numeric.c | 792 +++
.../SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c | 2411 +++++++
.../UMFPACK/Source/umfpack_report_control.c | 361 ++
.../UMFPACK/Source/umfpack_report_info.c | 611 ++
.../UMFPACK/Source/umfpack_report_matrix.c | 201 +
.../UMFPACK/Source/umfpack_report_numeric.c | 663 ++
.../UMFPACK/Source/umfpack_report_perm.c | 44 +
.../UMFPACK/Source/umfpack_report_status.c | 119 +
.../UMFPACK/Source/umfpack_report_symbolic.c | 228 +
.../UMFPACK/Source/umfpack_report_triplet.c | 99 +
.../UMFPACK/Source/umfpack_report_vector.c | 43 +
.../UMFPACK/Source/umfpack_save_numeric.c | 92 +
.../UMFPACK/Source/umfpack_save_symbolic.c | 95 +
src/C/SuiteSparse/UMFPACK/Source/umfpack_scale.c | 158 +
src/C/SuiteSparse/UMFPACK/Source/umfpack_solve.c | 245 +
.../SuiteSparse/UMFPACK/Source/umfpack_symbolic.c | 39 +
src/C/SuiteSparse/UMFPACK/Source/umfpack_tictoc.c | 106 +
src/C/SuiteSparse/UMFPACK/Source/umfpack_timer.c | 83 +
.../SuiteSparse/UMFPACK/Source/umfpack_transpose.c | 108 +
.../UMFPACK/Source/umfpack_triplet_to_col.c | 225 +
src/C/SuiteSparse_cvxopt_extra/README | 7 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_global.c | 1 +
src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_1.c | 3 +
src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_2.c | 3 +
src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_aat.c | 3 +
.../umfpack/amd_i_defaults.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_i_dump.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_i_order.c | 3 +
.../umfpack/amd_i_post_tree.c | 3 +
.../umfpack/amd_i_postorder.c | 3 +
.../umfpack/amd_i_preprocess.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_i_valid.c | 3 +
src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_1.c | 3 +
src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_2.c | 3 +
src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_aat.c | 3 +
.../umfpack/amd_l_defaults.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_l_dump.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_l_order.c | 3 +
.../umfpack/amd_l_post_tree.c | 3 +
.../umfpack/amd_l_postorder.c | 3 +
.../umfpack/amd_l_preprocess.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/amd_l_valid.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_di_2by2.c | 2 +
.../umfpack/umf_di_assemble.c | 2 +
.../umfpack/umf_di_assemble_fixq.c | 3 +
.../umfpack/umf_di_blas3_update.c | 2 +
.../umfpack/umf_di_build_tuples.c | 2 +
.../umfpack/umf_di_create_element.c | 2 +
.../umfpack/umf_di_extend_front.c | 2 +
.../umfpack/umf_di_garbage_collection.c | 2 +
.../umfpack/umf_di_get_memory.c | 2 +
.../umfpack/umf_di_grow_front.c | 2 +
.../umfpack/umf_di_init_front.c | 3 +
.../umfpack/umf_di_kernel.c | 2 +
.../umfpack/umf_di_kernel_init.c | 2 +
.../umfpack/umf_di_kernel_wrapup.c | 2 +
.../umfpack/umf_di_lhsolve.c | 3 +
.../umfpack/umf_di_local_search.c | 2 +
.../umfpack/umf_di_lsolve.c | 2 +
.../umfpack/umf_di_ltsolve.c | 2 +
.../umfpack/umf_di_mem_alloc_element.c | 2 +
.../umfpack/umf_di_mem_alloc_head_block.c | 2 +
.../umfpack/umf_di_mem_alloc_tail_block.c | 2 +
.../umfpack/umf_di_mem_free_tail_block.c | 2 +
.../umfpack/umf_di_mem_init_memoryspace.c | 2 +
.../umfpack/umf_di_row_search.c | 2 +
.../umfpack/umf_di_scale.c | 2 +
.../umfpack/umf_di_scale_column.c | 2 +
.../umfpack/umf_di_set_stats.c | 2 +
.../umfpack/umf_di_solve.c | 2 +
.../umfpack/umf_di_start_front.c | 2 +
.../umfpack/umf_di_store_lu.c | 2 +
.../umfpack/umf_di_store_lu_drop.c | 3 +
.../umfpack/umf_di_symbolic_usage.c | 2 +
.../umfpack/umf_di_transpose.c | 2 +
.../umfpack/umf_di_tuple_lengths.c | 2 +
.../umfpack/umf_di_uhsolve.c | 3 +
.../umfpack/umf_di_usolve.c | 2 +
.../umfpack/umf_di_utsolve.c | 2 +
.../umfpack/umf_di_valid_numeric.c | 2 +
.../umfpack/umf_di_valid_symbolic.c | 2 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_dl_2by2.c | 3 +
.../umfpack/umf_dl_assemble.c | 3 +
.../umfpack/umf_dl_assemble_fixq.c | 3 +
.../umfpack/umf_dl_blas3_update.c | 3 +
.../umfpack/umf_dl_build_tuples.c | 3 +
.../umfpack/umf_dl_create_elememt.c | 3 +
.../umfpack/umf_dl_extend_front.c | 3 +
.../umfpack/umf_dl_garbage_collection.c | 3 +
.../umfpack/umf_dl_get_memory.c | 3 +
.../umfpack/umf_dl_grow_front.c | 3 +
.../umfpack/umf_dl_init_front.c | 3 +
.../umfpack/umf_dl_kernel.c | 3 +
.../umfpack/umf_dl_kernel_init.c | 3 +
.../umfpack/umf_dl_kernel_wrapup.c | 3 +
.../umfpack/umf_dl_lhsolve.c | 4 +
.../umfpack/umf_dl_local_search.c | 3 +
.../umfpack/umf_dl_lsolve.c | 3 +
.../umfpack/umf_dl_ltsolve.c | 3 +
.../umfpack/umf_dl_mem_alloc_element.c | 3 +
.../umfpack/umf_dl_mem_alloc_head_block.c | 3 +
.../umfpack/umf_dl_mem_alloc_tail_block.c | 3 +
.../umfpack/umf_dl_mem_free_tail_block.c | 3 +
.../umfpack/umf_dl_mem_init_memoryspace.c | 3 +
.../umfpack/umf_dl_row_search.c | 3 +
.../umfpack/umf_dl_scale.c | 3 +
.../umfpack/umf_dl_scale_column.c | 3 +
.../umfpack/umf_dl_set_stats.c | 3 +
.../umfpack/umf_dl_solve.c | 3 +
.../umfpack/umf_dl_start_front.c | 3 +
.../umfpack/umf_dl_store_lu.c | 3 +
.../umfpack/umf_dl_store_lu_drop.c | 3 +
.../umfpack/umf_dl_symbolic_usage.c | 3 +
.../umfpack/umf_dl_transpose.c | 3 +
.../umfpack/umf_dl_tuple_lengths.c | 3 +
.../umfpack/umf_dl_uhsolve.c | 4 +
.../umfpack/umf_dl_usolve.c | 3 +
.../umfpack/umf_dl_utsolve.c | 3 +
.../umfpack/umf_dl_valid_numeric.c | 3 +
.../umfpack/umf_dl_valid_symbolic.c | 3 +
.../umfpack/umf_i_analyze.c | 2 +
.../umfpack/umf_i_apply_order.c | 2 +
.../umfpack/umf_i_colamd.c | 2 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_i_free.c | 2 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_i_fsize.c | 2 +
.../umfpack/umf_i_is_permutation.c | 2 +
.../umfpack/umf_i_malloc.c | 2 +
.../umfpack/umf_i_realloc.c | 2 +
.../umfpack/umf_i_singletons.c | 2 +
.../umfpack/umf_l_analyze.c | 3 +
.../umfpack/umf_l_apply_order.c | 2 +
.../umfpack/umf_l_colamd.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_l_free.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_l_fsize.c | 3 +
.../umfpack/umf_l_is_permutation.c | 3 +
.../umfpack/umf_l_malloc.c | 3 +
.../umfpack/umf_l_realloc.c | 3 +
.../umfpack/umf_l_singletons.c | 3 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_zi_2by2.c | 2 +
.../umfpack/umf_zi_assemble.c | 2 +
.../umfpack/umf_zi_assemble_fixq.c | 3 +
.../umfpack/umf_zi_blas3_update.c | 2 +
.../umfpack/umf_zi_build_tuples.c | 2 +
.../umfpack/umf_zi_create_element.c | 2 +
.../umfpack/umf_zi_extend_front.c | 2 +
.../umfpack/umf_zi_garbage_collection.c | 2 +
.../umfpack/umf_zi_get_memory.c | 2 +
.../umfpack/umf_zi_grow_front.c | 2 +
.../umfpack/umf_zi_init_front.c | 3 +
.../umfpack/umf_zi_kernel.c | 2 +
.../umfpack/umf_zi_kernel_init.c | 2 +
.../umfpack/umf_zi_kernel_wrapup.c | 2 +
.../umfpack/umf_zi_lhsolve.c | 3 +
.../umfpack/umf_zi_local_search.c | 2 +
.../umfpack/umf_zi_lsolve.c | 2 +
.../umfpack/umf_zi_ltsolve.c | 2 +
.../umfpack/umf_zi_mem_alloc_element.c | 2 +
.../umfpack/umf_zi_mem_alloc_head_block.c | 2 +
.../umfpack/umf_zi_mem_alloc_tail_block.c | 2 +
.../umfpack/umf_zi_mem_free_tail_block.c | 2 +
.../umfpack/umf_zi_mem_init_memoryspace.c | 2 +
.../umfpack/umf_zi_row_search.c | 2 +
.../umfpack/umf_zi_scale.c | 2 +
.../umfpack/umf_zi_scale_column.c | 2 +
.../umfpack/umf_zi_set_stats.c | 2 +
.../umfpack/umf_zi_solve.c | 2 +
.../umfpack/umf_zi_start_front.c | 2 +
.../umfpack/umf_zi_store_lu.c | 2 +
.../umfpack/umf_zi_store_lu_drop.c | 3 +
.../umfpack/umf_zi_symbolic_usage.c | 2 +
.../umfpack/umf_zi_transpose.c | 2 +
.../umfpack/umf_zi_tuple_lengths.c | 2 +
.../umfpack/umf_zi_uhsolve.c | 3 +
.../umfpack/umf_zi_usolve.c | 2 +
.../umfpack/umf_zi_utsolve.c | 2 +
.../umfpack/umf_zi_valid_numeric.c | 2 +
.../umfpack/umf_zi_valid_symbolic.c | 2 +
.../SuiteSparse_cvxopt_extra/umfpack/umf_zl_2by2.c | 3 +
.../umfpack/umf_zl_assemble.c | 3 +
.../umfpack/umf_zl_assemble_fixq.c | 3 +
.../umfpack/umf_zl_blas3_update.c | 3 +
.../umfpack/umf_zl_build_tuples.c | 3 +
.../umfpack/umf_zl_create_elememt.c | 3 +
.../umfpack/umf_zl_extend_front.c | 3 +
.../umfpack/umf_zl_garbage_collection.c | 3 +
.../umfpack/umf_zl_get_memory.c | 3 +
.../umfpack/umf_zl_grow_front.c | 3 +
.../umfpack/umf_zl_init_front.c | 3 +
.../umfpack/umf_zl_kernel.c | 3 +
.../umfpack/umf_zl_kernel_init.c | 3 +
.../umfpack/umf_zl_kernel_wrapup.c | 3 +
.../umfpack/umf_zl_lhsolve.c | 4 +
.../umfpack/umf_zl_local_search.c | 3 +
.../umfpack/umf_zl_lsolve.c | 3 +
.../umfpack/umf_zl_ltsolve.c | 3 +
.../umfpack/umf_zl_mem_alloc_element.c | 3 +
.../umfpack/umf_zl_mem_alloc_head_block.c | 3 +
.../umfpack/umf_zl_mem_alloc_tail_block.c | 3 +
.../umfpack/umf_zl_mem_free_tail_block.c | 3 +
.../umfpack/umf_zl_mem_init_memoryspace.c | 3 +
.../umfpack/umf_zl_row_search.c | 3 +
.../umfpack/umf_zl_scale.c | 3 +
.../umfpack/umf_zl_scale_column.c | 3 +
.../umfpack/umf_zl_set_stats.c | 3 +
.../umfpack/umf_zl_solve.c | 3 +
.../umfpack/umf_zl_start_front.c | 3 +
.../umfpack/umf_zl_store_lu.c | 3 +
.../umfpack/umf_zl_store_lu_drop.c | 3 +
.../umfpack/umf_zl_symbolic_usage.c | 3 +
.../umfpack/umf_zl_transpose.c | 3 +
.../umfpack/umf_zl_tuple_lengths.c | 3 +
.../umfpack/umf_zl_uhsolve.c | 4 +
.../umfpack/umf_zl_usolve.c | 3 +
.../umfpack/umf_zl_utsolve.c | 3 +
.../umfpack/umf_zl_valid_numeric.c | 3 +
.../umfpack/umf_zl_valid_symbolic.c | 3 +
.../umfpack/umfpack_di_free_numeric.c | 2 +
.../umfpack/umfpack_di_free_symbolic.c | 2 +
.../umfpack/umfpack_di_numeric.c | 2 +
.../umfpack/umfpack_di_qsymbolic.c | 2 +
.../umfpack/umfpack_di_solve.c | 2 +
.../umfpack/umfpack_di_symbolic.c | 2 +
.../umfpack/umfpack_dl_free_numeric.c | 3 +
.../umfpack/umfpack_dl_free_symbolic.c | 3 +
.../umfpack/umfpack_dl_numeric.c | 3 +
.../umfpack/umfpack_dl_qsymbolic.c | 3 +
.../umfpack/umfpack_dl_solve.c | 3 +
.../umfpack/umfpack_dl_symbolic.c | 2 +
.../umfpack/umfpack_zi_free_numeric.c | 2 +
.../umfpack/umfpack_zi_free_symbolic.c | 2 +
.../umfpack/umfpack_zi_numeric.c | 2 +
.../umfpack/umfpack_zi_qsymbolic.c | 2 +
.../umfpack/umfpack_zi_solve.c | 2 +
.../umfpack/umfpack_zi_symbolic.c | 2 +
.../umfpack/umfpack_zl_free_numeric.c | 3 +
.../umfpack/umfpack_zl_free_symbolic.c | 3 +
.../umfpack/umfpack_zl_numeric.c | 3 +
.../umfpack/umfpack_zl_qsymbolic.c | 3 +
.../umfpack/umfpack_zl_solve.c | 3 +
.../umfpack/umfpack_zl_symbolic.c | 2 +
src/C/amd.c | 198 +
src/C/base.c | 950 +++
src/C/blas.c | 3316 ++++++++++
src/C/blas_redefines.h | 140 +
src/C/cholmod.c | 947 +++
src/C/cvxopt.h | 127 +
src/C/dense.c | 2129 ++++++
src/C/dsdp.c | 437 ++
src/C/fftw.c | 290 +
src/C/glpk.c | 358 +
src/C/lapack.c | 5088 +++++++++++++++
src/C/misc.h | 85 +
src/C/mosek.c | 778 +++
src/C/random.c | 144 +
src/C/rngs/README.cvxopt | 3 +
src/C/rngs/rngs.c | 179 +
src/C/rngs/rngs.h | 19 +
src/C/rngs/rvgs.c | 218 +
src/C/rngs/rvgs.h | 28 +
src/C/sparse.c | 3992 ++++++++++++
src/C/umfpack.c | 448 ++
src/python/__init__.py | 2 +
src/python/coneprog.py | 2151 ++++++
src/python/cvxprog.py | 1074 +++
src/python/info.py | 41 +
src/python/misc.py | 515 ++
src/python/modeling.py | 3214 +++++++++
src/python/solvers.py | 24 +
src/setup.py | 165 +
898 files changed, 185779 insertions(+)
diff --git a/INSTALL b/INSTALL
new file mode 100644
index 0000000..a9ffc1a
--- /dev/null
+++ b/INSTALL
@@ -0,0 +1,74 @@
+Installation instructions for CVXOPT Version 0.8.2.
+
+The package requires version 2.3 or newer of Python, and is built
+from source, so the header files and libraries for Python must be
+installed, as well as the core binaries.
+
+The installation requires either ATLAS or BLAS + LAPACK. Using
+architecture optimized ATLAS libraries is recommended and gives a
+large performance improvement over standard BLAS & LAPACK libraries.
+Both header files and libraries must be installed.
+
+The following software libraries are optional.
+
+1) FFTW (www.fftw.org) is a C library for discrete Fourier transforms.
+
+1) GLPK (www.gnu.org/software/glpk/glpk.html) is a linear programming
+package.
+
+2) MOSEK version 4 (www.mosek.com) is a commercial library of convex
+optimization solvers.
+
+3) DSDP5.8 (www-unix.mcs.anl.gov/DSDP) is a semidefinite programming
+solver.
+
+
+Configuration script:
+---------------------
+Edit src/setup.py and update the following variables:
+
+- ATLAS_LIB_DIR: the directory containing the lapack and blas libraries
+
+- BUILD_FFTW: set this variable to 1 to enable FFTW support
+- FFTW_LIB_DIR: the directory containing the libfftw3
+- FFTW_INC_DIR: the directory containing fftw.h
+
+- BUILD_GLPK: set this variable to 1 to enable GLPK support
+- GLPK_LIB_DIR: the directory containing libglpk
+- GLPK_INC_DIR: the directory containing glpk.h
+
+- BUILD_MOSEK: set this variable to 1 to enable MOSEK support
+- MOSEK_LIB_DIR: the directory containing libmosek
+- MOSEK_INC_DIR: the directory containing mosek.h
+
+- BUILD_DSDP: set this variable to 1 to enable DSDP support
+- DSDP_LIB_DIR: the directory containing libdsdp
+- DSDP_INC_DIR: the directory containing dsdp5.h
+
+
+Compilation:
+------------
+CVXOPT can be installed globally (for all users on a UNIX system) by
+writing:
+
+ python setup.py install
+
+It can also be installed locally in the home directory by typing:
+
+ python setup.py install --home=~
+
+This will install the libraries in /home/username/lib/python. In this
+case PYTHONPATH must be updated, e.g., under Bash write
+
+ export PYTHONPATH=$PYTHONPATH:/home/username/lib/python
+
+
+Test it:
+--------
+To test that the installation was successful, go to the examples
+directory and try one of the examples, for example,
+
+ $ cd examples/doc
+ $ python acent
+
+If Python does not issue an error message installation was successful.
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..62afd96
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,319 @@
+CVXOPT version 0.8.2.
+Copyright (C) 2004-2007 J. Dahl and L. Vandenberghe.
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+A copy of the GNU General Public License is enclosed below.
+See also www.gnu.org/copyleft/gpl.html.
+------------------------------------------------------------------------
+
+The CVXOPT distribution includes source code for the following software
+libraries.
+
+AMD Version 2.0. Copyright (c) 2006 by Timothy A. Davis, Patrick R.
+Amestoy, and Iain S. Duff.
+See www.cise.ufl.edu/research/sparse/amd.
+
+CHOLMOD Version 1.4. Copyright (c) 2005-2006 by University of Florida,
+Timothy A. Davis and William W. Hager.
+See www.cise.ufl.edu/research/sparse/cholmod.
+
+COLAMD version 2.6. Copyright (c) 1998-2006 by Timothy A. Davis.
+See www.cise.ufl.edu/research/sparse/colamd.
+
+UMFPACK Version 5.0.2. Copyright (c) 1995-2006 by Timothy A. Davis.
+See www.cise.ufl.edu/research/sparse/umfpack.
+
+RNGS Random Number Generation - Multiple Streams (Sep. 22, 1998) by
+Steve Park & Dave Geyer.
+See www.cs.wm.edu/~va/software/park/park.html.
+------------------------------------------------------------------------
+
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
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diff --git a/doc/Makefile b/doc/Makefile
new file mode 100644
index 0000000..00879d3
--- /dev/null
+++ b/doc/Makefile
@@ -0,0 +1,14 @@
+MKHOWTO = /usr/lib/python2.4/doc/tools/mkhowto
+SOURCES = cvxopt.tex intro.tex base.tex blas.tex lapack.tex \
+ spsolvers.tex modeling.tex solvers.tex c-api.tex
+
+all: html
+
+ps: Makefile $(SOURCES)
+ $(MKHOWTO) --ps cvxopt.tex
+
+html: Makefile $(SOURCES)
+ $(MKHOWTO) --html --image-type gif cvxopt.tex
+
+clean:
+ rm -rf *.dvi *.idx *.ind *.l2h *.log *.toc *.aux *~ *.ps cvxopt
diff --git a/doc/README b/doc/README
new file mode 100644
index 0000000..f47740c
--- /dev/null
+++ b/doc/README
@@ -0,0 +1,2 @@
+python.sty in this directory is the style file from the standard Python
+distribution with lines 555--563 commented out.
diff --git a/doc/base.tex b/doc/base.tex
new file mode 100644
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+++ b/doc/base.tex
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+\chapter{Dense Matrices (\module{cvxopt.base})}\label{chap:matrix}
+
+The \module{cvxopt.base} module defines two new Python types:
+\mtrx\ objects, used for dense matrix computations, and
+\spmtrx\ objects, used for sparse matrix computations.
+In this chapter we describe the dense \mtrx\ object.
+
+\section{Creating Matrices}\label{s-creating-matrices}
+A \mtrx\ object is created by calling the function \function{matrix()}.
+The arguments specify the values of the coefficients, the
+dimensions, and the type (integer, double or complex) of the matrix.
+
+\begin{funcdesc}{matrix}{x\optional{, size\optional{, tc}}}
+\var{size} is a tuple of length two with the matrix dimensions.
+The number of rows and/or the number of columns can be zero.
+
+\var{tc} stands for typecode. The possible values are \itc, \dtc\ and
+\ztc, for integer, real (double) and complex matrices, respectively.
+
+\var{x} can be a number, a sequence of numbers, a dense or sparse
+matrix, a two-dimensional \module{numarray} array, or a list of
+lists of matrices and numbers.
+\BIT
+\item If \var{x} is a number (Python \intgr, \flt\ or \cmplx), a matrix
+is created with the dimensions specified by \var{size} and with all the
+coefficients equal to \var{x}.
+The default value of \var{size} is (1,1), and the default value
+of \var{tc} is the type of \var{x}.
+If necessary, the type of \var{x} is converted (from integer to double
+when used to create a matrix of type \dtc, and from integer or
+double to complex when used to create a matrix of type \ztc).
+
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> A = matrix(1, (1,4))
+>>> print A
+ 1 1 1 1
+>>> A = matrix(1.0, (1,4))
+>>> print A
+ 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00
+>>> A = matrix(1+1j)
+>>> print A
+ 1.0000e+00+j1.0000e+00
+\end{verbatim}
+
+\item If \var{x} is a sequence of numbers (list, tuple, \module{array}
+array, xrange object, one-dimensional \module{numarray} array, \ldots),
+then the numbers are interpreted as the coefficients of a matrix in
+column-major order. The length of \var{x} must be equal to the product
+of \var{size}[0] and \var{size}[1].
+If \var{size} is not specified, a matrix with one column is created.
+If \var{tc} is not specified, it is determined from the elements of
+\var{x} (and if that is impossible, for example because \var{x} is
+an empty list, a value \itc\ is used).
+Type conversion takes place as for scalar \var{x}.
+
+The following example shows several ways to define the same integer
+matrix.
+\begin{verbatim}
+>>> A = matrix([0, 1, 2, 3], (2,2))
+>>> A = matrix((0, 1, 2, 3), (2,2))
+>>> A = matrix(xrange(4), (2,2))
+>>> from array import array
+>>> A = matrix(array('i', [0,1,2,3]), (2,2))
+>>> print A
+ 0 2
+ 1 3
+\end{verbatim}
+
+\item If \var{x} is a dense or sparse matrix (a \mtrx\ or a \spmtrx\
+object), or a two-dimensional \module{numarray} array of type \itc,
+\dtc\ or \ztc, then the coefficients of \var{x} are copied, in
+column-major order, to a new matrix of the given size.
+The total number of elements in the new matrix (the product of
+\var{size}[0] and \var{size}[1]) must be the same as the product of
+the dimensions of \var{x}. If \var{size} is not specified, the
+dimensions of \var{x} are used.
+The default value of \var{tc} is the type of \var{x}.
+Type conversion takes place when the type of \var{x} differs from
+\var{tc}, in a similar way as for scalar \var{x}.
+
+\begin{verbatim}
+>>> A = matrix([1., 2., 3., 4., 5., 6.], (2,3))
+>>> print A
+ 1.0000e+00 3.0000e+00 5.0000e+00
+ 2.0000e+00 4.0000e+00 6.0000e+00
+>>> B = matrix(A, (3,2))
+>>> print B
+ 1.0000e+00 4.0000e+00
+ 2.0000e+00 5.0000e+00
+ 3.0000e+00 6.0000e+00
+>>> C = matrix(B, tc='z')
+>>> print C
+ 1.0000e+00-j0.0000e+00 4.0000e+00-j0.0000e+00
+ 2.0000e+00-j0.0000e+00 5.0000e+00-j0.0000e+00
+ 3.0000e+00-j0.0000e+00 6.0000e+00-j0.0000e+00
+>>> from numarray import array
+>>> x = array([1., 2., 3., 4., 5., 6.], shape=(2,3))
+>>> print x
+[[ 1. 2. 3.]
+ [ 4. 5. 6.]]
+>>> y = matrix(x)
+>>> print y
+ 1.0000e+00 2.0000e+00 3.0000e+00
+ 4.0000e+00 5.0000e+00 6.0000e+00
+\end{verbatim}
+
+\item If \var{x} is a list of lists of matrices
+(\mtrx\ or \spmtrx\ objects) or numbers (Python \intgr, \flt\ or
+\cmplx), then each element of \var{x} is interpreted as a
+block-column stored in column-major order.
+If \var{size} is not specified, the block-columns are juxtaposed
+to obtain a matrix with \code{len(\var{x})} block-columns.
+If \var{size} is specified, then the matrix with \code{len(\var{x})}
+block-columns is resized by copying its elements in column-major order
+into a matrix of the dimensions given by \var{size}.
+If \var{tc} is not specified, it is determined from the elements of
+\var{x} (and if that is impossible, for example because \var{x} is
+a list of empty lists, a value \itc\ is used).
+The same rules for type conversion apply as for scalar \var{x}.
+
+\begin{verbatim}
+>>> A = matrix([[1., 2.], [3., 4.], [5., 6.]])
+>>> print A
+ 1.0000e+00 3.0000e+00 5.0000e+00
+ 2.0000e+00 4.0000e+00 6.0000e+00
+>>> A1 = matrix([1, 2], (2,1))
+>>> B1 = matrix([6, 7, 8, 9, 10, 11], (2,3))
+>>> B2 = matrix([12, 13, 14, 15, 16, 17], (2,3))
+>>> B3 = matrix([18, 19, 20], (1,3))
+>>> print matrix([[A1, 3.0, 4.0, 5.0], [B1, B2, B3]])
+ 1.0000e+00 6.0000e+00 8.0000e+00 1.0000e+01
+ 2.0000e+00 7.0000e+00 9.0000e+00 1.1000e+01
+ 3.0000e+00 1.2000e+01 1.4000e+01 1.6000e+01
+ 4.0000e+00 1.3000e+01 1.5000e+01 1.7000e+01
+ 5.0000e+00 1.8000e+01 1.9000e+01 2.0000e+01
+\end{verbatim}
+
+A matrix with a single block-column can be represented by a single
+list (\ie, when the length of \var{x} is one, it can be replaced with
+\code{\var{x}[0]}).
+\begin{verbatim}
+>>> print matrix([B1, B2, B3])
+ 6 8 10
+ 7 9 11
+ 12 14 16
+ 13 15 17
+ 18 19 20
+\end{verbatim}
+\EIT
+\end{funcdesc}
+
+\section{Attributes and Methods}
+A \mtrx\ has the following attributes.
+
+\begin{memberdesc}[tuple]{size}
+A tuple with the dimensions of the matrix. This is a read-only
+attribute; operations that change the size of a matrix are not
+permitted.
+\end{memberdesc}
+
+\begin{memberdesc}[char]{typecode}
+A \ctype{char}, either \itc, \dtc, or \ztc, for integer, real
+and complex matrices, respectively. A read-only attribute.
+\end{memberdesc}
+
+\begin{methoddesc}{trans}{}
+Returns the transpose of the matrix as a new matrix.
+One can also use \code{A.T} instead of \code{A.trans()}.
+\end{methoddesc}
+
+\begin{methoddesc}{ctrans}{}
+Returns the conjugate transpose of the matrix as a new matrix.
+One can also use \code{A.H} instead of \code{A.ctrans()}.
+\end{methoddesc}
+
+\begin{methoddesc}{real}{}
+For complex matrices, returns the real part as a real matrix.
+For integer and real matrices, returns a copy of the matrix.
+\end{methoddesc}
+
+\begin{methoddesc}{imag}{}
+For complex matrices, returns the imaginary part as a real matrix.
+For integer and real matrices, returns an integer or real zero matrix.
+\end{methoddesc}
+
+\begin{memberdesc}[PyCObject]{\_\_array\_struct\_\_}
+A PyCObject implementing the NumPy array interface
+(see section~\ref{s-array-interface} for details).
+\end{memberdesc}
+
+\begin{methoddesc}{tofile}{f}
+Writes the elements of the matrix in column-major order to a binary
+file \var{f}.
+\end{methoddesc}
+
+\begin{methoddesc}{fromfile}{f}
+Reads the contents of a binary file \var{f} into the matrix object.
+\end{methoddesc}
+
+The last two methods are illustrated in the following example.
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> A = matrix([[1.,2.,3.], [4.,5.,6.]])
+>>> print A
+ 1.0000e+00 4.0000e+00
+ 2.0000e+00 5.0000e+00
+ 3.0000e+00 6.0000e+00
+>>> f = open('mat.bin','w')
+>>> A.tofile(f)
+>>> f.close()
+>>> B = matrix(0.0, (2,3))
+>>> f = open('mat.bin','r')
+>>> B.fromfile(f)
+>>> f.close()
+>>> print B
+ 1.0000e+00 3.0000e+00 5.0000e+00
+ 2.0000e+00 4.0000e+00 6.0000e+00
+\end{verbatim}
+
+Matrices can also be written to or read from files using the
+\function{dump()} and \function{load()} functions in the
+\module{pickle} module.
+
+
+\section{Arithmetic Operations} \label{s-arithmetic}
+The following table lists the arithmetic operations defined for
+dense matrices. In this table \var{A} and \var{B} are dense matrices
+with compatible dimensions, \var{c} is a scalar (a Python number
+or a dense 1 by 1 matrix), and \var{d} is a Python number.
+
+\begin{center}
+\begin{tabular}{l|l}
+Unary plus/minus & \code{+\var{A}}, \code{-\var{A}} \\
+Addition & \code{\var{A}+\var{B}}, \code{\var{A}+\var{c}},
+ \code{\var{c}+\var{A}}\\
+Subtraction & \code{\var{A}-\var{B}}, \code{\var{A}-\var{c}},
+ \code{\var{c}-\var{A}}\\
+Matrix multiplication & {\var{A}*\var{B}} \\
+Scalar multiplication and division & \code{\var{c}*\var{A}},
+ \code{\var{A}*\var{c}}, \code{\var{A}/\var{c}} \\
+Remainder after division & \code{\var{A}\%\var{c}} \\
+Elementwise exponentiation & \code{\var{A}**\var{d}}
+\end{tabular}
+\end{center}
+
+If \var{c} in the expressions \code{\var{A}+\var{c}},
+\code{\var{c}+\var{A}}, \code{\var{A}-\var{c}},
+\code{\var{c}-\var{A}} is a number, then it is interpreted as a
+matrix with the same dimensions as \var{A}, type given by the type
+of \var{c}, and all entries equal to \var{c}.
+If \var{c} is a 1 by 1 matrix and \var{A} is not 1 by 1, then \var{c}
+is interpreted as a matrix with the same size of \var{A} and all
+entries equal to \code{\var{c}[0]}.
+
+Postmultiplying a matrix with a number \var{c} means the same as
+premultiplying, \ie, scalar multiplication. Dividing a matrix by
+\var{c} means dividing all entries by \var{c}.
+If \var{c} is a 1 by 1 matrix and the product
+\code{\var{c}*\var{A}} or \code{\var{A}*\var{c}} cannot be
+interpreted as a matrix-matrix product, then it is interpreted as
+\code{\var{c}[0]*\var{A}}.
+The division \code{\var{A}/\var{c}} and remainder
+\code{\var{A}\%\var{c}} with \var{c} a 1 by 1 matrix are always
+interpreted as \code{\var{A}/\var{c}[0]}, resp.,
+\code{\var{A}\%\var{c}[0]}.
+
+If one of the operands in the arithmetic operations is integer
+(a scalar \intgr\ or a matrix of type \itc) and the other operand
+is double (a scalar \flt\ or a matrix of type \dtc), then the
+integer operand is converted to double, and the result is a matrix of
+type \dtc.
+If one of the operands is integer or double, and the other operand is
+complex (a scalar \cmplx\ or a matrix of type \ztc),
+then the first operand is converted to complex, and the result is
+a matrix of type \ztc.
+
+The result of \code{\var{A}**\var{d}} is a complex matrix
+if \var{A} or \var{d} are complex, and real otherwise.
+
+Note that Python rounds the result of an integer division towards minus
+infinity.
+
+The following in-place operations are also defined, but only if
+they do not change the type or the size of the matrix \var{A}:
+\begin{center}\begin{tabular}{l|l}
+ In-place addition &
+ \code{\var{A}+=\var{B}}, \code{\var{A}+=\var{c}} \\
+ In-place subtraction &
+ \code{\var{A}-=\var{B}}, \code{\var{A}-=\var{c}} \\
+ In-place scalar multiplication and division &
+ \code{\var{A}*=\var{c}}, \code{\var{A}/=\var{c}} \\
+ In-place remainder & \code{\var{A}\%=\var{c}}
+\end{tabular}\end{center}
+
+For example, if \var{A} has type \itc, then \code{\var{A}+=\var{B}}
+is allowed if \var{B} has type \itc.
+It is not allowed if \var{B} has type \dtc or \ztc because the
+addition \code{\var{A}+\var{B}} results in a matrix of
+type \dtc or \ztc and therefore cannot be assigned to \var{A}
+without changing its type.
+
+In-place matrix-matrix products are not allowed. (Except when
+\var{c} is a 1 by 1 matrix, in which case \code{\var{A}*=\var{c}} is
+interpreted as the scalar product \code{\var{A}*=\var{c}[0]}.)
+
+It is important to know when a matrix operation creates
+a new object. The following rules apply.
+\begin{itemize}
+\item A simple assignment (\samp{A = B}) is given the standard
+Python interpretation, \ie, it assigns to the variable \var{A} a
+reference (or pointer) to the object referenced by \var{B}.
+\begin{verbatim}
+>>> B = matrix([[1.,2.], [3.,4.]])
+>>> print B
+ 1.0000e+00 3.0000e+00
+ 2.0000e+00 4.0000e+00
+>>> A = B
+>>> A[0,0] = -1
+>>> print B # modifying A[0,0] also modified B[0,0]
+-1.0000e+00 3.0000e+00
+ 2.0000e+00 4.0000e+00
+\end{verbatim}
+
+\item The regular (\ie, not in-place) arithmetic operations always
+return new objects. Hence \samp{A = +B} is equivalent to
+\samp{A = matrix(B)}.
+\begin{verbatim}
+>>> B = matrix([[1.,2.], [3.,4.]])
+>>> A = +B
+>>> A[0,0] = -1
+>>> print B # modifying A[0,0] does not modify B[0,0]
+ 1.0000e+00 3.0000e+00
+ 2.0000e+00 4.0000e+00
+\end{verbatim}
+
+\item The in-place operations directly modify the
+ coefficients of the existing matrix object and do not create a new
+ object.
+\begin{verbatim}
+>>> B = matrix([[1.,2.], [3.,4.]])
+>>> A = B
+>>> A *= 2
+>>> print B # in-place operation also changed B
+ 2.0000e+00 6.0000e+00
+ 4.0000e+00 8.0000e+00
+>>> A = 2*A
+>>> print B # regular operation creates a new A, so does not change B
+ 2.0000e+00 6.0000e+00
+ 4.0000e+00 8.0000e+00
+\end{verbatim}
+\end{itemize}
+
+The restrictions on in-place operations follow the principle that once
+a matrix object is created, its size and type cannot be modified.
+The only matrix attributes that can be changed are the values of the
+elements. The values can be changed by in-place operations or by an
+indexed assignment, as explained in the next section.
+
+\section{Indexing and Slicing} \label{s-indexing}
+
+Matrices can be indexed using one or two arguments. In single-argument
+indexing of a matrix \var{A}, the index runs from
+\code{-len(\var{A})} to \code{len(\var{A})-1}, and is interpreted as an
+index in the one-dimensional array of coefficients of \var{A}
+in column-major order. Negative indices have the standard Python
+interpretation: for negative \var{k}, \code{\var{A}[\var{k}]} is the
+same element as \code{\var{A}[len(\var{A})+\var{k}]}.
+
+Four different types of one-argument indexing are implemented.
+\begin{enumerate}
+\item The index can be a single integer. This returns a
+number, \eg, \code{\var{A}[0]} is the first element of \var{A}.
+
+\item The index can be an integer matrix. This returns a
+column matrix: the command \samp{A[matrix([0,1,2,3])]}
+returns the 4 by 1 matrix consisting of the first four elements of
+\var{A}. The size of the index matrix is ignored:
+\samp{A[matrix([0,1,2,3], (2,2))]} returns the same 4 by 1 matrix.
+
+\item The index can be a list of integers. This returns a column
+matrix, \eg, \code{\var{A}[[0,1,2,3]]} is the 4 by 1 matrix consisting
+of elements 0, 1, 2, 3 of \var{A}.
+
+\item The index can be a Python slice. This returns a matrix with one
+column (possibly 0 by 1, or 1 by 1). For example, \code{\var{A}[::2]}
+is the column matrix defined by taking every other element of \var{A},
+stored in column-major order.
+\code{\var{A}[0:0]} is a matrix with size (0,1).
+\end{enumerate}
+Thus, single-argument indexing returns a scalar (if the index is an
+integer), or a matrix with one column. This is consistent with the
+interpretation that single-argument indexing accesses the matrix in
+column-major order.
+
+Note that an index list or an index matrix are equivalent,
+but they are both useful, especially when we perform operations on
+index sets. For example, if \var{I} and \var{J} are lists then
+\code{\var{I}+\var{J}} is the concatenated list, and \code{2*\var{I}}
+is \var{I} repeated twice. If they are matrices, these operations are
+interpreted as arithmetic operations.
+For large index sets, indexing with integer matrices is also faster
+than indexing with lists.
+
+The following example illustrates one-argument indexing.
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> A = matrix(range(16), (4,4), 'd')
+>>> print A
+ 0.0000e+00 4.0000e+00 8.0000e+00 1.2000e+01
+ 1.0000e+00 5.0000e+00 9.0000e+00 1.3000e+01
+ 2.0000e+00 6.0000e+00 1.0000e+01 1.4000e+01
+ 3.0000e+00 7.0000e+00 1.1000e+01 1.5000e+01
+>>> A[4]
+4.0
+>>> I = matrix([0, 5, 10, 15])
+>>> print A[I] # the diagonal
+ 0.0000e+00
+ 5.0000e+00
+ 1.0000e+01
+ 1.5000e+01
+>>> I = [0,2]; J = [1,3]
+>>> print A[2*I+J] # duplicate I and append J
+ 0.0000e+00
+ 2.0000e+00
+ 0.0000e+00
+ 2.0000e+00
+ 1.0000e+00
+ 3.0000e+00
+>>> I = matrix([0, 2]); J = matrix([1, 3])
+>>> print A[2*I+J] # multiply I by 2 and add J
+ 1.0000e+00
+ 7.0000e+00
+>>> print A[4::4] # get every fourth element skipping the first four
+ 4.0000e+00
+ 8.0000e+00
+ 1.2000e+01
+\end{verbatim}
+
+In two-argument indexing the arguments can be any combinations of the
+four types listed above. The first argument indexes the rows of
+the matrix and the second argument indexes the columns. If both
+indices are scalars, then a scalar is returned. In all other cases,
+a matrix is returned. We continue the example.
+\begin{verbatim}
+>>> print A[:,1]
+ 4.0000e+00
+ 5.0000e+00
+ 6.0000e+00
+ 7.0000e+00
+>>> J = matrix([0, 2])
+>>> print A[J,J]
+ 0.0000e+00 8.0000e+00
+ 2.0000e+00 1.0000e+01
+>>> print A[:2, -2:]
+ 8.0000e+00 1.2000e+01
+ 9.0000e+00 1.3000e+01
+\end{verbatim}
+
+Expressions of the form \code{\var{A}[\var{I}]} or
+\code{\var{A}[\var{I},\var{J}]} can also appear on the lefthand side
+of an assignment.
+The righthand side must be a scalar (\ie, a number or a 1 by 1 dense
+matrix), a sequence of numbers, or a dense or sparse matrix.
+If the righthand side is a scalar, it is interpreted as a
+matrix with identical entries and the dimensions of the lefthand side.
+If the righthand side is a sequence of numbers (list, tuple,
+\module{array} array, xrange object, \ldots) its values are
+interpreted as the coefficients of the lefthand side in column-major
+order. If the righthand side is a matrix (\mtrx\ or \spmtrx), it must
+have the same size as the lefthand side. Sparse matrices are
+converted to dense in the assignment.
+
+Indexed assignments are only allowed if they do not change the type of
+the matrix. For example, if \var{A} is a matrix with type \dtc, then
+\code{\var{A}[\var{I}] = \var{B}} is only permitted if \var{B} is
+an \intgr, a \flt, or a matrix of type \itc\ or \dtc.
+If \var{A} is an integer matrix, then \code{\var{A}[\var{I}] = \var{B}}
+is only permitted if \var{B} is an \intgr\ or an integer matrix.
+
+The following example illlustrates indexed assignment.
+\begin{verbatim}
+>>> A = matrix(range(16), (4,4))
+>>> A[::2,::2] = matrix([[-1, -2], [-3, -4]])
+>>> print A
+ -1 4 -3 12
+ 1 5 9 13
+ -2 6 -4 14
+ 3 7 11 15
+>>> A[::5] += 1
+>>> print A
+ 0 4 -3 12
+ 1 6 9 13
+ -2 6 -3 14
+ 3 7 11 16
+>>> A[0,:] = -1, 1, -1, 1
+>>> print A
+ -1 1 -1 1
+ 1 6 9 13
+ -2 6 -3 14
+ 3 7 11 16
+>>> A[2:,2:] = xrange(4)
+>>> print A
+ -1 1 -1 1
+ 1 6 9 13
+ -2 6 0 2
+ 3 7 1 3
+\end{verbatim}
+
+\section{Built-in Functions} \label{s-builtinfuncs}
+Many Python built-in functions and operations can be used with matrix
+arguments. We list some useful examples.
+
+\begin{funcdesc}{len}{x}
+Returns the product of the number of rows and the number of columns.
+\end{funcdesc}
+
+\begin{funcdesc}{bool}{\optional{x}}
+Returns \False\ if \var{x} is empty (\ie, \code{len(\var{x})} is zero)
+and \True\ otherwise.
+\end{funcdesc}
+
+\begin{funcdesc}{max}{x}
+Returns the maximum element of \var{x}.
+\end{funcdesc}
+
+\begin{funcdesc}{min}{x}
+Returns the minimum element of \var{x}.
+\end{funcdesc}
+
+\begin{funcdesc}{abs}{x}
+Returns a matrix with the absolute values of the elements of \var{x}.
+\end{funcdesc}
+
+\begin{funcdesc}{sum}{x\optional{, start=0.0}}
+Returns the sum of \var{start} and the elements of \var{x}.
+\end{funcdesc}
+
+Matrices can be used as arguments to the \function{list()},
+\function{tuple()}, \function{zip()}, \function{map()}, and
+\function{filter()} functions described in section 2.1 of the Python
+Library Reference. \code{list(\var{A})} and \code{tuple(\var{A})}
+construct a list, respectively a tuple, from the elements of \var{A}.
+\code{zip(\var{A},\var{B},\ldots)} returns a list of tuples,
+with the {\it i}th tuple containing the {\it i}th elements of \var{A},
+\var{B}, \ldots.
+
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> A = matrix([[-11., -5., -20.], [-6., -0., 7.]])
+>>> B = matrix(range(6), (3,2))
+>>> list(A)
+[-11.0, -5.0, -20.0, -6.0, 0.0, 7.0]
+>>> tuple(B)
+(0, 1, 2, 3, 4, 5)
+>>> zip(A,B)
+[(-11.0, 0), (-5.0, 1), (-20.0, 2), (-6.0, 3), (0.0, 4), (7.0, 5)]
+\end{verbatim}
+
+\code{map(\var{f},\var{A})}, where \var{f} is a function and \var{A}
+is a matrix, returns a list constructed by applying \var{f} to each
+element of \var{A}. Multiple arguments can be provided, for example,
+as in \code{map(\var{f},\var{A},\var{B})}, if \var{f} is a function
+with two arguments.
+\begin{verbatim}
+>>> A = matrix([[5, -4, 10, -7], [-1, -5, -6, 2], [6, 1, 5, 2], [-1, 2, -3, -7]])
+>>> B = matrix([[4,-15, 9, -14], [-4, -12, 1, -22], [-10, -9, 9, 12], [-9, -7,-11, -6]])
+>>> print matrix(map(max, A, B), (4,4)) # takes componentwise maximum
+ 5 -1 6 -1
+ -4 -5 1 2
+ 10 1 9 -3
+ -7 2 12 -6
+\end{verbatim}
+
+\code{filter(\var{f},\var{A})}, where \var{f} is a function and
+\var{A} is a matrix, returns a list containing the elements of \var{A}
+for which \var{f} is true.
+\begin{verbatim}
+>>> print filter(lambda x: x%2, A) # list of odd elements in A
+[5, -7, -1, -5, 1, 5, -1, -3, -7]
+>>> print filter(lambda x: -2 < x < 3, A) # list of elements between -2 and 3
+[-1, 2, 1, 2, -1, 2]
+\end{verbatim}
+
+It is also possible to iterate over matrix elements, as illustrated in
+the following example.
+\begin{verbatim}
+>>> A = matrix([[5, -3], [9, 11]])
+>>> for x in A: print max(x,0)
+...
+5
+0
+9
+11
+>>> [max(x,0) for x in A]
+[5, 0, 9, 11]
+\end{verbatim}
+
+The expression \samp{\var{x} in \var{A}} returns \True\ if an element
+of \var{A} is equal to \var{x} and \False\ otherwise.
+
+\section{Other Matrix Functions} \label{s-otherfuncs}
+The following functions of dense matrices can be imported from
+\module{cvxopt.base}.
+\begin{funcdesc}{sqrt}{x}
+The elementwise square root of \var{x}. The result is returned
+as a real matrix if \var{x} is an integer or real matrix and
+as a complex matrix if \var{x} is a complex matrix. Raises an
+exception when \var{x} is an integer or real matrix with negative
+elements.
+\end{funcdesc}
+
+\begin{funcdesc}{sin}{x}
+The sine function applied elementwise to \var{x}.
+The result is returned as a real matrix if \var{x} is an integer
+or real matrix and as a complex matrix otherwise.
+\end{funcdesc}
+
+\begin{funcdesc}{cos}{x}
+The cosine function applied elementwise to \var{x}.
+The result is returned as a real matrix if \var{x} is an integer
+or real matrix and as a complex matrix otherwise.
+\end{funcdesc}
+
+\begin{funcdesc}{exp}{x}
+The exponential function applied elementwise to \var{x}.
+The result is returned as a real matrix if \var{x} is an integer
+or real matrix and as a complex matrix otherwise.
+\end{funcdesc}
+
+\begin{funcdesc}{log}{x}
+The natural logarithm applied elementwise to \var{x}.
+The result is returned as a real matrix if \var{x} is an integer
+or real matrix and as a complex matrix otherwise.
+Raises an exception when \var{x} is an integer or real matrix with
+nonnegative elements, or a complex matrix with zero elements.
+\end{funcdesc}
+
+\begin{funcdesc}{mul}{x, y}
+The elementwise product of \var{x} and \var{y}.
+The two matrices must have the same size and type.
+\end{funcdesc}
+
+\begin{funcdesc}{div}{x, y}
+The elementwise division of \var{x} by \var{y}.
+The two matrices must have the same size and type.
+\end{funcdesc}
+
+
+\section{Randomly Generated Matrices} \label{s-random}
+The module \module{cvxopt.random} provides functions for generating
+random matrices. Two types of random matrices are defined:
+matrices with normally distributed entries and matrices with uniformly
+distributed entries.
+
+The pseudo-random number generators used to
+generate the random matrices are from the package described in the
+references below.
+\begin{seealso}
+\seelink{http://www.cs.wm.edu/\~{}va/software/park/park.html}
+{S. Park, Random Number Generators.}{}
+
+\seealso{S. Park, D. Geyer, Random Number Generators: Good Ones Are
+Hard To Find,
+Communications of the ACM, October 1988.}
+\end{seealso}
+
+\begin{funcdesc}{normal}{nrows\optional{, ncols\optional{,
+ mean\optional{, std}}}}
+Returns a type \dtc\ matrix of size \var{nrows} by
+\var{ncols} with random elements chosen from a normal distribution
+with mean \var{mean} and standard deviation \var{std}.
+The default values for the optional arguments are
+\var{ncols}=1, \var{mean}=0.0, \var{std}=1.0.
+\end{funcdesc}
+
+\begin{funcdesc}{uniform}{nrows\optional{, ncols\optional{,
+ a\optional{, b}}}}
+Returns a type \dtc\ matrix of size \var{nrows} by
+\var{ncols} matrix with random elements, uniformly distributed
+between \var{a} and \var{b}.
+The default values for the optional arguments are
+\var{ncols}=1, \var{a}=0.0, \var{b}=1.0.
+\end{funcdesc}
+
+\begin{funcdesc}{getseed}{}
+Returns the current seed value (the state of the random number
+generator).
+\end{funcdesc}
+
+\begin{funcdesc}{setseed}{\optional{value}}
+Sets the seed value. \var{value} must be a nonnegative integer.
+If \var{value} is absent or equal to zero, the seed value is taken
+from the system clock.
+\end{funcdesc}
+
+\section{The NumPy Array Interface} \label{s-array-interface}
+
+The CVXOPT \mtrx\ object is compatible with the NumPy Array Interface,
+which allows Python objects that represent multidimensional
+arrays to exchange data using information stored in the
+attribute \code{\_\_array\_struct\_\_}.
+
+\begin{seealso}
+\seelink{http://numpy.scipy.org/array_interface.shtml}
+{NumPy Array Interface Specification}{}
+
+\seelink{http://numpy.scipy.org}{NumPy home page}{}
+\end{seealso}
+
+As already mentioned in section~\ref{s-creating-matrices},
+a two-dimensional array object (for example, a 2D \module{numarray}
+array) can be converted to a \mtrx\ object by using the
+\function{matrix()} constructor.
+Conversely, CVXOPT matrices can be used as array-like objects
+in \module{numarray}. The following example illustrates the
+compatibility of CVXOPT matrices and \module{numarray} arrays.
+\begin{verbatim}
+>>> from cvxopt import matrix
+>>> a = matrix(range(6), (2,3), 'd')
+>>> print a
+ 0.0000e+00 2.0000e+00 4.0000e+00
+ 1.0000e+00 3.0000e+00 5.0000e+00
+>>> from numarray import array
+>>> b = array(a)
+>>> print b
+[[ 0. 2. 4.]
+ [ 1. 3. 5.]]
+>>> print a*b
+[[ 0. 4. 16.]
+ [ 1. 9. 25.]]
+\end{verbatim}
+In the last expression \code{a*b} is interpreted as a \module{numarray}
+multiplication (\ie, componentwise) even though one operand is a
+\mtrx\ object.
+
+\section{Printing Options}
+The format used for printing dense matrices (and the sparse matrices
+discussed in chapter~\ref{chap:spmatrix}) is controlled
+by the dictionary \member{cvxopt.base.print\_options}. The dictionary
+has three keys, \code{'iformat'}, \code{'dformat'}, \code{'zformat'}
+that control, respectively, how integer, double and complex numbers are
+printed. The fields are C printf format strings with default
+values \code{'5.4e'}\ for \dtc\ and \ztc\ matrices and \code{'5i'}\ for
+\itc\ matrices.
+\begin{verbatim}
+>>> from cvxopt.base import matrix, print_options
+>>> print_options
+{'zformat': '5.4e', 'iformat': '5i', 'dformat': '5.4e'}
+>>> A = matrix([1., 2., 3.])
+>>> print A
+ 1.0000e+00
+ 2.0000e+00
+ 3.0000e+00
+>>> print_options['dformat'] = 'f'
+>>> print A
+ 1.000000
+ 2.000000
+ 3.000000
+>>> print_options['dformat'] = '5.2e'
+>>> print A
+ 1.00e+00
+ 2.00e+00
+ 3.00e+00
+\end{verbatim}
diff --git a/doc/base_sparse.tex b/doc/base_sparse.tex
new file mode 100644
index 0000000..d0d7c6b
--- /dev/null
+++ b/doc/base_sparse.tex
@@ -0,0 +1,712 @@
+\chapter{Sparse Matrices (\module{cvxopt.base})}\label{chap:spmatrix}
+
+In this chapter we discuss the \spmtrx\ object defined in
+\module{cvxopt.base}.
+
+\section{Creating Sparse Matrices} \label{s-creating-spmatrix}
+A general \spmtrx\ object can be thought of as a \emph{triplet
+description} of a sparse matrix, \ie, a list of entries of the matrix,
+with for each entry the value, row index, and column index.
+Entries that are not included in the list are assumed to be zero.
+For example, the sparse matrix
+\BEQ \label{e-sparse-A}
+ A = \left[ \begin{array}{rrrrr}
+ 0 & 2 & 0 & 0 & 3 \\
+ 2 & 0 & 0 & 0 & 0 \\
+ -1 & -2 & 0 & 4 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \end{array} \right]
+\EEQ
+has the triplet description
+\[
+(2,1,0), \qquad (-1,2,0), \qquad (2,0,1), \qquad (-2,2,1), \qquad
+(1,3,2), \qquad (4,2,3), \qquad (3,0,4).
+\]
+The list may include entries with a zero value, so triplet
+descriptions are not necessarily unique.
+The list
+\[
+(2,1,0), \qquad (-1,2,0), \qquad (0,3,0), \qquad (2,0,1), \qquad
+ (-2,2,1), \qquad (1,3,2), \qquad (4,2,3), \qquad (3,0,4)
+\]
+is another triplet description of the same matrix.
+
+An \spmtrx\ object corresponds to a particular triplet
+description of a sparse matrix. We will refer to the entries in
+the triplet description as the \emph{nonzero entries} of the object,
+even though they may have a numerical value zero.
+
+Two functions are provided to create sparse matrices.
+The first, \function{spmatrix()}, constructs a sparse matrix from
+a triplet description.
+\begin{funcdesc}{spmatrix}{x, I, J\optional{, size\optional{, tc}}}
+
+\var{I} and \var{J} are sequences of integers (lists, tuples,
+\module{array} arrays, xrange objects, \ldots) or integer matrices
+(\mtrx\ objects with typecode \itc), containing the row and column
+indices of the nonzero entries.
+The lengths of \var{I} and \var{J} must be equal. If they
+are matrices, they are treated as lists of indices stored in
+column-major order, \ie, as lists \code{list(\var{I})}, respectively,
+\code{list(\var{J})}.
+
+\var{size} is a tuple of nonnegative integers with the row and column
+dimensions of the matrix.
+The \var{size} argument is only needed when creating a matrix with
+a zero last row or last column. If \var{size} is not specified, it
+is determined from \var{I} and \var{J}:
+the default value for \code{\var{size}[0]} is \code{max(\var{I})+1}
+if \var{I} is nonempty and zero otherwise.
+The default value for \code{\var{size}[1]} is
+\code{max(\var{J})+1} if \var{J} is nonempty and zero otherwise.
+
+\var{tc} is the typecode, \dtc\ or \ztc, for double and complex
+matrices, respectively. Integer sparse matrices are not implemented.
+
+\var{x} can be a number, a sequence of numbers, or a dense matrix.
+This argument specifies the numerical values of the nonzero entries.
+\BIT
+\item If \var{x} is a number (Python \intgr, \flt\ or \cmplx),
+a matrix is created with the sparsity pattern defined by \var{I} and
+\var{J}, and nonzero entries initialized to the value of \var{x}.
+The default value of \var{tc} is \dtc\ if \var{x} is \intgr\ or \flt,
+and \ztc\ if \var{x} is \cmplx.
+
+The following code creates a 4 by 4 sparse identity matrix.
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix
+>>> A = spmatrix(1.0, range(4), range(4))
+>>> print A
+SIZE: (4,4)
+(0, 0) 1.0000e+00
+(1, 1) 1.0000e+00
+(2, 2) 1.0000e+00
+(3, 3) 1.0000e+00
+\end{verbatim}
+
+\item If \var{x} is a sequence of numbers, a sparse matrix is created
+with the entries of \var{x} copied to the entries indexed by \var{I}
+and \var{J}. The list \var{x} must have the same length as \var{I} and
+\var{J}.
+The default value of \var{tc} is determined from the elements of
+\var{x}:
+\dtc\ if \var{x} contains integers and floating-point numbers or
+if \var{x} is an empty list,
+and \ztc\ if \var{x} contains at least one complex number.
+
+As an example, the matrix~(\ref{e-sparse-A}) can be created as follows.
+\begin{verbatim}
+>>> A = spmatrix([2,-1,2,-2,1,4,3], [1,2,0,2,3,2,0], [0,0,1,1,2,3,4])
+>>> print A
+SIZE: (4,5)
+(1, 0) 2.0000e+00
+(2, 0) -1.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(3, 2) 1.0000e+00
+(2, 3) 4.0000e+00
+(0, 4) 3.0000e+00
+\end{verbatim}
+
+\item If \var{x} is a dense matrix, a sparse matrix is created with
+all the entries of \var{x} copied, in column-major order, to the
+entries indexed by \var{I} and \var{J}.
+The matrix \var{x} must have the same length as \var{I} and \var{J}.
+The default value of \var{tc} is \dtc\ if \var{x} is an \itc\ or \dtc\
+matrix, and \ztc\ otherwise.
+\EIT
+
+If \var{I} and \var{J} contain repeated entries, the corresponding
+values of the coefficients are added.
+\end{funcdesc}
+
+The function \function{sparse()} constructs a sparse matrix from
+a block-matrix description.
+
+\begin{funcdesc}{sparse}{x\optional{, tc}}
+\var{tc} is the typecode, \dtc\ or \ztc, for double and complex
+matrices, respectively.
+
+\var{x} can be a \mtrx, \spmtrx, or a list of lists of matrices
+(\mtrx\ or \spmtrx\ objects) and numbers (Python \intgr, \flt\ or
+\cmplx).
+\BIT
+\item If \var{x} is a \mtrx\ or \spmtrx\ object, then a sparse matrix
+of the same size and the same numerical value is created.
+Numerical zeros in \var{x} are treated as structural zeros and removed
+from the triplet description of the new sparse matrix.
+
+\item If \var{x} is a list of lists of matrices (\mtrx\ or \spmtrx)
+and numbers (Python \intgr, \flt\ or \cmplx) then each element of
+\var{x} is interpreted as a (block-)column matrix stored in
+colum-major order, and a block-matrix is constructed by juxtaposing
+the \code{len(\var{x})} block-columns
+(as in \function{matrix()}, see section~\ref{s-creating-matrices}).
+Numerical zeros are removed from the triplet description of the new
+matrix.
+
+The following example shows how to construct a sparse block-matrix.
+\begin{verbatim}
+>>> from cvxopt.base import matrix, spmatrix, sparse
+>>> A = matrix([[1, 2, 0], [2, 1, 2], [0, 2, 1]])
+>>> B = spmatrix([], [], [], (3,3))
+>>> C = spmatrix([3, 4, 5], [0, 1, 2], [0, 1, 2])
+>>> print sparse([[A, B], [B, C]])
+SIZE: (6,6)
+(0, 0) 1.0000e+00
+(1, 0) 2.0000e+00
+(0, 1) 2.0000e+00
+(1, 1) 1.0000e+00
+(2, 1) 2.0000e+00
+(1, 2) 2.0000e+00
+(2, 2) 1.0000e+00
+(3, 3) 3.0000e+00
+(4, 4) 4.0000e+00
+(5, 5) 5.0000e+00
+\end{verbatim}
+
+A matrix with a single block-column can be represented by a single
+list.
+\begin{verbatim}
+>>> print sparse([A, C])
+SIZE: (6,3)
+(0, 0) 1.0000e+00
+(1, 0) 2.0000e+00
+(3, 0) 3.0000e+00
+(0, 1) 2.0000e+00
+(1, 1) 1.0000e+00
+(2, 1) 2.0000e+00
+(4, 1) 4.0000e+00
+(1, 2) 2.0000e+00
+(2, 2) 1.0000e+00
+(5, 2) 5.0000e+00
+\end{verbatim}
+\EIT
+
+\end{funcdesc}
+
+\section{Attributes and Methods}
+The following attributes and methods are defined for \spmtrx\ objects.
+
+\begin{memberdesc}[matrix]{V}
+A single-column dense matrix containing the numerical values of the
+nonzero entries in column-major order. Making an assignment to
+the attribute is an efficient way of changing the values of the sparse
+matrix, without changing the sparsity pattern.
+
+When the attribute \member{V} is read, a \emph{copy} of \member{V} is
+returned, as a new dense matrix.
+(This implies, for example, that an indexed assignment
+\samp{A.V[I] = B} does not work, or at least
+cannot be used to modify \var{A}. Instead the attribute \code{V}\
+will be read and returned as a new matrix; then the elements of this
+new matrix are modified.)
+\end{memberdesc}
+
+\begin{memberdesc}[spmatrix]{I}
+A single-column integer matrix with the row indices of the entries in
+\code{V}. A read-only attribute.
+\end{memberdesc}
+
+\begin{memberdesc}[matrix]{J}
+A single-column integer matrix with the column indices of the entries
+in \code{V}. A read-only attribute.
+\end{memberdesc}
+
+\begin{memberdesc}[tuple]{size}
+A tuple with the dimensions of the matrix. A read-only attribute.
+\end{memberdesc}
+
+\begin{methoddesc}{trans}{}
+Returns the transpose of a sparse matrix as a new sparse matrix.
+One can also use \code{A.T} instead of \code{A.trans()}.
+\end{methoddesc}
+
+\begin{methoddesc}{ctrans}{}
+Returns the complex conjugate transpose of a sparse matrix as a
+new sparse matrix.
+One can also use \code{A.H} instead of \code{A.ctrans()}.
+\end{methoddesc}
+
+In the following example we take the elementwise square root of
+the matrix
+\BEQ \label{e-spA-example}
+ A = \left[ \begin{array}{rrrrr}
+ 0 & 2 & 0 & 0 & 3 \\
+ 2 & 0 & 0 & 0 & 0 \\
+ 1 & 2 & 0 & 4 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \end{array} \right]
+\EEQ
+\begin{verbatim}
+>>> from cvxopt.base import sqrt
+>>> A = spmatrix([2,1,2,2,1,3,4], [1,2,0,2,3,0,2], [0,0,1,1,2,3,3])
+>>> B = spmatrix(sqrt(A.V), A.I, A.J)
+>>> print B
+SIZE: (4,4)
+(1, 0) 1.4142e+00
+(2, 0) 1.0000e+00
+(0, 1) 1.4142e+00
+(2, 1) 1.4142e+00
+(3, 2) 1.0000e+00
+(0, 3) 1.7321e+00
+(2, 3) 2.0000e+00
+\end{verbatim}
+
+The next example below illustrates assignments to \member{V}.
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix, matrix
+>>> A = spmatrix(range(5), [0,1,1,2,2], [0,0,1,1,2])
+>>> print A
+SIZE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 1.0000e+00
+(1, 1) 2.0000e+00
+(2, 1) 3.0000e+00
+(2, 2) 4.0000e+00
+>>> B = spmatrix(A.V, A.J, A.I, (4,4)) # transpose and add a zero row and column
+>>> print B
+SIZE: (4,4)
+(0, 0) 0.0000e+00
+(0, 1) 1.0000e+00
+(1, 1) 2.0000e+00
+(1, 2) 3.0000e+00
+(2, 2) 4.0000e+00
+>>> print matrix(B)
+ 0.0000e+00 1.0000e+00 0.0000e+00 0.0000e+00
+ 0.0000e+00 2.0000e+00 3.0000e+00 0.0000e+00
+ 0.0000e+00 0.0000e+00 4.0000e+00 0.0000e+00
+ 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
+>>> B.V[:] = 1., 7., 8., 6., 4. # assign new values to nonzero entries
+>>> print B
+SIZE: (4,4)
+(0, 0) 1.0000e+00
+(0, 1) 7.0000e+00
+(1, 1) 8.0000e+00
+(1, 2) 6.0000e+00
+(2, 2) 4.0000e+00
+>>> B.V += 1.0 # add 1 to the nonzero entries
+>>> print B
+SIZE: (4,4)
+(0, 0) 2.0000e+00
+(0, 1) 8.0000e+00
+(1, 1) 9.0000e+00
+(1, 2) 7.0000e+00
+(2, 2) 5.0000e+00
+\end{verbatim}
+
+The \member{V}, \member{I} and \member{J} attributes can be used for
+reading sparse matrices from or writing them to binary files.
+Suppose we want to write the matrix \var{A} defined above to a binary
+file.
+\begin{verbatim}
+>>> f = open('test.bin','w')
+>>> A.V.tofile(f)
+>>> A.I.tofile(f)
+>>> A.J.tofile(f)
+>>> f.close()
+\end{verbatim}
+A sparse matrix can be created from this file as follows.
+\begin{verbatim}
+>>> f = open('test.bin','r')
+>>> V = matrix(0.0, (5,1)); V.fromfile(f)
+>>> I = matrix(0, (5,1)); I.fromfile(f)
+>>> J = matrix(0, (5,1)); J.fromfile(f)
+>>> B = spmatrix(V, I, J)
+>>> print B
+SIZE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 1.0000e+00
+(1, 1) 2.0000e+00
+(2, 1) 3.0000e+00
+(2, 2) 4.0000e+00
+\end{verbatim}
+
+Note that the \module{pickle} module provides a convenient alternative
+to this method.
+
+\section{Arithmetic Operations} \label{s-spmatrix-arith}
+Most of the operations defined for dense \dtc\ and \ztc\ matrices
+(section~\ref{s-arithmetic}) are also defined for sparse matrices.
+In the following table, \var{A} is a sparse matrix,
+\var{B} is sparse or dense, and \var{c} is a scalar, defined as a
+Python number or a 1 by 1 dense matrix.
+
+\begin{center}
+\begin{tabular}{l|l}
+ Unary plus/minus & \code{+\var{A}}, \code{-\var{A}} \\
+ Addition & \code{\var{A}+\var{B}}, \code{\var{B}+\var{A}},
+ \code{\var{A}+\var{c}}, \code{\var{c}+\var{A}}\\
+ Subtraction & \code{\var{A}-\var{B}}, \code{\var{B}-\var{A}},
+ \code{\var{A}-\var{c}}, \code{\var{c}-\var{A}}\\
+ Matrix multiplication & \code{\var{A}*\var{B}},
+ \code{\var{B}*\var{A}} \\
+ Scalar multiplication and division & \code{\var{c}*\var{A}},
+ \code{\var{A}*\var{c}}, \code{\var{A}/\var{c}}
+ \end{tabular}
+\end{center}
+
+If \var{B} is a dense matrix, then the result of
+\code{\var{A}+\var{B}}, \code{\var{B}+\var{A}}, \code{\var{A}-\var{B}},
+\code{\var{B}-\var{A}} is a dense matrix.
+The typecode of the result is \dtc\ if \var{A} has typcode \dtc\ and
+\var{B} has typecode \itc\ or \dtc,
+and it is \ztc\ if \var{A} and/or \var{B} have typecode \ztc.
+
+If \var{B} is a sparse matrix, then the result of
+\code{\var{A}+\var{B}}, \code{\var{B}+\var{A}},
+\code{\var{A}-\var{B}}, \code{\var{B}-\var{A}} is a sparse
+matrix. The typecode of the result is \dtc\ if \var{A} and \var{B}
+have typecode \dtc, and \ztc\ otherwise.
+
+If \var{c} in \code{\var{A}+\var{c}}, \code{\var{A}-\var{c}},
+\code{\var{c}+\var{A}}, \code{\var{c}-\var{A}} is a number,
+then it is interpreted as a dense matrix with the same size as
+\var{A}, typecode given by the type of \var{c}, and all entries equal
+to \var{c}.
+If \var{c} is a 1 by 1 dense matrix and the size of \var{A} is not 1
+by 1, then \var{c}
+is interpreted as a dense matrix of the same size as \var{A},
+typecode given by the typecode of \var{c}, and all entries equal to
+\code{\var{c}[0]}.
+
+The result of a matrix-matrix product \code{\var{A}*\var{B}} or
+\code{\var{B}*\var{A}} is a dense matrix if \var{B} is dense, and sparse
+if \var{B} is sparse. The matrix-matrix product is not allowed if
+\var{B} is a dense \itc\ matrix.
+
+If \var{c} is a number (Python \intgr\, \flt\ or \cmplx), then the
+operations \code{\var{c}*\var{A}} and \code{\var{A}*\var{c}} define
+scalar multiplication and return a sparse matrix.
+
+If \var{c} is a 1 by 1 dense matrix, then, if possible, the products
+\code{\var{c}*\var{A}} and \code{\var{A}*\var{c}} are interpreted as
+matrix-matrix products and a dense matrix is returned.
+If the product cannot be interpreted as a matrix-matrix product
+(either because the dimensions of \var{A} are incompatible or because
+\var{c} has typecode \itc), then the product is interpreted as the
+scalar multiplication with \code{\var{c}[0]} and a sparse matrix is
+returned.
+
+The division \code{\var{A}/\var{c}} is interpreted as scalar
+multiplication with \code{1.0/\var{c}} if \var{c} is a number,
+or with \code{1.0/\var{c}[0]} if \var{c} is a 1 by 1 dense matrix.
+
+The following in-place operations are defined for a sparse matrix
+\var{A} if they do not change the dimensions or type of \var{A}.
+\begin{center}
+ \begin{tabular}{l|l}
+ In-place addition & \code{\var{A}+=\var{B}},
+ \code{\var{A}+=\var{c}} \\
+ In-place subtraction & \code{\var{A}-=\var{B}},
+ \code{\var{A}-=\var{c}} \\
+ In-place scalar multiplication and division &
+ \code{\var{A}*=\var{c}}, \code{\var{A}/=\var{c}}
+ \end{tabular}
+\end{center}
+
+For example, \samp{\var{A} += 1.0} is not allowed because the
+operation \samp{\var{A} = \var{A} + 1.0} results in a dense matrix,
+so it cannot be assigned to \var{A} without changing its type.
+
+In-place matrix-matrix products are not allowed. (Except when
+\var{c} is a 1 by 1 dense matrix, in which case \code{\var{A}*=\var{c}}
+is interpreted as a scalar product \code{\var{A}*=\var{c}[0]}.)
+
+As for dense operations, the in-place sparse operations do not return
+a new matrix but modify the existing object \var{A}.
+The restrictions on in-place operations follow the principle that once
+a sparse matrix is created, its size and type cannot be modified.
+The only attributes that can be modified are the sparsity pattern and
+the numerical values of the nonzero elements.
+These attributes can be modified by in-place operations or by indexed
+assignments.
+
+
+
+\section{Indexing and Slicing}
+Sparse matrices can be indexed the same way as dense matrices
+(see section~\ref{s-indexing} ).
+
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix
+>>> A = spmatrix([0,2,-1,2,-2,1], [0,1,2,0,2,1], [0,0,0,1,1,2])
+>>> print A[:,[0,1]]
+SIZE: (3,2)
+(0, 0) 0.0000e+00
+(1, 0) 2.0000e+00
+(2, 0) -1.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+>>> B = spmatrix([0,2*1j,0,-2], [1,2,1,2], [0,0,1,1,])
+>>> print B[-2:,-2:]
+SIZE: (2,2)
+(0, 0) 0.0000e+00-j0.0000e+00
+(1, 0) 2.0000e+00-j0.0000e+00
+(0, 1) 0.0000e+00-j0.0000e+00
+(1, 1) 0.0000e+00-j2.0000e+00
+\end{verbatim}
+
+An indexed sparse matrix \code{\var{A}[\var{I}]} or
+\code{\var{A}[\var{I},\var{J}]} can also be the target of an
+assignment. The righthand side of the assignment can be a scalar
+(a Python \intgr, \flt, or \cmplx, or a 1 by 1 dense matrix),
+a sequence of numbers, or a sparse or dense matrix of
+compatible dimensions.
+If the righthand side is a scalar, it is treated as a dense matrix of
+the same size as the lefthand side and with all its entries equal to
+the scalar.
+If the righthand side is a sequence of numbers, they are treated as
+the elements of a dense matrix in column-major order.
+
+We continue the example above.
+\begin{verbatim}
+>>> C = spmatrix([10,-20,30], [0,2,1], [0,0,1])
+>>> A[:,0] = C[:,0]
+>>> print A
+SIZE: (3,3)
+(0, 0) 1.0000e+01
+(2, 0) -2.0000e+01
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+>>> D = matrix(range(6), (3,2))
+>>> A[:,0] = D[:,0]
+>>> print A
+SIZE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 1.0000e+00
+(2, 0) 2.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+>>> A[:,0] = 1
+>>> print A
+SIZE: (3,3)
+(0, 0) 1.0000e+00
+(1, 0) 1.0000e+00
+(2, 0) 1.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+>>> A[:,0] = 0
+>>> print A
+TYPE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 0.0000e+00
+(2, 0) 0.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+\end{verbatim}
+
+
+\section{Built-In Functions}
+
+The functions described in the table of section~\ref{s-builtinfuncs}
+also work with sparse matrix arguments. The difference is that for a
+sparse matrix only the nonzero entries are considered.
+
+\begin{funcdesc}{len}{x}
+If \var{x} is a \spmtrx, returns the number of nonzero entries in
+\var{x}.
+\end{funcdesc}
+
+\begin{funcdesc}{bool}{\optional{x}}
+If \var{x} is a \spmtrx, returns \False\ if \var{x} has at least one
+nonzero entry; \False\ otherwise.
+\end{funcdesc}
+
+\begin{funcdesc}{max}{x}
+If \var{x} is a \spmtrx, returns the maximum nonzero entry of \var{x}.
+\end{funcdesc}
+
+\begin{funcdesc}{min}{x}
+If \var{x} is a \spmtrx, returns the minimum nonzero entry of \var{x}.
+\end{funcdesc}
+
+\begin{funcdesc}{abs}{x}
+If \var{x} is a \spmtrx, returns a sparse matrix with the absolute
+value of the elements of \var{x} and the same sparsity pattern.
+\end{funcdesc}
+
+\begin{funcdesc}{sum}{x\optional{, start=0.0}}
+If \var{x} is a \spmtrx, returns the sum of \var{start} and the
+elements of \var{x}.
+\end{funcdesc}
+
+The functions \function{list()}, \function{tuple()}, \function{zip()},
+\function{map()}, \function{filter()} also take sparse matrix arguments.
+They work as for dense matrices, again with the difference that only
+the nonzero entries are considered.
+
+In the following example we square the entries of the
+matrix~(\ref{e-spA-example}).
+
+\begin{verbatim}
+>>> A = spmatrix([2,1,2,2,1,3,4], [1,2,0,2,3,0,2], [0,0,1,1,2,3,3])
+>>> B = spmatrix(map(lambda x: x**2, A), A.I, A.J)
+>>> print B
+SIZE: (4,4)
+(1, 0) 4.0000e+00
+(2, 0) 1.0000e+00
+(0, 1) 4.0000e+00
+(2, 1) 4.0000e+00
+(3, 2) 1.0000e+00
+(0, 3) 9.0000e+00
+(2, 3) 1.6000e+01
+\end{verbatim}
+
+The expression \samp{\var{x} in \var{A}} returns \True\ if a nonzero
+entry of \var{A} is equal to \var{x} and \False\ otherwise.
+
+
+\section{Sparse BLAS Functions}
+The \module{cvxopt.base} module includes a few arithmetic functions
+that extend functions from \module{cvxopt.blas} to sparse matrices.
+These functions are faster than the corresponding operations
+implemented using the overloaded arithmetic described
+in~section~\ref{s-spmatrix-arith}.
+They also work in-place, \ie, they modify their arguments without
+creating new objects.
+
+
+\begin{funcdesc}{gemv}{A, x, y\optional{, trans='N'\optional{,
+ alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a general dense or sparse matrix:
+\[
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+y := \alpha A^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}),
+ \qquad
+y := \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}).
+\]
+If \var{A} is a dense matrix, this is identical to
+\function{blas.gemv()}. If \var{A} is sparse, the result is the same
+as when \function{blas.gemv()} is called with \code{matrix(A)} as
+argument, however, without explicitly converting \var{A} to dense.
+\end{funcdesc}
+
+\begin{funcdesc}{symv}{A, x, y\optional{, uplo='L'\optional{,
+alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a dense or sparse real symmetric matrix:
+\[
+ y := \alpha A x + \beta y.
+\]
+If \var{A} is a dense matrix, this is identical to
+\function{blas.symv()}. If \var{A} is sparse, the result is the same
+as when \function{blas.symv()} is called with \code{matrix(A)} as
+argument, however, without explicitly converting \var{A} to dense.
+\end{funcdesc}
+
+\begin{funcdesc}{gemm}{A, B, C\optional{, transA='N'\optional{,
+transB='N'\optional{, alpha=1.0\optional{, beta=0.0\optional{,
+partial=False}}}}}}
+Matrix-matrix product of two general sparse or dense matrices:
+\[
+ C := \alpha \op(A) \op(B) + \beta C
+\]
+where
+\[
+\op(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'} \end{array} \right.
+\qquad
+\op(B) = \left\{ \begin{array}{ll}
+ B & \mathrm{transB} = \mathrm{'N'} \\
+ B^T & \mathrm{transB} = \mathrm{'T'} \\
+ B^H & \mathrm{transB} = \mathrm{'C'}. \end{array} \right.
+\]
+If \var{A}, \var{B} and \var{C} are dense matrices, this is
+identical to \function{blas.gemm()}, described in section~\ref{s-blas3},
+and the argument \var{partial} is ignored.
+
+If \var{A} and/or \var{B} are sparse and \var{C} is dense, the result
+is the same as when \function{blas.gemm()} is called with
+\code{matrix(A)} and \code{matrix(B)} as arguments, without explicitly
+converting \var{A} and \var{B} to dense.
+The argument \var{partial} is ignored.
+
+If \var{C} is a sparse matrix, the matrix-matrix product in the
+definition of \function{blas.gemm()} is computed, but as a sparse
+matrix.
+If \var{partial} is \False, the result is stored in \var{C},
+and the sparsity pattern of \var{C} is modified if necessary.
+If \var{partial} is \True, the operation only updates the nonzero
+elements in \var{C}, even if the sparsity pattern of \var{C} differs
+from that of the matrix product.
+\end{funcdesc}
+
+\begin{funcdesc}{syrk}{A, C\optional{, uplo='L'\optional{,
+trans='N'\optional{, alpha=1.0\optional{, beta=0.0\optional{,
+partial=False}}}}}}
+Rank-{\it k} update of a sparse or dense real or complex symmetric
+matrix:
+\[
+ C := \alpha AA^T + \beta C \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+ C := \alpha A^TA + \beta C \quad (\mathrm{trans} = \mathrm{'T'}),
+\]
+If \var{A} and \var{C} are dense, this is identical to
+\function{blas.syrk()}, described in section~\ref{s-blas3},
+and the argument \var{partial} is ignored.
+
+If \var{A} is sparse and \var{C} is dense, the result is the same as
+when \function{blas.syrk()} is called with \code{matrix(A)} as
+argument, without explicitly converting \var{A} to dense.
+The argument \var{partial} is ignored.
+
+If \var{C} is sparse, the product in the definition of
+\function{blas.syrk()} is computed, but as a sparse matrix.
+If \var{partial} is \False, the result is stored in \var{C},
+and the sparsity pattern of \var{C} is modified if necessary.
+If \var{partial} is \True, the operation only updates the nonzero
+elements in \var{C}, even if the sparsity pattern of \var{C} differs
+from that of the matrix product.
+\end{funcdesc}
+
+In the following example, we first compute
+\[
+C = A^TB, \qquad
+A = \left[ \begin{array}{ccc}
+0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}\right],
+\qquad
+B = \left[ \begin{array}{ccc}
+ 0 & -1 & 0 \\ 2 & 0 & 2 \\ 0 & 3 & 0 \\ 2 & 0 & 0
+ \end{array}\right].
+\]
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix, gemm
+>>> A = spmatrix(1, [1,3,0,2,1], [0,0,1,1,2])
+>>> B = spmatrix([2,2,-1,3,2], [1,3,0,2,1], [0,0,1,1,2])
+>>> C = spmatrix([], [], [], size=(3,3))
+>>> gemm(A, B, C, transA='T')
+>>> print C
+SIZE: (3,3)
+(0, 0) 4.0000e+00
+(2, 0) 2.0000e+00
+(1, 1) 2.0000e+00
+(0, 2) 2.0000e+00
+(2, 2) 2.0000e+00
+\end{verbatim}
+Now suppose we want to replace {\it C}
+\[
+C = A^TD, \qquad
+D = \left[ \begin{array}{ccc}
+ 0 & 1 & 0 \\ 3 & 0 & -2 \\ 0 & 1 & 0 \\ 4 & 0 & 0
+ \end{array}\right].
+\]
+The new matrix has the same sparsity pattern as \var{C}, so we can
+use \function{gemm()} with the \code{partial=True} option.
+This saves time in large sparse matrix multiplications when the
+sparsity pattern of the result is known beforehand.
+\begin{verbatim}
+>>> D = spmatrix([3,4,1,1,-2], [1,3,0,2,1], [0,0,1,1,2])
+>>> gemm(A, D, C, transA='T', partial=True)
+>>> print C
+SIZE: (3,3)
+(0, 0) 7.0000e+00
+(2, 0) 3.0000e+00
+(1, 1) 2.0000e+00
+(0, 2) -2.0000e+00
+(2, 2) -2.0000e+00
+\end{verbatim}
diff --git a/doc/blas.tex b/doc/blas.tex
new file mode 100644
index 0000000..2d4531a
--- /dev/null
+++ b/doc/blas.tex
@@ -0,0 +1,755 @@
+\chapter{The BLAS Interface (\module{cvxopt.blas})}\label{chap:blas}
+The \module{cvxopt.blas} module provides an interface to the
+double-precision real and complex Basic Linear Algebra Subprograms
+(BLAS). The names and calling sequences of the Python functions in
+the interface closely match the corresponding Fortran BLAS routines
+(described in the references below) and their functionality is exactly
+the same.
+
+Many of the operations performed by the BLAS routines can be
+implemented in a more straightforward way by using the matrix
+arithmetic of section~\ref{s-arithmetic}, combined with the slicing
+and indexing of section~\ref{s-indexing}.
+As an example, \samp{C = A*B} gives the same result as the BLAS
+call \samp{gemm(A,B,C)}.
+The BLAS interface offers two advantages. First, some of the
+functions it includes are not easily implemented using the basic
+matrix arithmetic. For example, BLAS includes functions that
+efficiently exploit symmetry or triangular matrix structure.
+Second, there is a performance difference that can be significant for
+large matrices. Although our implementation of the basic matrix
+arithmetic makes internal calls to BLAS, it also often requires
+creating temporary matrices to store intermediate results.
+The BLAS functions on the other hand always operate directly
+on their matrix arguments and never require any copying to temporary
+matrices. Thus they can be viewed as generalizations of the in-place
+matrix addition and scalar multiplication of
+section~\ref{s-arithmetic} to more complicated operations.
+
+\begin{seealso}
+\seetext{C. L. Lawson, R. J. Hanson, D. R. Kincaid, F. T. Krogh,
+Basic Linear Algebra Subprograms for Fortran Use,
+ACM Transactions on Mathematical Software, 5(3), 309-323, 1975.}
+\seetext{J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson,
+An Extended Set of Fortran Basic Linear Algebra Subprograms,
+ACM Transactions on Mathematical Software, 14(1), 1-17, 1988.}
+\seetext{J. J. Dongarra, J. Du Croz, S. Hammarling, I. Duff,
+A Set of Level 3 Basic Linear Algebra Subprograms,
+ACM Transactions on Mathematical Software, 16(1), 1-17, 1990.}
+\end{seealso}
+
+\section{Matrix Classes} \label{s-conventions}
+
+The BLAS exploit several types of matrix structure: symmetric,
+Hermitian, triangular, and banded. We represent all these matrix
+classes by dense real or complex \mtrx\ objects, with additional
+arguments that specify the structure.
+
+\begin{description}
+\item[Vector]
+A real or complex {\it n}-vector is represented by a \mtrx\ of type
+\dtc\ or \ztc\ and length {\it n}, with the entries of the vector
+stored in column-major order.
+
+\item[General matrix]
+A general real or complex {\it m} by {\it n} matrix is represented by
+a real or complex \mtrx\ of size ({\it m}, {\it n}).
+
+\item[Symmetric matrix]
+A real or complex symmetric matrix of order {\it n} is represented
+by a real or complex \mtrx\ of size ({\it n}, {\it n}), and a character
+argument \var{uplo} with two possible values:
+\code{'L'} and \code{'U'}.
+If \var{uplo} is \code{'L'}, the lower triangular part of the
+symmetric matrix is stored; if \var{uplo} is \code{'U'}, the upper
+triangular part is stored. A square \mtrx\ {\var X} of size
+({\it n}, {\it n}) can therefore be used to represent the symmetric
+matrices
+\BEAS
+& \left[\begin{array}{ccccc}
+X[0,0] & X[1,0] & X[2,0] & \cdots & X[n-1,0] \\
+X[1,0] & X[1,1] & X[2,1] & \cdots & X[n-1,1] \\
+X[2,0] & X[2,1] & X[2,2] & \cdots & X[n-1,2] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+& \left[\begin{array}{ccccc}
+X[0,0] & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+X[0,1] & X[1,1] & X[1,2] & \cdots & X[1,n-1] \\
+X[0,2] & X[1,2] & X[2,2] & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[0,n-1] & X[1,n-1] & X[2,n-1] & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = U'}.
+\EEAS
+
+\item[Complex Hermitian matrix]
+A complex Hermitian matrix of order {\it n} is represented
+by a \mtrx\ of type \ztc\ and size ({\it n}, {\it n}), and
+a character argument \var{uplo} with the ame meaning as for symmetric
+matrices.
+A complex \mtrx\ {\var X} of size ({\it n}, {\it n}) can
+represent the Hermitian matrices
+\BEAS
+&
+\left[\begin{array}{ccccc}
+\Re X[0,0] & \bar X[1,0] & \bar X[2,0] & \cdots & \bar X[n-1,0] \\
+X[1,0] & \Re X[1,1] & \bar X[2,1] & \cdots & \bar X[n-1,1] \\
+X[2,0] & X[2,1] & \Re X[2,2] & \cdots & \bar X[n-1,2] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & \Re X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+& \left[\begin{array}{ccccc}
+\Re X[0,0] & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+\bar X[0,1] & \Re X[1,1] & X[1,2] & \cdots & X[1,n-1] \\
+\bar X[0,2] & \bar X[1,2] & \Re X[2,2] & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+\bar X[0,n-1] & \bar X[1,n-1] & \bar X[2,n-1] & \cdots & \Re X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'U'}.
+\EEAS
+
+\item[Triangular matrix]
+A real or complex triangular matrix of order {\it n} is represented
+by a real or complex \mtrx\ of size ({\it n}, {\it n}), and two
+character arguments: an argument \var{uplo} with possible values
+\code{'L'} and \code{'U'} to distinguish between lower and upper
+triangular matrices, and an argument \var{diag} with possible values
+\code{'U'} and \code{'N'} to distinguish between unit and non-unit
+triangular matrices. A square \mtrx\ {\var X} of size
+({\it n}, {\it n}) can represent the triangular matrices
+\BEAS
+& \left[\begin{array}{ccccc}
+X[0,0] & 0 & 0 & \cdots & 0 \\
+X[1,0] & X[1,1] & 0 & \cdots & 0 \\
+X[2,0] & X[2,1] & X[2,2] & \cdots & 0 \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'N'}, \\
+& \left[\begin{array}{ccccc}
+1 & 0 & 0 & \cdots & 0 \\
+X[1,0] & 1 & 0 & \cdots & 0 \\
+X[2,0] & X[2,1] & 1 & \cdots & 0 \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & 1
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'U'}, \\
+& \left[\begin{array}{ccccc}
+X[0,0] & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+0 & X[1,1] & X[1,2] & \cdots & X[1,n-1] \\
+0 & 0 & X[2,2] & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+0 & 0 & 0 & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'N'}, \\
+& \left[\begin{array}{ccccc}
+1 & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+0 & 1 & X[1,2] & \cdots & X[1,n-1] \\
+0 & 0 & 1 & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+0 & 0 & 0 & \cdots & 1
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'U'}.
+\EEAS
+
+\item[General band matrix]
+A general real or complex {\it m} by {\it n} band matrix with {\it kl}
+subdiagonals and {\it ku} superdiagonals is represented by a real or
+complex \mtrx\ \var{X} of size ({\it kl+ku+1}, {\it n}), and the two
+integers {\it m} and {\it kl}.
+The diagonals of the band matrix are stored in the rows of \var{X},
+starting at the top diagonal, and shifted horizontally so that the
+entries of the
+{\it k}th column of the band matrix are stored in column {\it k} of
+{\var X}. A \mtrx\ {\var X} of size ({\it kl+ku+1}, {\it n}) therefore
+represents the {\it m} by {\it n} band matrix
+\[
+\left[ \begin{array}{ccccccc}
+X[k_u,0] & X[k_u-1,1] & X[k_u-2,2] & \cdots & X[0,k_u] & 0 & \cdots \\
+X[k_u+1,0] & X[k_u,1] & X[k_u-1,2] & \cdots & X[1,k_u] & X[0,k_u+1] & \cdots \\
+X[k_u+2,0] & X[k_u+1,1] & X[k_u,2] & \cdots & X[2,k_u] & X[1,k_u+1] & \cdots \\
+ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[k_u+k_l,0] & X[k_u+k_l-1,1] & X[k_u+k_l-2,2] & \cdots & & & \\
+0 & X[k_u+k_l,1] & X[k_u+k_l-1,2] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right].
+\]
+
+\item[Symmetric band matrix]
+A real or complex symmetric band matrix of order {\it n} with {\it k}
+subdiagonals, is represented by a real or complex matrix \var{X} of
+size ({\it k}+1, {\it n}), and an argument {\it uplo} to indicate
+whether the subdiagonals ({\it uplo} is \code{'L'}) or superdiagonals
+({\it uplo} is \code{'U'}) are stored.
+The {\it k}+1 diagonals are stored as rows of \var{X}, starting at the top
+diagonal (\ie, the main diagonal if {\it uplo} is \code{'L'}, or
+the {\it k}th superdiagonal if {\it uplo} is \code{'U'}) and shifted
+horizontally so that the entries of the
+{\it k}th column of the band matrix are stored in column {\it k} of
+{\var X}. A \mtrx\ {\it X} of size ({\it k}+1, {\it n}) can therefore
+represent the band matrices
+\BEAS
+& \left[ \begin{array}{ccccccc}
+X[0,0] & X[1,0] & X[2,0] & \cdots & X[k,0] & 0 & \cdots \\
+X[1,0] & X[0,1] & X[1,1] & \cdots & X[k-1,1] & X[k,1] & \cdots \\
+X[2,0] & X[1,1] & X[0,2] & \cdots & X[k-2,2] & X[k-1,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & & & \\
+0 & X[k,1] & X[k-1,2] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+&
+\left[ \begin{array}{ccccccc}
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & X[0,k] & 0 & \cdots \\
+X[k-1,1] & X[k,1] & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+X[k-2,2] & X[k-1,2] & X[k,2] & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[0,k] & X[1,k] & X[2,k] & \cdots & & & \\
+0 & X[0,k+1] & X[1,k+1] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo='U'}.
+\EEAS
+
+\item[Hermitian band matrix]
+A complex Hermitian band matrix of order {\it n} with {\it k}
+subdiagonals is represented by a complex matrix of size
+({\it k+1}, {\it n}) and an argument \var{uplo}.
+A \mtrx\ {\it X} of size ({\it k}+1, {\it n}) can represent the band
+matrices
+\BEAS
+& \left[ \begin{array}{ccccccc}
+\Re X[0,0] & \bar X[1,0] & \bar X[2,0] & \cdots & \bar X[k,0] & 0 & \cdots \\
+X[1,0] & \Re X[0,1] & \bar X[1,1] & \cdots & \bar X[k-1,1] & \bar X[k,1] & \cdots \\
+X[2,0] & X[1,1] & \Re X[0,2] & \cdots & \bar X[k-2,2] & \bar X[k-1,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & & & \\
+0 & X[k,1] & X[k-1,2] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+&
+\left[ \begin{array}{ccccccc}
+\Re X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & X[0,k] & 0 & \cdots \\
+\bar X[k-1,1] & \Re X[k,1] & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+\bar X[k-2,2] & \bar X[k-1,2] & \Re X[k,2] & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+\bar X[0,k] & \bar X[1,k] & \bar X[2,k] & \cdots & & & \\
+0 & \bar X[0,k+1] & \bar X[1,k+1] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo='U'}.
+\EEAS
+
+\item[Triangular band matrix]
+A triangular band matrix of order {\it n} with {\it k} subdiagonals or
+superdiagonals is represented by a real complex matrix of size
+({\it k+1}, {\it n}) and two character arguments \var{uplo} and
+\var{diag}.
+A \mtrx\ {\it X} of size ({\it k}+1, {\it n}) can represent the band
+matrices
+\BEAS
+& \left[ \begin{array}{cccc}
+X[0,0] & 0 & 0 & \cdots \\
+X[1,0] & X[0,1] & 0 & \cdots \\
+X[2,0] & X[1,1] & X[0,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots \\
+0 & X[k,1] & X[k-1,1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'N'}, \\
+& \left[ \begin{array}{cccc}
+1 & 0 & 0 & \cdots \\
+X[1,0] & 1 & 0 & \cdots \\
+X[2,0] & X[1,1] & 1 & \cdots \\
+\vdots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots \\
+0 & X[k,1] & X[k-1,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'U'}, \\
+& \left[ \begin{array}{ccccccc}
+X[k,0] & X[k-1,1] & X[k-2,3] & \cdots & X[0,k] & 0 & \cdots\\
+0 & X[k,1] & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+0 & 0 & X[k,2] & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'N'}, \\
+& \left[ \begin{array}{ccccccc}
+1 & X[k-1,1] & X[k-2,3] & \cdots & X[0,k] & 0 & \cdots\\
+0 & 1 & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+0 & 0 & 1 & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'U'}.
+\EEAS
+\end{description}
+
+When discussing BLAS functions in the following sections we will
+omit several less important optional arguments that can
+be used to select submatrices for in-place operations.
+The complete specification is documented in the docstrings of the
+source code and the \program{pydoc} help program.
+
+\section{Level 1 BLAS} \label{s-blas1}
+The level 1 functions implement vector operations.
+
+\begin{funcdesc}{scal}{alpha, x}
+Scales a vector by a constant:
+\[
+x := \alpha x.
+\]
+If \var{x} is a real \mtrx, the scalar argument \var{alpha} must be a
+Python \intgr\ or \flt. If \var{x} is complex, \var{alpha} can be an
+\intgr, \flt, or \cmplx.
+\end{funcdesc}
+
+\begin{funcdesc}{nrm2}{x}
+Euclidean norm of a vector: returns
+\[
+ \|x\|_2.
+\]
+\end{funcdesc}
+
+\begin{funcdesc}{asum}{x}
+L-1 norm of a vector: returns
+\[
+\|x\|_1 \quad \mbox{($x$ real)}, \qquad
+\|\Re x\|_1 + \|\Im x\|_1 \quad \mbox{($x$ complex)}.
+\]
+\end{funcdesc}
+
+\begin{funcdesc}{iamax}{x}
+Returns
+\[
+ \argmax_{k=0,\ldots,n-1} |x_k| \quad \mbox{($x$ real)}, \qquad
+ \argmax_{k=0,\ldots,n-1} |\Re x_k| + |\Im x_k| \quad
+ \mbox{($x$ complex)}.
+\]
+If more than one coefficient achieves the maximum, the index of the
+first {\it k} is returned.
+\end{funcdesc}
+
+\begin{funcdesc}{swap}{x, y}
+Interchanges two vectors:
+\[
+ x \leftrightarrow y.
+\]
+\var{x} and \var{y} are matrices of the same type (\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{copy}{x, y}
+Copies a vector to another vector:
+\[
+ y := x.
+\]
+\var{x} and \var{y} are matrices of the same type (\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{axpy}{x, y\optional{,alpha=1.0}}
+Constant times a vector plus a vector:
+\[
+y := \alpha x + y.
+\]
+\var{x} and \var{y} are matrices of the same type (\dtc\ or \ztc).
+If \var{x} is real, the scalar argument \var{alpha} must be a Python
+\intgr\ or \flt. If \var{x} is complex, \var{alpha} can be an \intgr,
+\flt, or \cmplx.
+\end{funcdesc}
+
+\begin{funcdesc}{dot}{x, y}
+Returns
+\[
+x^Hy.
+\]
+\var{x} and \var{y} are matrices of the same type (\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{dotu}{x, y}
+Returns
+\[
+x^Ty.
+\]
+\var{x} and \var{y} are matrices of the same type (\dtc\ or \ztc).
+\end{funcdesc}
+
+
+\section{Level 2 BLAS} \label{s-blas2}
+The level 2 functions implement matrix-vector products and
+rank-1 and rank-2 matrix updates.
+Different types of matrix structure can be exploited using the
+conventions of section~\ref{s-conventions}.
+
+\begin{funcdesc}{gemv}{A, x, y\optional{, trans='N'\optional{,
+alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a general matrix:
+\[
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+y := \alpha A^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}),
+ \qquad
+y := \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}).
+\]
+The arguments \var{A}, \var{x} and {\var y} must have the same type
+(\dtc\ or \ztc). Complex values of \var{alpha} and \var{beta} are only
+allowed if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{symv}{A, x, y\optional{, uplo='L'\optional{,
+alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a real symmetric matrix:
+\[
+ y := \alpha A x + \beta y,
+\]
+where {\it A} is a real symmetric matrix.
+The arguments \var{A}, \var{x} and {\var y} must have
+type \dtc\ and \var{alpha} and \var{beta} must be real.
+\end{funcdesc}
+
+\begin{funcdesc}{hemv}{A, x, y\optional{, uplo='L'\optional{,
+alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a real symmetric or complex Hermitian
+matrix:
+\[
+ y := \alpha A x + \beta y,
+\]
+where {\it A} is real symmetric or complex Hermitian.
+The arguments \var{A}, \var{x} and {\var y} must have the same
+type (\dtc\ or \ztc).
+Complex values of \var{alpha} and \var{beta} are only
+allowed if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{trmv}{A, x\optional{, uplo='L'\optional{,
+trans='N'\optional{, diag='N'}}}}
+Matrix-vector product with a triangular matrix:
+\[
+x := Ax \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^T x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^H x \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is square and triangular.
+The arguments \var{A} and \var{x} must have the same type
+(\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{trsv}{A, x\optional{, uplo='L'\optional{,
+trans='N'\optional{, diag='N'}}}}
+Solution of a nonsingular triangular set of linear equations:
+\[
+x := A^{-1}x \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^{-T}x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^{-H}x \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is square and triangular with nonzero diagonal
+elements. The arguments \var{A} and \var{x} must have the same type
+(\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{gbmv}{A, m, kl, x, y\optional{, trans='N'
+\optional{, alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a general band matrix:
+\[
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha A^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}),
+\qquad
+y := \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is a rectangular band matrix with \var{m} rows and
+\var{kl} subdiagonals.
+The arguments \var{A}, \var{x} and {\var y} must have the same
+type (\dtc\ or \ztc).
+Complex values of \var{alpha} and \var{beta} are only allowed if \var{A} is
+ complex.
+\end{funcdesc}
+
+\begin{funcdesc}{sbmv}{A, x, y\optional{, uplo='L'\optional{,
+alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a real symmetric band matrix:
+\[
+ y := \alpha Ax + \beta y,
+\]
+where {\it A} is a real symmetric band matrix.
+The arguments \var{A}, \var{x} and {\var y} must have type \dtc\ and
+\var{alpha} and \var{beta} must be real.
+\end{funcdesc}
+
+\begin{funcdesc}{hbmv}{A, x, y\optional{, uplo='L'\optional{,
+alpha=1.0\optional{, beta=0.0}}}}
+Matrix-vector product with a real symmetric or complex Hermitian
+band matrix:
+\[
+ y := \alpha Ax + \beta y,
+\]
+where {\it A} is a real symmetric or complex Hermitian band matrix.
+The arguments \var{A}, \var{x} and {\var y} must have the same type
+(\dtc\ or \ztc).
+Complex values of \var{alpha} and \var{beta} are only allowed if
+\var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{tbmv}{A, x\optional{, uplo='L'\optional{,
+trans\optional{, diag}}}}
+Matrix-vector product with a triangular band matrix:
+\[
+x := Ax \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^T x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^H x \quad (\mathrm{trans} = \mathrm{'C'}).
+\]
+The arguments \var{A} and \var{x} must have the same type
+(\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{tbsv}{A, x\optional{, uplo='L'\optional{,
+trans\optional{, diag}}}}
+Solution of a triangular banded set of linear equations:
+\[
+x := A^{-1}x \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^{-T} x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^{-H} x \quad (\mathrm{trans} = \mathrm{'T'}),
+\]
+where {\it A} is a triangular band matrix of with nonzero diagonal
+elements.
+The arguments \var{A} and \var{x} must have the same type
+(\dtc\ or \ztc).
+\end{funcdesc}
+
+\begin{funcdesc}{ger}{x, y, A\optional{, alpha=1.0}}
+General rank-1 update:
+\[
+A := A + \alpha x y^H,
+\]
+where {\it A} is a general matrix.
+The arguments \var{A}, \var{x} and \var{y} must have the same type
+(\dtc\ or \ztc).
+Complex values of \var{alpha} are only allowed if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{geru}{x, y, A\optional{, alpha=1.0}}
+General rank-1 update:
+\[
+A := A + \alpha x y^T,
+\]
+where {\it A} is a general matrix.
+The arguments \var{A}, \var{x} and \var{y} must have the same type
+(\dtc\ or \ztc).
+Complex values of \var{alpha} are only allowed if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{syr}{x, A\optional{, uplo='L'\optional{, alpha=1.0}}}
+Symmetric rank-1 update:
+\[
+ A := A + \alpha xx^T,
+\]
+where {\it A} is a real symmetric matrix.
+The arguments \var{A} and \var{x} must have type \dtc.
+\var{alpha} must be a real number.
+\end{funcdesc}
+
+\begin{funcdesc}{her}{x, A\optional{, uplo='L'\optional{, alpha=1.0}}}
+Hermitian rank-1 update:
+\[
+ A := A + \alpha xx^H,
+\]
+where {\it A} is a real symmetric or complex Hermitian matrix.
+The arguments \var{A} and \var{x} must have the same type
+(\dtc\ or \ztc).
+\var{alpha} must be a real number.
+\end{funcdesc}
+
+\begin{funcdesc}{syr2}{x, y, A\optional{, uplo='L'\optional{,
+alpha=1.0}}}
+Symmetric rank-2 update:
+\[
+ A := A + \alpha (xy^T + yx^T),
+\]
+where {\it A} is a real symmetric matrix.
+The arguments \var{A}, \var{x} and \var{y} must have type \dtc.
+\var{alpha} must be real.
+\end{funcdesc}
+
+\begin{funcdesc}{her2}{x, y, A\optional{, uplo='L'\optional{,
+alpha=1.0}}}
+Symmetric rank-2 update:
+\[
+ A := A + \alpha xy^H + \bar \alpha yx^H,
+\]
+where {\it A} is a a real symmetric or complex Hermitian matrix.
+The arguments \var{A}, \var{x} and \var{y} must have the same type
+(\dtc\ or \ztc).
+Complex values of \var{alpha} are only allowed if \var{A} is complex.
+\end{funcdesc}
+
+As an example, the following code multiplies the tridiagonal matrix
+\[
+A = \left[\begin{array}{rrrr}
+ 1 & 6 & 0 & 0 \\
+ 2 & -4 & 3 & 0 \\
+ 0 & -3 & -1 & 1
+ \end{array}\right]
+\]
+with the vector {\it x} = (1,-1,2,-2).
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt.blas import gbmv
+>>> A = matrix([[0., 1., 2.], [6., -4., -3.], [3., -1., 0.], [1., 0., 0.]])
+>>> x = matrix([1., -1., 2., -2.])
+>>> y = matrix(0., (3,1))
+>>> gbmv(A, 3, 1, x, y)
+>>> print y
+-5.0000e+00
+ 1.2000e+01
+-1.0000e+00
+\end{verbatim}
+
+The following example illustrates the use of \function{tbsv()}.
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt.blas import tbsv
+>>> A = matrix([-6., 5., -1., 2.], (1,4))
+>>> x = matrix(1.0, (4,1))
+>>> tbsv(A, x) # x := diag(A)^{-1}*x
+>>> print x
+-1.6667e-01
+ 2.0000e-01
+-1.0000e+00
+ 5.0000e-01
+\end{verbatim}
+
+
+\section{Level 3 BLAS} \label{s-blas3}
+The level 3 BLAS include functions for matrix-matrix multiplication.
+
+\begin{funcdesc}{gemm}{A, B, C\optional{, transA='N'\optional{,
+transB='N'\optional{, alpha=1.0\optional{, beta=0.0}}}}}
+Matrix-matrix product of two general matrices:
+\[
+ C := \alpha \op(A) \op(B) + \beta C
+\]
+where
+\[
+\op(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'} \end{array} \right.
+\qquad
+\op(B) = \left\{ \begin{array}{ll}
+ B & \mathrm{transB} = \mathrm{'N'} \\
+ B^T & \mathrm{transB} = \mathrm{'T'} \\
+ B^H & \mathrm{transB} = \mathrm{'C'}. \end{array} \right.
+\]
+The arguments \var{A}, \var{B} and \var{C} must have the same type
+(\dtc\ or \ztc).
+Complex values of \var{alpha} and \var{beta} are only allowed
+if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{symm}{A, B, C\optional{, side='L'\optional{,
+uplo='L'\optional{, alpha=1.0\optional{, beta=0.0}}}}}
+Product of a real or complex symmetric matrix {\it A} and a general
+matrix {\it B}:
+\[
+ C := \alpha AB + \beta C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := \alpha BA + \beta C \quad (\mathrm{side} = \mathrm{'R'}).
+\]
+The arguments \var{A}, \var{B} and \var{C} must have the same type
+(\dtc\ or \ztc). Complex values of \var{alpha} and \var{beta} are
+only allowed if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{hemm}{A, B, C\optional{, side='L'\optional{,
+uplo='L'\optional{, alpha=1.0\optional{, beta=0.0}}}}}
+Product of a real symmetric or complex Hermitian matrix {\it A} and a
+general matrix {\it B}:
+\[
+ C := \alpha AB + \beta C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := \alpha BA + \beta C \quad (\mathrm{side} = \mathrm{'R'}).
+\]
+The arguments \var{A}, \var{B} and \var{C} must have the same type
+(\dtc\ or \ztc).
+Complex values of \var{alpha} and \var{beta} are only allowed if
+\var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{trmm}{A, B\optional{, side='L'\optional{,
+uplo='L'\optional{, transA='N'\optional{, diag='N'\optional{,
+alpha=1.0}}}}}}
+Product of a triangular matrix {\it A} and a general matrix {\it B}:
+\[
+ B := \alpha\op(A)B \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ B := \alpha B\op(A) \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \op(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'}. \end{array} \right.
+\]
+The arguments \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc). Complex values of \var{alpha} are only allowed if \var{A} is
+complex.
+\end{funcdesc}
+
+\begin{funcdesc}{trsm}{A, B\optional{, side='L'\optional{,
+uplo='L'\optional{, transA='N'\optional{, diag='N'\optional{,
+alpha=1.0}}}}}}
+Solution of a nonsingular triangular system of equations:
+\[
+ B := \alpha \op(A)^{-1}B \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ B := \alpha B\op(A)^{-1} \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \op(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'}, \end{array} \right.
+\]
+where {\it A} is triangular and {\it B} is a general matrix.
+The arguments \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc). Complex values of \var{alpha} are only allowed if \var{A} is
+complex.
+\end{funcdesc}
+
+\begin{funcdesc}{syrk}{A, C\optional{, uplo='L'\optional{,
+trans='N'\optional{, alpha=1.0\optional{, beta=0.0}}}}}
+Rank-{\it k} update of a real or complex symmetric matrix {\it C}:
+\[
+ C := \alpha AA^T + \beta C \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+ C := \alpha A^TA + \beta C \quad (\mathrm{trans} = \mathrm{'T'}),
+\]
+where {\it A} is a general matrix.
+The arguments \var{A} and \var{C} must have the same type (\dtc\ or
+\ztc). Complex values of \var{alpha} and \var{beta} are only allowed
+if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{herk}{A, C\optional{, uplo='L'\optional{,
+trans='N'\optional{, alpha=1.0\optional{, beta=0.0}}}}}
+Rank-{\it k} update of a real symmetric or complex Hermitian matrix
+{\it C}:
+\[
+ C := \alpha AA^H + \beta C \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+ C := \alpha A^HA + \beta C \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is a general matrix.
+The arguments \var{A} and \var{C} must have the same type (\dtc\ or
+\ztc). \var{alpha} and \var{beta} must be real.
+\end{funcdesc}
+
+\begin{funcdesc}{syr2k}{A, B, C\optional{, uplo='L'\optional{,
+trans='N'\optional{, alpha=1.0\optional{, beta=0.0}}}}}
+Rank-{\it 2k} update of a real or complex symmetric matrix {\it C}:
+\[
+ C := \alpha (AB^T + BA^T) + \beta C \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+ C := \alpha (A^TB + B^TA) + \beta C \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\]
+{\it A} and {\it B} are general real or complex matrices.
+The arguments \var{A}, \var{B} and \var{C} must have the same
+type. Complex values of \var{alpha} and \var{beta} are only
+allowed if \var{A} is complex.
+\end{funcdesc}
+
+\begin{funcdesc}{her2k}{A, B, C\optional{, uplo='L'\optional{,
+trans='N'\optional{, alpha=1.0\optional{ beta=0.0}}}}}
+Rank-{\it 2k} update of a real symmetric or complex Hermitian matrix
+{\it C}:
+\[
+ C := \alpha AB^H + \bar \alpha BA^H + \beta C \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+ C := \alpha A^HB + \bar\alpha B^HA + \beta C \quad
+ (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} and {\it B} are general matrices.
+The arguments \var{A}, \var{B} and \var{C} must have the same type
+(\dtc\ or \ztc). Complex values of \var{alpha} are only allowed if
+\var{A} is complex. \var{beta} must be real.
+\end{funcdesc}
diff --git a/doc/c-api.tex b/doc/c-api.tex
new file mode 100644
index 0000000..a836b51
--- /dev/null
+++ b/doc/c-api.tex
@@ -0,0 +1,194 @@
+\chapter{C API}\label{chap:c-api}
+The API can be used to extend CVXOPT with interfaces to
+external C routines and libraries.
+A C program that creates or manipulates the dense or sparse matrix
+objects defined in \module{cvxopt.base} must include the
+\file{cvxopt.h} header file in the \file{src} directory of the
+distribution.
+
+Before the C-API can be used in an extension module it must be
+initialized by calling the macro \cfunction{import\_cvxopt}.
+As an example
+we show the module initialization from the \module{cvxopt.blas} module,
+which itself uses the API:
+\begin{verbatim}
+PyMODINIT_FUNC initblas(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("cvxopt.blas", blas_functions, blas__doc__);
+
+ if (import_cvxopt() < 0)
+ return;
+}
+\end{verbatim}
+
+
+\section{Dense Matrices}
+As can be seen from the header file \file{cvxopt.h}, a \mtrx\ is
+essentially a structure with four fields.
+The fields \cdata{nrows} and \cdata{ncols} are two integers that
+specify the dimensions.
+The \cdata{id} field controls the type of the matrix and can have
+values \constant{DOUBLE}, \constant{INT} and \constant{COMPLEX}.
+The \cdata{buffer} field is an array that contains the matrix elements
+stored contiguously in column-major order.
+
+The following C functions can be used to create matrices.
+\begin{cfuncdesc}{matrix*}{Matrix\_New}{int nrows, int ncols, int id}
+Returns a \mtrx\ object of type \var{id} with \var{nrows} rows
+and \var{ncols} columns. The elements of the matrix are uninitialized.
+\end{cfuncdesc}
+
+\begin{cfuncdesc}{matrix*}{Matrix\_NewFromMatrix}{matrix *src, int id}
+Returns a copy of the matrix \var{src} converted to type \var{id}.
+The following type conversions are allowed: \itc\ to \dtc,
+\itc\ to \ztc\ and \dtc\ to \ztc.
+\end{cfuncdesc}
+
+\begin{cfuncdesc}{matrix*}{Matrix\_NewFromSequence}{PyListObject *x, int id}
+Creates a matrix of type \var{id} from the Python sequence type \var{x}. The
+returned matrix has size \code{(len(\var{x}),1)}.
+The size can be changed by modifying the \member{nrows} and
+\member{ncols} fields of the returned matrix.
+\end{cfuncdesc}
+
+To illustrate the creation and manipulation of dense matrices (as well
+as the Python C API), we show the code for the \function{uniform()}
+function from \module{cvxopt.random} described in
+section~\ref{s-random}.
+\begin{verbatim}
+PyObject * uniform(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *obj;
+ int i, nrows, ncols = 1;
+ double a = 0, b = 1;
+ char *kwlist[] = {"nrows", "ncols", "a", "b", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "i|idd", kwlist,
+ &nrows, &ncols, &a, &b)) return NULL;
+
+ if ((nrows<0) || (ncols<0)) {
+ PyErr_SetString(PyExc_TypeError, "dimensions must be non-negative");
+ return NULL;
+ }
+
+ if (!(obj = Matrix_New(nrows, ncols, DOUBLE)))
+ return PyErr_NoMemory();
+
+ for (i = 0; i < nrows*ncols; i++)
+ MAT_BUFD(obj)[i] = Uniform(a,b);
+
+ return (PyObject *)obj;
+}
+\end{verbatim}
+
+\section{Sparse Matrices}
+Sparse matrices are stored in compressed column storage (CCS)
+format. For a general \var{nrows} by \var{ncols} sparse matrix with
+\var{nnz} nonzero entries this means the following. The sparsity
+pattern and the nonzero values are stored in three fields:
+\begin{description}
+\item[values:] A \dtc\ or \ztc\ matrix of size \code{(\var{nnz},1)}
+ with the nonzero entries of the matrix stored columnwise.
+\item[rowind:] An array of integers of length \var{nnz} containing the
+row indices of the nonzero entries, stored in the same order as
+\var{values}.
+\item[colptr:] An array of integers of length \code{\var{ncols}+1} with
+for each column of the matrix the index of the first element in
+\var{values} from that column. More precisely,
+\code{\var{colptr}[0]} is \code{0}, and for
+\code{\var{k} = 0, 1, \ldots, \var{ncols}-1},
+\code{\var{colptr}[k+1]} is equal to \code{\var{colptr}[k]} plus the
+number of nonzeros in column \var{k} of the matrix.
+Thus, \code{\var{colptr}[\var{ncols}]} is equal to \var{nnz}, the
+number of nonzero entries.
+\end{description}
+
+For example, for the matrix
+\[
+A=\left [\begin{array}{cccc}
+ 1 & 0 & 0 & 5\\
+ 2 & 0 & 4 & 0\\
+ 0 & 0 & 0 & 6\\
+ 3 & 0 & 0 & 0
+\end{array}\right]
+\]
+the elements of \var{values}, \var{rowind} and \var{colptr} are:
+\begin{quote}
+ \var{values}: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, \qquad
+ \var{rowind}: 0, 1,3, 1, 0, 2, \qquad
+ \var{colptr}: 0, 3, 3, 4, 6.
+\end{quote}
+It is crucial that for each column the row indices in \var{rowind} are
+sorted; the equivalent representation
+\begin{quote}
+ \var{values}: 3.0, 2.0, 1.0, 4.0, 5.0, 6.0, \qquad
+ \var{rowind}: 3, 1, 0, 1, 0, 2, \qquad
+ \var{colptr}: 0, 3, 3, 4, 6
+\end{quote}
+is not allowed (and will likely cause the program to crash).
+
+The \cdata{nzmax} field specifies the number of non-zero elements the
+matrix can store. It is equal to the length of \var{rowind} and
+\var{values}; this number can be larger that
+\code{\var{colptr}[\var{nrows}]}, but never less.
+This field makes it possible to preallocate a certain amount of
+memory to avoid reallocations if the matrix is constructed
+sequentially by filling in elements.
+In general the \var{nzmax} field can safely be ignored, however, since
+it will always be adjusted automatically as the number of non-zero
+elements grows.
+
+The \cdata{id} field controls the type of the matrix and can have
+values \constant{DOUBLE} and \constant{COMPLEX}.
+
+Sparse matrices are created using the following functions from the API.
+\begin{cfuncdesc}{spmatrix*}{SpMatrix\_New}{int nrows, int ncols, int
+ nzmax, int id}
+ Returns a sparse zero matrix with \var{nrows} rows and
+ \var{ncols} columns. \var{nzmax} is the number of elements that will
+ be allocated (the length of the \var{values} and \var{rowind}
+ fields).
+\end{cfuncdesc}
+
+\begin{cfuncdesc}{spmatrix*}{SpMatrix\_NewFromMatrix}{spmatrix *src, int
+ id}
+ Returns a copy the sparse matrix \var{src}.
+\end{cfuncdesc}
+
+\begin{cfuncdesc}{spmatrix*}{SpMatrix\_NewFromIJV}{matrix *I, matrix *J,
+ matrix *V, int nrows, int ncols, int nzmax, int id}
+ Creates a sparse matrix with \var{nrows} rows and \var{ncols}
+ columns from a triplet description. \var{I} and \var{J}
+ must be integer matrices and \var{V} either a double or complex matrix,
+ or \constant{NULL}. If \var{V} is \constant{NULL} the values of the
+ entries in the matrix are undefined, otherwise they are
+ specified by \var{V}. Repeated entries in \var{V} are summed.
+ The number of allocated elements is given by \var{nzmax}, which is
+ adjusted if it is smaller than the required amount.
+\end{cfuncdesc}
+
+We illustrate use of the sparse matrix class by listing the source
+code for the \method{real()} method, which returns the real part of
+a sparse matrix:
+
+\begin{verbatim}
+static PyObject * spmatrix_real(spmatrix *self) {
+
+ if (SP_ID(self) != COMPLEX)
+ return (PyObject *)SpMatrix_NewFromMatrix(self, 0, SP_ID(self));
+
+ spmatrix *ret = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self),
+ SP_NNZ(self), DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i < SP_NNZ(self); i++)
+ SP_VALD(ret)[i] = creal(SP_VALZ(self)[i]);
+
+ memcpy(SP_COL(ret), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t));
+ memcpy(SP_ROW(ret), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
+ return (PyObject *)ret;
+}
+\end{verbatim}
diff --git a/doc/cvxopt.tex b/doc/cvxopt.tex
new file mode 100644
index 0000000..f0d4888
--- /dev/null
+++ b/doc/cvxopt.tex
@@ -0,0 +1,121 @@
+\documentclass{manual}
+\usepackage{graphicx}
+
+\def\BIT{\begin{itemize}}
+\def\EIT{\end{itemize}}
+\def\BEQ{\begin{equation}}
+\def\EEQ{\end{equation}}
+\def\reals{{\mbox{\bf R}}}
+\def\complex{{\mbox{\bf C}}}
+\newcommand{\eg}{{\em e.g.}}
+\newcommand{\ie}{{\em i.e.}}
+\newcommand{\BEA}{\begin{eqnarray}}
+\newcommand{\EEA}{\end{eqnarray}}
+\newcommand{\BEAS}{\begin{eqnarray*}}
+\newcommand{\EEAS}{\end{eqnarray*}}
+\newcommand{\Rank}{\mathop{\bf rank}}
+\newcommand{\Tr}{\mathop{\bf tr}}
+\newcommand{\lse}{\mathop{\bf lse}}
+\newcommand{\diag}{\mbox{\bf diag}\,}
+\newcommand{\ones}{{\bf 1}}
+\newcommand{\argmax}{\mathop{\rm argmax}}
+\newcommand{\symm}{{\mbox{\bf S}}}
+\newcommand{\op}{\mathop{\mathrm{op}}}
+
+% constants
+\newcommand{\dtc}{\code{'d'}}
+\newcommand{\itc}{\code{'i'}}
+\newcommand{\ztc}{\code{'z'}}
+\newcommand{\None}{\code{None}}
+\newcommand{\True}{\code{True}}
+\newcommand{\False}{\code{False}}
+
+% types
+\newcommand{\flt}{\pytype{float}}
+\newcommand{\chr}{\pytype{char}}
+\newcommand{\intgr}{\pytype{integer}}
+\newcommand{\cmplx}{\pytype{complex}}
+\newcommand{\mtrx}{\class{matrix}}
+\newcommand{\spmtrx}{\class{spmatrix}}
+
+%\makeindex
+
+\title{CVXOPT: A Python Package for Convex Optimization}
+\author{Joachim Dahl \& Lieven Vandenberghe \\
+{\tt joachim at kom.aau.dk}, {\tt vandenbe at ee.ucla.edu}}
+\date{February 6, 2007}
+\release{0.8.2}
+
+\begin{document}
+\maketitle
+
+\chapter*{Copyright and License}
+Copyright \copyright{2004-2007} J. Dahl \& L. Vandenberghe.
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the
+\ulink{GNU General Public License}{http://www.gnu.org/copyleft/gpl.html}
+as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+\ulink{GNU General Public License}{http://www.gnu.org/copyleft/gpl.html}
+for more details.
+
+\hrule
+The CVXOPT distribution includes source code for the following
+software libraries.
+\BIT
+\item Part of the SuiteSparse suite of sparse matrix algorithms,
+ including:
+\BIT
+\item AMD Version 2.0. Copyright (c) 2006 by Timothy A.\ Davis,
+ Patrick R.\ Amestoy, and Iain S.\ Duff.
+\item CHOLMOD Version 1.4.
+ Copyright (c) 2005-2006 by University of Florida, Timothy A. Davis
+ and W. Hager.
+\item COLAMD version 2.6. Copyright (c) 1998-2006 by Timothy A.\ Davis.
+\item UMFPACK Version 5.0.2.
+ Copyright (c) 1995-2006 by Timothy A.\ Davis.
+\EIT
+
+These packages are licensed under the terms of the
+\ulink{GNU Lesser General Public License}
+{http://www.gnu.org/copyleft/lesser.html} (UMFPACK, parts of CHOLMOD,
+AMD, COLAMD) and the \ulink{GNU General Public License}
+{http://www.gnu.org/copyleft/gpl.html} (parts of CHOLMOD).
+For details, consult the README files in the source directories or
+the website listed below.
+
+\begin{quote}
+Availability: \ulink{www.cise.ufl.edu/research/sparse}
+{http://www.cise.ufl.edu/research/sparse}.
+\end{quote}
+
+\item RNGS Random Number Generation --- Multiple Streams
+(Sep. 22, 1998) by Steve Park \& Dave Geyer.
+
+\begin{quote}
+Availability: \ulink{www.cs.wm.edu/\~{}va/software/park/park.html}
+{http://www.cs.wm.edu/\~{}va/software/park/park.html}.
+\end{quote}
+
+\EIT
+
+\tableofcontents
+
+\input{intro}
+\input{base}
+\input{blas}
+\input{lapack}
+\input{fftw}
+\input{base_sparse}
+\input{spsolvers}
+\input{solvers}
+\input{modeling}
+\input{c-api}
+\input{cvxopt.ind}
+\end{document}
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+<meta name='aesop' content='information' />
+<title>5. Discrete Transforms (cvxopt.fftw)</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="4.9 Example: Analytic Centering"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="node28.html">4.9 Example: Analytic Centering</A>
+<b class="navlabel">Up:</b>
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+<b class="navlabel">Next:</b>
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION007000000000000000000"></A> <A NAME="c-fftw"></A>
+<BR>
+5. Discrete Transforms (<tt class="module">cvxopt.fftw</tt>)
+</H1>
+
+<P>
+The <tt class="module">cvxopt.fftw</tt> module is an interface to the FFTW library
+and contains routines for discrete Fourier, cosine, and sine
+transforms. This module is optional, and only installed when
+the FFTW library is made available during the CVXOPT installation.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://www.fftw.org'
+ >FFTW3 code, documentation, copyright and
+license.</a></dt>
+ <dd></dd>
+ </dl>
+</div>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="node30.html">5.1 Discrete Fourier Transform</a>
+<LI><A href="node31.html">5.2 Discrete Cosine Transform</a>
+<LI><A href="node32.html">5.3 Discrete Sine Transform</a>
+</ul>
+<!--End of Table of Child-Links-->
+</div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="4.9 Example: Analytic Centering"
+ href="node28.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="CVXOPT: A Python Package"
+ href="cvxopt.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="5.1 Discrete Fourier Transform"
+ href="node30.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="node30.html">5.1 Discrete Fourier Transform</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
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+</HTML>
diff --git a/doc/cvxopt/c-spsolvers.html b/doc/cvxopt/c-spsolvers.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
+<link rel="next" href="node45.html" />
+<link rel="prev" href="node33.html" />
+<link rel="parent" href="cvxopt.html" />
+<link rel="next" href="s-orderings.html" />
+<meta name='aesop' content='information' />
+<title>7. Sparse Linear Equation Solvers</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="6.6 Sparse BLAS Functions"
+ href="node39.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="CVXOPT: A Python Package"
+ href="cvxopt.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="7.1 Matrix Orderings (cvxopt.amd)"
+ href="s-orderings.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="s-orderings.html">7.1 Matrix Orderings (cvxopt.amd)</A>
+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION009000000000000000000"></A> <A NAME="c-spsolvers"></A>
+<BR>
+7. Sparse Linear Equation Solvers
+</H1>
+In this section we describe routines for solving sparse sets of linear
+equations.
+
+<P>
+A real symmetric or complex Hermitian sparse matrix is stored as
+an <tt class="class">spmatrix</tt> object <var>X</var> of size (<I>n</I>, <I>n</I>) and an
+additional character argument <code>uplo</code> with possible values
+<code>'L'</code> and <code>'U'</code>.
+If <code>uplo</code> is <code>'L'</code>, the lower triangular part
+of <var>X</var> contains the lower triangular part of the
+symmetric or Hermitian matrix, and the upper triangular matrix
+of <var>X</var> is ignored.
+If <code>uplo</code> is <code>'U'</code>, the upper triangular part
+of <var>X</var> contains the upper triangular part of the
+matrix, and the lower triangular matrix of <var>X</var> is ignored.
+
+<P>
+A general sparse square matrix of order <I>n</I> is represented by an
+<tt class="class">spmatrix</tt> object of size (<I>n</I>, <I>n</I>).
+
+<P>
+Dense matrices, which appear as righthand sides of equations, are
+stored using the same conventions as in the BLAS and LAPACK modules.
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="s-orderings.html">7.1 Matrix Orderings (<tt class="module">cvxopt.amd</tt>)</a>
+<LI><A href="s-umfpack.html">7.2 General Linear Equations (<tt class="module">cvxopt.umfpack</tt>)</a>
+<LI><A href="s-cholmod.html">7.3 Positive Definite Linear Equations (<tt class="module">cvxopt.cholmod</tt>)</a>
+<LI><A href="e-covsel.html">7.4 Example: Covariance Selection</a>
+</ul>
+<!--End of Table of Child-Links-->
+</div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="6.6 Sparse BLAS Functions"
+ href="node39.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="CVXOPT: A Python Package"
+ href="cvxopt.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="7.1 Matrix Orderings (cvxopt.amd)"
+ href="s-orderings.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
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+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="node39.html">6.6 Sparse BLAS Functions</A>
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="s-orderings.html">7.1 Matrix Orderings (cvxopt.amd)</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
+
+</BODY>
+</HTML>
diff --git a/doc/cvxopt/contents.gif b/doc/cvxopt/contents.gif
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+++ b/doc/cvxopt/contents.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<link rel="prev" href="node1.html" />
+<link rel="parent" href="cvxopt.html" />
+<link rel="next" href="node3.html" />
+<meta name='aesop' content='information' />
+<title>Contents</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="Copyright and License"
+ href="node1.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="CVXOPT: A Python Package"
+ href="cvxopt.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="1. Introduction"
+ href="node3.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="node1.html">Copyright and License</A>
+<b class="navlabel">Up:</b>
+<a class="sectref" rel="parent" href="cvxopt.html">CVXOPT: A Python Package</A>
+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="node3.html">1. Introduction</A>
+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+<BR><h2><A NAME="SECTION002000000000000000000">
+Contents</A>
+</h2>
+<!--Table of Contents-->
+
+<UL CLASS="TofC">
+<LI><A href="node3.html">1. Introduction</a>
+<LI><A href="node4.html">2. Dense Matrices (cvxopt.base)</a>
+<UL>
+<LI><A href="s-creating-matrices.html">2.1 Creating Matrices</a>
+<LI><A href="node6.html">2.2 Attributes and Methods</a>
+<LI><A href="s-arithmetic.html">2.3 Arithmetic Operations</a>
+<LI><A href="s-indexing.html">2.4 Indexing and Slicing</a>
+<LI><A href="s-builtinfuncs.html">2.5 Built-in Functions</a>
+<LI><A href="s-otherfuncs.html">2.6 Other Matrix Functions</a>
+<LI><A href="s-random.html">2.7 Randomly Generated Matrices</a>
+<LI><A href="s-array-interface.html">2.8 The NumPy Array Interface</a>
+<LI><A href="node13.html">2.9 Printing Options</a>
+</ul>
+<LI><A href="node14.html">3. The BLAS Interface (cvxopt.blas)</a>
+<UL>
+<LI><A href="s-conventions.html">3.1 Matrix Classes</a>
+<LI><A href="s-blas1.html">3.2 Level 1 BLAS</a>
+<LI><A href="s-blas2.html">3.3 Level 2 BLAS</a>
+<LI><A href="s-blas3.html">3.4 Level 3 BLAS</a>
+</ul>
+<LI><A href="node19.html">4. The LAPACK Interface (cvxopt.lapack)</a>
+<UL>
+<LI><A href="node20.html">4.1 General Linear Equations</a>
+<LI><A href="e-kkt-example.html">4.2 Positive Definite Linear Equations</a>
+<LI><A href="node22.html">4.3 Symmetric and Hermitian Linear Equations</a>
+<LI><A href="node23.html">4.4 Triangular Linear Equations</a>
+<LI><A href="node24.html">4.5 Least-Squares and Least-Norm Problems</a>
+<LI><A href="node25.html">4.6 Symmetric and Hermitian Eigenvalue Decomposition</a>
+<LI><A href="e-gevd.html">4.7 Generalized Symmetric Definite Eigenproblems</a>
+<LI><A href="node27.html">4.8 Singular Value Decomposition</a>
+<LI><A href="node28.html">4.9 Example: Analytic Centering</a>
+</ul>
+<LI><A href="c-fftw.html">5. Discrete Transforms (cvxopt.fftw)</a>
+<UL>
+<LI><A href="node30.html">5.1 Discrete Fourier Transform</a>
+<LI><A href="node31.html">5.2 Discrete Cosine Transform</a>
+<LI><A href="node32.html">5.3 Discrete Sine Transform</a>
+</ul>
+<LI><A href="node33.html">6. Sparse Matrices (cvxopt.base)</a>
+<UL>
+<LI><A href="s-creating-spmatrix.html">6.1 Creating Sparse Matrices</a>
+<LI><A href="e-spA-example.html">6.2 Attributes and Methods</a>
+<LI><A href="s-spmatrix-arith.html">6.3 Arithmetic Operations</a>
+<LI><A href="node37.html">6.4 Indexing and Slicing</a>
+<LI><A href="node38.html">6.5 Built-In Functions</a>
+<LI><A href="node39.html">6.6 Sparse BLAS Functions</a>
+</ul>
+<LI><A href="c-spsolvers.html">7. Sparse Linear Equation Solvers</a>
+<UL>
+<LI><A href="s-orderings.html">7.1 Matrix Orderings (cvxopt.amd)</a>
+<LI><A href="s-umfpack.html">7.2 General Linear Equations (cvxopt.umfpack)</a>
+<LI><A href="s-cholmod.html">7.3 Positive Definite Linear Equations (cvxopt.cholmod)</a>
+<LI><A href="e-covsel.html">7.4 Example: Covariance Selection</a>
+</ul>
+<LI><A href="node45.html">8. Optimization Routines (cvxopt.solvers)</a>
+<UL>
+<LI><A href="s-lpsolver.html">8.1 Linear Programming</a>
+<LI><A href="node47.html">8.2 Quadratic Programming</a>
+<LI><A href="node48.html">8.3 Geometric Programming</a>
+<LI><A href="s-sdpsolver.html">8.4 Semidefinite Programming</a>
+<LI><A href="e-nlcp.html">8.5 Nonlinear Convex Programming</a>
+<LI><A href="node51.html">8.6 Exploiting Structure in LPs and SDPs</a>
+<LI><A href="node52.html">8.7 Exploiting Structure in Nonlinear Convex Programs</a>
+<LI><A href="s-external.html">8.8 Optional Solvers</a>
+<LI><A href="s-parameters.html">8.9 Algorithm Parameters</a>
+</ul>
+<LI><A href="node55.html">9. Modeling (cvxopt.modeling)</a>
+<UL>
+<LI><A href="s-variables.html">9.1 Variables</a>
+<LI><A href="s-functions.html">9.2 Functions</a>
+<LI><A href="node58.html">9.3 Constraints</a>
+<LI><A href="s-lp.html">9.4 Optimization Problems</a>
+<LI><A href="node60.html">9.5 Examples</a>
+</ul>
+<LI><A href="node61.html">10. C API</a>
+<UL>
+<LI><A href="node62.html">10.1 Dense Matrices</a>
+<LI><A href="node63.html">10.2 Sparse Matrices</a>
+</ul>
+<LI><A href="genindex.html">Index</a>
+</ul>
+<!--End of Table of Contents-->
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="Copyright and License"
+ href="node1.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="CVXOPT: A Python Package"
+ href="cvxopt.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="1. Introduction"
+ href="node3.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="node1.html">Copyright and License</A>
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+<a class="sectref" rel="next" href="node3.html">1. Introduction</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
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+</HTML>
diff --git a/doc/cvxopt/cvxopt.css b/doc/cvxopt/cvxopt.css
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+++ b/doc/cvxopt/cvxopt.css
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+/*
+ * The first part of this is the standard CSS generated by LaTeX2HTML,
+ * with the "empty" declarations removed.
+ */
+
+/* Century Schoolbook font is very similar to Computer Modern Math: cmmi */
+.math { font-family: "Century Schoolbook", serif; }
+.math i { font-family: "Century Schoolbook", serif;
+ font-weight: bold }
+.boldmath { font-family: "Century Schoolbook", serif;
+ font-weight: bold }
+
+/*
+ * Implement both fixed-size and relative sizes.
+ *
+ * I think these can be safely removed, as it doesn't appear that
+ * LaTeX2HTML ever generates these, even though these are carried
+ * over from the LaTeX2HTML stylesheet.
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+<div class="titlepage">
+<div class='center'>
+<h1>CVXOPT: A Python Package for Convex Optimization</h1>
+<p><b><font size="+2">Joachim Dahl & Lieven Vandenberghe</font></b></p>
+<p><i><TT>joachim at kom.aau.dk</TT>, <TT>vandenbe at ee.ucla.edu</TT></i></p>
+<p><strong>Release 0.8.2</strong><br />
+<strong>February 6, 2007</strong></p>
+<p></p>
+</div>
+</div>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="node1.html">Copyright and License</a>
+<LI><A href="contents.html">Contents</a>
+<LI><A href="node3.html">1. Introduction</a>
+<LI><A href="node4.html">2. Dense Matrices (<tt class="module">cvxopt.base</tt>)</a>
+<UL>
+<LI><A href="s-creating-matrices.html">2.1 Creating Matrices</a>
+<LI><A href="node6.html">2.2 Attributes and Methods</a>
+<LI><A href="s-arithmetic.html">2.3 Arithmetic Operations</a>
+<LI><A href="s-indexing.html">2.4 Indexing and Slicing</a>
+<LI><A href="s-builtinfuncs.html">2.5 Built-in Functions</a>
+<LI><A href="s-otherfuncs.html">2.6 Other Matrix Functions</a>
+<LI><A href="s-random.html">2.7 Randomly Generated Matrices</a>
+<LI><A href="s-array-interface.html">2.8 The NumPy Array Interface</a>
+<LI><A href="node13.html">2.9 Printing Options</a>
+</ul>
+<LI><A href="node14.html">3. The BLAS Interface (<tt class="module">cvxopt.blas</tt>)</a>
+<UL>
+<LI><A href="s-conventions.html">3.1 Matrix Classes</a>
+<LI><A href="s-blas1.html">3.2 Level 1 BLAS</a>
+<LI><A href="s-blas2.html">3.3 Level 2 BLAS</a>
+<LI><A href="s-blas3.html">3.4 Level 3 BLAS</a>
+</ul>
+<LI><A href="node19.html">4. The LAPACK Interface (<tt class="module">cvxopt.lapack</tt>)</a>
+<UL>
+<LI><A href="node20.html">4.1 General Linear Equations</a>
+<LI><A href="e-kkt-example.html">4.2 Positive Definite Linear Equations</a>
+<LI><A href="node22.html">4.3 Symmetric and Hermitian Linear Equations</a>
+<LI><A href="node23.html">4.4 Triangular Linear Equations</a>
+<LI><A href="node24.html">4.5 Least-Squares and Least-Norm Problems</a>
+<LI><A href="node25.html">4.6 Symmetric and Hermitian Eigenvalue Decomposition</a>
+<LI><A href="e-gevd.html">4.7 Generalized Symmetric Definite Eigenproblems</a>
+<LI><A href="node27.html">4.8 Singular Value Decomposition</a>
+<LI><A href="node28.html">4.9 Example: Analytic Centering</a>
+</ul>
+<LI><A href="c-fftw.html">5. Discrete Transforms (<tt class="module">cvxopt.fftw</tt>)</a>
+<UL>
+<LI><A href="node30.html">5.1 Discrete Fourier Transform</a>
+<LI><A href="node31.html">5.2 Discrete Cosine Transform</a>
+<LI><A href="node32.html">5.3 Discrete Sine Transform</a>
+</ul>
+<LI><A href="node33.html">6. Sparse Matrices (<tt class="module">cvxopt.base</tt>)</a>
+<UL>
+<LI><A href="s-creating-spmatrix.html">6.1 Creating Sparse Matrices</a>
+<LI><A href="e-spA-example.html">6.2 Attributes and Methods</a>
+<LI><A href="s-spmatrix-arith.html">6.3 Arithmetic Operations</a>
+<LI><A href="node37.html">6.4 Indexing and Slicing</a>
+<LI><A href="node38.html">6.5 Built-In Functions</a>
+<LI><A href="node39.html">6.6 Sparse BLAS Functions</a>
+</ul>
+<LI><A href="c-spsolvers.html">7. Sparse Linear Equation Solvers</a>
+<UL>
+<LI><A href="s-orderings.html">7.1 Matrix Orderings (<tt class="module">cvxopt.amd</tt>)</a>
+<LI><A href="s-umfpack.html">7.2 General Linear Equations (<tt class="module">cvxopt.umfpack</tt>)</a>
+<LI><A href="s-cholmod.html">7.3 Positive Definite Linear Equations (<tt class="module">cvxopt.cholmod</tt>)</a>
+<LI><A href="e-covsel.html">7.4 Example: Covariance Selection</a>
+</ul>
+<LI><A href="node45.html">8. Optimization Routines (<tt class="module">cvxopt.solvers</tt>)</a>
+<UL>
+<LI><A href="s-lpsolver.html">8.1 Linear Programming</a>
+<LI><A href="node47.html">8.2 Quadratic Programming</a>
+<LI><A href="node48.html">8.3 Geometric Programming</a>
+<LI><A href="s-sdpsolver.html">8.4 Semidefinite Programming</a>
+<LI><A href="e-nlcp.html">8.5 Nonlinear Convex Programming</a>
+<LI><A href="node51.html">8.6 Exploiting Structure in LPs and SDPs</a>
+<LI><A href="node52.html">8.7 Exploiting Structure in Nonlinear Convex Programs</a>
+<LI><A href="s-external.html">8.8 Optional Solvers</a>
+<LI><A href="s-parameters.html">8.9 Algorithm Parameters</a>
+</ul>
+<LI><A href="node55.html">9. Modeling (<tt class="module">cvxopt.modeling</tt>)</a>
+<UL>
+<LI><A href="s-variables.html">9.1 Variables</a>
+<LI><A href="s-functions.html">9.2 Functions</a>
+<LI><A href="node58.html">9.3 Constraints</a>
+<LI><A href="s-lp.html">9.4 Optimization Problems</a>
+<LI><A href="node60.html">9.5 Examples</a>
+</ul>
+<LI><A href="node61.html">10. C API</a>
+<UL>
+<LI><A href="node62.html">10.1 Dense Matrices</a>
+<LI><A href="node63.html">10.2 Sparse Matrices</a>
+</ul>
+<LI><A href="genindex.html">Index</a>
+<LI><A href="about.html">About this document ...</a>
+</ul>
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diff --git a/doc/cvxopt/e-covsel.html b/doc/cvxopt/e-covsel.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<title>7.4 Example: Covariance Selection</title>
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+
+<H1><A NAME="SECTION009400000000000000000">
+7.4 Example: Covariance Selection</A>
+</H1>
+This example illustrates the use of the routines for sparse Cholesky
+factorization. We consider the problem
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+\begin{array}{ll}
+ \mbox{minimize} & -\log\det K + \mathop{\bf tr}(KY)\\
+ \mbox{subject to} & K_{ij}=0,\quad (i,j) \not \in S.
+ \end{array}
+\end{equation}
+ -->
+<A NAME="e-covsel"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-covsel"></A><IMG
+ WIDTH="227" HEIGHT="45" BORDER="0"
+ SRC="img104.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & -\log\det K + \mathop{...
+...box{subject to} & K_{ij}=0,\quad (i,j) \not \in S.
+\end{array}\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(7.5)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+The optimization variable is a symmetric matrix <I>K</I> of order <I>n</I>
+and the domain of the problem is the set of positive definite matrices.
+The matrix <SPAN CLASS="MATH"><IMG
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img105.gif"
+ ALT="$Y$"></SPAN> and the index set <SPAN CLASS="MATH"><IMG
+ WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img106.gif"
+ ALT="$S$"></SPAN> are given. We assume that all
+the diagonal positions are included in <SPAN CLASS="MATH"><IMG
+ WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img106.gif"
+ ALT="$S$"></SPAN>.
+This problem arises in maximum likelihood estimation of the covariance
+matrix of a zero-mean normal distribution, with constraints
+that specify that pairs of variables are conditionally independent.
+
+<P>
+We can express <I>K</I> as
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+K(x) = E_1\mbox{\bf diag}\,(x)E_2^T+E_2\mbox{\bf diag}\,(x)E_1^T
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="265" HEIGHT="28" BORDER="0"
+ SRC="img107.gif"
+ ALT="\begin{displaymath}
+K(x) = E_1\mbox{\bf diag}\,(x)E_2^T+E_2\mbox{\bf diag}\,(x)E_1^T
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>x</I> are the nonzero elements in the lower triangular part
+of <I>K</I>, with the diagonal elements scaled by 1/2,
+and
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+E_1 = \left[ \begin{array}{cccc}
+ e_{i_1} & e_{i_2} & \cdots & e_{i_q} \end{array}\right], \qquad
+ E_2 = \left[ \begin{array}{cccc}
+ e_{j_1} & e_{j_2} & \cdots & e_{j_q} \end{array}\right],
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="436" HEIGHT="30" BORDER="0"
+ SRC="img108.gif"
+ ALT="\begin{displaymath}
+E_1 = \left[ \begin{array}{cccc}
+e_{i_1} & e_{i_2} & \cdot...
+...cc}
+e_{j_1} & e_{j_2} & \cdots & e_{j_q} \end{array}\right],
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where (<I>i_k</I>, <I>j_k</I>) are the positions of the nonzero
+entries in the lower-triangular part of <I>K</I>.
+With this notation, we can solve problem (<A HREF="#e-covsel">7.5</A>) by solving
+the unconstrained problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & f(x) = -\log\det K(x) + \mathop{\bf tr}(K(x)Y).
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="325" HEIGHT="30" BORDER="0"
+ SRC="img109.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & f(x) = -\log\det K(x) + \mathop{\bf tr}(K(x)Y).
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The code below implements Newton's method with a backtracking line
+search. The gradient and Hessian of the objective function are given
+by
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+\nabla f(x)
+&=& 2 \mbox{\bf diag}\,( E_1^T (Y - K(x)^{-1}) E_2)) \\
+&=& 2\mbox{\bf diag}\,(Y_{IJ} - \left(K(x)^{-1}\right)_{IJ})\\
+\nabla^2 f(x) & = &
+ 2 (E_1^T K(x)^{-1} E_1) \circ (E_2^T K(x)^{-1} E_2)
+ + 2 (E_1^T K(x)^{-1} E_2) \circ (E_2^T K(x)^{-1} E_1) \\
+&=& 2 \left(K(x)^{-1}\right)_{II} \circ
+ \left(K(x)^{-1}\right)_{JJ}
+ +2 \left(K(x)^{-1}\right)_{IJ} \circ
+ \left(K(x)^{-1}\right)_{JI},
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="588" HEIGHT="105" BORDER="0"
+ SRC="img110.gif"
+ ALT="\begin{eqnarray*}
+\nabla f(x)
+&=& 2 \mbox{\bf diag}\,( E_1^T (Y - K(x)^{-1}) E_...
+...\left(K(x)^{-1}\right)_{IJ} \circ
+\left(K(x)^{-1}\right)_{JI},
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+where <code>o</code> denotes Hadamard product.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt.base import matrix, spmatrix, log, mul
+from cvxopt import blas, lapack, amd, cholmod
+
+def covsel(Y):
+ """
+ Returns the solution of
+
+ minimize -logdet K + Tr(KY)
+ subject to K_{ij}=0, (i,j) not in indices listed in I,J.
+
+ Y is a symmetric sparse matrix with nonzero diagonal elements.
+ I = Y.I, J = Y.J.
+ """
+
+ I, J = Y.I, Y.J
+ n, m = Y.size[0], len(I)
+ N = I + J*n # non-zero positions for one-argument indexing
+ D = [k for k in xrange(m) if I[k]==J[k]] # position of diagonal elements
+
+ # starting point: symmetric identity with nonzero pattern I,J
+ K = spmatrix(0, I, J)
+ K[::n+1] = 1
+
+ # Kn is used in the line search
+ Kn = spmatrix(0, I, J)
+
+ # symbolic factorization of K
+ F = cholmod.symbolic(K)
+
+ # Kinv will be the inverse of K
+ Kinv = matrix(0.0, (n,n))
+
+ for iters in xrange(100):
+
+ # numeric factorization of K
+ cholmod.numeric(K, F)
+ d = cholmod.diag(F)
+
+ # compute Kinv by solving K*X = I
+ Kinv[:] = 0
+ Kinv[::n+1] = 1
+ cholmod.solve(F, Kinv)
+
+ # solve Newton system
+ grad = 2*(Y.V - Kinv[N])
+ hess = 2*(mul(Kinv[I,J],Kinv[J,I]) + mul(Kinv[I,I],Kinv[J,J]))
+ v = -grad
+ lapack.posv(hess,v)
+
+ # stopping criterion
+ sqntdecr = -blas.dot(grad,v)
+ print "Newton decrement squared:%- 7.5e" %sqntdecr
+ if (sqntdecr < 1e-12):
+ print "number of iterations: ", iters+1
+ break
+
+ # line search
+ dx = +v
+ dx[D] *= 2 # scale the diagonal elems
+ f = -2.0 * sum(log(d)) # f = -log det K
+ s = 1
+ for lsiter in xrange(50):
+ Kn.V = K.V + s*dx
+ try:
+ cholmod.numeric(Kn, F)
+ except ArithmeticError:
+ s *= 0.5
+ else:
+ d = cholmod.diag(F)
+ fn = -2.0 * sum(log(d)) + 2*s*blas.dot(v,Y.V)
+ if (fn < f - 0.01*s*sqntdecr):
+ break
+ s *= 0.5
+
+ K.V = Kn.V
+
+ return K
+</pre></div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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diff --git a/doc/cvxopt/e-gevd.html b/doc/cvxopt/e-gevd.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+
+<H1><A NAME="SECTION006700000000000000000">
+4.7 Generalized Symmetric Definite Eigenproblems</A>
+</H1>
+Three types of generalized eigenvalue problems can be solved:
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+AZ = BZ\mbox{\bf diag}\,(\lambda)\quad \mbox{(type 1)}, \qquad
+ ABZ = Z\mbox{\bf diag}\,(\lambda) \quad \mbox{(type 2)}, \qquad
+ BAZ = Z\mbox{\bf diag}\,(\lambda) \quad \mbox{(type 3)},
+\end{equation}
+ -->
+<A NAME="e-gevd"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-gevd"></A><IMG
+ WIDTH="649" HEIGHT="28" BORDER="0"
+ SRC="img66.gif"
+ ALT="\begin{displaymath}
+AZ = BZ\mbox{\bf diag}\,(\lambda)\quad \mbox{(type 1)}, \qq...
+...ad
+BAZ = Z\mbox{\bf diag}\,(\lambda) \quad \mbox{(type 3)},
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(4.2)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+with <SPAN CLASS="MATH"><IMG
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img53.gif"
+ ALT="$A$"></SPAN> and <SPAN CLASS="MATH"><IMG
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img67.gif"
+ ALT="$B$"></SPAN> real symmetric or complex Hermitian, and <SPAN CLASS="MATH"><IMG
+ WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img67.gif"
+ ALT="$B$"></SPAN> positive
+definite.
+The matrix of eigenvectors is normalized as follows:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+Z^H BZ = I \quad \mbox{(types 1 and 2)}, \qquad
+ Z^H B^{-1}Z = I \quad \mbox{(type 3)}.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="392" HEIGHT="27" BORDER="0"
+ SRC="img68.gif"
+ ALT="\begin{displaymath}
+Z^H BZ = I \quad \mbox{(types 1 and 2)}, \qquad
+Z^H B^{-1}Z = I \quad \mbox{(type 3)}.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-105' xml:id='l2h-105' class="function">sygv</tt></b>(</nobr></td>
+ <td><var>A, B, W</var><big>[</big><var>, itype=1</var><big>[</big><var>,
+jobz='N'</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves the generalized eigenproblem (<A HREF="#e-gevd">4.2</A>) for real symmetric
+matrices of order <I>n</I>, stored in real matrices <var>A</var> and <var>B</var>.
+<var>itype</var> is an integer with possible values 1, 2, 3, and specifies
+the type of eigenproblem.
+<var>W</var> is a real matrix of length at least <I>n</I>.
+On exit, it contains the eigenvalues in ascending order.
+On exit, <var>B</var> contains the Cholesky factor of <I>B</I>.
+If <var>jobz</var> is <code>'V'</code>, the eigenvectors are computed
+and returned in <var>A</var>.
+If <var>jobz</var> is <code>'N'</code>, the eigenvectors are not returned and the
+contents of <var>A</var> are destroyed.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-106' xml:id='l2h-106' class="function">hegv</tt></b>(</nobr></td>
+ <td><var>A, B, W</var><big>[</big><var>, itype=1</var><big>[</big><var>,
+jobz='N'</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Generalized eigenvalue problem (<A HREF="#e-gevd">4.2</A>) of real symmetric or
+complex Hermitian matrix of order <var>n</var>.
+The calling sequence is identical to <tt class="function">sygv()</tt>,
+except that <var>A</var> and <var>B</var> can be real or complex.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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+
+<H1><A NAME="SECTION006200000000000000000">
+4.2 Positive Definite Linear Equations</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-72' xml:id='l2h-72' class="function">posv</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="64" HEIGHT="27" BORDER="0"
+ SRC="img41.gif"
+ ALT="\begin{displaymath}
+A X = B,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric or complex Hermitian positive
+definite matrix.
+On exit, <var>B</var> is replaced by the solution, and <var>A</var> is
+overwritten with the Cholesky factor.
+The matrices <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>).
+Raises an <code>ArithmeticError</code> if the matrix is not positive definite.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-73' xml:id='l2h-73' class="function">potrf</tt></b>(</nobr></td>
+ <td><var>A</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Cholesky factorization
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = LL^T \qquad \mbox{or} \qquad A = LL^H
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="207" HEIGHT="24" BORDER="0"
+ SRC="img46.gif"
+ ALT="\begin{displaymath}
+A = LL^T \qquad \mbox{or} \qquad A = LL^H
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+of a positive definite real symmetric or complex Hermitian matrix
+<I>A</I>. On exit, the lower triangular part of <var>A</var>
+(if <var>uplo</var> is <code>'L'</code>) or the upper triangular part
+(if <var>uplo</var> is <code>'U'</code>) is overwritten with the Cholesky factor
+or its (conjugate) transpose.
+Raises an <code>ArithmeticError</code> if the matrix is not positive definite.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-74' xml:id='l2h-74' class="function">potrs</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with a positive
+definite real symmetric or complex Hermitian matrix,
+given the Cholesky factorization computed by
+<tt class="function">posv()</tt> or <tt class="function">potrf()</tt>.
+On entry, <var>A</var> contains the triangular factor, as computed by
+<tt class="function">posv()</tt> or <tt class="function">potrf()</tt>. On exit, <var>B</var> is replaced
+by the solution.
+<var>B</var> must have the same type as <var>A</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-75' xml:id='l2h-75' class="function">potri</tt></b>(</nobr></td>
+ <td><var>A</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes the inverse of a positive definite matrix.
+On entry, <var>A</var> contains the Cholesky factorization computed
+by <tt class="function">potrf()</tt> or <tt class="function">posv()</tt>. On exit, it contains
+the inverse.
+</dl>
+
+<P>
+As an example, we use <tt class="function">posv()</tt> to solve the linear system
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+\left[ \begin{array}{cc}
+ -\mbox{\bf diag}\,(d)^2 & A \\
+ A^T & 0 \end{array} \right]
+ \left[ \begin{array}{c} x_1 \\x_2 \end{array} \right]
+ = \left[ \begin{array}{c} b_1 \\b_2 \end{array} \right]
+\end{equation}
+ -->
+<A NAME="e-kkt-example"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-kkt-example"></A><IMG
+ WIDTH="244" HEIGHT="45" BORDER="0"
+ SRC="img48.gif"
+ ALT="\begin{displaymath}
+\left[ \begin{array}{cc}
+-\mbox{\bf diag}\,(d)^2 & A \\
+...
+...ght]
+= \left[ \begin{array}{c} b_1 \\ b_2 \end{array} \right]
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(4.1)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+by block-elimination.
+We first pick a random problem.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix, div
+>>> from cvxopt.random import normal, uniform
+>>> from cvxopt.blas import syrk, gemv
+>>> from cvxopt.lapack import posv
+>>> m, n = 100, 50
+>>> A = normal(m,n)
+>>> b1, b2 = normal(m), normal(n)
+>>> d = uniform(m)
+</pre></div>
+We then solve the equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A^T \mbox{\bf diag}\,(d)^{-2}A x_2 = b_2 + A^T \mbox{\bf diag}\,(d)^{-2} b_1, \qquad
+ \mbox{\bf diag}\,(d)^2 x_1 = Ax_2 - b_1.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="481" HEIGHT="28" BORDER="0"
+ SRC="img49.gif"
+ ALT="\begin{displaymath}
+A^T \mbox{\bf diag}\,(d)^{-2}A x_2 = b_2 + A^T \mbox{\bf di...
+...(d)^{-2} b_1, \qquad
+\mbox{\bf diag}\,(d)^2 x_1 = Ax_2 - b_1.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> Asc = div(A, d[:, n*[0]]) # Asc := diag(d)^{-1}*A
+>>> B = matrix(0.0, (n,n))
+>>> syrk(Asc, B, trans='T') # B := Asc^T * Asc = A^T * diag(d)^{-2} * A
+>>> x1 = div(b1, d) # x1 := diag(d)^{-1}*b1
+>>> x2 = +b2
+>>> gemv(Asc, x1, x2, trans='T', beta=1.0) # x2 := x2 + Asc^T*x1 = b2 + A^T*diag(d)^{-2}*b1
+>>> posv(B, x2) # x2 := B^{-1}*x2 = B^{-1}*(b2 + A^T*diag(d)^{-2}*b1)
+>>> gemv(Asc, x2, x1, beta=-1.0) # x1 := Asc*x2 - x1 = diag(d)^{-1} * (A*x2 - b1)
+>>> x1 = div(x1, d) # x1 := diag(d)^{-1}*x1 = diag(d)^{-2} * (A*x2 - b1)
+</pre></div>
+
+<P>
+There are separate routines for equations with positive definite band
+matrices.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-76' xml:id='l2h-76' class="function">pbsv</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric or complex Hermitian positive definite
+band matrix. On entry, the diagonals of <I>A</I> are stored in <var>A</var>,
+using the BLAS format for symmetric or Hermitian band matrices
+(see section <A href="s-conventions.html#s-conventions">3.1</A>). On exit, <var>B</var> is replaced by the
+solution, and <var>A</var> is overwritten with the Cholesky factor (in the
+BLAS format for triangular band matrices). The matrices <var>A</var> and
+<var>B</var> must have the same type (<code>'d'</code> or <code>'z'</code>).
+Raises an <code>ArithmeticError</code> if the matrix is not positive definite.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-77' xml:id='l2h-77' class="function">pbtrf</tt></b>(</nobr></td>
+ <td><var>A</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Cholesky factorization
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = LL^T \qquad \mbox{or} \qquad A = LL^H
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="207" HEIGHT="24" BORDER="0"
+ SRC="img46.gif"
+ ALT="\begin{displaymath}
+A = LL^T \qquad \mbox{or} \qquad A = LL^H
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+of a positive definite real symmetric or complex Hermitian band matrix
+<I>A</I>. On entry, the diagonals of <I>A</I> are stored in <var>A</var>,
+using the BLAS format for symmetric or Hermitian band matrices.
+On exit, <var>A</var> contains the Cholesky factor, in the BLAS format
+for triangular band matrices.
+Raises an <code>ArithmeticError</code> if the matrix is not positive definite.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-78' xml:id='l2h-78' class="function">pbtrs</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with a positive definite real symmetric or complex Hermitian band matrix,
+given the Cholesky factorization computed by <tt class="function">pbsv()</tt> or
+<tt class="function">pbtrf()</tt>.
+On entry, <var>A</var> contains the triangular factor, as computed by
+<tt class="function">pbsv()</tt> or <tt class="function">pbtrf()</tt>. On exit, <var>B</var> is replaced
+by the solution. <var>B</var> must have the same type as <var>A</var>.
+</dl>
+
+<P>
+The following functions are useful for tridiagonal systems.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-79' xml:id='l2h-79' class="function">ptsv</tt></b>(</nobr></td>
+ <td><var>d, e, B</var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="64" HEIGHT="27" BORDER="0"
+ SRC="img41.gif"
+ ALT="\begin{displaymath}
+A X = B,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is an <I>n</I> by <I>n</I> real symmetric or complex
+Hermitian tridiagonal matrix, with diagonal <var>d</var> (a <code>'d'</code> matrix of
+length <I>n</I>) and subdiagonal <var>e</var> (a <code>'d'</code> or <code>'z'</code> matrix of length
+<I>n</I>-1).
+The arguments <var>e</var> and <var>B</var> must have the same type.
+On exit <var>d</var> contains the diagonal elements of <I>D</I> in
+the LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img50.gif"
+ ALT="${}\mathrm{^T}$"></SPAN> or LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img51.gif"
+ ALT="${}\mathrm{^H}$"></SPAN> factorization
+of <I>A</I>, and <var>e</var> contains the subdiagonal elements of the unit
+lower bidiagonal matrix <I>L</I>.
+<var>B</var> is overwritten with the solution <I>X</I>.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-80' xml:id='l2h-80' class="function">pttrf</tt></b>(</nobr></td>
+ <td><var>d, e</var>)</td></tr></table></dt>
+<dd>
+LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img50.gif"
+ ALT="${}\mathrm{^T}$"></SPAN> or LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img51.gif"
+ ALT="${}\mathrm{^H}$"></SPAN> factorization of an <I>n</I> by
+<I>n</I> real symmetric or complex Hermitian tridiagonal matrix <I>A</I>.
+On entry, the argument <var>d</var> is a <code>'d'</code> matrix with the diagonal elements
+of <I>A</I>. The argument <var>e</var> is <code>'d'</code> or <code>'z'</code> matrix with
+the subdiagonal elements of <I>A</I>.
+On exit <var>d</var> contains the diagonal elements of <I>D</I>, and <var>e</var>
+contains the subdiagonal elements of the unit lower bidiagonal matrix
+<I>L</I>. Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-81' xml:id='l2h-81' class="function">gttrs</tt></b>(</nobr></td>
+ <td><var>d, e, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is an <I>n</I> by <I>n</I> real symmetric or complex
+Hermitian tridiagonal matrix, given its LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img50.gif"
+ ALT="${}\mathrm{^T}$"></SPAN> or
+LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img51.gif"
+ ALT="${}\mathrm{^H}$"></SPAN> factorization.
+The argument <var>d</var> is the diagonal of the diagonal matrix <I>D</I>.
+The argument <var>uplo</var> only matters for complex matrices.
+If <var>uplo</var> is <code>'L'</code>, then <var>e</var> contains the subdiagonal
+elements of the unit bidiagonal matrix <I>L</I>.
+If <var>uplo</var> is <code>'U'</code>, then <var>e</var> contains the complex
+conjugates of the elements of the unit bidiagonal matrix <I>L</I>.
+On exit, <var>B</var> is overwritten with the solution <I>X</I>.
+<var>B</var> must have the same type as <var>e</var>.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="4.1 General Linear Equations"
+ href="node20.html"><img src='previous.gif'
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<title>8.5 Nonlinear Convex Programming</title>
+</head>
+<body>
+<DIV CLASS="navigation">
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+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0010500000000000000000">
+8.5 Nonlinear Convex Programming</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-149' xml:id='l2h-149' class="function">cp</tt></b>(</nobr></td>
+ <td><var>F</var><big>[</big><var>, G, h</var><big>[</big><var>, A, b</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves an optimization problem
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+\begin{array}{ll}
+ \mbox{minimize} & f_0(x) \\
+ \mbox{subject to} & f_k(x) \leq 0, \quad k=1,\ldots,m \\
+ & G x \preceq h \\
+ & A x = b,
+ \end{array}
+\end{equation}
+ -->
+<A NAME="e-nlcp"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-nlcp"></A><IMG
+ WIDTH="254" HEIGHT="83" BORDER="0"
+ SRC="img138.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & f_0(x) \\
+\mbox{subj...
+... k=1,\ldots,m \\
+& G x \preceq h \\
+& A x = b,
+\end{array}\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(8.3)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+with <!-- MATH
+ $f=(f_0,\ldots,f_m)$
+ -->
+<SPAN CLASS="MATH"><IMG
+ WIDTH="117" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ SRC="img139.gif"
+ ALT="$f=(f_0,\ldots,f_m)$"></SPAN> convex and twice differentiable.
+
+<P>
+<var>F</var> is a function that evaluates the objective and nonlinear
+constraint functions. It must handle the following calling sequences.
+
+<P>
+
+<UL>
+<LI><code>F()</code> returns a tuple (<var>m</var>, <var>x0</var>), where <var>m</var> is
+ the number of nonlinear constraints and <var>x0</var> is a point in the
+ domain of <I>f</I>. <var>x0</var> is a dense real matrix of size
+ (<var>n</var>,1).
+
+<P>
+</LI>
+<LI><code>F(x)</code>, with <var>x</var> a dense real matrix of size
+ (<var>n</var>,1), returns a tuple (<var>f</var>, <var>Df</var>).
+ <var>f</var> is a dense real matrix of size (<var>m</var>+1,1), with
+ <code><var>f</var>[<var>k</var>]</code> equal to <I>f_k(x)</I>.
+ (If <I>m</I> is zero, <var>f</var> can also be returned as a number.)
+ <var>Df</var> is a dense or sparse real matrix of size (<var>m</var>+1,<var>n</var>)
+ with <code><var>Df</var>[<var>k</var>,:]</code> equal to the transpose of the gradient
+ of <I>f_k</I> at <I>x</I>.
+ If <var>x</var> is not in the domain of <I>f</I>, <code>F(x)</code> returns
+ <code>None</code> or a tuple (<code>None</code>,<code>None</code>).
+
+<P>
+</LI>
+<LI><code>F(x,z)</code>, with <var>x</var> a dense real matrix of size
+ (<var>n</var>,1) and <var>z</var> a positive dense real matrix of size
+ (<var>m</var>+1,1) returns a tuple (<var>f</var>, <var>Df</var>, <var>H</var>).
+ <var>f</var> and <var>Df</var> are defined as above.
+ <var>H</var> is a square dense or sparse real matrix of size
+ (<I>n</I>, <I>n</I>), whose lower triangular part contains the lower
+ triangular part of
+ <BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+z_0 \nabla^2f_0(x) + z_1 \nabla^2f_1(x) + \cdots + z_m \nabla^2f_m(x).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="303" HEIGHT="28" BORDER="0"
+ SRC="img140.gif"
+ ALT="\begin{displaymath}
+z_0 \nabla^2f_0(x) + z_1 \nabla^2f_1(x) + \cdots + z_m \nabla^2f_m(x).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>F</var> is called with two arguments, it can be assumed that
+ <var>x</var> is in the domain of <I>f</I>.
+</LI>
+</UL>
+
+<P>
+<var>G</var> and <var>A</var> are dense or sparse real matrices with <var>n</var>
+columns. Their default values are matrices of size (0,<var>n</var>).
+<var>h</var> and <var>b</var> are dense real matrices with one column, and the
+same number of rows as <var>G</var> and <var>A</var>, respectively.
+Their default values are matrices of size (0,1).
+
+<P>
+<tt class="function">cp()</tt> returns a dictionary with keys <code>'status'</code>,
+<code>'x'</code>, <code>'snl'</code>, <code>'sl'</code>, <code>'y'</code>, <code>'znl'</code>,
+<code>'zl'</code>.
+The possible values of the <code>'status'</code> key are:
+<DL>
+<DT><STRONG><code>'optimal'</code></STRONG></DT>
+<DD>In this case the
+<code>'x'</code> entry of the dictionary is the primal optimal solution,
+ the <code>'snl'</code> and <code>'sl'</code> entries are the corresponding
+ slacks in the nonlinear and linear inequality constraints, and the
+<code>'znl'</code>, <code>'zl'</code> and <code>'y'</code> entries are the optimal
+values of the dual variables associated with the nonlinear
+inequalities, the linear inequalities, and the linear equality
+constraints. These vectors approximately satisfy the Karush-
+Kuhn-Tucker (KKT) conditions
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\nabla f_0(x) + D\tilde f(x)^T z_\mathrm{nl} +
+ G^T z_\mathrm{l} + A^T y = 0, \qquad
+\tilde f(x) + s_\mathrm{nl} = 0, \quad k=1,\ldots,m, \qquad
+ Gx + s_\mathrm{l} = h, \qquad
+ Ax = b,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="701" HEIGHT="28" BORDER="0"
+ SRC="img141.gif"
+ ALT="\begin{displaymath}
+\nabla f_0(x) + D\tilde f(x)^T z_\mathrm{nl} +
+G^T z_\mat...
+... k=1,\ldots,m, \qquad
+Gx + s_\mathrm{l} = h, \qquad
+Ax = b,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <!-- MATH
+ $\tilde f = (f_1,\ldots, f_m)$
+ -->
+<SPAN CLASS="MATH"><IMG
+ WIDTH="117" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ SRC="img142.gif"
+ ALT="$\tilde f = (f_1,\ldots, f_m)$"></SPAN>,
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+s_\mathrm{nl}\succeq 0, \qquad s_\mathrm{l}\succeq 0, \qquad
+z_\mathrm{nl} \succeq 0, \qquad z_\mathrm{l} \succeq 0, \qquad
+s_\mathrm{nl}^T z_\mathrm{nl} + s_\mathrm{l}^T z_\mathrm{l} = 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="453" HEIGHT="28" BORDER="0"
+ SRC="img125.gif"
+ ALT="\begin{displaymath}
+s_\mathrm{nl}\succeq 0, \qquad s_\mathrm{l}\succeq 0, \qquad...
+...\mathrm{nl}^T z_\mathrm{nl} + s_\mathrm{l}^T z_\mathrm{l} = 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'unknown'</code></STRONG></DT>
+<DD>This indicates that the algorithm reached
+the maximum number of iterations before a solution was found.
+The <code>'x'</code>, <code>'snl'</code>, <code>'sl'</code>,
+<code>'y'</code>, <code>'znl'</code> and <code>'zl'</code> entries are <code>None</code>.
+</DD>
+</DL>
+
+<P>
+</dl>
+
+<P>
+<DL>
+<DT><STRONG>Example: equality constrained analytic centering</STRONG></DT>
+<DD><P>
+The equality constrained analytic centering problem is defined as
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & -\sum_{i=1}^m \log x_i \\
+ \mbox{subject to} & Ax = b.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="169" HEIGHT="45" BORDER="0"
+ SRC="img143.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & -\sum_{i=1}^m \log x_i \\
+\mbox{subject to} & Ax = b.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The function <tt class="function">acent()</tt> defined below solves the problem,
+assumping it is solvable.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, log
+
+def acent(A, b):
+ m, n = A.size
+ def F(x=None, z=None):
+ if x is None: return 0, matrix(1.0, (n,1))
+ if min(x) <= 0.0: return None
+ f = -sum(log(x))
+ Df = -(x**-1).T
+ if z is None: return f, Df
+ H = z[0] * spmatrix(x**-2, range(n), range(n))
+ return f, Df, H
+ return solvers.cp(F, A=A, b=b)['x']
+</pre></div>
+
+<P>
+</DD>
+<DT><STRONG>Example: robust least-squares</STRONG></DT>
+<DD><P>
+The function <tt class="function">robls()</tt> defined below solves the unconstrained
+problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \sum_{k=1}^m \phi((Ax-b)_k),
+\end{array} \qquad \mbox{where} \quad A \in{\mbox{\bf R}}^{m\times n}, \quad
+\phi(u) = \sqrt{\rho + u^2}.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="519" HEIGHT="30" BORDER="0"
+ SRC="img144.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \sum_{k=1}^m \phi((Ax-b)...
+...{\mbox{\bf R}}^{m\times n}, \quad
+\phi(u) = \sqrt{\rho + u^2}.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, sqrt, div
+
+def robls(A, b, rho):
+ m, n = A.size
+ def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (n,1))
+ y = A*x-b
+ w = sqrt(rho + y**2)
+ f = sum(w)
+ Df = div(y, w).T * A
+ if z is None: return f, Df
+ H = A.T * spmatrix(z[0]*rho*(w**-3), range(m), range(m)) * A
+ return f, Df, H
+ return solvers.cp(F)['x']
+</pre></div>
+
+<P>
+</DD>
+<DT><STRONG>Example: floor planning</STRONG></DT>
+<DD><P>
+This example is the floor planning problem of section 8.8.2 in the book
+<em class="citetitle"><a
+ href="http://www.stanford.edu/~boyd/cvxbook"
+ title="Convex Optimization"
+ >Convex Optimization</a></em>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & W + H \\
+ \mbox{subject to} & A_{\mathrm{min}, k}/h_k - w_k \leq 0,
+ \quad k=1,\ldots, 5 \\
+ & x_1 \geq 0, \quad x_2 \geq 0, \quad x_4 \geq 0 \\
+ & x_1 + w_1 + \rho \leq x_3, \quad x_2 + w_2 + \rho \leq x_3, \quad
+ x_3 + w_3 + \rho \leq x_5, \quad x_4 + w_4 + \rho \leq x_5, \quad
+ x_5 + w_5 \leq W \\
+ & y_2 \geq 0, \quad y_3 \geq 0, \quad y_5 \geq 0 \\
+ & y_2 + h_2 + \rho \leq y_1, \quad y_1 + h_1 + \rho \leq y_4, \quad
+ y_3 + h_3 + \rho \leq y_4, \quad y_4 + h_4 \leq H, \quad
+ y_5 + h_5 \leq H \\
+ & h_k/\gamma \leq w_k \leq \gamma h_k, \quad k=1,\ldots,5.
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="740" HEIGHT="140" BORDER="0"
+ SRC="img145.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & W + H \\
+\mbox{subjec...
+...gamma \leq w_k \leq \gamma h_k, \quad k=1,\ldots,5.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+This problem has 22 variables
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+W, \qquad H, \qquad x\in{\mbox{\bf R}}^5, \qquad y\in{\mbox{\bf R}}^5, \qquad
+w\in{\mbox{\bf R}}^5, \qquad h\in{\mbox{\bf R}}^5,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="417" HEIGHT="27" BORDER="0"
+ SRC="img146.gif"
+ ALT="\begin{displaymath}
+W, \qquad H, \qquad x\in{\mbox{\bf R}}^5, \qquad y\in{\mbox{...
+...}^5, \qquad
+w\in{\mbox{\bf R}}^5, \qquad h\in{\mbox{\bf R}}^5,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+5 nonlinear inequality constraints, and 26 linear inequality
+constraints. The code belows defines a function
+<tt class="function">floorplan()</tt> that solves the problem by calling
+<tt class="function">cp()</tt>, then applies it to 4 instances, and creates
+a figure.
+
+<P>
+<div class="verbatim"><pre>
+import pylab
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, mul, div
+
+def floorplan(Amin):
+
+ # minimize W+H
+ # subject to Amink / hk <= wk, k = 1,..., 5
+ # x1 >= 0, x2 >= 0, x4 >= 0
+ # x1 + w1 + rho <= x3
+ # x2 + w2 + rho <= x3
+ # x3 + w3 + rho <= x5
+ # x4 + w4 + rho <= x5
+ # x5 + w5 <= W
+ # y2 >= 0, y3 >= 0, y5 >= 0
+ # y2 + h2 + rho <= y1
+ # y1 + h1 + rho <= y4
+ # y3 + h3 + rho <= y4
+ # y4 + h4 <= H
+ # y5 + h5 <= H
+ # hk/gamma <= wk <= gamma*hk, k = 1, ..., 5
+ #
+ # 22 Variables W, H, x (5), y (5), w (5), h (5).
+ #
+ # W, H: scalars; bounding box width and height
+ # x, y: 5-vectors; coordinates of bottom left corners of blocks
+ # w, h: 5-vectors; widths and heigths of the 5 blocks
+
+ rho, gamma = 1.0, 5.0 # min spacing, min aspect ratio
+
+ # The objective is to minimize W + H. There are five nonlinear
+ # constraints
+ #
+ # -wk + Amink / hk <= 0, k = 1, ..., 5
+
+ def F(x=None, z=None):
+ if x is None: return 5, matrix(17*[0.0] + 5*[1.0])
+ if min(x[17:]) <= 0.0: return None
+ f = matrix(0.0, (6,1))
+ f[0] = x[0] + x[1]
+ f[1:] = -x[12:17] + div(Amin, x[17:])
+ Df = matrix(0.0, (6,22))
+ Df[0, [0,1]] = 1.0
+ Df[1:,12:17] = spmatrix(-1.0, range(5), range(5))
+ Df[1:,17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
+ if z is None: return f, Df
+ H = spmatrix( 2.0* mul(z[1:], div(Amin, x[17::]**3)), range(17,22), range(17,22) )
+ return f, Df, H
+
+ G = matrix(0.0, (26,22))
+ h = matrix(0.0, (26,1))
+ G[0,2] = -1.0 # -x1 <= 0
+ G[1,3] = -1.0 # -x2 <= 0
+ G[2,5] = -1.0 # -x4 <= 0
+ G[3, [2, 4, 12]], h[3] = [1.0, -1.0, 1.0], -rho # x1 - x3 + w1 <= -rho
+ G[4, [3, 4, 13]], h[4] = [1.0, -1.0, 1.0], -rho # x2 - x3 + w2 <= -rho
+ G[5, [4, 6, 14]], h[5] = [1.0, -1.0, 1.0], -rho # x3 - x5 + w3 <= -rho
+ G[6, [5, 6, 15]], h[6] = [1.0, -1.0, 1.0], -rho # x4 - x5 + w4 <= -rho
+ G[7, [0, 6, 16]] = -1.0, 1.0, 1.0 # -W + x5 + w5 <= 0
+ G[8,8] = -1.0 # -y2 <= 0
+ G[9,9] = -1.0 # -y3 <= 0
+ G[10,11] = -1.0 # -y5 <= 0
+ G[11, [7, 8, 18]], h[11] = [-1.0, 1.0, 1.0], -rho # -y1 + y2 + h2 <= -rho
+ G[12, [7, 10, 17]], h[12] = [1.0, -1.0, 1.0], -rho # y1 - y4 + h1 <= -rho
+ G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho # y3 - y4 + h3 <= -rho
+ G[14, [1, 10, 20]] = -1.0, 1.0, 1.0 # -H + y4 + h4 <= 0
+ G[15, [1, 11, 21]] = -1.0, 1.0, 1.0 # -H + y5 + h5 <= 0
+ G[16, [12, 17]] = -1.0, 1.0/gamma # -w1 + h1/gamma <= 0
+ G[17, [12, 17]] = 1.0, -gamma # w1 - gamma * h1 <= 0
+ G[18, [13, 18]] = -1.0, 1.0/gamma # -w2 + h2/gamma <= 0
+ G[19, [13, 18]] = 1.0, -gamma # w2 - gamma * h2 <= 0
+ G[20, [14, 18]] = -1.0, 1.0/gamma # -w3 + h3/gamma <= 0
+ G[21, [14, 19]] = 1.0, -gamma # w3 - gamma * h3 <= 0
+ G[22, [15, 19]] = -1.0, 1.0/gamma # -w4 + h4/gamma <= 0
+ G[23, [15, 20]] = 1.0, -gamma # w4 - gamma * h4 <= 0
+ G[24, [16, 21]] = -1.0, 1.0/gamma # -w5 + h5/gamma <= 0
+ G[25, [16, 21]] = 1.0, -gamma # w5 - gamma * h5 <= 0.0
+
+ # solve and return W, H, x, y, w, h
+ sol = solvers.cp(F, G, h)
+ return sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], sol['x'][12:17], sol['x'][17:]
+
+pylab.figure(facecolor='w')
+pylab.subplot(221)
+Amin = matrix([100., 100., 100., 100., 100.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]], '#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(222)
+Amin = matrix([20., 50., 80., 150., 200.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]], '#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(223)
+Amin = matrix([180., 80., 80., 80., 80.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]],'#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(224)
+Amin = matrix([20., 150., 20., 200., 110.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]],'#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.show()
+</pre></div>
+
+<P>
+<DIV ALIGN="CENTER">
+<IMG
+ WIDTH="680" HEIGHT="511" ALIGN="BOTTOM" BORDER="0"
+ SRC="img147.gif"
+ ALT="\includegraphics[width=15cm]{figures/floorplan.eps}">
+
+</DIV>
+</DD>
+</DL>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+</head>
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+</DIV>
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+
+<H1><A NAME="SECTION008200000000000000000">
+6.2 Attributes and Methods</A>
+</H1>
+The following attributes and methods are defined for <tt class="class">spmatrix</tt> objects.
+
+<P>
+<dl><dt><b><tt id='l2h-117' xml:id='l2h-117' class="member">V</tt></b></dt>
+<dd>
+A single-column dense matrix containing the numerical values of the
+nonzero entries in column-major order. Making an assignment to
+the attribute is an efficient way of changing the values of the sparse
+matrix, without changing the sparsity pattern.
+
+<P>
+When the attribute <tt class="member">V</tt> is read, a <em>copy</em> of <tt class="member">V</tt> is
+returned, as a new dense matrix.
+(This implies, for example, that an indexed assignment
+"<tt class="samp">A.V[I] = B</tt>" does not work, or at least
+cannot be used to modify <var>A</var>. Instead the attribute <code>V</code>
+will be read and returned as a new matrix; then the elements of this
+new matrix are modified.)
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-118' xml:id='l2h-118' class="member">I</tt></b></dt>
+<dd>
+A single-column integer matrix with the row indices of the entries in
+<code>V</code>. A read-only attribute.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-119' xml:id='l2h-119' class="member">J</tt></b></dt>
+<dd>
+A single-column integer matrix with the column indices of the entries
+in <code>V</code>. A read-only attribute.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-120' xml:id='l2h-120' class="member">size</tt></b></dt>
+<dd>
+A tuple with the dimensions of the matrix. A read-only attribute.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-121' xml:id='l2h-121' class="method">trans</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns the transpose of a sparse matrix as a new sparse matrix.
+One can also use <code>A.T</code> instead of <code>A.trans()</code>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-122' xml:id='l2h-122' class="method">ctrans</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns the complex conjugate transpose of a sparse matrix as a
+new sparse matrix.
+One can also use <code>A.H</code> instead of <code>A.ctrans()</code>.
+</dl>
+
+<P>
+In the following example we take the elementwise square root of
+the matrix
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+A = \left[ \begin{array}{rrrrr}
+ 0 & 2 & 0 & 0 & 3 \\
+ 2 & 0 & 0 & 0 & 0 \\
+ 1 & 2 & 0 & 4 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \end{array} \right]
+\end{equation}
+ -->
+<A NAME="e-spA-example"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-spA-example"></A><IMG
+ WIDTH="168" HEIGHT="83" BORDER="0"
+ SRC="img81.gif"
+ ALT="\begin{displaymath}
+A = \left[ \begin{array}{rrrrr}
+0 & 2 & 0 & 0 & 3 \\
+2 &...
+...
+1 & 2 & 0 & 4 & 0 \\
+0 & 0 & 1 & 0 & 0 \end{array} \right]
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(6.2)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import sqrt
+>>> A = spmatrix([2,1,2,2,1,3,4], [1,2,0,2,3,0,2], [0,0,1,1,2,3,3])
+>>> B = spmatrix(sqrt(A.V), A.I, A.J)
+>>> print B
+SIZE: (4,4)
+(1, 0) 1.4142e+00
+(2, 0) 1.0000e+00
+(0, 1) 1.4142e+00
+(2, 1) 1.4142e+00
+(3, 2) 1.0000e+00
+(0, 3) 1.7321e+00
+(2, 3) 2.0000e+00
+</pre></div>
+
+<P>
+The next example below illustrates assignments to <tt class="member">V</tt>.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix, matrix
+>>> A = spmatrix(range(5), [0,1,1,2,2], [0,0,1,1,2])
+>>> print A
+SIZE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 1.0000e+00
+(1, 1) 2.0000e+00
+(2, 1) 3.0000e+00
+(2, 2) 4.0000e+00
+>>> B = spmatrix(A.V, A.J, A.I, (4,4)) # transpose and add a zero row and column
+>>> print B
+SIZE: (4,4)
+(0, 0) 0.0000e+00
+(0, 1) 1.0000e+00
+(1, 1) 2.0000e+00
+(1, 2) 3.0000e+00
+(2, 2) 4.0000e+00
+>>> print matrix(B)
+ 0.0000e+00 1.0000e+00 0.0000e+00 0.0000e+00
+ 0.0000e+00 2.0000e+00 3.0000e+00 0.0000e+00
+ 0.0000e+00 0.0000e+00 4.0000e+00 0.0000e+00
+ 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00
+>>> B.V[:] = 1., 7., 8., 6., 4. # assign new values to nonzero entries
+>>> print B
+SIZE: (4,4)
+(0, 0) 1.0000e+00
+(0, 1) 7.0000e+00
+(1, 1) 8.0000e+00
+(1, 2) 6.0000e+00
+(2, 2) 4.0000e+00
+>>> B.V += 1.0 # add 1 to the nonzero entries
+>>> print B
+SIZE: (4,4)
+(0, 0) 2.0000e+00
+(0, 1) 8.0000e+00
+(1, 1) 9.0000e+00
+(1, 2) 7.0000e+00
+(2, 2) 5.0000e+00
+</pre></div>
+
+<P>
+The <tt class="member">V</tt>, <tt class="member">I</tt> and <tt class="member">J</tt> attributes can be used for
+reading sparse matrices from or writing them to binary files.
+Suppose we want to write the matrix <var>A</var> defined above to a binary
+file.
+<div class="verbatim"><pre>
+>>> f = open('test.bin','w')
+>>> A.V.tofile(f)
+>>> A.I.tofile(f)
+>>> A.J.tofile(f)
+>>> f.close()
+</pre></div>
+A sparse matrix can be created from this file as follows.
+<div class="verbatim"><pre>
+>>> f = open('test.bin','r')
+>>> V = matrix(0.0, (5,1)); V.fromfile(f)
+>>> I = matrix(0, (5,1)); I.fromfile(f)
+>>> J = matrix(0, (5,1)); J.fromfile(f)
+>>> B = spmatrix(V, I, J)
+>>> print B
+SIZE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 1.0000e+00
+(1, 1) 2.0000e+00
+(2, 1) 3.0000e+00
+(2, 2) 4.0000e+00
+</pre></div>
+
+<P>
+Note that the <tt class="module">pickle</tt> module provides a convenient alternative
+to this method.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
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+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+<br />
+
+<h2><A NAME="SECTION0013000000000000000000">
+Index</A>
+</h2><hr /><center>
+<b><a href="#letter-Symbols">Symbols</a></b> |
+<b><a href="#letter-a">a</a></b> |
+<b><a href="#letter-b">b</a></b> |
+<b><a href="#letter-c">c</a></b> |
+<b><a href="#letter-d">d</a></b> |
+<b><a href="#letter-e">e</a></b> |
+<b><a href="#letter-f">f</a></b> |
+<b><a href="#letter-g">g</a></b> |
+<b><a href="#letter-h">h</a></b> |
+<b><a href="#letter-i">i</a></b> |
+<b><a href="#letter-j">j</a></b> |
+<b><a href="#letter-l">l</a></b> |
+<b><a href="#letter-m">m</a></b> |
+<b><a href="#letter-n">n</a></b> |
+<b><a href="#letter-o">o</a></b> |
+<b><a href="#letter-p">p</a></b> |
+<b><a href="#letter-q">q</a></b> |
+<b><a href="#letter-r">r</a></b> |
+<b><a href="#letter-s">s</a></b> |
+<b><a href="#letter-t">t</a></b> |
+<b><a href="#letter-u">u</a></b> |
+<b><a href="#letter-v">v</a></b></center>
+
+<hr />
+<h2 id="letter-Symbols">Symbols</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node6.html#l2h-8">\_\_array\_struct\_\_ (PyCObject attribute)</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-a">A</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-builtinfuncs.html#l2h-15">abs()</a>,
+ <a href="node38.html#l2h-127">[Link]</a>
+<dt><a href="s-lp.html#l2h-170">addconstraint() (lp method)</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas1.html#l2h-30">asum()</a>
+<dt><a href="s-blas1.html#l2h-34">axpy()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-b">B</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-builtinfuncs.html#l2h-12">bool()</a>,
+ <a href="node38.html#l2h-124">[Link]</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-c">C</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node51.html#l2h-150">conelp()</a>
+<dt><a href="s-lp.html#l2h-166">constraints() (lp method)</a>
+<dt><a href="s-blas1.html#l2h-33">copy()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-otherfuncs.html#l2h-19">cos()</a>
+<dt><a href="e-nlcp.html#l2h-149">cp()</a>
+<dt><a href="node6.html#l2h-5">ctrans()</a>,
+ <a href="e-spA-example.html#l2h-122">[Link]</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-d">D</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node31.html#l2h-111">dct()</a>
+<dt><a href="s-lp.html#l2h-169">delconstraint() (lp method)</a>
+<dt><a href="node30.html#l2h-109">dft()</a>
+<dt><a href="s-cholmod.html#l2h-144">diag()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-otherfuncs.html#l2h-23">div()</a>
+<dt><a href="s-blas1.html#l2h-35">dot()</a>,
+ <a href="s-functions.html#l2h-158">[Link]</a>
+<dt><a href="s-blas1.html#l2h-36">dotu()</a>
+<dt><a href="node32.html#l2h-113">dst()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-e">E</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-lp.html#l2h-168">equalities() (lp method)</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-otherfuncs.html#l2h-20">exp()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-f">F</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node6.html#l2h-10">fromfile()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-lp.html#l2h-173">fromfile() (lp method)</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-g">G</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas2.html#l2h-42">gbmv()</a>
+<dt><a href="node20.html#l2h-66">gbsv()</a>
+<dt><a href="node20.html#l2h-67">gbtrf()</a>
+<dt><a href="node20.html#l2h-68">gbtrs()</a>
+<dt><a href="node24.html#l2h-93">gels()</a>
+<dt><a href="s-blas3.html#l2h-53">gemm()</a>,
+ <a href="node39.html#l2h-131">[Link]</a>
+<dt><a href="s-blas2.html#l2h-37">gemv()</a>,
+ <a href="node39.html#l2h-129">[Link]</a>
+<dt><a href="node24.html#l2h-94">geqrf()</a>
+<dt><a href="s-blas2.html#l2h-47">ger()</a>
+<dt><a href="s-blas2.html#l2h-48">geru()</a>
+<dt><a href="node27.html#l2h-108">gesdd()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="node20.html#l2h-62">gesv()</a>
+<dt><a href="node27.html#l2h-107">gesvd()</a>
+<dt><a href="node20.html#l2h-63">getrf()</a>
+<dt><a href="node20.html#l2h-65">getri()</a>
+<dt><a href="node20.html#l2h-64">getrs()</a>
+<dt><a href="s-random.html#l2h-26">getseed()</a>
+<dt><a href="node48.html#l2h-147">gp()</a>
+<dt><a href="node20.html#l2h-69">gtsv()</a>
+<dt><a href="node20.html#l2h-70">gttrf()</a>
+<dt><a href="e-kkt-example.html#l2h-81">gttrs()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-h">H</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas2.html#l2h-44">hbmv()</a>
+<dt><a href="node25.html#l2h-101">heev()</a>
+<dt><a href="node25.html#l2h-102">heevd()</a>
+<dt><a href="node25.html#l2h-104">heevr()</a>
+<dt><a href="node25.html#l2h-103">heevx()</a>
+<dt><a href="e-gevd.html#l2h-106">hegv()</a>
+<dt><a href="s-blas3.html#l2h-55">hemm()</a>
+<dt><a href="s-blas2.html#l2h-39">hemv()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas2.html#l2h-50">her()</a>
+<dt><a href="s-blas2.html#l2h-52">her2()</a>
+<dt><a href="s-blas3.html#l2h-61">her2k()</a>
+<dt><a href="s-blas3.html#l2h-59">herk()</a>
+<dt><a href="node22.html#l2h-86">hesv()</a>
+<dt><a href="node22.html#l2h-87">hetrf()</a>
+<dt><a href="node22.html#l2h-89">hetri()</a>
+<dt><a href="node22.html#l2h-88">hetrs()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-i">I</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="e-spA-example.html#l2h-118">I (spmatrix attribute)</a>
+<dt><a href="s-blas1.html#l2h-31">iamax()</a>
+<dt><a href="node31.html#l2h-112">idct()</a>
+<dt><a href="node30.html#l2h-110">idft()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="node32.html#l2h-114">idst()</a>
+<dt><a href="node6.html#l2h-7">imag()</a>
+<dt><a href="s-lp.html#l2h-167">inequalities() (lp method)</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-j">J</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="e-spA-example.html#l2h-119">J (matrix attribute)</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-l">L</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-builtinfuncs.html#l2h-11">len()</a>,
+ <a href="node38.html#l2h-123">[Link]</a>
+<dt><a href="s-umfpack.html#l2h-134">linsolve()</a>,
+ <a href="s-cholmod.html#l2h-138">[Link]</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-otherfuncs.html#l2h-21">log()</a>
+<dt><a href="s-lpsolver.html#l2h-145">lp()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-m">M</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-creating-matrices.html#l2h-1">matrix()</a>
+<dt><a href="node62.html#l2h-174">Matrix\_New()</a>
+<dt><a href="node62.html#l2h-175">Matrix\_NewFromMatrix()</a>
+<dt><a href="node62.html#l2h-176">Matrix\_NewFromSequence()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-builtinfuncs.html#l2h-13">max()</a>,
+ <a href="node38.html#l2h-125">[Link]</a>
+<dt><a href="s-builtinfuncs.html#l2h-14">min()</a>,
+ <a href="node38.html#l2h-126">[Link]</a>
+<dt><a href="s-otherfuncs.html#l2h-22">mul()</a>
+<dt><a href="node58.html#l2h-161">multiplier (constraint attribute)</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-n">N</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node58.html#l2h-162">name (constraint attribute)</a>
+<dt><a href="s-variables.html#l2h-153">name (variable attribute)</a>
+<dt><a href="node52.html#l2h-151">nlcp()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-random.html#l2h-24">normal()</a>
+<dt><a href="s-blas1.html#l2h-29">nrm2()</a>
+<dt><a href="s-umfpack.html#l2h-136">numeric()</a>,
+ <a href="s-cholmod.html#l2h-141">[Link]</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-o">O</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-lp.html#l2h-164">objective (op attribute)</a>
+<dt><a href="s-lp.html#l2h-163">op (class in )</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-orderings.html#l2h-133">order()</a>
+<dt><a href="node24.html#l2h-95">ormqr()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-p">P</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="e-kkt-example.html#l2h-76">pbsv()</a>
+<dt><a href="e-kkt-example.html#l2h-77">pbtrf()</a>
+<dt><a href="e-kkt-example.html#l2h-78">pbtrs()</a>
+<dt><a href="e-kkt-example.html#l2h-72">posv()</a>
+<dt><a href="e-kkt-example.html#l2h-73">potrf()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="e-kkt-example.html#l2h-75">potri()</a>
+<dt><a href="e-kkt-example.html#l2h-74">potrs()</a>
+<dt><a href="e-kkt-example.html#l2h-79">ptsv()</a>
+<dt><a href="e-kkt-example.html#l2h-80">pttrf()</a>
+<dt><a href="node20.html#l2h-71">pttrs()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-q">Q</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node47.html#l2h-146">qp()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-r">R</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="node6.html#l2h-6">real()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-s">S</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas2.html#l2h-43">sbmv()</a>
+<dt><a href="s-blas1.html#l2h-28">scal()</a>
+<dt><a href="s-sdpsolver.html#l2h-148">sdp()</a>
+<dt><a href="s-random.html#l2h-27">setseed()</a>
+<dt><a href="s-otherfuncs.html#l2h-18">sin()</a>
+<dt><a href="node6.html#l2h-2">size (tuple attribute)</a>,
+ <a href="e-spA-example.html#l2h-120">[Link]</a>
+<dt><a href="s-umfpack.html#l2h-137">solve()</a>,
+ <a href="s-cholmod.html#l2h-142">[Link]</a>
+<dt><a href="s-lp.html#l2h-171">solve() (op method)</a>
+<dt><a href="s-creating-spmatrix.html#l2h-116">sparse()</a>
+<dt><a href="s-cholmod.html#l2h-139">splinsolve()</a>
+<dt><a href="s-creating-spmatrix.html#l2h-115">spmatrix()</a>
+<dt><a href="node63.html#l2h-177">SpMatrix\_New()</a>
+<dt><a href="node63.html#l2h-179">SpMatrix\_NewFromIJV()</a>
+<dt><a href="node63.html#l2h-178">SpMatrix\_NewFromMatrix()</a>
+<dt><a href="s-cholmod.html#l2h-143">spsolve()</a>
+<dt><a href="s-otherfuncs.html#l2h-17">sqrt()</a>
+<dt><a href="s-builtinfuncs.html#l2h-16">sum()</a>,
+ <a href="node38.html#l2h-128">[Link]</a>,
+ <a href="s-functions.html#l2h-157">[Link]</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas1.html#l2h-32">swap()</a>
+<dt><a href="node25.html#l2h-97">syev()</a>
+<dt><a href="node25.html#l2h-98">syevd()</a>
+<dt><a href="node25.html#l2h-100">syevr()</a>
+<dt><a href="node25.html#l2h-99">syevx()</a>
+<dt><a href="e-gevd.html#l2h-105">sygv()</a>
+<dt><a href="s-umfpack.html#l2h-135">symbolic()</a>,
+ <a href="s-cholmod.html#l2h-140">[Link]</a>
+<dt><a href="s-blas3.html#l2h-54">symm()</a>
+<dt><a href="s-blas2.html#l2h-38">symv()</a>,
+ <a href="node39.html#l2h-130">[Link]</a>
+<dt><a href="s-blas2.html#l2h-49">syr()</a>
+<dt><a href="s-blas2.html#l2h-51">syr2()</a>
+<dt><a href="s-blas3.html#l2h-60">syr2k()</a>
+<dt><a href="s-blas3.html#l2h-58">syrk()</a>,
+ <a href="node39.html#l2h-132">[Link]</a>
+<dt><a href="node22.html#l2h-82">sysv()</a>
+<dt><a href="node22.html#l2h-83">sytrf()</a>
+<dt><a href="node22.html#l2h-85">sytri()</a>
+<dt><a href="node22.html#l2h-84">sytrs()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-t">T</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas2.html#l2h-45">tbmv()</a>
+<dt><a href="s-blas2.html#l2h-46">tbsv()</a>
+<dt><a href="node23.html#l2h-92">tbtrs()</a>
+<dt><a href="node6.html#l2h-9">tofile()</a>
+<dt><a href="s-lp.html#l2h-172">tofile() (op method)</a>
+<dt><a href="node6.html#l2h-4">trans()</a>,
+ <a href="e-spA-example.html#l2h-121">[Link]</a>
+<dt><a href="s-blas3.html#l2h-56">trmm()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-blas2.html#l2h-40">trmv()</a>
+<dt><a href="s-blas3.html#l2h-57">trsm()</a>
+<dt><a href="s-blas2.html#l2h-41">trsv()</a>
+<dt><a href="node23.html#l2h-91">trtri()</a>
+<dt><a href="node23.html#l2h-90">trtrs()</a>
+<dt><a href="node58.html#l2h-159">type() (constraint method)</a>
+<dt><a href="node6.html#l2h-3">typecode (char attribute)</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-u">U</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-random.html#l2h-25">uniform()</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="node24.html#l2h-96">unmqr()</a>
+</dl>
+</td>
+</tr></table>
+<hr />
+<h2 id="letter-v">V</h2>
+
+<table width="100%"><tr valign="top"><td width="50%">
+<dl compact='compact'>
+<dt><a href="e-spA-example.html#l2h-117">V (matrix attribute)</a>
+<dt><a href="node58.html#l2h-160">value() (constraint method)</a>
+<dt><a href="s-variables.html#l2h-154">value (variable attribute)</a>
+<dt><a href="s-functions.html#l2h-156">value() (variable method)</a>
+</dl>
+</td><td width="50%">
+<dl compact='compact'>
+<dt><a href="s-variables.html#l2h-152">variable (class in )</a>
+<dt><a href="s-lp.html#l2h-165">variables() (lp method)</a>
+<dt><a href="s-functions.html#l2h-155">variables() (variable method)</a>
+</dl>
+</td>
+</tr></table>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="10.2 Sparse Matrices"
+ href="node63.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="CVXOPT: A Python Package"
+ href="cvxopt.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="About this document ..."
+ href="about.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="node63.html">10.2 Sparse Matrices</A>
+<b class="navlabel">Up:</b>
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="about.html">About this document ...</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
+
+</BODY>
+</HTML>
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+<div class="titlepage">
+<div class='center'>
+<h1>CVXOPT: A Python Package for Convex Optimization</h1>
+<p><b><font size="+2">Joachim Dahl & Lieven Vandenberghe</font></b></p>
+<p><i><TT>joachim at kom.aau.dk</TT>, <TT>vandenbe at ee.ucla.edu</TT></i></p>
+<p><strong>Release 0.8.2</strong><br />
+<strong>February 6, 2007</strong></p>
+<p></p>
+</div>
+</div>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="node1.html">Copyright and License</a>
+<LI><A href="contents.html">Contents</a>
+<LI><A href="node3.html">1. Introduction</a>
+<LI><A href="node4.html">2. Dense Matrices (<tt class="module">cvxopt.base</tt>)</a>
+<UL>
+<LI><A href="s-creating-matrices.html">2.1 Creating Matrices</a>
+<LI><A href="node6.html">2.2 Attributes and Methods</a>
+<LI><A href="s-arithmetic.html">2.3 Arithmetic Operations</a>
+<LI><A href="s-indexing.html">2.4 Indexing and Slicing</a>
+<LI><A href="s-builtinfuncs.html">2.5 Built-in Functions</a>
+<LI><A href="s-otherfuncs.html">2.6 Other Matrix Functions</a>
+<LI><A href="s-random.html">2.7 Randomly Generated Matrices</a>
+<LI><A href="s-array-interface.html">2.8 The NumPy Array Interface</a>
+<LI><A href="node13.html">2.9 Printing Options</a>
+</ul>
+<LI><A href="node14.html">3. The BLAS Interface (<tt class="module">cvxopt.blas</tt>)</a>
+<UL>
+<LI><A href="s-conventions.html">3.1 Matrix Classes</a>
+<LI><A href="s-blas1.html">3.2 Level 1 BLAS</a>
+<LI><A href="s-blas2.html">3.3 Level 2 BLAS</a>
+<LI><A href="s-blas3.html">3.4 Level 3 BLAS</a>
+</ul>
+<LI><A href="node19.html">4. The LAPACK Interface (<tt class="module">cvxopt.lapack</tt>)</a>
+<UL>
+<LI><A href="node20.html">4.1 General Linear Equations</a>
+<LI><A href="e-kkt-example.html">4.2 Positive Definite Linear Equations</a>
+<LI><A href="node22.html">4.3 Symmetric and Hermitian Linear Equations</a>
+<LI><A href="node23.html">4.4 Triangular Linear Equations</a>
+<LI><A href="node24.html">4.5 Least-Squares and Least-Norm Problems</a>
+<LI><A href="node25.html">4.6 Symmetric and Hermitian Eigenvalue Decomposition</a>
+<LI><A href="e-gevd.html">4.7 Generalized Symmetric Definite Eigenproblems</a>
+<LI><A href="node27.html">4.8 Singular Value Decomposition</a>
+<LI><A href="node28.html">4.9 Example: Analytic Centering</a>
+</ul>
+<LI><A href="c-fftw.html">5. Discrete Transforms (<tt class="module">cvxopt.fftw</tt>)</a>
+<UL>
+<LI><A href="node30.html">5.1 Discrete Fourier Transform</a>
+<LI><A href="node31.html">5.2 Discrete Cosine Transform</a>
+<LI><A href="node32.html">5.3 Discrete Sine Transform</a>
+</ul>
+<LI><A href="node33.html">6. Sparse Matrices (<tt class="module">cvxopt.base</tt>)</a>
+<UL>
+<LI><A href="s-creating-spmatrix.html">6.1 Creating Sparse Matrices</a>
+<LI><A href="e-spA-example.html">6.2 Attributes and Methods</a>
+<LI><A href="s-spmatrix-arith.html">6.3 Arithmetic Operations</a>
+<LI><A href="node37.html">6.4 Indexing and Slicing</a>
+<LI><A href="node38.html">6.5 Built-In Functions</a>
+<LI><A href="node39.html">6.6 Sparse BLAS Functions</a>
+</ul>
+<LI><A href="c-spsolvers.html">7. Sparse Linear Equation Solvers</a>
+<UL>
+<LI><A href="s-orderings.html">7.1 Matrix Orderings (<tt class="module">cvxopt.amd</tt>)</a>
+<LI><A href="s-umfpack.html">7.2 General Linear Equations (<tt class="module">cvxopt.umfpack</tt>)</a>
+<LI><A href="s-cholmod.html">7.3 Positive Definite Linear Equations (<tt class="module">cvxopt.cholmod</tt>)</a>
+<LI><A href="e-covsel.html">7.4 Example: Covariance Selection</a>
+</ul>
+<LI><A href="node45.html">8. Optimization Routines (<tt class="module">cvxopt.solvers</tt>)</a>
+<UL>
+<LI><A href="s-lpsolver.html">8.1 Linear Programming</a>
+<LI><A href="node47.html">8.2 Quadratic Programming</a>
+<LI><A href="node48.html">8.3 Geometric Programming</a>
+<LI><A href="s-sdpsolver.html">8.4 Semidefinite Programming</a>
+<LI><A href="e-nlcp.html">8.5 Nonlinear Convex Programming</a>
+<LI><A href="node51.html">8.6 Exploiting Structure in LPs and SDPs</a>
+<LI><A href="node52.html">8.7 Exploiting Structure in Nonlinear Convex Programs</a>
+<LI><A href="s-external.html">8.8 Optional Solvers</a>
+<LI><A href="s-parameters.html">8.9 Algorithm Parameters</a>
+</ul>
+<LI><A href="node55.html">9. Modeling (<tt class="module">cvxopt.modeling</tt>)</a>
+<UL>
+<LI><A href="s-variables.html">9.1 Variables</a>
+<LI><A href="s-functions.html">9.2 Functions</a>
+<LI><A href="node58.html">9.3 Constraints</a>
+<LI><A href="s-lp.html">9.4 Optimization Problems</a>
+<LI><A href="node60.html">9.5 Examples</a>
+</ul>
+<LI><A href="node61.html">10. C API</a>
+<UL>
+<LI><A href="node62.html">10.1 Dense Matrices</a>
+<LI><A href="node63.html">10.2 Sparse Matrices</a>
+</ul>
+<LI><A href="genindex.html">Index</a>
+<LI><A href="about.html">About this document ...</a>
+</ul>
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+
+<H1><A NAME="SECTION001000000000000000000">
+Copyright and License</A>
+</H1>
+Copyright ©2004-2007 J. Dahl & L. Vandenberghe.
+
+<P>
+This program is free software; you can redistribute it and/or modify
+it under the terms of the
+<a class="ulink" href="http://www.gnu.org/copyleft/gpl.html"
+ >GNU General Public License</a>
+as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+<P>
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+<a class="ulink" href="http://www.gnu.org/copyleft/gpl.html"
+ >GNU General Public License</a>
+for more details.
+
+<P>
+<HR>The CVXOPT distribution includes source code for the following
+software libraries.
+
+<UL>
+<LI>Part of the SuiteSparse suite of sparse matrix algorithms,
+ including:
+
+<UL>
+<LI>AMD Version 2.0. Copyright (c) 2006 by Timothy A. Davis,
+ Patrick R. Amestoy, and Iain S. Duff.
+</LI>
+<LI>CHOLMOD Version 1.4.
+ Copyright (c) 2005-2006 by University of Florida, Timothy A. Davis
+ and W. Hager.
+</LI>
+<LI>COLAMD version 2.6. Copyright (c) 1998-2006 by Timothy A. Davis.
+</LI>
+<LI>UMFPACK Version 5.0.2.
+ Copyright (c) 1995-2006 by Timothy A. Davis.
+</LI>
+</UL>
+
+<P>
+These packages are licensed under the terms of the
+<a class="ulink" href="http://www.gnu.org/copyleft/lesser.html"
+ >GNU Lesser General Public License</a> (UMFPACK, parts of CHOLMOD,
+AMD, COLAMD) and the <a class="ulink" href="http://www.gnu.org/copyleft/gpl.html"
+ >GNU General Public License</a> (parts of CHOLMOD).
+For details, consult the README files in the source directories or
+the website listed below.
+
+<P>
+<BLOCKQUOTE>
+Availability: <a class="ulink" href="http://www.cise.ufl.edu/research/sparse"
+ >www.cise.ufl.edu/research/sparse</a>.
+
+</BLOCKQUOTE>
+
+<P>
+</LI>
+<LI>RNGS Random Number Generation -- Multiple Streams
+(Sep. 22, 1998) by Steve Park & Dave Geyer.
+
+<P>
+<BLOCKQUOTE>
+Availability: <a class="ulink" href="http://www.cs.wm.edu/~va/software/park/park.html"
+ >www.cs.wm.edu/~va/software/park/park.html</a>.
+
+</BLOCKQUOTE>
+
+<P>
+</LI>
+</UL>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
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+
+<H1><A NAME="SECTION004900000000000000000">
+2.9 Printing Options</A>
+</H1>
+The format used for printing dense matrices (and the sparse matrices
+discussed in chapter <A HREF="node33.html#chap:spmatrix">6</A>) is controlled
+by the dictionary <tt class="member">cvxopt.base.print_options</tt>. The dictionary
+has three keys, <code>'iformat'</code>, <code>'dformat'</code>, <code>'zformat'</code>
+that control, respectively, how integer, double and complex numbers are
+printed. The fields are C printf format strings with default
+values <code>'5.4e'</code> for <code>'d'</code> and <code>'z'</code> matrices and <code>'5i'</code> for
+<code>'i'</code> matrices.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix, print_options
+>>> print_options
+{'zformat': '5.4e', 'iformat': '5i', 'dformat': '5.4e'}
+>>> A = matrix([1., 2., 3.])
+>>> print A
+ 1.0000e+00
+ 2.0000e+00
+ 3.0000e+00
+>>> print_options['dformat'] = 'f'
+>>> print A
+ 1.000000
+ 2.000000
+ 3.000000
+>>> print_options['dformat'] = '5.2e'
+>>> print A
+ 1.00e+00
+ 2.00e+00
+ 3.00e+00
+</pre></div>
+
+<DIV CLASS="navigation">
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+</DIV>
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+
+<H1><A NAME="SECTION005000000000000000000"></A><A NAME="chap:blas"></A>
+<BR>
+3. The BLAS Interface (<tt class="module">cvxopt.blas</tt>)
+</H1>
+The <tt class="module">cvxopt.blas</tt> module provides an interface to the
+double-precision real and complex Basic Linear Algebra Subprograms
+(BLAS). The names and calling sequences of the Python functions in
+the interface closely match the corresponding Fortran BLAS routines
+(described in the references below) and their functionality is exactly
+the same.
+
+<P>
+Many of the operations performed by the BLAS routines can be
+implemented in a more straightforward way by using the matrix
+arithmetic of section <A href="s-arithmetic.html#s-arithmetic">2.3</A>, combined with the slicing
+and indexing of section <A href="s-indexing.html#s-indexing">2.4</A>.
+As an example, "<tt class="samp">C = A*B</tt>" gives the same result as the BLAS
+call "<tt class="samp">gemm(A,B,C)</tt>".
+The BLAS interface offers two advantages. First, some of the
+functions it includes are not easily implemented using the basic
+matrix arithmetic. For example, BLAS includes functions that
+efficiently exploit symmetry or triangular matrix structure.
+Second, there is a performance difference that can be significant for
+large matrices. Although our implementation of the basic matrix
+arithmetic makes internal calls to BLAS, it also often requires
+creating temporary matrices to store intermediate results.
+The BLAS functions on the other hand always operate directly
+on their matrix arguments and never require any copying to temporary
+matrices. Thus they can be viewed as generalizations of the in-place
+matrix addition and scalar multiplication of
+section <A href="s-arithmetic.html#s-arithmetic">2.3</A> to more complicated operations.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<div class="seetext"><p>C. L. Lawson, R. J. Hanson, D. R. Kincaid, F. T. Krogh,
+Basic Linear Algebra Subprograms for Fortran Use,
+ACM Transactions on Mathematical Software, 5(3), 309-323, 1975.</p></div>
+<div class="seetext"><p>J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson,
+An Extended Set of Fortran Basic Linear Algebra Subprograms,
+ACM Transactions on Mathematical Software, 14(1), 1-17, 1988.</p></div>
+<div class="seetext"><p>J. J. Dongarra, J. Du Croz, S. Hammarling, I. Duff,
+A Set of Level 3 Basic Linear Algebra Subprograms,
+ACM Transactions on Mathematical Software, 16(1), 1-17, 1990.</p></div>
+</div>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="s-conventions.html">3.1 Matrix Classes</a>
+<LI><A href="s-blas1.html">3.2 Level 1 BLAS</a>
+<LI><A href="s-blas2.html">3.3 Level 2 BLAS</a>
+<LI><A href="s-blas3.html">3.4 Level 3 BLAS</a>
+</ul>
+<!--End of Table of Child-Links-->
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+
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+<div class='online-navigation'>
+<p></p><hr />
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+
+<H1><A NAME="SECTION006000000000000000000"></A>
+<A NAME="chap:lapack"></A>
+<BR>
+4. The LAPACK Interface (<tt class="module">cvxopt.lapack</tt>)
+</H1>
+
+<P>
+The module <tt class="module">cvxopt.lapack</tt> includes functions for
+solving dense sets of linear equations, for the corresponding matrix
+factorizations (LU, Cholesky, LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img40.gif"
+ ALT="$\mathrm{{}^T}$"></SPAN>),
+for solving least-squares and least-norm problems, for QR
+factorization, for symmetric eigenvalue problems and for singular
+value decomposition.
+
+<P>
+In this chapter we briefly describe the Python calling sequences.
+For further details on the underlying LAPACK functions we refer to the
+LAPACK Users' Guide and manual pages.
+
+<P>
+The BLAS conventional storage scheme of section <A href="s-conventions.html#s-conventions">3.1</A> is
+used. As in the previous chapter, we omit from the function definitions
+less important arguments that are useful for selecting submatrices.
+The complete definitions are documented in the docstrings in the
+source code.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://www.netlib.org/lapack/lug/lapack_lug.html'
+ >LAPACK
+Users' Guide, Third Edition, SIAM, 1999.</a></dt>
+ <dd></dd>
+ </dl>
+</div>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="node20.html">4.1 General Linear Equations</a>
+<LI><A href="e-kkt-example.html">4.2 Positive Definite Linear Equations</a>
+<LI><A href="node22.html">4.3 Symmetric and Hermitian Linear Equations</a>
+<LI><A href="node23.html">4.4 Triangular Linear Equations</a>
+<LI><A href="node24.html">4.5 Least-Squares and Least-Norm Problems</a>
+<LI><A href="node25.html">4.6 Symmetric and Hermitian Eigenvalue Decomposition</a>
+<LI><A href="e-gevd.html">4.7 Generalized Symmetric Definite Eigenproblems</a>
+<LI><A href="node27.html">4.8 Singular Value Decomposition</a>
+<LI><A href="node28.html">4.9 Example: Analytic Centering</a>
+</ul>
+<!--End of Table of Child-Links-->
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+
+<DIV CLASS="navigation">
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+
+<H1><A NAME="SECTION006100000000000000000">
+4.1 General Linear Equations</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-62' xml:id='l2h-62' class="function">gesv</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, ipiv=None</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="64" HEIGHT="27" BORDER="0"
+ SRC="img41.gif"
+ ALT="\begin{displaymath}
+A X = B,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> and <I>B</I> are real or complex matrices, with <I>A</I>
+square and nonsingular. On exit, <var>B</var> is replaced by the solution.
+The arguments <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>).
+The optional argument <var>ipiv</var> is an integer matrix of length at
+least <var>n</var>.
+If <var>ipiv</var> is provided, then <tt class="function">gesv()</tt> solves the system,
+replaces <var>A</var> with its triangular factors, and returns the
+permutation matrix in <var>ipiv</var>.
+If <var>ipiv</var> is not specified, then <tt class="function">gesv()</tt> solves the
+system but does not return the LU factorization and does not
+modify <var>A</var>.
+For example,
+<div class="verbatim"><pre>
+>>> gesv(A, B)
+</pre></div>
+solves the system without modifying <var>A</var> and returns the solution
+in <var>B</var>.
+<div class="verbatim"><pre>
+>>> gesv(A, B, ipiv)
+</pre></div>
+returns the solution in <var>B</var> and also returns the details of the
+LU factorization in <var>A</var> and <var>ipiv</var>.
+
+<P>
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-63' xml:id='l2h-63' class="function">getrf</tt></b>(</nobr></td>
+ <td><var>A, ipiv</var>)</td></tr></table></dt>
+<dd>
+LU factorization of a general, possibly rectangular, real or
+complex matrix,
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = PLU
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="68" HEIGHT="24" BORDER="0"
+ SRC="img42.gif"
+ ALT="\begin{displaymath}
+A = PLU
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is <var>m</var> by <var>n</var>.
+The argument <var>ipiv</var> is an integer matrix of length at least
+min{<var>m</var>, <var>n</var>}.
+On exit, the lower triangular part of <var>A</var> is replaced by <I>L</I>,
+the upper triangular part by <I>U</I>, and the permutation matrix is
+returned in <var>ipiv</var>.
+Raises an <code>ArithmeticError</code> if the matrix is not full rank.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-64' xml:id='l2h-64' class="function">getrs</tt></b>(</nobr></td>
+ <td><var>A, ipiv, B</var><big>[</big><var>, trans='N'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a general set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+given the LU factorization computed by <tt class="function">gesv()</tt> or
+<tt class="function">getrf()</tt>.
+On entry, <var>A</var> and <var>ipiv</var> must contain the factorization
+as computed by <tt class="function">gesv()</tt> or <tt class="function">getrf()</tt>.
+On exit, <var>B</var> is overwritten with the solution.
+<var>B</var> must have the same type as <var>A</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-65' xml:id='l2h-65' class="function">getri</tt></b>(</nobr></td>
+ <td><var>A, ipiv</var>)</td></tr></table></dt>
+<dd>
+Computes the inverse of a matrix.
+On entry, <var>A</var> and <var>ipiv</var> must contain the factorization
+as computed by <tt class="function">gesv()</tt> or <tt class="function">getrf()</tt>. On exit,
+<var>A</var> contains the inverse.
+</dl>
+
+<P>
+In the following example we compute
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x = (A^{-1} + A^{-T})b
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="129" HEIGHT="28" BORDER="0"
+ SRC="img44.gif"
+ ALT="\begin{displaymath}
+x = (A^{-1} + A^{-T})b
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+for randomly generated problem data, factoring the coefficient matrix
+once.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt.random import normal
+>>> from cvxopt.lapack import gesv, getrs
+>>> n = 10
+>>> A = normal(n,n)
+>>> b = normal(n)
+>>> ipiv = matrix(0, (n,1))
+>>> x = +b
+>>> gesv(A, x, ipiv) # x = A^{-1}*b
+>>> x2 = +b
+>>> getrs(A, ipiv, x2, trans='T') # x2 = A^{-T}*b
+>>> x += x2
+</pre></div>
+
+<P>
+Separate functions are provided for equations with band matrices.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-66' xml:id='l2h-66' class="function">gbsv</tt></b>(</nobr></td>
+ <td><var>A, kl, B</var><big>[</big><var>, ipiv=None</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="64" HEIGHT="27" BORDER="0"
+ SRC="img41.gif"
+ ALT="\begin{displaymath}
+A X = B,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> and <I>B</I> are real or complex matrices, with <I>A</I>
+<I>n</I> by <I>n</I> and banded with <var>kl</var> subdiagonals.
+The arguments <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>).
+
+<P>
+The optional argument <var>ipiv</var> is an integer matrix of length at least
+<I>n</I>.
+If <var>ipiv</var> is provided, then <var>A</var> must have
+2<var>kl</var> + <var>ku</var> + 1 rows. On entry the diagonals of <I>A</I> are
+stored in rows <var>kl</var> + 1 to 2<var>kl</var> + <var>ku</var> +1 of the <var>A</var>, using
+the BLAS format for general band matrices (see section <A href="s-conventions.html#s-conventions">3.1</A>).
+On exit, the factorization is returned in <var>A</var> and <var>ipiv</var>.
+
+<P>
+If <var>ipiv</var> is not provided, then <var>A</var> must have <var>kl</var> + <var>ku</var> +
+1 rows. On entry the diagonals of <I>A</I> are stored in the rows of
+<var>A</var>, following the standard format for general band matrices.
+In this case, <tt class="function">gbsv()</tt> does not modify <var>A</var> on exit and does
+not return the factorization.
+
+<P>
+On exit, <var>B</var> is replaced by the solution <I>X</I>.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-67' xml:id='l2h-67' class="function">gbtrf</tt></b>(</nobr></td>
+ <td><var>A, m, kl, ipiv</var>)</td></tr></table></dt>
+<dd>
+LU factorization of a general <I>m</I> by <I>n</I> real or complex band
+matrix with <var>kl</var> subdiagonals.
+The matrix is stored using the BLAS format for general band matrices
+(see section <A href="s-conventions.html#s-conventions">3.1</A>), by providing the
+diagonals (stored as rows of a <var>ku</var> + <var>kl</var> + 1 by <I>n</I> matrix),
+the number of rows <var>m</var>, and the number of subdiagonals <var>kl</var>.
+The argument <var>ipiv</var> is an integer matrix of length at least
+min{<I>m</I>, <I>n</I>}.
+On exit, <var>A</var> and <var>ipiv</var> contain the details of the factorization.
+Raises an <code>ArithmeticError</code> if the matrix is not full rank.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-68' xml:id='l2h-68' class="function">gbtrs</tt></b>(</nobr></td>
+ <td><var>A, kl, ipiv, B</var><big>[</big><var>, trans='N'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with <I>A</I> a general band matrix with <var>kl</var> subdiagonals, given the
+LU factorization computed by <tt class="function">gbsv()</tt> or <tt class="function">gbtrf()</tt>.
+On entry, <var>A</var> and <var>ipiv</var> must contain the factorization
+as computed by <tt class="function">gbsv()</tt> or <tt class="function">gbtrf()</tt>.
+On exit, <var>B</var> is overwritten with the solution.
+<var>B</var> must have the same type as <var>A</var>.
+</dl>
+
+<P>
+As an example, we solve a linear equation with
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = \left[ \begin{array}{cccc}
+ 1 & 2 & 0 & 0 \\
+ 3 & 4 & 5 & 0 \\
+ 6 & 7 & 8 & 9 \\
+ 0 & 10 & 11 & 12
+ \end{array}\right], \qquad x = \left[\begin{array}{c} 1 \\1 \\1 \\1
+ \end{array}\right].
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="297" HEIGHT="83" BORDER="0"
+ SRC="img45.gif"
+ ALT="\begin{displaymath}
+A = \left[ \begin{array}{cccc}
+1 & 2 & 0 & 0 \\
+3 & 4 & ...
+...= \left[\begin{array}{c} 1 \\ 1 \\ 1 \\ 1
+\end{array}\right].
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt.lapack import gbsv, gbtrf, gbtrs
+>>> n, kl, ku = 4, 2, 1
+>>> A = matrix([[0., 1., 3., 6.], [2., 4., 7., 10.], [5., 8., 11., 0.], [9., 12., 0., 0.]])
+>>> x = matrix(1.0, (4,1))
+>>> gbsv(A, kl, x)
+>>> print x
+ 7.1429e-02
+ 4.6429e-01
+ -2.1429e-01
+ -1.0714e-01
+</pre></div>
+The code below illustrates how one can reuse the factorization returned
+by <tt class="function">gbsv()</tt>.
+<div class="verbatim"><pre>
+>>> Ac = matrix(0.0, (2*kl+ku+1,n))
+>>> Ac[kl:,:] = A
+>>> ipiv = matrix(0, (n,1))
+>>> x = matrix(1.0, (4,1))
+>>> gbsv(Ac, kl, x, ipiv) # solves A*x = 1
+>>> print x
+ 7.1429e-02
+ 4.6429e-01
+ -2.1429e-01
+ -1.0714e-01
+>>> x = matrix(1.0, (4,1))
+>>> gbtrs(Ac, kl, ipiv, x, trans='T') # solve A^T*x = 1
+>>> print x
+ 7.1429e-02
+ 2.3810e-02
+ 1.4286e-01
+ -2.3810e-02
+</pre></div>
+An alternative method uses <tt class="function">getrf()</tt> for the factorization.
+<div class="verbatim"><pre>
+>>> Ac[kl:,:] = A
+>>> gbtrf(Ac, n, kl, ipiv)
+>>> x = matrix(1.0, (4,1))
+>>> gbtrs(Ac, kl, ipiv, x) # solve A^T*x = 1
+>>> print x
+ 7.1429e-02
+ 4.6429e-01
+ -2.1429e-01
+ -1.0714e-01
+>>> x = matrix(1.0, (4,1))
+>>> gbtrs(Ac, kl, ipiv, x, trans='T') # solve A^T*x = 1
+>>> print x
+ 7.1429e-02
+ 2.3810e-02
+ 1.4286e-01
+ -2.3810e-02
+</pre></div>
+
+<P>
+The following functions can be used for tridiagonal matrices They use a
+simpler matrix format, that stores the diagonals in three separate
+vectors.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-69' xml:id='l2h-69' class="function">gtsv</tt></b>(</nobr></td>
+ <td><var>dl, d, du, B)</var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="64" HEIGHT="27" BORDER="0"
+ SRC="img41.gif"
+ ALT="\begin{displaymath}
+A X = B,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is an <I>n</I> by <I>n</I> tridiagonal matrix,
+with subdiagonal <var>dl</var> (a matrix of length <I>n</I>-1),
+diagonal <var>d</var> (a matrix of length <I>n</I>), and superdiagonal
+<var>du</var> (a matrix of length <I>n</I>-1).
+The four arguments must have the same type (<code>'d'</code> or <code>'z'</code>).
+On exit <var>dl</var>, <var>d</var>, <var>du</var> are overwritten with the details of
+the LU factorization of <I>A</I>, and <var>B</var> is overwritten with the
+solution <I>X</I>.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-70' xml:id='l2h-70' class="function">gttrf</tt></b>(</nobr></td>
+ <td><var>dl, d, du, du2, ipiv</var>)</td></tr></table></dt>
+<dd>
+LU factorization of an <I>n</I> by <I>n</I> tridiagonal matrix with
+subdiagonal <var>dl</var>, diagonal <var>d</var> and superdiagonal <var>du</var>.
+<var>dl</var>, <var>d</var> and <var>du</var> must have the same type.
+<var>du2</var> is a matrix of length <I>n</I>-2, and of the same type as
+<var>dl</var>.
+<var>ipiv</var> is an <code>'i'</code> matrix of length <I>n</I>.
+On exit, the five arguments contain the details of the factorization.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-71' xml:id='l2h-71' class="function">pttrs</tt></b>(</nobr></td>
+ <td><var>dl, d, du, du2, ipiv, B</var><big>[</big><var>, trans='N'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is an <I>n</I> by <I>n</I> tridiagonal matrix.
+The arguments <var>dl</var>, <var>d</var>, <var>du</var>, <var>du2</var> and <var>ipiv</var>
+contain the details of the LU factorization as returned by
+<tt class="function">gttrf()</tt>.
+On exit, <var>B</var> is overwritten with the solution <I>X</I>.
+<var>B</var> must have the same type as <var>dl</var>.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
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+
+<H1><A NAME="SECTION006300000000000000000">
+4.3 Symmetric and Hermitian Linear Equations</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-82' xml:id='l2h-82' class="function">sysv</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, ipiv=None</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real or complex symmetric matrix of order <I>n</I>.
+On exit, <var>B</var> is replaced by the solution.
+The matrices <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>).
+The optional argument <var>ipiv</var> is an integer matrix of length at
+least equal to <I>n</I>.
+If <var>ipiv</var> is provided, <tt class="function">sysv()</tt> solves the system and
+returns the factorization in <var>A</var> and <var>ipiv</var>.
+If <var>ipiv</var> is not specified, <tt class="function">sysv()</tt> solves the
+system but does not return the factorization and does not modify
+<var>A</var>.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-83' xml:id='l2h-83' class="function">sytrf</tt></b>(</nobr></td>
+ <td><var>A, ipiv</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img50.gif"
+ ALT="${}\mathrm{^T}$"></SPAN> factorization
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+PAP^T = LDL^T
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="112" HEIGHT="24" BORDER="0"
+ SRC="img52.gif"
+ ALT="\begin{displaymath}
+PAP^T = LDL^T
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+of a real or complex symmetric matrix <SPAN CLASS="MATH"><IMG
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img53.gif"
+ ALT="$A$"></SPAN> of order <I>n</I>.
+<var>ipiv</var> is an <code>'i'</code> matrix of length at least <I>n</I>.
+On exit, <var>A</var> and <var>ipiv</var> contain the factorization.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-84' xml:id='l2h-84' class="function">sytrs</tt></b>(</nobr></td>
+ <td><var>A, ipiv, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+given the LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img50.gif"
+ ALT="${}\mathrm{^T}$"></SPAN> factorization computed by
+<tt class="function">sytrf()</tt> or <tt class="function">sysv()</tt>. <var>B</var> must have the same
+type as <var>A</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-85' xml:id='l2h-85' class="function">sytri</tt></b>(</nobr></td>
+ <td><var>A, ipiv</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes the inverse of a real or complex symmetric matrix.
+On entry, <var>A</var> and <var>ipiv</var> contain the LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img50.gif"
+ ALT="${}\mathrm{^T}$"></SPAN>
+factorization computed by <tt class="function">sytrf()</tt> or <tt class="function">sysv()</tt>.
+On exit, <var>A</var> contains the inverse.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-86' xml:id='l2h-86' class="function">hesv</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, ipiv=<code>None</code></var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric or complex Hermitian of order <I>n</I>.
+On exit, <var>B</var> is replaced by the solution.
+The matrices <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>).
+The optional argument <var>ipiv</var> is an integer matrix of length at
+least <var>n</var>.
+If <var>ipiv</var> is provided, then <tt class="function">hesv()</tt> solves the system and
+returns the factorization in <var>A</var> and <var>ipiv</var>.
+If <var>ipiv</var> is not specified, then <tt class="function">hesv()</tt> solves the
+system but does not return the factorization and does not modify
+<var>A</var>.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-87' xml:id='l2h-87' class="function">hetrf</tt></b>(</nobr></td>
+ <td><var>A, ipiv</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img51.gif"
+ ALT="${}\mathrm{^H}$"></SPAN> factorization
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+PAP^T = LDL^H
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="115" HEIGHT="24" BORDER="0"
+ SRC="img54.gif"
+ ALT="\begin{displaymath}
+PAP^T = LDL^H
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+of a real symmetric or complex Hermitian matrix of order <I>n</I>.
+<var>ipiv</var> is an <code>'i'</code> matrix of length at least <var>n</var>.
+On exit, <var>A</var> and <var>ipiv</var> contain the factorization.
+Raises an <code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-88' xml:id='l2h-88' class="function">hetrs</tt></b>(</nobr></td>
+ <td><var>A, ipiv, B</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A X = B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+given the LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img51.gif"
+ ALT="${}\mathrm{^H}$"></SPAN> factorization computed by
+<tt class="function">hetrf()</tt> or <tt class="function">hesv()</tt>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-89' xml:id='l2h-89' class="function">hetri</tt></b>(</nobr></td>
+ <td><var>A, ipiv</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes the inverse of a real symmetric or complex Hermitian matrix.
+On entry, <var>A</var> and <var>ipiv</var> contain the LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img51.gif"
+ ALT="${}\mathrm{^H}$"></SPAN>
+factorization computed by <tt class="function">hetrf()</tt> or <tt class="function">hesv()</tt>.
+On exit, <var>A</var> contains the inverse.
+</dl>
+
+<P>
+As an example we solve the KKT system (<A href="e-kkt-example.html#e-kkt-example">4.1</A>).
+<div class="verbatim"><pre>
+>>> from cvxopt.lapack import sysv
+>>> K = matrix(0.0, (m+n,m+n))
+>>> K[: (m+n)*m : m+n+1] = -d**2
+>>> K[:m, m:] = A
+>>> x = matrix(0.0, (m+n,1))
+>>> x[:m], x[m:] = b1, b2
+>>> sysv(K, x, uplo='U')
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
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@@ -0,0 +1,182 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
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+<link rel='help' href='about.html' title='About this document...' />
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+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION006400000000000000000">
+4.4 Triangular Linear Equations</A>
+</H1>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-90' xml:id='l2h-90' class="function">trtrs</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, diag='N'</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a triangular set of equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is real or complex and triangular of order <I>n</I>,
+and <var>B</var> is a matrix with <I>n</I> rows.
+<var>A</var> and <var>B</var> are matrices with the same type (<code>'d'</code> or <code>'z'</code>).
+<tt class="function">trtrs()</tt> is similar to <tt class="function">blas.trsm()</tt>, except
+that it raises an <code>ArithmeticError</code> if a diagonal element of
+<var>A</var> is zero (whereas <tt class="function">blas.trsm()</tt> returns <code>inf</code>
+values).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-91' xml:id='l2h-91' class="function">trtri</tt></b>(</nobr></td>
+ <td><var>A</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, diag='N'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes the inverse of a real or complex triangular matrix <I>A</I>.
+On exit, <var>A</var> contains the inverse.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-92' xml:id='l2h-92' class="function">tbtrs</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='T'</var><big>[</big><var>,diag='N'</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a triangular set of equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is real or complex triangular band matrix of order <I>n</I>,
+and <var>B</var> is a matrix with <I>n</I> rows.
+The diagonals of <I>A</I> are stored in <var>A</var> using the BLAS conventions
+for triangular band matrices.
+<var>A</var> and <var>B</var> are matrices with the same type (<code>'d'</code> or <code>'z'</code>).
+On exit, <var>B</var> is replaced by the solution <I>X</I>.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+
+<H1><A NAME="SECTION006500000000000000000">
+4.5 Least-Squares and Least-Norm Problems</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-93' xml:id='l2h-93' class="function">gels</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, trans='N'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves least-squares and least-norm problems with a full rank
+<I>m</I> by <I>n</I> matrix <I>A</I>.
+
+<P>
+
+<OL>
+<LI><var>trans</var> is <code>'N'</code>. If <I>m</I> is greater than or equal
+to <I>n</I>, <tt class="function">gels()</tt> solves the least-squares problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|AX-B\|_F.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="165" HEIGHT="30" BORDER="0"
+ SRC="img55.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert AX-B\Vert _F.
+\end{array}
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <I>m</I> is less than or equal to <I>n</I>, <tt class="function">gels()</tt> solves
+the least-norm problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|X\|_F \\
+ \mbox{subject to} & AX = B.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="141" HEIGHT="45" BORDER="0"
+ SRC="img56.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert X\Vert _F \\
+\mbox{subject to} & AX = B.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</LI>
+<LI><var>trans</var> is <code>'T'</code> or <code>'C'</code> and <var>A</var> and <var>B</var>
+are real. If <I>m</I> is greater than or equal to <I>n</I>,
+<tt class="function">gels()</tt> solves the least-norm problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|X\|_F \\
+ \mbox{subject to} & A^TX=B.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="151" HEIGHT="45" BORDER="0"
+ SRC="img57.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert X\Vert _F \\
+\mbox{subject to} & A^TX=B.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <I>m</I> is less than or equal to <I>n</I>, <tt class="function">gels()</tt> solves
+the least-squares problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|A^TX-B\|_F.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="175" HEIGHT="30" BORDER="0"
+ SRC="img58.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert A^TX-B\Vert _F.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</LI>
+<LI><var>trans</var> is <code>'C'</code> and <var>A</var> and <var>B</var>
+are complex. If <I>m</I> is greater than or equal to <I>n</I>,
+<tt class="function">gels()</tt> solves the least-norm problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|X\|_F \\
+ \mbox{subject to} & A^HX=B.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="153" HEIGHT="45" BORDER="0"
+ SRC="img59.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert X\Vert _F \\
+\mbox{subject to} & A^HX=B.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <I>m</I> is less than or equal to <I>n</I>, <tt class="function">gels()</tt> solves
+the least-squares problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|A^HX-B\|_F.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="177" HEIGHT="30" BORDER="0"
+ SRC="img60.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert A^HX-B\Vert _F.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+</LI>
+</OL>
+<var>A</var> and <var>B</var> must have the same typecode (<code>'d'</code> or <code>'z'</code>).
+<var>trans</var> = <code>'T'</code> is not allowed if <var>A</var> is complex.
+On exit, the solution <I>X</I> is stored as the leading submatrix
+of <var>B</var>.
+The array <var>A</var> is overwritten with details of the QR or the LQ
+factorization of <I>A</I>.
+Note that <tt class="function">gels()</tt> does not check whether <SPAN CLASS="MATH"><IMG
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img53.gif"
+ ALT="$A$"></SPAN> is full rank.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-94' xml:id='l2h-94' class="function">geqrf</tt></b>(</nobr></td>
+ <td><var>A, tau</var>)</td></tr></table></dt>
+<dd>
+QR factorization of a real or complex matrix <var>A</var>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = Q R.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="61" HEIGHT="27" BORDER="0"
+ SRC="img61.gif"
+ ALT="\begin{displaymath}
+A = Q R.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>A</var> is <I>m</I> by <I>n</I>, then <I>Q</I> is <I>m</I> by <I>m</I>
+and orthogonal/unitary, and <var>R</var> is <I>m</I> by <I>n</I>
+and upper triangular (if <var>m</var> is greater than or equal to <var>n</var>),
+or upper trapezoidal (if <var>m</var> is less than or equal to <var>n</var>).
+<var>tau</var> is a matrix of the same type as <var>A</var> and of length at
+least min{<var>m</var>, <var>n</var>}.
+On exit, <I>R</I> is stored in the upper triangular part of <var>A</var>.
+The matrix <I>Q</I> is stored as a product of min{<var>m</var>, <var>n</var>}
+elementary reflectors in the first min{<var>m</var>, <var>n</var>} columns
+of <var>A</var> and in <var>tau</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-95' xml:id='l2h-95' class="function">ormqr</tt></b>(</nobr></td>
+ <td><var>A, tau, C</var><big>[</big><var>, side='L'</var><big>[</big><var>,
+trans='N'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Product with a real orthogonal matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \mathop{\mathrm{op}}(Q)C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := C\mathop{\mathrm{op}}(Q) \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \mathop{\mathrm{op}}(Q) = \left\{ \begin{array}{ll}
+ Q & \mathrm{trans} = \mathrm{'N'} \\
+ Q^T & \mathrm{trans} = \mathrm{'T'},
+\end{array}\right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="658" HEIGHT="45" BORDER="0"
+ SRC="img62.gif"
+ ALT="\begin{displaymath}
+C := \mathop{\mathrm{op}}(Q)C \quad (\mathrm{side} = \mathr...
+...} \\
+Q^T & \mathrm{trans} = \mathrm{'T'},
+\end{array}\right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>Q</I> is square and orthogonal.
+<I>Q</I> is stored in <var>A</var> and <var>tau</var> as a product
+of min{<var>A</var>.<tt class="member">size</tt>[0], <var>A</var>.<tt class="member">size</tt>[1]}
+elementary reflectors, as computed by <tt class="function">geqrf()</tt>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-96' xml:id='l2h-96' class="function">unmqr</tt></b>(</nobr></td>
+ <td><var>A, tau, C</var><big>[</big><var>, side='L'</var><big>[</big><var>,
+trans='N'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Product with a real orthogonal or complex unitary matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \mathop{\mathrm{op}}(Q)C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := C\mathop{\mathrm{op}}(Q) \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \mathop{\mathrm{op}}(Q) = \left\{ \begin{array}{ll}
+ Q & \mathrm{trans} = \mathrm{'N'} \\
+ Q^T & \mathrm{trans} = \mathrm{'T'} \\
+ Q^H & \mathrm{trans} = \mathrm{'C'},
+\end{array}\right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="662" HEIGHT="64" BORDER="0"
+ SRC="img63.gif"
+ ALT="\begin{displaymath}
+C := \mathop{\mathrm{op}}(Q)C \quad (\mathrm{side} = \mathr...
+...} \\
+Q^H & \mathrm{trans} = \mathrm{'C'},
+\end{array}\right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<I>Q</I> is square and orthogonal or unitary.
+<I>Q</I> is stored in <var>A</var> and <var>tau</var> as a product of
+min{<var>A</var>.<tt class="member">size</tt>[0], <var>A</var>.<tt class="member">size</tt>[1]}
+elementary reflectors, as computed by <tt class="function">geqrf()</tt>.
+The arrays <var>A</var>, <var>tau</var> and <var>C</var> must have the same type.
+<code><var>trans</var> = 'T'</code> is only allowed if the typecode is <code>'d'</code>.
+</dl>
+
+<P>
+In the following example, we solve a least-squares problem
+by a direct call to <tt class="function">gels()</tt>, and by separate calls to
+<tt class="function">geqrf()</tt>, <tt class="function">ormqr()</tt>, and <tt class="function">trtrs()</tt>.
+<div class="verbatim"><pre>
+>>> from cvxopt import random, blas, lapack
+>>> from cvxopt.base import matrix
+>>> m, n = 10, 5
+>>> A, b = random.normal(m,n), random.normal(m,1)
+>>> x1 = +b
+>>> lapack.gels(+A, x1) # x1[:n] minimizes ||A*x1[:n] - b||_2
+>>> tau = matrix(0.0, (n,1))
+>>> lapack.geqrf(A, tau) # A = [Q1, Q2] * [R1; 0]
+>>> x2 = +b
+>>> lapack.ormqr(A, tau, x2, trans='T') # x2 := [Q1, Q2]' * b
+>>> lapack.trtrs(A[:n,:], x2, uplo='U') # x2[:n] := R1^{-1}*x2[:n]
+>>> blas.nrm2(x1[:n] - x2[:n])
+3.0050798580569307e-16
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION006600000000000000000">
+4.6 Symmetric and Hermitian Eigenvalue Decomposition</A>
+</H1>
+The first four routines compute all or selected eigenvalues and
+eigenvectors of a real symmetric matrix <SPAN CLASS="MATH"><IMG
+ WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img53.gif"
+ ALT="$A$"></SPAN>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = V\mbox{\bf diag}\,(\lambda)V^T,\qquad V^TV = I.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="229" HEIGHT="28" BORDER="0"
+ SRC="img64.gif"
+ ALT="\begin{displaymath}
+A = V\mbox{\bf diag}\,(\lambda)V^T,\qquad V^TV = I.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-97' xml:id='l2h-97' class="function">syev</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Eigenvalue decomposition of a real symmetric matrix of order <I>n</I>.
+<var>W</var> is a real matrix of length at least <I>n</I>.
+On exit, <var>W</var> contains the eigenvalues in ascending order.
+If <var>jobz</var> is <code>'V'</code>, the eigenvectors are also computed
+and returned in <var>A</var>.
+If <var>jobz</var> is <code>'N'</code>, the eigenvectors are not returned and the
+contents of <var>A</var> are destroyed.
+Raises an <code>ArithmeticError</code> if the eigenvalue decomposition fails.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-98' xml:id='l2h-98' class="function">syevd</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+This is an alternative to <tt class="function">syev()</tt>, based on a different
+algorithm. It is faster on large problems, but also uses more memory.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-99' xml:id='l2h-99' class="function">syevx</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>,
+range='A'</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, vl=0.0, vu=0.0</var><big>[</big><var>,
+il=1, iu=1</var><big>[</big><var>, Z=<code>None</code></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes selected eigenvalues and eigenvectors of a real symmetric
+matrix <var>A</var> of order <I>n</I>.
+
+<P>
+<var>W</var> is a real matrix of length at least <var>n</var>.
+On exit, <var>W</var> contains the eigenvalues in ascending order.
+If <var>range</var> is <code>'A'</code>, all the eigenvalues are computed.
+If <var>range</var> is <code>'I'</code>, eigenvalues <var>il</var> through <var>iu</var>
+are computed, where <var>1</var> <code><=</code> <var>il</var> <code><=</code> <var>iu</var>
+<code><=</code> <var>n</var>.
+If <var>range</var> is <code>'V'</code>, the eigenvalues in the interval
+<code>(<var>vl</var>,<var>vu</var>]</code> are computed.
+
+<P>
+If <var>jobz</var> is <code>'V'</code>, the (normalized) eigenvectors are
+computed, and returned in <var>Z</var>. If <var>jobz</var> is <code>'N'</code>, the
+eigenvectors are not computed. In both cases, the contents of <var>A</var>
+are destroyed on exit.
+<var>Z</var> is optional (and not referenced) if <var>jobz</var> is <code>'N'</code>.
+It is required if <var>jobz</var> is <code>'V'</code> and must have at least
+<var>n</var> columns if <var>range</var> is <code>'A'</code> or <code>'V'</code> and at
+least <code><var>iu</var>-<var>il</var>+1</code> columns if <var>range</var> is <code>'I'</code>.
+
+<P>
+<tt class="function">syevx()</tt> returns the number of computed eigenvalues.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-100' xml:id='l2h-100' class="function">syevr</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>,
+range='A'</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, vl=0.0, vu=0.0</var><big>[</big><var>,
+il=1, iu=n</var><big>[</big><var>, Z=<code>None</code></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+This is an alternative to <tt class="function">syevx()</tt>.
+<tt class="function">syevr()</tt> is the most recent LAPACK routine for symmetric
+eigenvalue problems, and expected to supersede the three other
+routines in future releases.
+</dl>
+
+<P>
+The next four routines can be used to compute eigenvalues and
+eigenvectors for complex Hermitian matrices:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = V\mbox{\bf diag}\,(\lambda)V^H,\qquad V^HV = I.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="233" HEIGHT="28" BORDER="0"
+ SRC="img65.gif"
+ ALT="\begin{displaymath}
+A = V\mbox{\bf diag}\,(\lambda)V^H,\qquad V^HV = I.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+For real symmetric matrices they are identical to the corresponding
+<tt class="function">syev_()</tt> routines.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-101' xml:id='l2h-101' class="function">heev</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Eigenvalue decomposition of a real symmetric or complex Hermitian
+matrix of order <I>n</I>.
+The calling sequence is identical to <tt class="function">syev()</tt>, except that
+<var>A</var> can be real or complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-102' xml:id='l2h-102' class="function">heevd</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+This is an alternative to <tt class="function">heev()</tt>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-103' xml:id='l2h-103' class="function">heevx</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>,
+range='A'</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, vl=0.0, vu=0.0 </var><big>[</big><var>,
+il=1, iu=n</var><big>[</big><var>, Z=<code>None</code></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes selected eigenvalues and eigenvectors of a real symmetric
+or complex Hermitian matrix of order <I>n</I>.
+The calling sequence is identical to <tt class="function">syevx()</tt>,
+except that <var>A</var> can be real or complex.
+<var>Z</var> must have the same type as <var>A</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-104' xml:id='l2h-104' class="function">heevr</tt></b>(</nobr></td>
+ <td><var>A, W</var><big>[</big><var>, jobz='N'</var><big>[</big><var>,
+range='A'</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, vl=0.0, vu=0.0</var><big>[</big><var>,
+il=1, iu=n</var><big>[</big><var>, Z=<code>None</code></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+This is an alternative to <tt class="function">heevx()</tt>.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION006800000000000000000">
+4.8 Singular Value Decomposition</A>
+</H1>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-107' xml:id='l2h-107' class="function">gesvd</tt></b>(</nobr></td>
+ <td><var>A, S</var><big>[</big><var>, jobu='N'</var><big>[</big><var>,
+jobvt='N'</var><big>[</big><var>, U=<code>None</code></var><big>[</big><var>, Vt=<code>None</code></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Singular value decomposition
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = U \Sigma V^T, \qquad A = U \Sigma V^H
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="200" HEIGHT="27" BORDER="0"
+ SRC="img69.gif"
+ ALT="\begin{displaymath}
+A = U \Sigma V^T, \qquad A = U \Sigma V^H
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+of a real or complex <I>m</I> by <I>n</I> matrix <var>A</var>.
+
+<P>
+<var>S</var> is a real matrix of length at least min{<I>m</I>, <I>n</I>}.
+On exit, its first min{<I>m</I>, <I>n</I>} elements are the
+singular values in descending order.
+
+<P>
+The argument <var>jobu</var> controls how many left singular vectors are
+computed. The possible values are <code>'N'</code>, <code>'A'</code>, <code>'S'</code>
+and <code>'O'</code>.
+If <var>jobu</var> is <code>'N'</code>, no left singular vectors are
+computed.
+If <var>jobu</var> is <code>'A'</code>, all left singular vectors are computed
+and returned as columns of <var>U</var>.
+If <var>jobu</var> is <code>'S'</code>, the first min{<I>m</I>,<I>n</I>} left
+singular vectors are computed and returned as columns of <var>U</var>.
+If <var>jobu</var> is <code>'O'</code>, the first min{<I>m</I>,<I>n</I>} left
+singular vectors are computed and returned as columns of <var>A</var>.
+The argument <var>U</var> is <code>None</code> (if <var>jobu</var> is <code>'N'</code>
+or <code>'A'</code>) or a matrix of the same type as <var>A</var>.
+
+<P>
+The argument <var>jobvt</var> controls how many right singular vectors are
+computed. The possible values are <code>'N'</code>, <code>'A'</code>, <code>'S'</code>
+and <code>'O'</code>.
+If <var>jobvt</var> is <code>'N'</code>, no right singular vectors are
+computed. If <var>jobvt</var> is <code>'A'</code>, all right singular vectors
+are computed and returned as rows of <var>Vt</var>.
+If <var>jobvt</var> is <code>'S'</code>, the first min{<I>m</I>,<I>n</I>} right
+singular vectors are computed and their (conjugate) transposes are
+returned as rows of <var>Vt</var>.
+If <var>jobvt</var> is <code>'O'</code>, the first min{<I>m</I>, <I>n</I>} right
+singular vectors are computed and their (conjugate) transposes
+are returned as rows of <var>A</var>.
+Note that the (conjugate) transposes of the right singular vectors
+(<EM>i.e.</EM>, the matrix <SPAN CLASS="MATH"><IMG
+ WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img70.gif"
+ ALT="$V^H$"></SPAN>) are returned in <var>Vt</var> or <var>A</var>.
+The argument <var>Vt</var> can be <code>None</code> (if <var>jobvt</var> is <code>'N'</code>
+or <code>'A'</code>) or a matrix of the same type as <var>A</var>.
+
+<P>
+On exit, the contents of <var>A</var> are destroyed.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-108' xml:id='l2h-108' class="function">gesdd</tt></b>(</nobr></td>
+ <td><var>A, S</var><big>[</big><var>, jobz='N'</var><big>[</big><var>,
+U=<code>None</code></var><big>[</big><var>, Vt=<code>None</code></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Singular value decomposition of a real or complex <I>m</I> by <I>n</I>
+matrix <var>A</var>. This function is based on a divide-and-conquer
+algorithm and is faster than <tt class="function">gesvd()</tt>.
+
+<P>
+<var>S</var> is a real matrix of length at least min{<I>m</I>, <I>n</I>}.
+On exit, its first min{<I>m</I>, <I>n</I>} elements are the
+singular values in descending order.
+
+<P>
+The argument <var>jobz</var> controls how many singular vectors are
+computed. The possible values are <code>'N'</code>, <code>'A'</code>, <code>'S'</code>
+and <code>'O'</code>.
+If <var>jobz</var> is <code>'N'</code>, no singular vectors are computed.
+If <var>jobz</var> is <code>'A'</code>, all <I>m</I> left singular vectors are
+computed and returned as columns of <var>U</var> and all <I>n</I> right
+singular vectors are computed and returned as rows of <var>Vt</var>.
+If <var>jobz</var> is <code>'S'</code>, the first min{<I>m</I>, <I>n</I>} left
+and right singular vectors are computed and returned as columns of
+<var>U</var> and rows of <var>Vt</var>.
+If <var>jobz</var> is <code>'O'</code> and <I>m</I> is greater than or equal
+to <I>n</I>, the first <I>n</I> left singular vectors are returned as
+columns of <var>A</var> and the <I>n</I> right singular vectors are returned
+as rows of <var>Vt</var>. If <var>jobz</var> is <code>'O'</code> and <I>m</I> is less
+than <I>n</I>, the <I>m</I> left singular vectors are returned as columns
+of <var>U</var> and the first <I>m</I> right singular vectors are returned
+as rows of <var>A</var>.
+Note that the (conjugate) transposes of the right singular vectors
+are returned in <var>Vt</var> or <var>A</var>.
+
+<P>
+The argument <var>U</var> can be <code>None</code> (if <var>jobz</var> is <code>'N'</code>
+or <code>'A'</code> of <var>jobz</var> is <code>'O'</code> and <I>m</I> is greater than
+or equal to <I>n</I>) or a matrix of the same type as <var>A</var>.
+The argument <var>Vt</var> can be <code>None</code> (if <var>jobz</var> is <code>'N'</code>
+or <code>'A'</code> or <var>jobz</var> is <code>'O'</code> and <I>m</I> is less than
+<I>n</I>) or a matrix of the same type as <var>A</var>.
+
+<P>
+On exit, the contents of <var>A</var> are destroyed.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+
+<H1><A NAME="SECTION006900000000000000000">
+4.9 Example: Analytic Centering</A>
+</H1>
+The analytic centering problem is defined as
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & -\sum_{i=1}^m \log(b_i-a_i^Tx).
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="227" HEIGHT="30" BORDER="0"
+ SRC="img71.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & -\sum_{i=1}^m \log(b_i-a_i^Tx).
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+In the code below we solve the problem using Newton's method.
+At each iteration the Newton direction is computed by solving
+a positive definite set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A^T \mbox{\bf diag}\,(b-Ax)^{-2} A v = -\mbox{\bf diag}\,(b-Ax)^{-1}{\bf 1}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="301" HEIGHT="28" BORDER="0"
+ SRC="img72.gif"
+ ALT="\begin{displaymath}
+A^T \mbox{\bf diag}\,(b-Ax)^{-2} A v = -\mbox{\bf diag}\,(b-Ax)^{-1}{\bf 1}
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+(where <I>A</I> has rows <SPAN CLASS="MATH"><IMG
+ WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ SRC="img73.gif"
+ ALT="$a_i^T$"></SPAN>), and a suitable step size is determined
+by a backtracking line search.
+
+<P>
+We use the level-3 BLAS function <tt class="function">syrk()</tt> to form the Hessian
+matrix and the LAPACK function <tt class="function">posv()</tt> to solving the Newton
+system. The code can be further optimized by replacing the
+matrix-vector products with the level-2 BLAS function <tt class="function">gemv()</tt>.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt.base import matrix, log, mul, div
+from cvxopt import blas, lapack, random
+from math import sqrt
+
+def acent(A,b):
+ """
+ Returns the analytic center of A*x <= b.
+ We assume that b > 0 and the feasible set is bounded.
+ """
+
+ MAXITERS = 100
+ ALPHA = 0.01
+ BETA = 0.5
+ TOL = 1e-8
+
+ m, n = A.size
+ x = matrix(0.0, (n,1))
+ H = matrix(0.0, (n,n))
+ g = matrix(0.0, (n,1))
+
+ for iter in xrange(MAXITERS):
+
+ # Gradient is g = A^T * (1./(b-A*x)).
+ d = (b-A*x)**-1
+ g = A.T * d
+
+ # Hessian is H = A^T * diag(d)^2 * A.
+ Asc = mul( d[:,n*[0]], A )
+ blas.syrk(Asc, H, trans='T')
+
+ # Newton step is v = -H^-1 * g.
+ v = -g
+ lapack.posv(H, v)
+
+ # Terminate if Newton decrement is less than TOL.
+ lam = blas.dot(g, v)
+ if sqrt(-lam) < TOL: return x
+
+ # Backtracking line search.
+ y = mul(A*v, d)
+ step = 1.0
+ while 1-step*max(y) < 0: step *= BETA
+ while True:
+ if -sum(log(1-step*y)) < ALPHA*step*lam: break
+ step *= BETA
+ x += step*v
+</pre></div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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diff --git a/doc/cvxopt/node3.html b/doc/cvxopt/node3.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<link rel="parent" href="cvxopt.html" />
+<link rel="next" href="node4.html" />
+<meta name='aesop' content='information' />
+<title>1. Introduction</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+ href="node4.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="node4.html">2. Dense Matrices (cvxopt.base)</A>
+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION003000000000000000000"></A><A NAME="chap:intro"></A>
+<BR>
+1. Introduction
+</H1>
+
+<P>
+CVXOPT is a free software package for convex optimization based on
+the Python programming language.
+It can be used with the interactive Python interpreter,
+on the command line by executing Python scripts, or integrated in
+other software via Python extension modules.
+Its main purpose is to make the development of software for convex
+optimization applications straightforward by building on Python's
+extensive standard library and on the strengths of Python as a
+high-level programming language.
+
+<P>
+Release 0.8.2 of CVXOPT includes routines for basic linear algebra
+calculations,
+interfaces to efficient libraries for solving dense and sparse linear
+equations,
+convex optimization solvers written in Python,
+interfaces to a few other optimization libraries,
+and a modeling tool for piecewise-linear convex optimization problems.
+These components are organized in different modules.
+<DL>
+<DT><STRONG><tt class="module">cvxopt.base</tt></STRONG></DT>
+<DD>This module defines a Python type
+ <tt class="class">matrix</tt> for storing and manipulating dense matrices,
+ a Python type <tt class="class">spmatrix</tt> for storing and manipulating sparse
+ matrices, and routines for sparse matrix-vector and matrix-matrix
+ multiplication (see chapters <A HREF="node4.html#chap:matrix">2</A>
+ and <A HREF="node33.html#chap:spmatrix">6</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.random</tt></STRONG></DT>
+<DD>Routines for generating random matrices
+ with uniformly or normally distributed entries
+ (see section <A href="s-random.html#s-random">2.7</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.blas</tt></STRONG></DT>
+<DD>Interface to most of the double-precision
+ real and complex BLAS (chapter <A HREF="node14.html#chap:blas">3</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.lapack</tt></STRONG></DT>
+<DD>Interface to the dense double-precision
+ real and complex linear equation solvers and eigenvalue routines
+ from LAPACK (chapter <A HREF="node19.html#chap:lapack">4</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.fftw</tt></STRONG></DT>
+<DD>An optional interface to the
+ discrete transform routines from FFTW (section <A href="c-fftw.html#c-fftw">5</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.amd</tt></STRONG></DT>
+<DD>Interface to the approximate minimum degree
+ ordering routine from AMD (chapter <A href="s-orderings.html#s-orderings">7.1</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.umfpack</tt></STRONG></DT>
+<DD>Interface to the sparse LU solver
+ from UMFPACK (section <A href="s-umfpack.html#s-umfpack">7.2</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.cholmod</tt></STRONG></DT>
+<DD>Interface to the sparse Cholesky
+ solver from CHOLMOD (section <A href="s-cholmod.html#s-cholmod">7.3</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.solvers</tt></STRONG></DT>
+<DD>Convex optimization routines
+ and optional interfaces to solvers from GLPK, MOSEK and DSDP5
+ (chapter <A HREF="node45.html#chap:solvers">8</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.modeling</tt></STRONG></DT>
+<DD>Routines for specifying and solving
+ linear programs and convex optimization problems with piecewise-linear
+ cost and constraint functions (chapter <A HREF="node55.html#chap:modeling">9</A>).
+</DD>
+<DT><STRONG><tt class="module">cvxopt.info</tt></STRONG></DT>
+<DD>Defines a string <code>version</code> with
+ the version number of the CVXOPT installation and a function
+ <tt class="function">license()</tt> that prints the CVXOPT license.
+</DD>
+</DL>
+The modules are described in detail in this manual and in the
+on-line Python help facility <b class="program">pydoc</b>. Several example scripts
+are included in the distribution.
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="Contents"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
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+<link rel='help' href='about.html' title='About this document...' />
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+<link rel="parent" href="c-fftw.html" />
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+</head>
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+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION007100000000000000000">
+5.1 Discrete Fourier Transform</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-109' xml:id='l2h-109' class="function">dft</tt></b>(</nobr></td>
+ <td><var>X</var>)</td></tr></table></dt>
+<dd>
+Replaces the columns of a dense complex matrix with their discrete
+Fourier transforms: if <var>X</var> has <I>n</I> rows,
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+X[k,:] := \sum_{j=0}^{n-1} e^{-2\pi j k \sqrt{-1}/n} X[j,:],
+ \qquad k=0,\ldots,n-1.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="375" HEIGHT="58" BORDER="0"
+ SRC="img74.gif"
+ ALT="\begin{displaymath}
+X[k,:] := \sum_{j=0}^{n-1} e^{-2\pi j k \sqrt{-1}/n} X[j,:],
+\qquad k=0,\ldots,n-1.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-110' xml:id='l2h-110' class="function">idft</tt></b>(</nobr></td>
+ <td><var>X</var>)</td></tr></table></dt>
+<dd>
+Replaces the columns of a dense complex matrix with their inverse
+discrete Fourier transforms: if <var>X</var> has <I>n</I> rows,
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+X[k,:] :=
+ \frac{1}{n} \sum_{j=0}^{n-1} e^{2\pi j k \sqrt{-1}/n} X[j,:],
+ \qquad k=0,\ldots,n-1.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="382" HEIGHT="58" BORDER="0"
+ SRC="img75.gif"
+ ALT="\begin{displaymath}
+X[k,:] :=
+\frac{1}{n} \sum_{j=0}^{n-1} e^{2\pi j k \sqrt{-1}/n} X[j,:],
+\qquad k=0,\ldots,n-1.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<td class='online-navigation'><a rel="next" title="5.3 Discrete Sine Transform"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
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+
+<H1><A NAME="SECTION007200000000000000000">
+5.2 Discrete Cosine Transform</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-111' xml:id='l2h-111' class="function">dct</tt></b>(</nobr></td>
+ <td><var>X</var><big>[</big><var>, type=2</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Replaces the columns of a dense real matrix with their discrete
+cosine transforms. The second argument, an integer between 1 and 4,
+denotes the type of transform (DCT-I, DCT-II, DCT-III, DCT-IV).
+The DCT-I transform requires that the row dimension of <var>X</var> is at
+least 2.
+These transforms are defined as follows
+(for a matrix with <I>n</I> rows).
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+\mbox{DCT-I:} \qquad
+ X[k,:] & := & X[0,:] + (-1)^k X[n-1,:] +
+ 2 \sum_{j=1}^{n-2} X[j,:] \cos(\pi j k /(n-1)),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DCT-II:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \cos(\pi(j+1/2)k/n),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DCT-III:} \qquad
+ X[k,:] & := & X[0,:] + 2 \sum_{j=1}^{n-1} X[j,:] \cos(\pi j(k+1/2)/n),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DCT-IV:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \cos(\pi (j+1/2)(k+1/2)/n),
+ \qquad k=0,\ldots,n-1.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="724" HEIGHT="230" BORDER="0"
+ SRC="img76.gif"
+ ALT="\begin{eqnarray*}
+\mbox{DCT-I:} \qquad
+X[k,:] & := & X[0,:] + (-1)^k X[n-1,:] +...
+...n-1} X[j,:] \cos(\pi (j+1/2)(k+1/2)/n),
+\qquad k=0,\ldots,n-1.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-112' xml:id='l2h-112' class="function">idct</tt></b>(</nobr></td>
+ <td><var>X</var><big>[</big><var>, type=2</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Replaces the columns of a dense real matrix with the inverses
+of the discrete cosine transforms defined above.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
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+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+
+<H1><A NAME="SECTION007300000000000000000">
+5.3 Discrete Sine Transform</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-113' xml:id='l2h-113' class="function">dst</tt></b>(</nobr></td>
+ <td><var>X</var><big>[</big><var>, type=1</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Replaces the columns of a dense real matrix with their discrete
+sine transforms. The second argument, an integer between 1 and 4,
+denotes the type of transform (DST-I, DST-II, DST-III, DST-IV).
+These transforms are defined as follows
+(for a matrix with <I>n</I> rows).
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+\mbox{DST-I:} \qquad
+ X[k,:] & := &
+ 2 \sum_{j=0}^{n-1} X[j,:] \sin(\pi(j+1)(k+1)/(n+1)),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DST-II:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \sin(\pi(j+1/2)(k+1)/n),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DST-III:} \qquad
+ X[k,:] & := & (-1)^k X[n-1,:] + 2 \sum_{j=0}^{n-2}
+ X[j,:] \sin(\pi(j+1)(k+1/2)/n),
+ \qquad k=0,\ldots,n-1. \\
+\mbox{DST-IV:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \sin(\pi (j+1/2)(k+1/2)/n),
+ \qquad k=0,\ldots,n-1.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="714" HEIGHT="230" BORDER="0"
+ SRC="img77.gif"
+ ALT="\begin{eqnarray*}
+\mbox{DST-I:} \qquad
+X[k,:] & := &
+2 \sum_{j=0}^{n-1} X[j,:...
+...n-1} X[j,:] \sin(\pi (j+1/2)(k+1/2)/n),
+\qquad k=0,\ldots,n-1.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-114' xml:id='l2h-114' class="function">idst</tt></b>(</nobr></td>
+ <td><var>X</var><big>[</big><var>, type=1</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Replaces the columns of a dense real matrix with the inverses
+of the discrete sine transforms defined above.
+</dl>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="5.2 Discrete Cosine Transform"
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+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION008000000000000000000"></A><A NAME="chap:spmatrix"></A>
+<BR>
+6. Sparse Matrices (<tt class="module">cvxopt.base</tt>)
+</H1>
+
+<P>
+In this chapter we discuss the <tt class="class">spmatrix</tt> object defined in
+<tt class="module">cvxopt.base</tt>.
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="s-creating-spmatrix.html">6.1 Creating Sparse Matrices</a>
+<LI><A href="e-spA-example.html">6.2 Attributes and Methods</a>
+<LI><A href="s-spmatrix-arith.html">6.3 Arithmetic Operations</a>
+<LI><A href="node37.html">6.4 Indexing and Slicing</a>
+<LI><A href="node38.html">6.5 Built-In Functions</a>
+<LI><A href="node39.html">6.6 Sparse BLAS Functions</a>
+</ul>
+<!--End of Table of Child-Links-->
+</div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
+<link rel="next" href="node38.html" />
+<link rel="prev" href="s-spmatrix-arith.html" />
+<link rel="parent" href="node33.html" />
+<link rel="next" href="node38.html" />
+<meta name='aesop' content='information' />
+<title>6.4 Indexing and Slicing</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="6.3 Arithmetic Operations"
+ href="s-spmatrix-arith.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="6. Sparse Matrices (cvxopt.base)"
+ href="node33.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="6.5 Built-In Functions"
+ href="node38.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
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+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION008400000000000000000">
+6.4 Indexing and Slicing</A>
+</H1>
+Sparse matrices can be indexed the same way as dense matrices
+(see section <A href="s-indexing.html#s-indexing">2.4</A> ).
+
+<P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix
+>>> A = spmatrix([0,2,-1,2,-2,1], [0,1,2,0,2,1], [0,0,0,1,1,2])
+>>> print A[:,[0,1]]
+SIZE: (3,2)
+(0, 0) 0.0000e+00
+(1, 0) 2.0000e+00
+(2, 0) -1.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+>>> B = spmatrix([0,2*1j,0,-2], [1,2,1,2], [0,0,1,1,])
+>>> print B[-2:,-2:]
+SIZE: (2,2)
+(0, 0) 0.0000e+00-j0.0000e+00
+(1, 0) 2.0000e+00-j0.0000e+00
+(0, 1) 0.0000e+00-j0.0000e+00
+(1, 1) 0.0000e+00-j2.0000e+00
+</pre></div>
+
+<P>
+An indexed sparse matrix <code><var>A</var>[<var>I</var>]</code> or
+<code><var>A</var>[<var>I</var>,<var>J</var>]</code> can also be the target of an
+assignment. The righthand side of the assignment can be a scalar
+(a Python integer, float, or complex, or a 1 by 1 dense matrix),
+a sequence of numbers, or a sparse or dense matrix of
+compatible dimensions.
+If the righthand side is a scalar, it is treated as a dense matrix of
+the same size as the lefthand side and with all its entries equal to
+the scalar.
+If the righthand side is a sequence of numbers, they are treated as
+the elements of a dense matrix in column-major order.
+
+<P>
+We continue the example above.
+<div class="verbatim"><pre>
+>>> C = spmatrix([10,-20,30], [0,2,1], [0,0,1])
+>>> A[:,0] = C[:,0]
+>>> print A
+SIZE: (3,3)
+(0, 0) 1.0000e+01
+(2, 0) -2.0000e+01
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+>>> D = matrix(range(6), (3,2))
+>>> A[:,0] = D[:,0]
+>>> print A
+SIZE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 1.0000e+00
+(2, 0) 2.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+>>> A[:,0] = 1
+>>> print A
+SIZE: (3,3)
+(0, 0) 1.0000e+00
+(1, 0) 1.0000e+00
+(2, 0) 1.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+>>> A[:,0] = 0
+>>> print A
+TYPE: (3,3)
+(0, 0) 0.0000e+00
+(1, 0) 0.0000e+00
+(2, 0) 0.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(1, 2) 1.0000e+00
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="6.3 Arithmetic Operations"
+ href="s-spmatrix-arith.html"><img src='previous.gif'
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@@ -0,0 +1,184 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<meta name='aesop' content='information' />
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+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td class='online-navigation'><a rel="next" title="6.6 Sparse BLAS Functions"
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION008500000000000000000">
+6.5 Built-In Functions</A>
+</H1>
+
+<P>
+The functions described in the table of section <A href="s-builtinfuncs.html#s-builtinfuncs">2.5</A>
+also work with sparse matrix arguments. The difference is that for a
+sparse matrix only the nonzero entries are considered.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-123' xml:id='l2h-123' class="function">len</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+If <var>x</var> is a <tt class="class">spmatrix</tt>, returns the number of nonzero entries in
+<var>x</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-124' xml:id='l2h-124' class="function">bool</tt></b>(</nobr></td>
+ <td><var></var><big>[</big><var>x</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+If <var>x</var> is a <tt class="class">spmatrix</tt>, returns <code>False</code> if <var>x</var> has at least one
+nonzero entry; <code>False</code> otherwise.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-125' xml:id='l2h-125' class="function">max</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+If <var>x</var> is a <tt class="class">spmatrix</tt>, returns the maximum nonzero entry of <var>x</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-126' xml:id='l2h-126' class="function">min</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+If <var>x</var> is a <tt class="class">spmatrix</tt>, returns the minimum nonzero entry of <var>x</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-127' xml:id='l2h-127' class="function">abs</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+If <var>x</var> is a <tt class="class">spmatrix</tt>, returns a sparse matrix with the absolute
+value of the elements of <var>x</var> and the same sparsity pattern.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-128' xml:id='l2h-128' class="function">sum</tt></b>(</nobr></td>
+ <td><var>x</var><big>[</big><var>, start=0.0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+If <var>x</var> is a <tt class="class">spmatrix</tt>, returns the sum of <var>start</var> and the
+elements of <var>x</var>.
+</dl>
+
+<P>
+The functions <tt class="function">list()</tt>, <tt class="function">tuple()</tt>, <tt class="function">zip()</tt>,
+<tt class="function">map()</tt>, <tt class="function">filter()</tt> also take sparse matrix arguments.
+They work as for dense matrices, again with the difference that only
+the nonzero entries are considered.
+
+<P>
+In the following example we square the entries of the
+matrix (<A href="e-spA-example.html#e-spA-example">6.2</A>).
+
+<P>
+<div class="verbatim"><pre>
+>>> A = spmatrix([2,1,2,2,1,3,4], [1,2,0,2,3,0,2], [0,0,1,1,2,3,3])
+>>> B = spmatrix(map(lambda x: x**2, A), A.I, A.J)
+>>> print B
+SIZE: (4,4)
+(1, 0) 4.0000e+00
+(2, 0) 1.0000e+00
+(0, 1) 4.0000e+00
+(2, 1) 4.0000e+00
+(3, 2) 1.0000e+00
+(0, 3) 9.0000e+00
+(2, 3) 1.6000e+01
+</pre></div>
+
+<P>
+The expression "<tt class="samp"><var>x</var> in <var>A</var></tt>" returns <code>True</code> if a nonzero
+entry of <var>A</var> is equal to <var>x</var> and <code>False</code> otherwise.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="6.4 Indexing and Slicing"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+ href="node33.html"><img src='up.gif'
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+<td class='online-navigation'><a rel="next" title="7. Sparse Linear Equation"
+ href="c-spsolvers.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
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+<b class="navlabel">Next:</b>
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION008600000000000000000">
+6.6 Sparse BLAS Functions</A>
+</H1>
+The <tt class="module">cvxopt.base</tt> module includes a few arithmetic functions
+that extend functions from <tt class="module">cvxopt.blas</tt> to sparse matrices.
+These functions are faster than the corresponding operations
+implemented using the overloaded arithmetic described
+in section <A href="s-spmatrix-arith.html#s-spmatrix-arith">6.3</A>.
+They also work in-place, <EM>i.e.</EM>, they modify their arguments without
+creating new objects.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-129' xml:id='l2h-129' class="function">gemv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, trans='N'</var><big>[</big><var>,
+ alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a general dense or sparse matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+y := \alpha A^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}),
+ \qquad
+y := \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="707" HEIGHT="28" BORDER="0"
+ SRC="img17.gif"
+ ALT="\begin{displaymath}
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'...
+...\alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>A</var> is a dense matrix, this is identical to
+<tt class="function">blas.gemv()</tt>. If <var>A</var> is sparse, the result is the same
+as when <tt class="function">blas.gemv()</tt> is called with <code>matrix(A)</code> as
+argument, however, without explicitly converting <var>A</var> to dense.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-130' xml:id='l2h-130' class="function">symv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a dense or sparse real symmetric matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha A x + \beta y.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="106" HEIGHT="27" BORDER="0"
+ SRC="img82.gif"
+ ALT="\begin{displaymath}
+y := \alpha A x + \beta y.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>A</var> is a dense matrix, this is identical to
+<tt class="function">blas.symv()</tt>. If <var>A</var> is sparse, the result is the same
+as when <tt class="function">blas.symv()</tt> is called with <code>matrix(A)</code> as
+argument, however, without explicitly converting <var>A</var> to dense.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-131' xml:id='l2h-131' class="function">gemm</tt></b>(</nobr></td>
+ <td><var>A, B, C</var><big>[</big><var>, transA='N'</var><big>[</big><var>,
+transB='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>[</big><var>,
+partial=False</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-matrix product of two general sparse or dense matrices:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha \mathop{\mathrm{op}}(A) \mathop{\mathrm{op}}(B) + \beta C
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="177" HEIGHT="28" BORDER="0"
+ SRC="img31.gif"
+ ALT="\begin{displaymath}
+C := \alpha \mathop{\mathrm{op}}(A) \mathop{\mathrm{op}}(B) + \beta C
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\mathop{\mathrm{op}}(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'} \end{array} \right.
+\qquad
+\mathop{\mathrm{op}}(B) = \left\{ \begin{array}{ll}
+ B & \mathrm{transB} = \mathrm{'N'} \\
+ B^T & \mathrm{transB} = \mathrm{'T'} \\
+ B^H & \mathrm{transB} = \mathrm{'C'}. \end{array} \right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="474" HEIGHT="64" BORDER="0"
+ SRC="img32.gif"
+ ALT="\begin{displaymath}
+\mathop{\mathrm{op}}(A) = \left\{ \begin{array}{ll}
+A & \ma...
+...\\
+B^H & \mathrm{transB} = \mathrm{'C'}. \end{array} \right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>A</var>, <var>B</var> and <var>C</var> are dense matrices, this is
+identical to <tt class="function">blas.gemm()</tt>, described in section <A href="s-blas3.html#s-blas3">3.4</A>,
+and the argument <var>partial</var> is ignored.
+
+<P>
+If <var>A</var> and/or <var>B</var> are sparse and <var>C</var> is dense, the result
+is the same as when <tt class="function">blas.gemm()</tt> is called with
+<code>matrix(A)</code> and <code>matrix(B)</code> as arguments, without explicitly
+converting <var>A</var> and <var>B</var> to dense.
+The argument <var>partial</var> is ignored.
+
+<P>
+If <var>C</var> is a sparse matrix, the matrix-matrix product in the
+definition of <tt class="function">blas.gemm()</tt> is computed, but as a sparse
+matrix.
+If <var>partial</var> is <code>False</code>, the result is stored in <var>C</var>,
+and the sparsity pattern of <var>C</var> is modified if necessary.
+If <var>partial</var> is <code>True</code>, the operation only updates the nonzero
+elements in <var>C</var>, even if the sparsity pattern of <var>C</var> differs
+from that of the matrix product.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-132' xml:id='l2h-132' class="function">syrk</tt></b>(</nobr></td>
+ <td><var>A, C</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>[</big><var>,
+partial=False</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Rank-<I>k</I> update of a sparse or dense real or complex symmetric
+matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha AA^T + \beta C \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+ C := \alpha A^TA + \beta C \quad (\mathrm{trans} = \mathrm{'T'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="501" HEIGHT="28" BORDER="0"
+ SRC="img36.gif"
+ ALT="\begin{displaymath}
+C := \alpha AA^T + \beta C \quad (\mathrm{trans} = \mathrm{...
+... \alpha A^TA + \beta C \quad (\mathrm{trans} = \mathrm{'T'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>A</var> and <var>C</var> are dense, this is identical to
+<tt class="function">blas.syrk()</tt>, described in section <A href="s-blas3.html#s-blas3">3.4</A>,
+and the argument <var>partial</var> is ignored.
+
+<P>
+If <var>A</var> is sparse and <var>C</var> is dense, the result is the same as
+when <tt class="function">blas.syrk()</tt> is called with <code>matrix(A)</code> as
+argument, without explicitly converting <var>A</var> to dense.
+The argument <var>partial</var> is ignored.
+
+<P>
+If <var>C</var> is sparse, the product in the definition of
+<tt class="function">blas.syrk()</tt> is computed, but as a sparse matrix.
+If <var>partial</var> is <code>False</code>, the result is stored in <var>C</var>,
+and the sparsity pattern of <var>C</var> is modified if necessary.
+If <var>partial</var> is <code>True</code>, the operation only updates the nonzero
+elements in <var>C</var>, even if the sparsity pattern of <var>C</var> differs
+from that of the matrix product.
+</dl>
+
+<P>
+In the following example, we first compute
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C = A^TB, \qquad
+A = \left[ \begin{array}{ccc}
+0 & 1 & 0 \\1 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \end{array}\right],
+\qquad
+B = \left[ \begin{array}{ccc}
+ 0 & -1 & 0 \\2 & 0 & 2 \\0 & 3 & 0 \\2 & 0 & 0
+ \end{array}\right].
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="418" HEIGHT="83" BORDER="0"
+ SRC="img83.gif"
+ ALT="\begin{displaymath}
+C = A^TB, \qquad
+A = \left[ \begin{array}{ccc}
+0 & 1 & 0 \\ ...
+...0 \\ 2 & 0 & 2 \\ 0 & 3 & 0 \\ 2 & 0 & 0
+\end{array}\right].
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix, gemm
+>>> A = spmatrix(1, [1,3,0,2,1], [0,0,1,1,2])
+>>> B = spmatrix([2,2,-1,3,2], [1,3,0,2,1], [0,0,1,1,2])
+>>> C = spmatrix([], [], [], size=(3,3))
+>>> gemm(A, B, C, transA='T')
+>>> print C
+SIZE: (3,3)
+(0, 0) 4.0000e+00
+(2, 0) 2.0000e+00
+(1, 1) 2.0000e+00
+(0, 2) 2.0000e+00
+(2, 2) 2.0000e+00
+</pre></div>
+Now suppose we want to replace <I>C</I>
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C = A^TD, \qquad
+D = \left[ \begin{array}{ccc}
+ 0 & 1 & 0 \\3 & 0 & -2 \\0 & 1 & 0 \\4 & 0 & 0
+ \end{array}\right].
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="252" HEIGHT="83" BORDER="0"
+ SRC="img84.gif"
+ ALT="\begin{displaymath}
+C = A^TD, \qquad
+D = \left[ \begin{array}{ccc}
+0 & 1 & 0 \\ 3 & 0 & -2 \\ 0 & 1 & 0 \\ 4 & 0 & 0
+\end{array}\right].
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The new matrix has the same sparsity pattern as <var>C</var>, so we can
+use <tt class="function">gemm()</tt> with the <code>partial=True</code> option.
+This saves time in large sparse matrix multiplications when the
+sparsity pattern of the result is known beforehand.
+<div class="verbatim"><pre>
+>>> D = spmatrix([3,4,1,1,-2], [1,3,0,2,1], [0,0,1,1,2])
+>>> gemm(A, D, C, transA='T', partial=True)
+>>> print C
+SIZE: (3,3)
+(0, 0) 7.0000e+00
+(2, 0) 3.0000e+00
+(1, 1) 2.0000e+00
+(0, 2) -2.0000e+00
+(2, 2) -2.0000e+00
+</pre></div>
+
+<DIV CLASS="navigation">
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+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+</head>
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION004000000000000000000"></A><A NAME="chap:matrix"></A>
+<BR>
+2. Dense Matrices (<tt class="module">cvxopt.base</tt>)
+</H1>
+
+<P>
+The <tt class="module">cvxopt.base</tt> module defines two new Python types:
+<tt class="class">matrix</tt> objects, used for dense matrix computations, and
+<tt class="class">spmatrix</tt> objects, used for sparse matrix computations.
+In this chapter we describe the dense <tt class="class">matrix</tt> object.
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="s-creating-matrices.html">2.1 Creating Matrices</a>
+<LI><A href="node6.html">2.2 Attributes and Methods</a>
+<LI><A href="s-arithmetic.html">2.3 Arithmetic Operations</a>
+<LI><A href="s-indexing.html">2.4 Indexing and Slicing</a>
+<LI><A href="s-builtinfuncs.html">2.5 Built-in Functions</a>
+<LI><A href="s-otherfuncs.html">2.6 Other Matrix Functions</a>
+<LI><A href="s-random.html">2.7 Randomly Generated Matrices</a>
+<LI><A href="s-array-interface.html">2.8 The NumPy Array Interface</a>
+<LI><A href="node13.html">2.9 Printing Options</a>
+</ul>
+<!--End of Table of Child-Links-->
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+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+
+<H1><A NAME="SECTION0010000000000000000000"></A>
+<A NAME="chap:solvers"></A>
+<BR>
+8. Optimization Routines (<tt class="module">cvxopt.solvers</tt>)
+</H1>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="s-lpsolver.html">8.1 Linear Programming</a>
+<LI><A href="node47.html">8.2 Quadratic Programming</a>
+<LI><A href="node48.html">8.3 Geometric Programming</a>
+<LI><A href="s-sdpsolver.html">8.4 Semidefinite Programming</a>
+<LI><A href="e-nlcp.html">8.5 Nonlinear Convex Programming</a>
+<LI><A href="node51.html">8.6 Exploiting Structure in LPs and SDPs</a>
+<LI><A href="node52.html">8.7 Exploiting Structure in Nonlinear Convex Programs</a>
+<LI><A href="s-external.html">8.8 Optional Solvers</a>
+<LI><A href="s-parameters.html">8.9 Algorithm Parameters</a>
+</ul>
+<!--End of Table of Child-Links-->
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+<DIV CLASS="navigation">
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+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+
+<H1><A NAME="SECTION0010200000000000000000">
+8.2 Quadratic Programming</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-146' xml:id='l2h-146' class="function">qp</tt></b>(</nobr></td>
+ <td><var>P, q, </var><big>[</big><var>, G, h </var><big>[</big><var>, A, b</var><big>[</big><var>,
+solver</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a convex quadratic program
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & (1/2) x^TPx + q^T x \\
+\mbox{subject to} & Gx \preceq h \\& Ax = b.
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="199" HEIGHT="64" BORDER="0"
+ SRC="img116.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & (1/2) x^TPx + q^T x \\
+\mbox{subject to} & Gx \preceq h \\ & Ax = b.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+<var>P</var> is a square dense or sparse real matrix, representing a
+symmetric matrix in <code>'L'</code> storage, <EM>i.e.</EM>, only the lower
+triangular part of <var>P</var> is referenced.
+<var>G</var> and <var>A</var> are dense or sparse real matrices.
+Their default values are sparse matrices with zero columns.
+<var>q</var>, <var>h</var> and <var>b</var> are single-column real dense matrices.
+The default values of <var>h</var> and <var>b</var> are matrices of size (0,1).
+
+<P>
+The default CVXOPT solver is used when the <var>solver</var> argument
+is absent or <code>None</code>. The MOSEK solver (if installed) can be
+selected by setting <var>solver</var>=<code>'mosek'</code>.
+
+<P>
+<tt class="function">qp()</tt> returns a dictionary with keys
+<code>'status'</code>, <code>'x'</code>, <code>'s'</code>, <code>'y'</code>, <code>'z'</code>.
+The possible values of the <code>'status'</code> key are as follows.
+<DL>
+<DT><STRONG><code>'optimal'</code></STRONG></DT>
+<DD>In this case the
+<code>'x'</code> entry is the primal optimal solution,
+the <code>'s'</code> entry is the corresponding slack in the inequality
+constraints, the <code>'z'</code> and <code>'y'</code> entries are the optimal
+values of the dual variables associated with the linear inequality
+and linear equality constraints.
+These values (approximately) satisfy the optimality conditions
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+Px + q + G^T z + A^T y = 0, \qquad Gx + s = h, \qquad
+ Ax = b, \qquad s \succeq 0, \qquad z \succeq 0, \qquad s^T z = 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="603" HEIGHT="27" BORDER="0"
+ SRC="img117.gif"
+ ALT="\begin{displaymath}
+Px + q + G^T z + A^T y = 0, \qquad Gx + s = h, \qquad
+Ax = b, \qquad s \succeq 0, \qquad z \succeq 0, \qquad s^T z = 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'primal infeasible'</code></STRONG></DT>
+<DD>This only applies when
+<var>solver</var> is <code>'mosek'</code>, and means that a certificate of
+primal infeasibility has been found. The <code>'x'</code> and <code>'s'</code>
+entries are <code>None</code>, and the
+<code>'z'</code> and <code>'y'</code> entries are vectors that approximately satisfy
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+G^Tz + A^T y = 0, \qquad h^Tz + b^Ty = -1, \qquad z \succeq 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="340" HEIGHT="27" BORDER="0"
+ SRC="img113.gif"
+ ALT="\begin{displaymath}
+G^T z + A^T y = 0, \qquad h^T z + b^T y = -1, \qquad z \succeq 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'dual infeasible'</code></STRONG></DT>
+<DD>This only applies when
+<var>solver</var> is <code>'mosek'</code>, and means that a certificate of
+dual infeasibility has been found. The <code>'z'</code> and <code>'y'</code>
+entries are <code>None</code>, and the <code>'x'</code> and <code>'s'</code> entries are
+vectors that approximately satisfy
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+Px = 0, \qquad q^Tx = -1, \qquad Gx + s = 0, \qquad Ax=0, \qquad
+ s \succeq 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="442" HEIGHT="27" BORDER="0"
+ SRC="img118.gif"
+ ALT="\begin{displaymath}
+Px = 0, \qquad q^Tx = -1, \qquad Gx + s = 0, \qquad Ax=0, \qquad
+s \succeq 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'unknown'</code></STRONG></DT>
+<DD>This means that the algorithm reached
+the maximum number of iterations before a solution was found.
+The <code>'x'</code>, <code>'s'</code>, <code>'y'</code>, <code>'z'</code> entries are <code>None</code>.
+</DD>
+</DL>
+</dl>
+
+<P>
+As an example we compute the trade-off curve on page 187
+of the book <em class="citetitle"><a
+ href="http://www.stanford.edu/~boyd/cvxbook"
+ title="Convex
+Optimization"
+ >Convex
+Optimization</a></em>, by solving the quadratic program
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & -\bar p^T x + \mu x^T S x \\
+\mbox{subject to} & {\bf 1}^T x = 1, \quad x \succeq 0
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="195" HEIGHT="45" BORDER="0"
+ SRC="img119.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & -\bar p^T x + \mu x^T S ...
+...ox{subject to} & {\bf 1}^T x = 1, \quad x \succeq 0
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+for a sequence of positive values of <I>mu</I>.
+The code below computes the trade-off curve and produces two figures
+using the <a class="ulink" href="http://matplotlib.sourceforge.net"
+ >Matplotlib</a> package.
+<DIV ALIGN="CENTER">
+<IMG
+ WIDTH="453" HEIGHT="340" ALIGN="BOTTOM" BORDER="0"
+ SRC="img120.gif"
+ ALT="\includegraphics[width=10cm]{figures/portfolio1.eps}">
+
+<IMG
+ WIDTH="453" HEIGHT="340" ALIGN="BOTTOM" BORDER="0"
+ SRC="img121.gif"
+ ALT="\includegraphics[width=10cm]{figures/portfolio2.eps}">
+
+</DIV>
+
+<P>
+<div class="verbatim"><pre>
+from math import sqrt
+from cvxopt.base import matrix
+from cvxopt.blas import dot
+from cvxopt.solvers import qp
+import pylab
+
+# Problem data.
+n = 4
+S = matrix([[ 4e-2, 6e-3, -4e-3, 0.0 ],
+ [ 6e-3, 1e-2, 0.0, 0.0 ],
+ [-4e-3, 0.0, 2.5e-3, 0.0 ],
+ [ 0.0, 0.0, 0.0, 0.0 ]])
+pbar = matrix([.12, .10, .07, .03])
+G = matrix(0.0, (n,n))
+G[::n+1] = -1.0
+h = matrix(0.0, (n,1))
+A = matrix(1.0, (1,n))
+b = matrix(1.0)
+
+# Compute trade-off.
+N = 100
+mus = [ 10**(5.0*t/N-1.0) for t in xrange(N) ]
+portfolios = [ qp(mu*S, -pbar, G, h, A, b)['x'] for mu in mus ]
+returns = [ dot(pbar,x) for x in portfolios ]
+risks = [ sqrt(dot(x, S*x)) for x in portfolios ]
+
+# Plot trade-off curve and optimal allocations.
+pylab.figure(1, facecolor='w')
+pylab.plot(risks, returns)
+pylab.xlabel('standard deviation')
+pylab.ylabel('expected return')
+pylab.axis([0, 0.2, 0, 0.15])
+pylab.title('Risk-return trade-off curve (fig 4.12)')
+pylab.yticks([0.00, 0.05, 0.10, 0.15])
+
+pylab.figure(2, facecolor='w')
+c1 = [ x[0] for x in portfolios ]
+c2 = [ x[0] + x[1] for x in portfolios ]
+c3 = [ x[0] + x[1] + x[2] for x in portfolios ]
+c4 = [ x[0] + x[1] + x[2] + x[3] for x in portfolios ]
+pylab.fill(risks + [.20], c1 + [0.0], '#F0F0F0')
+pylab.fill(risks[-1::-1] + risks, c2[-1::-1] + c1, '#D0D0D0')
+pylab.fill(risks[-1::-1] + risks, c3[-1::-1] + c2, '#F0F0F0')
+pylab.fill(risks[-1::-1] + risks, c4[-1::-1] + c3, '#D0D0D0')
+pylab.axis([0.0, 0.2, 0.0, 1.0])
+pylab.xlabel('standard deviation')
+pylab.ylabel('allocation')
+pylab.text(.15,.5,'x1')
+pylab.text(.10,.7,'x2')
+pylab.text(.05,.7,'x3')
+pylab.text(.01,.7,'x4')
+pylab.title('Optimal allocations (fig 4.12)')
+pylab.show()
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
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+
+<H1><A NAME="SECTION0010300000000000000000">
+8.3 Geometric Programming</A>
+</H1>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-147' xml:id='l2h-147' class="function">gp</tt></b>(</nobr></td>
+ <td><var>K, F, g </var><big>[</big><var>, G, h </var><big>[</big><var>, A, b</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a geometric program in convex form
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & f_0(x) = \mathop{\bf lse}(F_0x+g_0) \\
+\mbox{subject to} & f_i(x) = \mathop{\bf lse}(F_ix+g_i) \leq 0,\quad i=1,\ldots,m \\
+ & Gx \preceq h \\
+ & Ax=b
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="359" HEIGHT="83" BORDER="0"
+ SRC="img122.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & f_0(x) = \mathop{\bf lse...
+...,\quad i=1,\ldots,m \\
+& Gx \preceq h \\
+& Ax=b
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\mathop{\bf lse}(u) = \log \sum_k \exp(u_k), \qquad
+ F = \left[ \begin{array}{cccc}
+ F_0^T & F_1^T & \cdots & F_m^T \end{array}\right]^T, \qquad
+ g = \left[ \begin{array}{cccc}
+ g_0^T & g_1^T & \cdots & g_m^T \end{array}\right]^T.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="649" HEIGHT="45" BORDER="0"
+ SRC="img123.gif"
+ ALT="\begin{displaymath}
+\mathop{\bf lse}(u) = \log \sum_k \exp(u_k), \qquad
+F = \l...
+...}{cccc}
+g_0^T & g_1^T & \cdots & g_m^T \end{array}\right]^T.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<var>K</var> is a list of <var>m</var>+1 positive integers with
+<code><var>K</var>[<var>i</var>]</code>
+equal to the number of rows in <I>Fi</I>.
+<var>F</var> is a dense or sparse real matrix of size
+<code>(sum(<var>K</var>),<var>n</var>)</code>.
+<var>g</var> is a dense real matrix of size <code>(sum(<var>K</var>),1)</code>.
+<var>G</var> and <var>A</var> are dense or sparse real matrices.
+Their default values are sparse matrices with zero rows.
+<var>h</var> and <var>b</var> are dense real matrices with one column.
+Their default values are matrices of size (0,1).
+
+<P>
+<tt class="function">gp()</tt> returns a dictionary with keys
+<code>'status'</code>, <code>'x'</code>, <code>'snl'</code>, <code>'sl'</code>,
+<code>'y'</code>, <code>'znl'</code> and <code>'zl'</code>.
+The possible values of the <code>'status'</code> key are:
+<DL>
+<DT><STRONG><code>'optimal'</code></STRONG></DT>
+<DD>In this case the
+<code>'x'</code> entry is the primal optimal solution,
+the <code>'snl'</code> and <code>'sl'</code> entries are the corresponding slacks
+in the nonlinear and linear inequality constraints.
+The <code>'znl'</code>, <code>'zl'</code> and <code>'y'</code> entries are the optimal
+values of the dual variables associated with the nonlinear and linear
+inequality constraints and the linear equality constraints.
+These values approximately satisfy
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\nabla f_0(x) + \sum_{k=1}^m z_{\mathrm{nl},k}
+ \nabla f_k(x) + G^T z_\mathrm{l} + A^T y = 0, \qquad
+ f_k(x) + s_{\mathrm{nl},k} = 0, \quad k=1,\ldots,m, \qquad
+ Gx + s_\mathrm{l} = h, \qquad Ax=b
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="747" HEIGHT="53" BORDER="0"
+ SRC="img124.gif"
+ ALT="\begin{displaymath}
+\nabla f_0(x) + \sum_{k=1}^m z_{\mathrm{nl},k}
+\nabla f_k...
+...quad k=1,\ldots,m, \qquad
+Gx + s_\mathrm{l} = h, \qquad Ax=b
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+and
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+s_\mathrm{nl}\succeq 0, \qquad s_\mathrm{l}\succeq 0, \qquad
+z_\mathrm{nl} \succeq 0, \qquad z_\mathrm{l} \succeq 0, \qquad
+s_\mathrm{nl}^T z_\mathrm{nl} + s_\mathrm{l}^T z_\mathrm{l} = 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="453" HEIGHT="28" BORDER="0"
+ SRC="img125.gif"
+ ALT="\begin{displaymath}
+s_\mathrm{nl}\succeq 0, \qquad s_\mathrm{l}\succeq 0, \qquad...
+...\mathrm{nl}^T z_\mathrm{nl} + s_\mathrm{l}^T z_\mathrm{l} = 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'unknown'</code></STRONG></DT>
+<DD>This means that the algorithm reached
+the maximum number of iterations before a solution was found.
+The <code>'x'</code>, <code>'snl'</code>, <code>'sl'</code>, <code>'y'</code>, <code>'znl'</code>
+and <code>'zl'</code> entries are <code>None</code>.
+</DD>
+</DL>
+</dl>
+
+<P>
+As an example, we solve the small GP on page 8 of the paper
+<em class="citetitle"><a
+ href="http://www.stanford.edu/~boyd/gp_tutorial"
+ title="A Tutorial on Geometric Programming"
+ >A Tutorial on Geometric Programming</a></em>.
+The posynomial form of the problem is
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & w^{-1} h^{-1} d^{-1} \\
+ \mbox{subject to}
+ & (2/A_\mathrm{wall}) hw + (2/A_\mathrm{wall})hd \leq 1 \\
+ & (1/A_\mathrm{flr}) wd \leq 1 \\
+ & \alpha wh^{-1} \leq 1 \\
+ & (1/\beta) hw^{-1} \leq 1 \\
+ & \gamma wd^{-1} \leq 1 \\
+ & (1/\delta)dw^{-1} \leq 1
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="288" HEIGHT="140" BORDER="0"
+ SRC="img126.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & w^{-1} h^{-1} d^{-1} \...
+...mma wd^{-1} \leq 1 \\
+& (1/\delta)dw^{-1} \leq 1
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with variables <I>h</I>, <I>w</I>, <I>d</I>.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt.base import matrix, log, exp
+from cvxopt import solvers
+
+Aflr = 1000.0
+Awall = 100.0
+alpha = 0.5
+beta = 2.0
+gamma = 0.5
+delta = 2.0
+
+F = matrix( [[-1., 1., 1., 0., -1., 1., 0., 0.],
+ [-1., 1., 0., 1., 1., -1., 1., -1.],
+ [-1., 0., 1., 1., 0., 0., -1., 1.]])
+g = log( matrix( [1.0, 2/Awall, 2/Awall, 1/Aflr, alpha, 1/beta, gamma, 1/delta]) )
+K = [1, 2, 1, 1, 1, 1, 1]
+h, w, d = exp( solvers.gp(K, F, g)['x'] )
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="8.2 Quadratic Programming"
+ href="node47.html"><img src='previous.gif'
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+
+<H1><A NAME="SECTION0010600000000000000000">
+8.6 Exploiting Structure in LPs and SDPs</A>
+</H1>
+The solvers <tt class="function">lp()</tt> and <tt class="function">sdp()</tt> are interfaces to
+a common function <tt class="function">conelp()</tt>, which can also be called
+directly. When calling <tt class="function">conelp()</tt>, the user must provide
+functions for evaluating the constraint functions and for
+solving the linear equations (KKT equations) that are solved in
+each iteration of the algorithm.
+This is useful for LPs and SDPs that possess some interesting
+structure that makes it possible to solve the KKT equations fast.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-150' xml:id='l2h-150' class="function">conelp</tt></b>(</nobr></td>
+ <td><var>c, kktsolver</var><big>[</big><var>, Gl, hl</var><big>[</big><var>,
+Gs, hs</var><big>[</big><var>, A, b</var><big>[</big><var>, primalstart</var><big>[</big><var>, dualstart</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves the pair of primal and dual SDPs (<A href="s-sdpsolver.html#e-sdp">8.2</A>).
+The arguments <var>c</var>, <var>hl</var>, <var>hs</var>, <var>b</var>,
+<var>primalstart</var>, <var>dualstart</var> have the same meaning as in
+<tt class="function">sdp()</tt>.
+The arguments <var>kktsolver</var>, <var>Gl</var>, <var>Gs</var>, <var>A</var> are
+functions that must handle the following calling sequences.
+
+<P>
+
+<UL>
+<LI><tt class="function">kktsolver</tt>(<var>d</var>, <var>R</var>) with <var>d</var> a positive
+dense real matrix of size (<I>ml</I>,<I>1</I>), and
+<var>R</var> a list of <I>N</I> square dense real matrices
+<code><var>R</var>[k]</code> of order <I>m_k</I>, returns a function for
+solving the equation
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+A^T u_y + G_\mathrm{l}^T u_{z_\mathrm{l}} +
+ G_\mathrm{s}^T(u_{z_\mathrm{s}}) & = & b_x \\
+ A u_x & = & b_y \\
+G_\mathrm{l}u_x - \mbox{\bf diag}\,(d)^{-2} u_{z_\mathrm{l}} & = &
+ b_{z_\mathrm{l}} \\
+G_\mathrm{s}(u_x) - R^{-T} R^{-1} u_{z_\mathrm{s}} R^{-T} R^{-1}
+ & = & b_{z_\mathrm{s}}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="276" HEIGHT="100" BORDER="0"
+ SRC="img148.gif"
+ ALT="\begin{eqnarray*}
+A^T u_y + G_\mathrm{l}^T u_{z_\mathrm{l}} +
+G_\mathrm{s}^T(...
+...} R^{-1} u_{z_\mathrm{s}} R^{-T} R^{-1}
+& = & b_{z_\mathrm{s}}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+The function created by "<tt class="samp">f = kktsolver(d, R)</tt>" will be
+called as "<tt class="samp">f(bx, by, bzl, bzs)</tt>".
+On entry, <var>bx</var>, <var>by</var>, <var>bzl</var> and <var>bzs</var> contain the
+righthand side. On exit, they should contain the solution of the KKT
+system, with <I>uzl</I> and <I>uzs</I> scaled:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+b_x := u_x, \qquad
+ b_y := u_y, \qquad
+ b_{z_\mathrm{l}} := \mbox{\bf diag}\,(d)^{-1} u_{z_\mathrm{l}}, \qquad
+ b_{z_\mathrm{s}} := R^{-1} u_{z_\mathrm{s}} R^{-T}.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="494" HEIGHT="29" BORDER="0"
+ SRC="img149.gif"
+ ALT="\begin{displaymath}
+b_x := u_x, \qquad
+b_y := u_y, \qquad
+b_{z_\mathrm{l}} :=...
+...}, \qquad
+b_{z_\mathrm{s}} := R^{-1} u_{z_\mathrm{s}} R^{-T}.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</LI>
+<LI><tt class="function">Gl</tt>(<var>x</var>, <var>y</var><big>[</big>,
+<var>alpha</var>=1.0<big>[</big>, <var>beta</var>=0.0<big>[</big>,
+<var>trans</var>=<code>'N'</code><big>]</big><big>]</big><big>]</big>) evaluates the matrix-vector products
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha G_\mathrm{l}x + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha G_\mathrm{l}^T x + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="475" HEIGHT="28" BORDER="0"
+ SRC="img150.gif"
+ ALT="\begin{displaymath}
+y := \alpha G_\mathrm{l}x + \beta y \quad
+(\mathrm{trans} ...
+...thrm{l}^T x + \beta y \quad
+(\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</LI>
+<LI><tt class="function">Gs</tt>(<var>x</var>, <var>y</var><big>[</big>,
+<var>alpha</var>=1.0<big>[</big>, <var>beta</var>=0.0<big>[</big>,
+<var>trans</var>=<code>'N'</code><big>]</big><big>]</big><big>]</big>)
+evaluates the linear mappings
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha G_\mathrm{s}(x) + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha G_\mathrm{s}^T(x) + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="501" HEIGHT="28" BORDER="0"
+ SRC="img151.gif"
+ ALT="\begin{displaymath}
+y := \alpha G_\mathrm{s}(x) + \beta y \quad
+(\mathrm{trans...
+...hrm{s}^T(x) + \beta y \quad
+(\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</LI>
+<LI><tt class="function">A</tt>(<var>x</var>, <var>y</var><big>[</big>,
+<var>alpha</var>=1.0<big>[</big>, <var>beta</var>=0.0<big>[</big>,
+<var>trans</var>=<code>'N'</code><big>]</big><big>]</big><big>]</big>)
+evaluates the matrix vector products
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha A^Tx + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="469" HEIGHT="28" BORDER="0"
+ SRC="img152.gif"
+ ALT="\begin{displaymath}
+y := \alpha Ax + \beta y \quad
+(\mathrm{trans} = \mathrm{'...
+...\alpha A^Tx + \beta y \quad
+(\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+</LI>
+</UL>
+</dl>
+
+<P>
+<DL>
+<DT><STRONG>Example: 1-norm approximation</STRONG></DT>
+<DD><P>
+The optimization problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|Pu-q\|_1
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="147" HEIGHT="30" BORDER="0"
+ SRC="img153.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert Pu-q\Vert _1
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+can be formulated as an LP
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & {\bf 1}^T v \\
+ \mbox{subject to} & -v \preceq Pu - q \preceq v.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="201" HEIGHT="45" BORDER="0"
+ SRC="img154.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & {\bf 1}^T v \\
+\mbox{subject to} & -v \preceq Pu - q \preceq v.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+By exploiting the structure in the inequalities, the cost of
+an iteration of an interior-point method can be reduced
+to the cost of least-squares problem of the same dimensions.
+(See section 11.8.2 in the book
+<em class="citetitle"><a
+ href="http://www.ee.ucla.edu/~vandenbe/cvxbook"
+ title="Convex Optimization"
+ >Convex Optimization</a></em>.)
+The code belows taks advantage of this fact.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt import base, blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, mul, div
+
+def l1(P, q):
+ """
+
+ Returns the solution u, w of the l1 approximation problem
+
+ (primal) minimize ||P*u - q||_1
+
+ (dual) maximize q'*w
+ subject to P'*w = 0
+ ||w||_infty <= 1.
+ """
+
+ m, n = P.size
+
+ # Solve equivalent LP
+ #
+ # minimize [0; 1]' * [u; v]
+ # subject to [P, -I; -P, -I] * [u; v] <= [q; -q]
+ #
+ # maximize -[q; -q]' * z
+ # subject to [P', -P']*z = 0
+ # [-I, -I]*z + 1 = 0
+ # z >= 0
+
+ c = matrix(n*[0.0] + m*[1.0])
+ h = matrix([q, -q])
+
+ def Fi(x, y, alpha=1.0, beta=0.0, trans='N'):
+ if trans=='N':
+ # y := alpha * [P, -I; -P, -I] * x + beta*y
+ u = P*x[:n]
+ y[:m] = alpha * ( u - x[n:]) + beta*y[:m]
+ y[m:] = alpha * (-u - x[n:]) + beta*y[m:]
+
+ else:
+ # y := alpha * [P', -P'; -I, -I] * x + beta*y
+ y[:n] = alpha * P.T * (x[:m] - x[m:]) + beta*y[:n]
+ y[n:] = -alpha * (x[:m] + x[m:]) + beta*y[n:]
+
+
+ def kktsolver(d, R):
+
+ # Returns a function f(x,y,zl,zs) that solves
+ #
+ # [ 0 0 P' -P' ] [ x[:n] ] [ bx[:n] ]
+ # [ 0 0 -I -I ] [ x[n:] ] [ bx[n:] ]
+ # [ P -I -D1^{-1} 0 ] [ zl[:m]] = [ bzl[:m] ]
+ # [-P -I 0 -D2^{-1} ] [ zl[m:]] [ bzl[m:] ]
+ #
+ # where D1 = diag(d[:m])^2, D2 = diag(d[m:])^2.
+ #
+ # On entry bx, bzl are stored in x, zl.
+ # On exit x, zl contain the solution, with zl scaled: zl./d is
+ # returned instead of zl.
+
+ # Factor A = 4*P'*D*P where D = d1.*d2 ./(d1+d2) and
+ # d1 = d[:m].^2, d2 = d[m:].^2.
+
+ d1, d2 = d[:m]**2, d[m:]**2
+ D = div( mul(d1,d2), d1+d2 )
+ A = P.T * spmatrix(4*D, range(m), range(m)) * P
+ lapack.potrf(A)
+
+ def f(x, y, zl, zs):
+
+ # Solve for x[:n]:
+ #
+ # A*x[:n] = bx[:n] + P' * ( ((D1-D2)*(D1+D2)^{-1})*bx[n:]
+ # + (2*D1*D2*(D1+D2)^{-1}) * (bzl[:m] - bzl[m:]) ).
+ x[:n] += P.T * ( mul(div(d1-d2, d1+d2), x[n:]) + mul(2*D, zl[:m]-zl[m:]) )
+ lapack.potrs(A, x)
+
+ # x[n:] := (D1+D2)^{-1} * (bx[n:] - D1*bzl[:m] - D2*bzl[m:] + (D1-D2)*P*x[:n])
+ u = P*x[:n]
+ x[n:] = div(x[n:] - mul(d1, zl[:m]) - mul(d2, zl[m:]) + mul(d1-d2, u), d1+d2)
+
+ # z[:m] := d1[:m] .* ( P*x[:n] - x[n:] - bzl[:m])
+ # z[m:] := d2[m:] .* (-P*x[:n] - x[n:] - bzl[m:])
+ zl[:m] = mul(d[:m], u-x[n:]-zl[:m])
+ zl[m:] = mul(d[m:], -u-x[n:]-zl[m:])
+
+ return f
+
+ sol = solvers.conelp(c, kktsolver, Gl=Fi, hl=h)
+ return sol['x'][:n], sol['zl'][m:] - sol['zl'][:m]
+</pre></div>
+
+<P>
+</DD>
+<DT><STRONG>Example: SDP with diagonal linear term</STRONG></DT>
+<DD><P>
+The SDP
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & {\bf 1}^T x \\
+ \mbox{subject to} & W + \mbox{\bf diag}\,(x) \succeq 0
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="195" HEIGHT="45" BORDER="0"
+ SRC="img155.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & {\bf 1}^T x \\
+\mbox{subject to} & W + \mbox{\bf diag}\,(x) \succeq 0
+\end{array}
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+can be solved efficiently by exploiting properties of the diag operator.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt import base, blas, lapack, solvers
+from cvxopt.base import matrix
+
+def mcsdp(w):
+ """
+ Returns solution x, z to
+
+ (primal) minimize sum(x)
+ subject to w + diag(x) >= 0
+
+ (dual) maximize -tr(w*z)
+ subject to diag(z) = 1
+ z >= 0.
+ """
+
+ n = w.size[0]
+
+ def Fs(x, y, alpha=1.0, beta=0.0, trans='N'):
+ """
+ y := alpha*(-diag(x)) + beta*y.
+ """
+ if trans=='N':
+ # x is a vector; y[0] is a matrix.
+ y[0] *= beta
+ y[0][::n+1] -= alpha * x
+ else:
+ # x[0] is a matrix; y is a vector.
+ y *= beta
+ y -= alpha * x[::n+1]
+
+
+ def cngrnc(r, x, alpha=1.0):
+ """
+ Congruence transformation
+
+ x := alpha * r'*x*r.
+
+ r and x are square 'd' matrices.
+ """
+
+ # Scale diagonal of x by 1/2.
+ x[::n+1] *= 0.5
+
+ # a := tril(x)*r
+ a = +r
+ blas.trmm(x, a, side='L')
+
+ # x := alpha*(a*r' + r*a')
+ blas.syr2k(r, a, x, trans='T', alpha=alpha)
+
+
+ def kktsolver(d, r):
+
+ # t = r*r' as a nonsymmetric matrix.
+ t = matrix(0.0, (n,n))
+ blas.gemm(r[0], r[0], t, transB='T')
+
+ # Cholesky factorization of tsq = t.*t.
+ tsq = t**2
+ lapack.potrf(tsq)
+
+ def f(x, y, zl, zs):
+ """
+ Solve
+ -diag(zs) = bx
+ -diag(x) - inv(r*r')*zs*inv(r*r') = bs.
+
+ On entry, x and zs contain bx and bs.
+ On exit, they contain the solution, with zs scaled
+ (inv(r)'*zs*inv(r) is returned instead of zs).
+
+ We solve
+
+ ((r*r') .* (r*r')) * x = bx - diag(t*bs*t)
+
+ and take zs = -r' * (diag(x) + bs) * r.
+ """
+
+ # tbst := t * zs * t = t * bs * t
+ tbst = +zs[0]
+ cngrnc(t, tbst)
+
+ # x := x - diag(tbst) = bx - diag(r*r' * bs * r*r')
+ x -= tbst[::n+1]
+
+ # x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
+ lapack.potrs(tsq, x)
+
+ # zs := zs + diag(x) = bs + diag(x)
+ zs[0][::n+1] += x
+
+ # zs := -r' * zs * r = -r' * (diag(x) + bs) * r
+ cngrnc(r[0], zs[0], alpha=-1.0)
+
+ return f
+
+ c = matrix(1.0, (n,1))
+ sol = solvers.conelp(c, kktsolver, Gs=Fs, hs=[w])
+ return sol['x'], sol['zs'][0]
+</pre></div>
+</DD>
+</DL>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="8.5 Nonlinear Convex Programming"
+ href="e-nlcp.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="8. Optimization Routines (cvxopt.solvers)"
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+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="8.7 Exploiting Structure in"
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+
+<H1><A NAME="SECTION0010700000000000000000">
+8.7 Exploiting Structure in Nonlinear Convex Programs</A>
+</H1>
+The solvers <tt class="function">gp()</tt>, <tt class="function">gp()</tt> and <tt class="function">cp()</tt> are
+interfaces to <tt class="function">nlcp()</tt>, which can also be called directly
+but requires user-provided functions for evaluating the constraint
+and for solving the KKT equations.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-151' xml:id='l2h-151' class="function">nlcp</tt></b>(</nobr></td>
+ <td><var>kktsolver, F</var><big>[</big><var>, G, h</var><big>[</big><var>, A, b</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves the nonlinear convex optimization problem (<A href="e-nlcp.html#e-nlcp">8.3</A>).
+
+<P>
+The meaning of the arguments <var>h</var> and <var>b</var> is the same
+as for <tt class="function">cp()</tt>.
+The arguments <var>kktsolver</var>, <var>F</var>, <var>G</var> and <var>A</var> are
+functions that must handle the following calling sequences.
+
+<UL>
+<LI><tt class="function">kktsolver</tt>(<var>x</var>, <var>z</var>, <var>dnl</var>, <var>dl</var>),
+returns a function for solving KKT systems
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+\sum_{k=0}^m z_k \nabla^2 f_k(x)u_x + A^T u_y +
+ D \tilde f(x)^T u_{z_\mathrm{nl}} +
+ G_\mathrm{l}^T u_{z_\mathrm{l}} & = & b_x \\
+ A x & = & b_y \\
+ D\tilde f(x) x - \mbox{\bf diag}\,(d_\mathrm{nl})^{-2} z_\mathrm{nl} & = &
+ b_{z_\mathrm{nl}} \\
+ G_\mathrm{l}x - \mbox{\bf diag}\,(d_\mathrm{l})^{-2} z_\mathrm{l} & = &
+ b_{z_\mathrm{l}}
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="402" HEIGHT="125" BORDER="0"
+ SRC="img156.gif"
+ ALT="\begin{eqnarray*}
+\sum_{k=0}^m z_k \nabla^2 f_k(x)u_x + A^T u_y +
+D \tilde f(...
+...diag}\,(d_\mathrm{l})^{-2} z_\mathrm{l} & = &
+b_{z_\mathrm{l}}
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+where <!-- MATH
+ $\tilde f = (f_1, \ldots, f_m)$
+ -->
+<SPAN CLASS="MATH"><IMG
+ WIDTH="117" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ SRC="img142.gif"
+ ALT="$\tilde f = (f_1,\ldots, f_m)$"></SPAN>.
+The arguments are single-column real dense matrices. <var>x</var> is in the
+domain of the objective and constraint functions. <var>z</var>, <var>dnl</var>
+and <var>dl</var> are positive vectors.
+
+<P>
+The function <var>f</var> created by
+"<tt class="samp">f = kktsolver(bx, by, bznl, bzl)</tt>" will be
+called as "<tt class="samp">f(bx, by, bznl, bzl)</tt>".
+On entry, the arguments contain the righthand sides. On exit, they
+should be replaced by the solution.
+
+<P>
+</LI>
+<LI>Called with no arguments, <code><tt class="function">F</tt>()</code> returns a tuple
+(<var>m</var>, <var>x0</var>), where <var>m</var> is the number of nonlinear
+inequality constraints) and <var>x0</var> is a point in the domain
+of <I>f</I>).
+
+<P>
+Called with one argument, <tt class="function">F(<var>x</var>)</tt> returns a tuple
+(<var>f</var>, <var>Df</var>). <var>f</var> is a dense matrix of size (<I>m</I>+1,1)
+with the function values of the objective function and the
+nonlinear constraint functions at <var>x</var>.
+<var>Df</var> is a dense or sparse real matrix of size (<var>m</var>+1,<var>n</var>)
+with <code><var>Df</var>[<var>k</var>,:]</code> equal to the transpose of the gradient
+of <I>f_k</I> at <I>x</I>.
+Alternatively, <var>Df</var> can be given as a function. In that case
+the function call <tt class="function">Df</tt>(<var>u</var>,<var>v</var>),
+where <var>u</var> and <var>v</var> are dense column vectors, should evaluate
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+v := \sum_{k=0}^m u_k \nabla f_k(x) + v.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="157" HEIGHT="53" BORDER="0"
+ SRC="img157.gif"
+ ALT="\begin{displaymath}
+v := \sum_{k=0}^m u_k \nabla f_k(x) + v.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+If <var>x</var> is not in the domain of <I>f</I>, <tt class="function">F</tt>(<var>x</var>)
+returns <code>None</code> or (<code>None</code>,<code>None</code>).
+
+<P>
+</LI>
+<LI><tt class="function">G</tt>(<var>x</var>, <var>y</var><big>[</big>,
+<var>alpha</var>=1.0<big>[</big>, <var>beta</var>=0.0<big>[</big>,
+<var>trans</var>=<code>'N'</code><big>]</big><big>]</big><big>]</big>) evaluates the matrix-vector products
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha G x + \beta y \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha G^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="471" HEIGHT="28" BORDER="0"
+ SRC="img158.gif"
+ ALT="\begin{displaymath}
+y := \alpha G x + \beta y \quad (\mathrm{trans} = \mathrm{'N...
+... \alpha G^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+Alternatively, <var>G</var> can be specified as a real sparse or dense
+matrix.
+
+<P>
+</LI>
+<LI><tt class="function">A</tt>(<var>x</var>, <var>y</var><big>[</big>,
+<var>alpha</var>=1.0<big>[</big>, <var>beta</var>=0.0<big>[</big>,
+<var>trans</var>=<code>'N'</code><big>]</big><big>]</big><big>]</big>) evaluates the matrix vector products
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha A^Tx + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="469" HEIGHT="28" BORDER="0"
+ SRC="img152.gif"
+ ALT="\begin{displaymath}
+y := \alpha Ax + \beta y \quad
+(\mathrm{trans} = \mathrm{'...
+...\alpha A^Tx + \beta y \quad
+(\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+Alternatively, <var>A</var> can be specified as a real sparse or dense
+matrix.
+</LI>
+</UL>
+</dl>
+
+<P>
+As an example, we consider the 1-norm regularized least-squares problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \|Ax - y\|_2^2 + \|x\|_1
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="199" HEIGHT="30" BORDER="0"
+ SRC="img159.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert Ax - y\Vert _2^2 + \Vert x\Vert _1
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with variable <I>x</I>. The problem is equivalent to the quadratic
+program
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|Ax - y\|_2^2 + {\bf 1}^T u \\
+ \mbox{subject to} & -u \preceq x \preceq u
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="197" HEIGHT="45" BORDER="0"
+ SRC="img160.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert Ax - y\Vert _2^2...
+... u \\
+\mbox{subject to} & -u \preceq x \preceq u
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with variables <I>x</I> and <I>u</I>. The implementation below is
+efficient when <I>A</I> has many more columns than rows.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt.base import matrix, spmatrix, mul, div
+from cvxopt import blas, lapack, solvers
+
+m, n = A.size
+def F(x=None):
+ """
+ Function and gradient evaluation of
+
+ f = || A*x[:n] - y ||_2^2 + sum(x[n:])
+ """
+
+ nvars = 2*n
+ if x is None: return 0, matrix(0.0, (nvars,1))
+ r = A*x[:n] - y
+ f = blas.nrm2(r)**2 + sum(x[n:])
+ gradf = matrix(1.0, (1,2*n))
+ blas.gemv(A, r, gradf, alpha=2.0, trans='T')
+ return f, +gradf
+
+
+def G(u, v, alpha=1.0, beta=0.0, trans='N'):
+ """
+ v := alpha*[I, -I; -I, -I] * u + beta * v (trans = 'N' or 'T')
+ """
+
+ v *= beta
+ v[:n] += alpha*(u[:n] - u[n:])
+ v[n:] += alpha*(-u[:n] - u[n:])
+
+h = matrix(0.0, (2*n,1))
+
+
+# Customized solver for the KKT system
+#
+# [ 2.0*z[0]*A'*A 0 I -I ] [x[:n] ] [bx[:n] ]
+# [ 0 0 -I -I ] [x[n:] ] = [bx[n:] ].
+# [ I -I -D1^-1 0 ] [zl[:n]] [bzl[:n]]
+# [ -I -I 0 -D2^-1 ] [zl[n:]] [bzl[n:]]
+#
+#
+# We first eliminate zl and x[n:]:
+#
+# ( 2*z[0]*A'*A + 4*D1*D2*(D1+D2)^-1 ) * x[:n] = bx[:n] - (D2-D1)*(D1+D2)^-1 * bx[n:]
+# + D1 * ( I + (D2-D1)*(D1+D2)^-1 ) * bzl[:n] - D2 * ( I - (D2-D1)*(D1+D2)^-1 ) * bzl[n:]
+#
+# x[n:] = (D1+D2)^-1 * ( bx[n:] - D1*bzl[:n] - D2*bzl[n:] ) - (D2-D1)*(D1+D2)^-1 * x[:n]
+# zl[:n] = D1 * ( x[:n] - x[n:] - bzl[:n] )
+# zl[n:] = D2 * (-x[:n] - x[n:] - bzl[n:] ).
+#
+# The first equation has the form
+#
+# (z[0]*A'*A + D)*x[:n] = rhs
+#
+# and is equivalent to
+#
+# [ D A' ] [ x:n] ] = [ rhs ]
+# [ A -1/z[0]*I ] [ v ] [ 0 ].
+#
+# It can be solved as
+#
+# ( A*D^-1*A' + 1/z[0]*I ) * v = A * D^-1 * rhs
+# x[:n] = D^-1 * ( rhs - A'*v ).
+
+S = matrix(0.0, (m,m))
+Asc = matrix(0.0, (m,n))
+v = matrix(0.0, (m,1))
+def kktsolver(x, z, dnl, dl):
+
+ # Factor
+ #
+ # S = A*D^-1*A' + 1/z[0]*I
+ #
+ # where D = 2*D1*D2*(D1+D2)^-1, D1 = dl[:n]**2, D2 = dl[n:]**2.
+
+ d1, d2 = dl[:n]**2, dl[n:]**2 # d1 = diag(D1), d2 = diag(D2)
+ # ds is square root of diagonal of D
+ ds = sqrt(2.0) * div( mul(dl[:n], dl[n:]), sqrt(d1+d2) )
+ d3 = div(d2 - d1, d1 + d2)
+
+ # Asc = A*diag(d)^-1/2
+ Asc = A * spmatrix( ds**-1, range(n), range(n))
+
+ # S = 1/z[0]*I + A * D^-1 * A'
+ blas.syrk(Asc, S)
+ S[::m+1] += 1.0 / z[0]
+ lapack.potrf(S)
+
+ def g(x, y, znl, zl):
+
+ x[:n] = 0.5 * ( x[:n] - mul(d3, x[n:]) + mul(d1, zl[:n] + mul(d3, zl[:n])) - mul(d2, zl[n:] - mul(d3, zl[n:])) )
+ x[:n] = div( x[:n], ds)
+
+ # Solve
+ #
+ # S * v = 0.5 * A * D^-1 * ( bx[:n] - (D2-D1)*(D1+D2)^-1 * bx[n:]
+ # + D1 * ( I + (D2-D1)*(D1+D2)^-1 ) * bzl[:n] - D2 * ( I - (D2-D1)*(D1+D2)^-1 ) * bzl[n:] )
+
+ blas.gemv(Asc, x, v)
+ lapack.potrs(S, v)
+
+ # x[:n] = D^-1 * ( rhs - A'*v ).
+ blas.gemv(Asc, v, x, alpha=-1.0, beta=1.0, trans='T')
+ x[:n] = div(x[:n], ds)
+
+ # x[n:] = (D1+D2)^-1 * ( bx[n:] - D1*bzl[:n] - D2*bzl[n:] ) - (D2-D1)*(D1+D2)^-1 * x[:n]
+ x[n:] = div( x[n:] - mul(d1, zl[:n]) - mul(d2, zl[n:]), d1+d2 ) - mul( d3, x[:n] )
+
+ # zl[:n] = D1 * ( x[:n] - x[n:] - bzl[:n] )
+ # zl[n:] = D2 * ( -x[:n] - x[n:] - bzl[n:] ).
+ zl[:n] = mul( d1, x[:n] - x[n:] - zl[:n] )
+ zl[n:] = mul( d2, -x[:n] - x[n:] - zl[n:] )
+
+ return g
+
+x = solvers.nlcp(kktsolver, F, G, h)['x'][:n]
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+</head>
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0011000000000000000000"></A>
+<A NAME="chap:modeling"></A>
+<BR>
+9. Modeling (<tt class="module">cvxopt.modeling</tt>)
+</H1>
+The module <tt class="module">cvxopt.modeling</tt> can be used to specify and solve
+optimization problems with convex piecewise-linear objective and
+constraint functions.
+
+<P>
+To specify an optimization problem one first defines
+the optimization variables (see section <A href="s-variables.html#s-variables">9.1</A>),
+and then defines the objective and constraint functions
+using linear operations (vector addition and subtraction,
+matrix-vector multiplication, indexing and slicing)
+and nested evaluations of <tt class="function">max()</tt>, <tt class="function">min()</tt>,
+<tt class="function">abs()</tt> and <tt class="function">sum()</tt> (see section <A href="s-functions.html#s-functions">9.2</A>).
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="s-variables.html">9.1 Variables</a>
+<LI><A href="s-functions.html">9.2 Functions</a>
+<LI><A href="node58.html">9.3 Constraints</a>
+<LI><A href="s-lp.html">9.4 Optimization Problems</a>
+<LI><A href="node60.html">9.5 Examples</a>
+</ul>
+<!--End of Table of Child-Links-->
+</div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="8.9 Algorithm Parameters"
+ href="s-parameters.html"><img src='previous.gif'
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+</div>
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+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<link rel="parent" href="node55.html" />
+<link rel="next" href="s-lp.html" />
+<meta name='aesop' content='information' />
+<title>9.3 Constraints</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="9.2 Functions"
+ href="s-functions.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
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+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0011300000000000000000">
+9.3 Constraints</A>
+</H1>
+Linear equality and inequality constraints of the form
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+f(x_1,\ldots,x_n) = 0, \qquad f(x_1,\ldots,x_n) \preceq 0,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="283" HEIGHT="28" BORDER="0"
+ SRC="img174.gif"
+ ALT="\begin{displaymath}
+f(x_1,\ldots,x_n) = 0, \qquad f(x_1,\ldots,x_n) \preceq 0,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <SPAN CLASS="MATH"><IMG
+ WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="img175.gif"
+ ALT="$f$"></SPAN> is a convex function, are represented by constraint
+objects. Equality constraints are created by expressions of the form
+<BLOCKQUOTE>
+<code><var>f1</var> == <var>f2</var></code>.
+
+</BLOCKQUOTE>
+Here <var>f1</var> and <var>f2</var> can be any objects for which the
+difference <code><var>f1</var>-<var>f2</var></code> yields an affine function.
+Inequality constraints are created by expressions of the form
+<BLOCKQUOTE>
+<code><var>f1</var> <= <var>f2</var></code>, <code><var>f2</var> >= <var>f1</var></code>,
+
+</BLOCKQUOTE>
+where <var>f1</var> and <var>f2</var> can be any objects for which the difference
+<code><var>f1</var>-<var>f2</var></code> yields a convex piecewise-linear function.
+The comparison operators first convert the expressions to
+<code><var>f1</var>-<var>f2</var> == 0</code>, resp. <code><var>f1</var>-<var>f2</var> <= 0</code>,
+and then return a new constraint object with constraint
+function
+<code><var>f1</var>-<var>f2</var></code>.
+
+<P>
+In the following example we create three constraints
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+0 \preceq x \preceq {\bf 1}, \qquad {\bf 1}^T x = 2,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="168" HEIGHT="27" BORDER="0"
+ SRC="img176.gif"
+ ALT="\begin{displaymath}
+0 \preceq x \preceq {\bf 1}, \qquad {\bf 1}^T x = 2,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+for a variable of length 5.
+<div class="verbatim"><pre>
+>>> x = variable(5,'x')
+>>> c1 = (x <= 1)
+>>> c2 = (x >= 0)
+>>> c3 = (sum(x) == 2)
+</pre></div>
+
+<P>
+The built-in fucntion <tt class="function">len()</tt> returns the dimension of the
+constraint function.
+
+<P>
+Constraints have four public attributes.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-159' xml:id='l2h-159' class="method">type</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns <code>'='</code> if the constraint is an equality constraint,
+and <code>'<'</code> if the constraint is an inequality constraint.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-160' xml:id='l2h-160' class="method">value</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns the value of the constraint function.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-161' xml:id='l2h-161' class="member">multiplier</tt></b></dt>
+<dd>
+For a constraint <var>c</var>, <var>c</var>.<tt class="member">multiplier</tt> is a
+variable object of dimension <code>len(<var>c</var>)</code>.
+It is used to represent the Lagrange multiplier or dual variable
+associated with the constraint.
+Its value is initialized as <code>None</code>, and can be modified
+by making an assignment to <var>c</var>.<tt class="member">multiplier</tt>.<tt class="member">value</tt>.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-162' xml:id='l2h-162' class="member">name</tt></b></dt>
+<dd>
+The name of the constraint. Changing the name of a constraint
+also changes the name of the multiplier of <var>c</var>.
+For example, the command <code><var>c</var>.<tt class="member">name</tt> = 'newname'</code> also
+changes
+<var>c</var>.<tt class="member">multiplier</tt>.<tt class="member">name</tt> to <code>'newname_mul'</code>.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="9.2 Functions"
+ href="s-functions.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="9. Modeling (cvxopt.modeling)"
+ href="node55.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="9.4 Optimization Problems"
+ href="s-lp.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
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+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
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diff --git a/doc/cvxopt/node6.html b/doc/cvxopt/node6.html
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@@ -0,0 +1,200 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
+<link rel="next" href="s-arithmetic.html" />
+<link rel="prev" href="s-creating-matrices.html" />
+<link rel="parent" href="node4.html" />
+<link rel="next" href="s-arithmetic.html" />
+<meta name='aesop' content='information' />
+<title>2.2 Attributes and Methods</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="2.1 Creating Matrices"
+ href="s-creating-matrices.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="2. Dense Matrices (cvxopt.base)"
+ href="node4.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="2.3 Arithmetic Operations"
+ href="s-arithmetic.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="s-creating-matrices.html">2.1 Creating Matrices</A>
+<b class="navlabel">Up:</b>
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="s-arithmetic.html">2.3 Arithmetic Operations</A>
+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION004200000000000000000">
+2.2 Attributes and Methods</A>
+</H1>
+A <tt class="class">matrix</tt> has the following attributes.
+
+<P>
+<dl><dt><b><tt id='l2h-2' xml:id='l2h-2' class="member">size</tt></b></dt>
+<dd>
+A tuple with the dimensions of the matrix. This is a read-only
+attribute; operations that change the size of a matrix are not
+permitted.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-3' xml:id='l2h-3' class="member">typecode</tt></b></dt>
+<dd>
+A <tt class="ctype">char</tt>, either <code>'i'</code>, <code>'d'</code>, or <code>'z'</code>, for integer, real
+and complex matrices, respectively. A read-only attribute.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-4' xml:id='l2h-4' class="method">trans</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns the transpose of the matrix as a new matrix.
+One can also use <code>A.T</code> instead of <code>A.trans()</code>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-5' xml:id='l2h-5' class="method">ctrans</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns the conjugate transpose of the matrix as a new matrix.
+One can also use <code>A.H</code> instead of <code>A.ctrans()</code>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-6' xml:id='l2h-6' class="method">real</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+For complex matrices, returns the real part as a real matrix.
+For integer and real matrices, returns a copy of the matrix.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-7' xml:id='l2h-7' class="method">imag</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+For complex matrices, returns the imaginary part as a real matrix.
+For integer and real matrices, returns an integer or real zero matrix.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-8' xml:id='l2h-8' class="member">__array_struct__</tt></b></dt>
+<dd>
+A PyCObject implementing the NumPy array interface
+(see section <A href="s-array-interface.html#s-array-interface">2.8</A> for details).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-9' xml:id='l2h-9' class="method">tofile</tt></b>(</nobr></td>
+ <td><var>f</var>)</td></tr></table></dt>
+<dd>
+Writes the elements of the matrix in column-major order to a binary
+file <var>f</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-10' xml:id='l2h-10' class="method">fromfile</tt></b>(</nobr></td>
+ <td><var>f</var>)</td></tr></table></dt>
+<dd>
+Reads the contents of a binary file <var>f</var> into the matrix object.
+</dl>
+
+<P>
+The last two methods are illustrated in the following example.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> A = matrix([[1.,2.,3.], [4.,5.,6.]])
+>>> print A
+ 1.0000e+00 4.0000e+00
+ 2.0000e+00 5.0000e+00
+ 3.0000e+00 6.0000e+00
+>>> f = open('mat.bin','w')
+>>> A.tofile(f)
+>>> f.close()
+>>> B = matrix(0.0, (2,3))
+>>> f = open('mat.bin','r')
+>>> B.fromfile(f)
+>>> f.close()
+>>> print B
+ 1.0000e+00 3.0000e+00 5.0000e+00
+ 2.0000e+00 4.0000e+00 6.0000e+00
+</pre></div>
+
+<P>
+Matrices can also be written to or read from files using the
+<tt class="function">dump()</tt> and <tt class="function">load()</tt> functions in the
+<tt class="module">pickle</tt> module.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="2.1 Creating Matrices"
+ href="s-creating-matrices.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="2. Dense Matrices (cvxopt.base)"
+ href="node4.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="2.3 Arithmetic Operations"
+ href="s-arithmetic.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+ href="contents.html"><img src='contents.gif'
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+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="s-creating-matrices.html">2.1 Creating Matrices</A>
+<b class="navlabel">Up:</b>
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+<a class="sectref" rel="next" href="s-arithmetic.html">2.3 Arithmetic Operations</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
+
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+</HTML>
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+
+<H1><A NAME="SECTION0011500000000000000000">
+9.5 Examples</A>
+</H1>
+
+<P>
+<DL>
+<DT><STRONG>Norm and Penalty Approximation</STRONG></DT>
+<DD><P>
+In the first example we solve the norm approximation problems
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \|Ax - b\|_\infty,
+ \end{array} \qquad
+ \begin{array}{ll}
+ \mbox{minimize} & \|Ax - b\|_1
+ \end{array},
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="364" HEIGHT="30" BORDER="0"
+ SRC="img178.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert Ax - b\Vert _\i...
+...ay}{ll}
+\mbox{minimize} & \Vert Ax - b\Vert _1
+\end{array},
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+and the penalty approximation problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & \sum_k \phi((Ax-b)_k),
+ \end{array} \qquad
+ \phi(u) = \left\{\begin{array}{ll}
+ 0 & |u| \leq 3/4 \\
+ |u|-3/4 & 3/4 \leq |u| \leq 3/2 \\
+ 2|u|-9/4 & |u| \geq 3/2.\end{array}\right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="503" HEIGHT="64" BORDER="0"
+ SRC="img179.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \sum_k \phi((Ax-b)_k)...
+...
+2\vert u\vert-9/4 & \vert u\vert \geq 3/2.\end{array}\right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+We use randomly generated data.
+
+<P>
+The code uses the <a class="ulink" href="http://matplotlib.sourceforge.net"
+ >Matplotlib</a>
+package for plotting the histograms of the residual vectors for the
+two solutions. It generates the figure shown below.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt.random import normal
+from cvxopt.modeling import variable, op, max, sum
+import pylab
+
+m, n = 500, 100
+A = normal(m,n)
+b = normal(m)
+
+x1 = variable(n)
+op(max(abs(A*x1-b))).solve()
+
+x2 = variable(n)
+op(sum(abs(A*x2-b))).solve()
+
+x3 = variable(n)
+op(sum(max(0, abs(A*x3-b)-0.75, 2*abs(A*x3-b)-2.25))).solve()
+
+pylab.subplot(311)
+pylab.hist(A*x1.value-b, m/5)
+pylab.subplot(312)
+pylab.hist(A*x2.value-b, m/5)
+pylab.subplot(313)
+pylab.hist(A*x3.value-b, m/5)
+pylab.show()
+</pre></div>
+
+<P>
+<DIV ALIGN="CENTER">
+<IMG
+ WIDTH="556" HEIGHT="418" ALIGN="BOTTOM" BORDER="0"
+ SRC="img180.gif"
+ ALT="\includegraphics[width=\linewidth]{figures/normappr.eps}">
+
+</DIV>
+
+<P>
+Equivalently, we can formulate and solve the problems as LPs.
+<div class="verbatim"><pre>
+t = variable()
+x1 = variable(n)
+op(t, [-t <= A*x1-b, A*x1-b<=t]).solve()
+
+u = variable(m)
+x2 = variable(n)
+op(sum(u), [-u <= A*x2+b, A*x2+b <= u]).solve()
+
+v = variable(m)
+x3 = variable(n)
+op(sum(v), [v >= 0, v >= A*x3+b-0.75, v >= -(A*x3+b)-0.75, v >= 2*(A*x3-b)-2.25, v >= -2*(A*x3-b)-2.25]).solve()
+</pre></div>
+
+<P>
+</DD>
+<DT><STRONG>Robust Linear Programming</STRONG></DT>
+<DD>The robust LP
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & c^T x \\
+ \mbox{subject to} & \sup_{\|v\|_\infty \leq 1}
+ (a_i+v)^T x \leq b_i, \qquad i=1,\ldots,m
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="379" HEIGHT="46" BORDER="0"
+ SRC="img181.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & c^T x \\
+\mbox{subje...
+...leq 1}
+(a_i+v)^T x \leq b_i, \qquad i=1,\ldots,m
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+is equivalent to the problem
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & c^Tx \\
+ \mbox{subject to} & a_i^Tx + \|x\|_1 \leq b_i, \qquad i=1,\ldots,m.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="315" HEIGHT="45" BORDER="0"
+ SRC="img182.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & c^Tx \\
+\mbox{subjec...
+...x + \Vert x\Vert _1 \leq b_i, \qquad i=1,\ldots,m.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The following code computes the solution and the solution of
+the equivalent LP
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & c^Tx \\
+ \mbox{subject to} & a_i^Tx + {\bf 1}^Ty \leq b_i, \qquad i=1,\ldots,m \\
+& -y \preceq x \preceq y
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="308" HEIGHT="64" BORDER="0"
+ SRC="img183.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & c^Tx \\
+\mbox{subjec...
+...i, \qquad i=1,\ldots,m \\
+& -y \preceq x \preceq y
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+for randomly generated data.
+
+<P>
+<div class="verbatim"><pre>
+from cvxopt.random import normal, uniform
+from cvxopt.modeling import variable, dot, op, sum
+from cvxopt.blas import nrm2
+
+m, n = 500, 100
+A = normal(m,n)
+b = uniform(m)
+c = normal(n)
+
+x = variable(n)
+op(dot(c,x), A*x+sum(abs(x)) <= b).solve()
+
+x2 = variable(n)
+y = variable(n)
+op(dot(c,x2), [A*x2+sum(y) <= b, -y <= x2, x2 <= y]).solve()
+</pre></div>
+
+<P>
+</DD>
+<DT><STRONG>1-Norm Support Vector Classifier</STRONG></DT>
+<DD><P>
+The following problem arises in classification:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \|x\|_1 + {\bf 1}^Tu \\
+\mbox{subject to} & Ax \succeq {\bf 1}-u \\
+& u \succeq 0.
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="157" HEIGHT="64" BORDER="0"
+ SRC="img184.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & \Vert x\Vert _1 + {\bf 1...
+...bject to} & Ax \succeq {\bf 1}-u \\
+& u \succeq 0.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+It can be solved as follows.
+<div class="verbatim"><pre>
+x = variable(A.size[1],'x')
+u = variable(A.size[0],'u')
+op(sum(abs(x)) + sum(u), [A*x >= 1-u, u >= 0]).solve()
+</pre></div>
+An equivalent unconstrained formulation is
+<div class="verbatim"><pre>
+x = variable(A.size[1],'x')
+op(sum(abs(x)) + sum(max(0,1-A*x))).solve()
+</pre></div>
+</DD>
+</DL>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0012000000000000000000"></A><A NAME="chap:c-api"></A>
+<BR>
+10. C API
+</H1>
+The API can be used to extend CVXOPT with interfaces to
+external C routines and libraries.
+A C program that creates or manipulates the dense or sparse matrix
+objects defined in <tt class="module">cvxopt.base</tt> must include the
+<span class="file">cvxopt.h</span> header file in the <span class="file">src</span> directory of the
+distribution.
+
+<P>
+Before the C-API can be used in an extension module it must be
+initialized by calling the macro <tt class="cfunction">import_cvxopt</tt>.
+As an example
+we show the module initialization from the <tt class="module">cvxopt.blas</tt> module,
+which itself uses the API:
+<div class="verbatim"><pre>
+PyMODINIT_FUNC initblas(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("cvxopt.blas", blas_functions, blas__doc__);
+
+ if (import_cvxopt() < 0)
+ return;
+}
+</pre></div>
+
+<P>
+
+<p><br /></p><hr class='online-navigation' />
+<div class='online-navigation'>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
+
+<UL CLASS="ChildLinks">
+<LI><A href="node62.html">10.1 Dense Matrices</a>
+<LI><A href="node63.html">10.2 Sparse Matrices</a>
+</ul>
+<!--End of Table of Child-Links-->
+</div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+ href="node60.html"><img src='previous.gif'
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+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+
+<H1><A NAME="SECTION0012100000000000000000">
+10.1 Dense Matrices</A>
+</H1>
+As can be seen from the header file <span class="file">cvxopt.h</span>, a <tt class="class">matrix</tt> is
+essentially a structure with four fields.
+The fields <tt class="cdata">nrows</tt> and <tt class="cdata">ncols</tt> are two integers that
+specify the dimensions.
+The <tt class="cdata">id</tt> field controls the type of the matrix and can have
+values <tt class="constant">DOUBLE</tt>, <tt class="constant">INT</tt> and <tt class="constant">COMPLEX</tt>.
+The <tt class="cdata">buffer</tt> field is an array that contains the matrix elements
+stored contiguously in column-major order.
+
+<P>
+The following C functions can be used to create matrices.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline"><td><nobr>matrix* <b><tt id='l2h-174' xml:id='l2h-174' class="cfunction">Matrix_New</tt></b>(</nobr></td><td>int <var>nrows</var>, int <var>ncols</var>, int <var>id</var>)</td></tr></table></dt>
+<dd>
+Returns a <tt class="class">matrix</tt> object of type <var>id</var> with <var>nrows</var> rows
+and <var>ncols</var> columns. The elements of the matrix are uninitialized.
+</dd></dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline"><td><nobr>matrix* <b><tt id='l2h-175' xml:id='l2h-175' class="cfunction">Matrix_NewFromMatrix</tt></b>(</nobr></td><td>matrix *<var>src</var>, int <var>id</var>)</td></tr></table></dt>
+<dd>
+Returns a copy of the matrix <var>src</var> converted to type <var>id</var>.
+The following type conversions are allowed: <code>'i'</code> to <code>'d'</code>,
+<code>'i'</code> to <code>'z'</code> and <code>'d'</code> to <code>'z'</code>.
+</dd></dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline"><td><nobr>matrix* <b><tt id='l2h-176' xml:id='l2h-176' class="cfunction">Matrix_NewFromSequence</tt></b>(</nobr></td><td>PyListObject *<var>x</var>, int <var>id</var>)</td></tr></table></dt>
+<dd>
+Creates a matrix of type <var>id</var> from the Python sequence type <var>x</var>. The
+returned matrix has size <code>(len(<var>x</var>),1)</code>.
+The size can be changed by modifying the <tt class="member">nrows</tt> and
+<tt class="member">ncols</tt> fields of the returned matrix.
+</dd></dl>
+
+<P>
+To illustrate the creation and manipulation of dense matrices (as well
+as the Python C API), we show the code for the <tt class="function">uniform()</tt>
+function from <tt class="module">cvxopt.random</tt> described in
+section <A href="s-random.html#s-random">2.7</A>.
+<div class="verbatim"><pre>
+PyObject * uniform(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *obj;
+ int i, nrows, ncols = 1;
+ double a = 0, b = 1;
+ char *kwlist[] = {"nrows", "ncols", "a", "b", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "i|idd", kwlist,
+ &nrows, &ncols, &a, &b)) return NULL;
+
+ if ((nrows<0) || (ncols<0)) {
+ PyErr_SetString(PyExc_TypeError, "dimensions must be non-negative");
+ return NULL;
+ }
+
+ if (!(obj = Matrix_New(nrows, ncols, DOUBLE)))
+ return PyErr_NoMemory();
+
+ for (i = 0; i < nrows*ncols; i++)
+ MAT_BUFD(obj)[i] = Uniform(a,b);
+
+ return (PyObject *)obj;
+}
+</pre></div>
+
+<P>
+
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+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+
+<H1><A NAME="SECTION0012200000000000000000">
+10.2 Sparse Matrices</A>
+</H1>
+Sparse matrices are stored in compressed column storage (CCS)
+format. For a general <var>nrows</var> by <var>ncols</var> sparse matrix with
+<var>nnz</var> nonzero entries this means the following. The sparsity
+pattern and the nonzero values are stored in three fields:
+<DL>
+<DT><STRONG>values:</STRONG></DT>
+<DD>A <code>'d'</code> or <code>'z'</code> matrix of size <code>(<var>nnz</var>,1)</code>
+ with the nonzero entries of the matrix stored columnwise.
+</DD>
+<DT><STRONG>rowind:</STRONG></DT>
+<DD>An array of integers of length <var>nnz</var> containing the
+row indices of the nonzero entries, stored in the same order as
+<var>values</var>.
+</DD>
+<DT><STRONG>colptr:</STRONG></DT>
+<DD>An array of integers of length <code><var>ncols</var>+1</code> with
+for each column of the matrix the index of the first element in
+<var>values</var> from that column. More precisely,
+<code><var>colptr</var>[0]</code> is <code>0</code>, and for
+<code><var>k</var> = 0, 1, ..., <var>ncols</var>-1</code>,
+<code><var>colptr</var>[k+1]</code> is equal to <code><var>colptr</var>[k]</code> plus the
+number of nonzeros in column <var>k</var> of the matrix.
+Thus, <code><var>colptr</var>[<var>ncols</var>]</code> is equal to <var>nnz</var>, the
+number of nonzero entries.
+</DD>
+</DL>
+
+<P>
+For example, for the matrix
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A=\left [\begin{array}{cccc}
+ 1 & 0 & 0 & 5\\
+ 2 & 0 & 4 & 0\\
+ 0 & 0 & 0 & 6\\
+ 3 & 0 & 0 & 0
+\end{array}\right]
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="144" HEIGHT="83" BORDER="0"
+ SRC="img185.gif"
+ ALT="\begin{displaymath}
+A=\left [\begin{array}{cccc}
+1 & 0 & 0 & 5\\
+2 & 0 & 4 & 0\\
+0 & 0 & 0 & 6\\
+3 & 0 & 0 & 0
+\end{array}\right]
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+the elements of <var>values</var>, <var>rowind</var> and <var>colptr</var> are:
+<BLOCKQUOTE>
+<var>values</var>: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0,
+ <var>rowind</var>: 0, 1,3, 1, 0, 2,
+ <var>colptr</var>: 0, 3, 3, 4, 6.
+
+</BLOCKQUOTE>
+It is crucial that for each column the row indices in <var>rowind</var> are
+sorted; the equivalent representation
+<BLOCKQUOTE>
+<var>values</var>: 3.0, 2.0, 1.0, 4.0, 5.0, 6.0,
+ <var>rowind</var>: 3, 1, 0, 1, 0, 2,
+ <var>colptr</var>: 0, 3, 3, 4, 6
+
+</BLOCKQUOTE>
+is not allowed (and will likely cause the program to crash).
+
+<P>
+The <tt class="cdata">nzmax</tt> field specifies the number of non-zero elements the
+matrix can store. It is equal to the length of <var>rowind</var> and
+<var>values</var>; this number can be larger that
+<code><var>colptr</var>[<var>nrows</var>]</code>, but never less.
+This field makes it possible to preallocate a certain amount of
+memory to avoid reallocations if the matrix is constructed
+sequentially by filling in elements.
+In general the <var>nzmax</var> field can safely be ignored, however, since
+it will always be adjusted automatically as the number of non-zero
+elements grows.
+
+<P>
+The <tt class="cdata">id</tt> field controls the type of the matrix and can have
+values <tt class="constant">DOUBLE</tt> and <tt class="constant">COMPLEX</tt>.
+
+<P>
+Sparse matrices are created using the following functions from the API.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline"><td><nobr>spmatrix* <b><tt id='l2h-177' xml:id='l2h-177' class="cfunction">SpMatrix_New</tt></b>(</nobr></td><td>int <var>nrows</var>, int <var>ncols</var>, int
+ <var>nzmax</var>, int <var>id</var>)</td></tr></table></dt>
+<dd>
+ Returns a sparse zero matrix with <var>nrows</var> rows and
+ <var>ncols</var> columns. <var>nzmax</var> is the number of elements that will
+ be allocated (the length of the <var>values</var> and <var>rowind</var>
+ fields).
+</dd></dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline"><td><nobr>spmatrix* <b><tt id='l2h-178' xml:id='l2h-178' class="cfunction">SpMatrix_NewFromMatrix</tt></b>(</nobr></td><td>spmatrix *<var>src</var>, int
+ <var>id</var>)</td></tr></table></dt>
+<dd>
+ Returns a copy the sparse matrix <var>src</var>.
+</dd></dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline"><td><nobr>spmatrix* <b><tt id='l2h-179' xml:id='l2h-179' class="cfunction">SpMatrix_NewFromIJV</tt></b>(</nobr></td><td>matrix *I, matrix *J,
+ matrix *V, int <var>nrows</var>, int <var>ncols</var>, int <var>nzmax</var>, int <var>id</var>)</td></tr></table></dt>
+<dd>
+ Creates a sparse matrix with <var>nrows</var> rows and <var>ncols</var>
+ columns from a triplet description. <var>I</var> and <var>J</var>
+ must be integer matrices and <var>V</var> either a double or complex matrix,
+ or <tt class="constant">NULL</tt>. If <var>V</var> is <tt class="constant">NULL</tt> the values of the
+ entries in the matrix are undefined, otherwise they are
+ specified by <var>V</var>. Repeated entries in <var>V</var> are summed.
+ The number of allocated elements is given by <var>nzmax</var>, which is
+ adjusted if it is smaller than the required amount.
+</dd></dl>
+
+<P>
+We illustrate use of the sparse matrix class by listing the source
+code for the <tt class="method">real()</tt> method, which returns the real part of
+a sparse matrix:
+
+<P>
+<div class="verbatim"><pre>
+static PyObject * spmatrix_real(spmatrix *self) {
+
+ if (SP_ID(self) != COMPLEX)
+ return (PyObject *)SpMatrix_NewFromMatrix(self, 0, SP_ID(self));
+
+ spmatrix *ret = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self),
+ SP_NNZ(self), DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i < SP_NNZ(self); i++)
+ SP_VALD(ret)[i] = creal(SP_VALZ(self)[i]);
+
+ memcpy(SP_COL(ret), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t));
+ memcpy(SP_ROW(ret), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
+ return (PyObject *)ret;
+}
+</pre></div>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+
+<H1><A NAME="SECTION004300000000000000000"></A> <A NAME="s-arithmetic"></A>
+<BR>
+2.3 Arithmetic Operations
+</H1>
+The following table lists the arithmetic operations defined for
+dense matrices. In this table <var>A</var> and <var>B</var> are dense matrices
+with compatible dimensions, <var>c</var> is a scalar (a Python number
+or a dense 1 by 1 matrix), and <var>d</var> is a Python number.
+
+<P>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1">
+<TR><TD ALIGN="LEFT">Unary plus/minus</TD>
+<TD ALIGN="LEFT"><code>+<var>A</var></code>, <code>-<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Addition</TD>
+<TD ALIGN="LEFT"><code><var>A</var>+<var>B</var></code>, <code><var>A</var>+<var>c</var></code>,
+ <code><var>c</var>+<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Subtraction</TD>
+<TD ALIGN="LEFT"><code><var>A</var>-<var>B</var></code>, <code><var>A</var>-<var>c</var></code>,
+ <code><var>c</var>-<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Matrix multiplication</TD>
+<TD ALIGN="LEFT"><var>A</var>*<var>B</var></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Scalar multiplication and division</TD>
+<TD ALIGN="LEFT"><code><var>c</var>*<var>A</var></code>,
+ <code><var>A</var>*<var>c</var></code>, <code><var>A</var>/<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Remainder after division</TD>
+<TD ALIGN="LEFT"><code><var>A</var>%<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Elementwise exponentiation</TD>
+<TD ALIGN="LEFT"><code><var>A</var>**<var>d</var></code></TD>
+</TR>
+</TABLE>
+</DIV>
+
+<P>
+If <var>c</var> in the expressions <code><var>A</var>+<var>c</var></code>,
+<code><var>c</var>+<var>A</var></code>, <code><var>A</var>-<var>c</var></code>,
+<code><var>c</var>-<var>A</var></code> is a number, then it is interpreted as a
+matrix with the same dimensions as <var>A</var>, type given by the type
+of <var>c</var>, and all entries equal to <var>c</var>.
+If <var>c</var> is a 1 by 1 matrix and <var>A</var> is not 1 by 1, then <var>c</var>
+is interpreted as a matrix with the same size of <var>A</var> and all
+entries equal to <code><var>c</var>[0]</code>.
+
+<P>
+Postmultiplying a matrix with a number <var>c</var> means the same as
+premultiplying, <EM>i.e.</EM>, scalar multiplication. Dividing a matrix by
+<var>c</var> means dividing all entries by <var>c</var>.
+If <var>c</var> is a 1 by 1 matrix and the product
+<code><var>c</var>*<var>A</var></code> or <code><var>A</var>*<var>c</var></code> cannot be
+interpreted as a matrix-matrix product, then it is interpreted as
+<code><var>c</var>[0]*<var>A</var></code>.
+The division <code><var>A</var>/<var>c</var></code> and remainder
+<code><var>A</var>%<var>c</var></code> with <var>c</var> a 1 by 1 matrix are always
+interpreted as <code><var>A</var>/<var>c</var>[0]</code>, resp.,
+<code><var>A</var>%<var>c</var>[0]</code>.
+
+<P>
+If one of the operands in the arithmetic operations is integer
+(a scalar integer or a matrix of type <code>'i'</code>) and the other operand
+is double (a scalar float or a matrix of type <code>'d'</code>), then the
+integer operand is converted to double, and the result is a matrix of
+type <code>'d'</code>.
+If one of the operands is integer or double, and the other operand is
+complex (a scalar complex or a matrix of type <code>'z'</code>),
+then the first operand is converted to complex, and the result is
+a matrix of type <code>'z'</code>.
+
+<P>
+The result of <code><var>A</var>**<var>d</var></code> is a complex matrix
+if <var>A</var> or <var>d</var> are complex, and real otherwise.
+
+<P>
+Note that Python rounds the result of an integer division towards minus
+infinity.
+
+<P>
+The following in-place operations are also defined, but only if
+they do not change the type or the size of the matrix <var>A</var>:
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1">
+<TR><TD ALIGN="LEFT">In-place addition</TD>
+<TD ALIGN="LEFT"><code><var>A</var>+=<var>B</var></code>, <code><var>A</var>+=<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">In-place subtraction</TD>
+<TD ALIGN="LEFT"><code><var>A</var>-=<var>B</var></code>, <code><var>A</var>-=<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">In-place scalar multiplication and division</TD>
+<TD ALIGN="LEFT"><code><var>A</var>*=<var>c</var></code>, <code><var>A</var>/=<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">In-place remainder</TD>
+<TD ALIGN="LEFT"><code><var>A</var>%=<var>c</var></code></TD>
+</TR>
+</TABLE>
+</DIV>
+
+<P>
+For example, if <var>A</var> has type <code>'i'</code>, then <code><var>A</var>+=<var>B</var></code>
+is allowed if <var>B</var> has type <code>'i'</code>.
+It is not allowed if <var>B</var> has type <code>'d'</code>or <code>'z'</code>because the
+addition <code><var>A</var>+<var>B</var></code> results in a matrix of
+type <code>'d'</code>or <code>'z'</code>and therefore cannot be assigned to <var>A</var>
+without changing its type.
+
+<P>
+In-place matrix-matrix products are not allowed. (Except when
+<var>c</var> is a 1 by 1 matrix, in which case <code><var>A</var>*=<var>c</var></code> is
+interpreted as the scalar product <code><var>A</var>*=<var>c</var>[0]</code>.)
+
+<P>
+It is important to know when a matrix operation creates
+a new object. The following rules apply.
+
+<UL>
+<LI>A simple assignment ("<tt class="samp">A = B</tt>") is given the standard
+Python interpretation, <EM>i.e.</EM>, it assigns to the variable <var>A</var> a
+reference (or pointer) to the object referenced by <var>B</var>.
+<div class="verbatim"><pre>
+>>> B = matrix([[1.,2.], [3.,4.]])
+>>> print B
+ 1.0000e+00 3.0000e+00
+ 2.0000e+00 4.0000e+00
+>>> A = B
+>>> A[0,0] = -1
+>>> print B # modifying A[0,0] also modified B[0,0]
+-1.0000e+00 3.0000e+00
+ 2.0000e+00 4.0000e+00
+</pre></div>
+
+<P>
+</LI>
+<LI>The regular (<EM>i.e.</EM>, not in-place) arithmetic operations always
+return new objects. Hence "<tt class="samp">A = +B</tt>" is equivalent to
+"<tt class="samp">A = matrix(B)</tt>".
+<div class="verbatim"><pre>
+>>> B = matrix([[1.,2.], [3.,4.]])
+>>> A = +B
+>>> A[0,0] = -1
+>>> print B # modifying A[0,0] does not modify B[0,0]
+ 1.0000e+00 3.0000e+00
+ 2.0000e+00 4.0000e+00
+</pre></div>
+
+<P>
+</LI>
+<LI>The in-place operations directly modify the
+ coefficients of the existing matrix object and do not create a new
+ object.
+<div class="verbatim"><pre>
+>>> B = matrix([[1.,2.], [3.,4.]])
+>>> A = B
+>>> A *= 2
+>>> print B # in-place operation also changed B
+ 2.0000e+00 6.0000e+00
+ 4.0000e+00 8.0000e+00
+>>> A = 2*A
+>>> print B # regular operation creates a new A, so does not change B
+ 2.0000e+00 6.0000e+00
+ 4.0000e+00 8.0000e+00
+</pre></div>
+</LI>
+</UL>
+
+<P>
+The restrictions on in-place operations follow the principle that once
+a matrix object is created, its size and type cannot be modified.
+The only matrix attributes that can be changed are the values of the
+elements. The values can be changed by in-place operations or by an
+indexed assignment, as explained in the next section.
+
+<P>
+
+<DIV CLASS="navigation">
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+
+<H1><A NAME="SECTION004800000000000000000"></A> <A NAME="s-array-interface"></A>
+<BR>
+2.8 The NumPy Array Interface
+</H1>
+
+<P>
+The CVXOPT <tt class="class">matrix</tt> object is compatible with the NumPy Array Interface,
+which allows Python objects that represent multidimensional
+arrays to exchange data using information stored in the
+attribute <code>__array_struct__</code>.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://numpy.scipy.org/array_interface.shtml'
+ >NumPy Array Interface Specification</a></dt>
+ <dd></dd>
+ </dl>
+
+<P>
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://numpy.scipy.org'
+ >NumPy home page</a></dt>
+ <dd></dd>
+ </dl>
+</div>
+
+<P>
+As already mentioned in section <A href="s-creating-matrices.html#s-creating-matrices">2.1</A>,
+a two-dimensional array object (for example, a 2D <tt class="module">numarray</tt>
+array) can be converted to a <tt class="class">matrix</tt> object by using the
+<tt class="function">matrix()</tt> constructor.
+Conversely, CVXOPT matrices can be used as array-like objects
+in <tt class="module">numarray</tt>. The following example illustrates the
+compatibility of CVXOPT matrices and <tt class="module">numarray</tt> arrays.
+<div class="verbatim"><pre>
+>>> from cvxopt import matrix
+>>> a = matrix(range(6), (2,3), 'd')
+>>> print a
+ 0.0000e+00 2.0000e+00 4.0000e+00
+ 1.0000e+00 3.0000e+00 5.0000e+00
+>>> from numarray import array
+>>> b = array(a)
+>>> print b
+[[ 0. 2. 4.]
+ [ 1. 3. 5.]]
+>>> print a*b
+[[ 0. 4. 16.]
+ [ 1. 9. 25.]]
+</pre></div>
+In the last expression <code>a*b</code> is interpreted as a <tt class="module">numarray</tt>
+multiplication (<EM>i.e.</EM>, componentwise) even though one operand is a
+<tt class="class">matrix</tt> object.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel="parent" href="node14.html" />
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+<title>3.2 Level 1 BLAS</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+ href="contents.html"><img src='contents.gif'
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+ border='0' height='32' alt='Index' width='32' /></A></td>
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+<hr /></div>
+</DIV>
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+
+<H1><A NAME="SECTION005200000000000000000"></A> <A NAME="s-blas1"></A>
+<BR>
+3.2 Level 1 BLAS
+</H1>
+The level 1 functions implement vector operations.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-28' xml:id='l2h-28' class="function">scal</tt></b>(</nobr></td>
+ <td><var>alpha, x</var>)</td></tr></table></dt>
+<dd>
+Scales a vector by a constant:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x := \alpha x.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="56" HEIGHT="24" BORDER="0"
+ SRC="img8.gif"
+ ALT="\begin{displaymath}
+x := \alpha x.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If <var>x</var> is a real <tt class="class">matrix</tt>, the scalar argument <var>alpha</var> must be a
+Python integer or float. If <var>x</var> is complex, <var>alpha</var> can be an
+integer, float, or complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-29' xml:id='l2h-29' class="function">nrm2</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+Euclidean norm of a vector: returns
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\|x\|_2.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="33" HEIGHT="28" BORDER="0"
+ SRC="img9.gif"
+ ALT="\begin{displaymath}
+\Vert x\Vert _2.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-30' xml:id='l2h-30' class="function">asum</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+L-1 norm of a vector: returns
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\|x\|_1 \quad \mbox{($x$\ real)}, \qquad
+\|\Re x\|_1 + \|\Im x\|_1 \quad \mbox{($x$\ complex)}.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="337" HEIGHT="28" BORDER="0"
+ SRC="img10.gif"
+ ALT="\begin{displaymath}
+\Vert x\Vert _1 \quad \mbox{($x$\ real)}, \qquad
+\Vert\Re x\Vert _1 + \Vert\Im x\Vert _1 \quad \mbox{($x$\ complex)}.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-31' xml:id='l2h-31' class="function">iamax</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+Returns
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\mathop{\rm argmax}_{k=0,\ldots,n-1} |x_k| \quad \mbox{($x$\ real)}, \qquad
+ \mathop{\rm argmax}_{k=0,\ldots,n-1} |\Re x_k| + |\Im x_k| \quad
+ \mbox{($x$\ complex)}.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="457" HEIGHT="41" BORDER="0"
+ SRC="img11.gif"
+ ALT="\begin{displaymath}
+\mathop{\rm argmax}_{k=0,\ldots,n-1} \vert x_k\vert \quad \...
+...e x_k\vert + \vert\Im x_k\vert \quad
+\mbox{($x$\ complex)}.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+If more than one coefficient achieves the maximum, the index of the
+first <I>k</I> is returned.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-32' xml:id='l2h-32' class="function">swap</tt></b>(</nobr></td>
+ <td><var>x, y</var>)</td></tr></table></dt>
+<dd>
+Interchanges two vectors:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x \leftrightarrow y.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="44" HEIGHT="27" BORDER="0"
+ SRC="img12.gif"
+ ALT="\begin{displaymath}
+x \leftrightarrow y.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<var>x</var> and <var>y</var> are matrices of the same type (<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-33' xml:id='l2h-33' class="function">copy</tt></b>(</nobr></td>
+ <td><var>x, y</var>)</td></tr></table></dt>
+<dd>
+Copies a vector to another vector:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := x.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="47" HEIGHT="27" BORDER="0"
+ SRC="img13.gif"
+ ALT="\begin{displaymath}
+y := x.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<var>x</var> and <var>y</var> are matrices of the same type (<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-34' xml:id='l2h-34' class="function">axpy</tt></b>(</nobr></td>
+ <td><var>x, y</var><big>[</big><var>,alpha=1.0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Constant times a vector plus a vector:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha x + y.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="85" HEIGHT="27" BORDER="0"
+ SRC="img14.gif"
+ ALT="\begin{displaymath}
+y := \alpha x + y.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<var>x</var> and <var>y</var> are matrices of the same type (<code>'d'</code> or <code>'z'</code>).
+If <var>x</var> is real, the scalar argument <var>alpha</var> must be a Python
+integer or float. If <var>x</var> is complex, <var>alpha</var> can be an integer,
+float, or complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-35' xml:id='l2h-35' class="function">dot</tt></b>(</nobr></td>
+ <td><var>x, y</var>)</td></tr></table></dt>
+<dd>
+Returns
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x^Hy.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="32" HEIGHT="27" BORDER="0"
+ SRC="img15.gif"
+ ALT="\begin{displaymath}
+x^Hy.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<var>x</var> and <var>y</var> are matrices of the same type (<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-36' xml:id='l2h-36' class="function">dotu</tt></b>(</nobr></td>
+ <td><var>x, y</var>)</td></tr></table></dt>
+<dd>
+Returns
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x^Ty.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="30" HEIGHT="27" BORDER="0"
+ SRC="img16.gif"
+ ALT="\begin{displaymath}
+x^Ty.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<var>x</var> and <var>y</var> are matrices of the same type (<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="3.1 Matrix Classes"
+ href="s-conventions.html"><img src='previous.gif'
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+<td class='online-navigation'><a rel="contents" title="Table of Contents"
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@@ -0,0 +1,661 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
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+</head>
+<body>
+<DIV CLASS="navigation">
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+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td class='online-navigation'><a rel="next" title="3.4 Level 3 BLAS"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+ href="contents.html"><img src='contents.gif'
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+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
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+<b class="navlabel">Next:</b>
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION005300000000000000000"></A> <A NAME="s-blas2"></A>
+<BR>
+3.3 Level 2 BLAS
+</H1>
+The level 2 functions implement matrix-vector products and
+rank-1 and rank-2 matrix updates.
+Different types of matrix structure can be exploited using the
+conventions of section <A href="s-conventions.html#s-conventions">3.1</A>.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-37' xml:id='l2h-37' class="function">gemv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, trans='N'</var><big>[</big><var>,
+alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a general matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+y := \alpha A^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}),
+ \qquad
+y := \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="707" HEIGHT="28" BORDER="0"
+ SRC="img17.gif"
+ ALT="\begin{displaymath}
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'...
+...\alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>). Complex values of <var>alpha</var> and <var>beta</var> are only
+allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-38' xml:id='l2h-38' class="function">symv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a real symmetric matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha A x + \beta y,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="107" HEIGHT="27" BORDER="0"
+ SRC="img18.gif"
+ ALT="\begin{displaymath}
+y := \alpha A x + \beta y,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have
+type <code>'d'</code> and <var>alpha</var> and <var>beta</var> must be real.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-39' xml:id='l2h-39' class="function">hemv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a real symmetric or complex Hermitian
+matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha A x + \beta y,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="107" HEIGHT="27" BORDER="0"
+ SRC="img18.gif"
+ ALT="\begin{displaymath}
+y := \alpha A x + \beta y,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is real symmetric or complex Hermitian.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same
+type (<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> and <var>beta</var> are only
+allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-40' xml:id='l2h-40' class="function">trmv</tt></b>(</nobr></td>
+ <td><var>A, x</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, diag='N'</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a triangular matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x := Ax \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^T x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^H x \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="586" HEIGHT="28" BORDER="0"
+ SRC="img19.gif"
+ ALT="\begin{displaymath}
+x := Ax \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A...
+...'}), \qquad
+x := A^H x \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is square and triangular.
+The arguments <var>A</var> and <var>x</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-41' xml:id='l2h-41' class="function">trsv</tt></b>(</nobr></td>
+ <td><var>A, x</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, diag='N'</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solution of a nonsingular triangular set of linear equations:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x := A^{-1}x \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^{-T}x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^{-H}x \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="623" HEIGHT="28" BORDER="0"
+ SRC="img20.gif"
+ ALT="\begin{displaymath}
+x := A^{-1}x \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x...
+..., \qquad
+x := A^{-H}x \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is square and triangular with nonzero diagonal
+elements. The arguments <var>A</var> and <var>x</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-42' xml:id='l2h-42' class="function">gbmv</tt></b>(</nobr></td>
+ <td><var>A, m, kl, x, y</var><big>[</big><var>, trans='N'
+</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a general band matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha A^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}),
+\qquad
+y := \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="708" HEIGHT="28" BORDER="0"
+ SRC="img21.gif"
+ ALT="\begin{displaymath}
+y := \alpha Ax + \beta y \quad (\mathrm{trans} = \mathrm{'N'...
+... \alpha A^H x + \beta y \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a rectangular band matrix with <var>m</var> rows and
+<var>kl</var> subdiagonals.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same
+type (<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> and <var>beta</var> are only allowed if <var>A</var> is
+ complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-43' xml:id='l2h-43' class="function">sbmv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a real symmetric band matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="107" HEIGHT="27" BORDER="0"
+ SRC="img18.gif"
+ ALT="\begin{displaymath}
+y := \alpha A x + \beta y,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric band matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have type <code>'d'</code> and
+<var>alpha</var> and <var>beta</var> must be real.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-44' xml:id='l2h-44' class="function">hbmv</tt></b>(</nobr></td>
+ <td><var>A, x, y</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a real symmetric or complex Hermitian
+band matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+y := \alpha Ax + \beta y,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="107" HEIGHT="27" BORDER="0"
+ SRC="img18.gif"
+ ALT="\begin{displaymath}
+y := \alpha A x + \beta y,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric or complex Hermitian band matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> and <var>beta</var> are only allowed if
+<var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-45' xml:id='l2h-45' class="function">tbmv</tt></b>(</nobr></td>
+ <td><var>A, x</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans</var><big>[</big><var>, diag</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-vector product with a triangular band matrix:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x := Ax \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^T x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^H x \quad (\mathrm{trans} = \mathrm{'C'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="585" HEIGHT="28" BORDER="0"
+ SRC="img22.gif"
+ ALT="\begin{displaymath}
+x := Ax \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A...
+...}), \qquad
+x := A^H x \quad (\mathrm{trans} = \mathrm{'C'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The arguments <var>A</var> and <var>x</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-46' xml:id='l2h-46' class="function">tbsv</tt></b>(</nobr></td>
+ <td><var>A, x</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans</var><big>[</big><var>, diag</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solution of a triangular banded set of linear equations:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x := A^{-1}x \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x := A^{-T} x \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+x := A^{-H} x \quad (\mathrm{trans} = \mathrm{'T'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="623" HEIGHT="28" BORDER="0"
+ SRC="img23.gif"
+ ALT="\begin{displaymath}
+x := A^{-1}x \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+x...
+..., \qquad
+x := A^{-H} x \quad (\mathrm{trans} = \mathrm{'T'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a triangular band matrix of with nonzero diagonal
+elements.
+The arguments <var>A</var> and <var>x</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-47' xml:id='l2h-47' class="function">ger</tt></b>(</nobr></td>
+ <td><var>x, y, A</var><big>[</big><var>, alpha=1.0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+General rank-1 update:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A := A + \alpha x y^H,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="112" HEIGHT="27" BORDER="0"
+ SRC="img24.gif"
+ ALT="\begin{displaymath}
+A := A + \alpha x y^H,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a general matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> are only allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-48' xml:id='l2h-48' class="function">geru</tt></b>(</nobr></td>
+ <td><var>x, y, A</var><big>[</big><var>, alpha=1.0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+General rank-1 update:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A := A + \alpha x y^T,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="110" HEIGHT="27" BORDER="0"
+ SRC="img25.gif"
+ ALT="\begin{displaymath}
+A := A + \alpha x y^T,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a general matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> are only allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-49' xml:id='l2h-49' class="function">syr</tt></b>(</nobr></td>
+ <td><var>x, A</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, alpha=1.0</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Symmetric rank-1 update:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A := A + \alpha xx^T,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="112" HEIGHT="27" BORDER="0"
+ SRC="img26.gif"
+ ALT="\begin{displaymath}
+A := A + \alpha xx^T,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric matrix.
+The arguments <var>A</var> and <var>x</var> must have type <code>'d'</code>.
+<var>alpha</var> must be a real number.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-50' xml:id='l2h-50' class="function">her</tt></b>(</nobr></td>
+ <td><var>x, A</var><big>[</big><var>, uplo='L'</var><big>[</big><var>, alpha=1.0</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Hermitian rank-1 update:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A := A + \alpha xx^H,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="114" HEIGHT="27" BORDER="0"
+ SRC="img27.gif"
+ ALT="\begin{displaymath}
+A := A + \alpha xx^H,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric or complex Hermitian matrix.
+The arguments <var>A</var> and <var>x</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+<var>alpha</var> must be a real number.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-51' xml:id='l2h-51' class="function">syr2</tt></b>(</nobr></td>
+ <td><var>x, y, A</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Symmetric rank-2 update:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A := A + \alpha (xy^T + yx^T),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="170" HEIGHT="28" BORDER="0"
+ SRC="img28.gif"
+ ALT="\begin{displaymath}
+A := A + \alpha (xy^T + yx^T),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a real symmetric matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have type <code>'d'</code>.
+<var>alpha</var> must be real.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-52' xml:id='l2h-52' class="function">her2</tt></b>(</nobr></td>
+ <td><var>x, y, A</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+alpha=1.0</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Symmetric rank-2 update:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A := A + \alpha xy^H + \bar \alpha yx^H,
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="172" HEIGHT="27" BORDER="0"
+ SRC="img29.gif"
+ ALT="\begin{displaymath}
+A := A + \alpha xy^H + \bar \alpha yx^H,
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a a real symmetric or complex Hermitian matrix.
+The arguments <var>A</var>, <var>x</var> and <var>y</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> are only allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+As an example, the following code multiplies the tridiagonal matrix
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+A = \left[\begin{array}{rrrr}
+ 1 & 6 & 0 & 0 \\
+ 2 & -4 & 3 & 0 \\
+ 0 & -3 & -1 & 1
+ \end{array}\right]
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="169" HEIGHT="64" BORDER="0"
+ SRC="img30.gif"
+ ALT="\begin{displaymath}
+A = \left[\begin{array}{rrrr}
+1 & 6 & 0 & 0 \\
+2 & -4 & 3 & 0 \\
+0 & -3 & -1 & 1
+\end{array}\right]
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with the vector <I>x</I> = (1,-1,2,-2).
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt.blas import gbmv
+>>> A = matrix([[0., 1., 2.], [6., -4., -3.], [3., -1., 0.], [1., 0., 0.]])
+>>> x = matrix([1., -1., 2., -2.])
+>>> y = matrix(0., (3,1))
+>>> gbmv(A, 3, 1, x, y)
+>>> print y
+-5.0000e+00
+ 1.2000e+01
+-1.0000e+00
+</pre></div>
+
+<P>
+The following example illustrates the use of <tt class="function">tbsv()</tt>.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt.blas import tbsv
+>>> A = matrix([-6., 5., -1., 2.], (1,4))
+>>> x = matrix(1.0, (4,1))
+>>> tbsv(A, x) # x := diag(A)^{-1}*x
+>>> print x
+-1.6667e-01
+ 2.0000e-01
+-1.0000e+00
+ 5.0000e-01
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION005400000000000000000"></A> <A NAME="s-blas3"></A>
+<BR>
+3.4 Level 3 BLAS
+</H1>
+The level 3 BLAS include functions for matrix-matrix multiplication.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-53' xml:id='l2h-53' class="function">gemm</tt></b>(</nobr></td>
+ <td><var>A, B, C</var><big>[</big><var>, transA='N'</var><big>[</big><var>,
+transB='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Matrix-matrix product of two general matrices:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha \mathop{\mathrm{op}}(A) \mathop{\mathrm{op}}(B) + \beta C
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="177" HEIGHT="28" BORDER="0"
+ SRC="img31.gif"
+ ALT="\begin{displaymath}
+C := \alpha \mathop{\mathrm{op}}(A) \mathop{\mathrm{op}}(B) + \beta C
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\mathop{\mathrm{op}}(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'} \end{array} \right.
+\qquad
+\mathop{\mathrm{op}}(B) = \left\{ \begin{array}{ll}
+ B & \mathrm{transB} = \mathrm{'N'} \\
+ B^T & \mathrm{transB} = \mathrm{'T'} \\
+ B^H & \mathrm{transB} = \mathrm{'C'}. \end{array} \right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="474" HEIGHT="64" BORDER="0"
+ SRC="img32.gif"
+ ALT="\begin{displaymath}
+\mathop{\mathrm{op}}(A) = \left\{ \begin{array}{ll}
+A & \ma...
+...\\
+B^H & \mathrm{transB} = \mathrm{'C'}. \end{array} \right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The arguments <var>A</var>, <var>B</var> and <var>C</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> and <var>beta</var> are only allowed
+if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-54' xml:id='l2h-54' class="function">symm</tt></b>(</nobr></td>
+ <td><var>A, B, C</var><big>[</big><var>, side='L'</var><big>[</big><var>,
+uplo='L'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Product of a real or complex symmetric matrix <I>A</I> and a general
+matrix <I>B</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha AB + \beta C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := \alpha BA + \beta C \quad (\mathrm{side} = \mathrm{'R'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="462" HEIGHT="28" BORDER="0"
+ SRC="img33.gif"
+ ALT="\begin{displaymath}
+C := \alpha AB + \beta C \quad (\mathrm{side} = \mathrm{'L'...
+... := \alpha BA + \beta C \quad (\mathrm{side} = \mathrm{'R'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The arguments <var>A</var>, <var>B</var> and <var>C</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>). Complex values of <var>alpha</var> and <var>beta</var> are
+only allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-55' xml:id='l2h-55' class="function">hemm</tt></b>(</nobr></td>
+ <td><var>A, B, C</var><big>[</big><var>, side='L'</var><big>[</big><var>,
+uplo='L'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Product of a real symmetric or complex Hermitian matrix <I>A</I> and a
+general matrix <I>B</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha AB + \beta C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := \alpha BA + \beta C \quad (\mathrm{side} = \mathrm{'R'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="462" HEIGHT="28" BORDER="0"
+ SRC="img33.gif"
+ ALT="\begin{displaymath}
+C := \alpha AB + \beta C \quad (\mathrm{side} = \mathrm{'L'...
+... := \alpha BA + \beta C \quad (\mathrm{side} = \mathrm{'R'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The arguments <var>A</var>, <var>B</var> and <var>C</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>).
+Complex values of <var>alpha</var> and <var>beta</var> are only allowed if
+<var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-56' xml:id='l2h-56' class="function">trmm</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, side='L'</var><big>[</big><var>,
+uplo='L'</var><big>[</big><var>, transA='N'</var><big>[</big><var>, diag='N'</var><big>[</big><var>,
+alpha=1.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Product of a triangular matrix <I>A</I> and a general matrix <I>B</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+B := \alpha\mathop{\mathrm{op}}(A)B \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ B := \alpha B\mathop{\mathrm{op}}(A) \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \mathop{\mathrm{op}}(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'}. \end{array} \right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="696" HEIGHT="64" BORDER="0"
+ SRC="img34.gif"
+ ALT="\begin{displaymath}
+B := \alpha\mathop{\mathrm{op}}(A)B \quad (\mathrm{side} = ...
+...\\
+A^H & \mathrm{transA} = \mathrm{'C'}. \end{array} \right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The arguments <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>). Complex values of <var>alpha</var> are only allowed if <var>A</var> is
+complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-57' xml:id='l2h-57' class="function">trsm</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, side='L'</var><big>[</big><var>,
+uplo='L'</var><big>[</big><var>, transA='N'</var><big>[</big><var>, diag='N'</var><big>[</big><var>,
+alpha=1.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solution of a nonsingular triangular system of equations:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+B := \alpha \mathop{\mathrm{op}}(A)^{-1}B \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ B := \alpha B\mathop{\mathrm{op}}(A)^{-1} \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \mathop{\mathrm{op}}(A) = \left\{ \begin{array}{ll}
+ A & \mathrm{transA} = \mathrm{'N'} \\
+ A^T & \mathrm{transA} = \mathrm{'T'} \\
+ A^H & \mathrm{transA} = \mathrm{'C'}, \end{array} \right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="731" HEIGHT="64" BORDER="0"
+ SRC="img35.gif"
+ ALT="\begin{displaymath}
+B := \alpha \mathop{\mathrm{op}}(A)^{-1}B \quad (\mathrm{si...
+...\\
+A^H & \mathrm{transA} = \mathrm{'C'}, \end{array} \right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is triangular and <I>B</I> is a general matrix.
+The arguments <var>A</var> and <var>B</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>). Complex values of <var>alpha</var> are only allowed if <var>A</var> is
+complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-58' xml:id='l2h-58' class="function">syrk</tt></b>(</nobr></td>
+ <td><var>A, C</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Rank-<I>k</I> update of a real or complex symmetric matrix <I>C</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha AA^T + \beta C \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+ C := \alpha A^TA + \beta C \quad (\mathrm{trans} = \mathrm{'T'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="501" HEIGHT="28" BORDER="0"
+ SRC="img36.gif"
+ ALT="\begin{displaymath}
+C := \alpha AA^T + \beta C \quad (\mathrm{trans} = \mathrm{...
+... \alpha A^TA + \beta C \quad (\mathrm{trans} = \mathrm{'T'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a general matrix.
+The arguments <var>A</var> and <var>C</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>). Complex values of <var>alpha</var> and <var>beta</var> are only allowed
+if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-59' xml:id='l2h-59' class="function">herk</tt></b>(</nobr></td>
+ <td><var>A, C</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Rank-<I>k</I> update of a real symmetric or complex Hermitian matrix
+<I>C</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha AA^H + \beta C \quad (\mathrm{trans} = \mathrm{'N'}),
+ \qquad
+ C := \alpha A^HA + \beta C \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="505" HEIGHT="28" BORDER="0"
+ SRC="img37.gif"
+ ALT="\begin{displaymath}
+C := \alpha AA^H + \beta C \quad (\mathrm{trans} = \mathrm{...
+...= \alpha A^HA + \beta C \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> is a general matrix.
+The arguments <var>A</var> and <var>C</var> must have the same type (<code>'d'</code> or
+<code>'z'</code>). <var>alpha</var> and <var>beta</var> must be real.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-60' xml:id='l2h-60' class="function">syr2k</tt></b>(</nobr></td>
+ <td><var>A, B, C</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var>, beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Rank-<I>2k</I> update of a real or complex symmetric matrix <I>C</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha (AB^T + BA^T) + \beta C \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+ C := \alpha (A^TB + B^TA) + \beta C \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="607" HEIGHT="28" BORDER="0"
+ SRC="img38.gif"
+ ALT="\begin{displaymath}
+C := \alpha (AB^T + BA^T) + \beta C \quad
+(\mathrm{trans}...
+...TB + B^TA) + \beta C \quad
+(\mathrm{trans} = \mathrm{'T'}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<I>A</I> and <I>B</I> are general real or complex matrices.
+The arguments <var>A</var>, <var>B</var> and <var>C</var> must have the same
+type. Complex values of <var>alpha</var> and <var>beta</var> are only
+allowed if <var>A</var> is complex.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-61' xml:id='l2h-61' class="function">her2k</tt></b>(</nobr></td>
+ <td><var>A, B, C</var><big>[</big><var>, uplo='L'</var><big>[</big><var>,
+trans='N'</var><big>[</big><var>, alpha=1.0</var><big>[</big><var> beta=0.0</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Rank-<I>2k</I> update of a real symmetric or complex Hermitian matrix
+<I>C</I>:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+C := \alpha AB^H + \bar \alpha BA^H + \beta C \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+ C := \alpha A^HB + \bar\alpha B^HA + \beta C \quad
+ (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="612" HEIGHT="28" BORDER="0"
+ SRC="img39.gif"
+ ALT="\begin{displaymath}
+C := \alpha AB^H + \bar \alpha BA^H + \beta C \quad
+(\mat...
+...alpha B^HA + \beta C \quad
+(\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>A</I> and <I>B</I> are general matrices.
+The arguments <var>A</var>, <var>B</var> and <var>C</var> must have the same type
+(<code>'d'</code> or <code>'z'</code>). Complex values of <var>alpha</var> are only allowed if
+<var>A</var> is complex. <var>beta</var> must be real.
+</dl>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="3.3 Level 2 BLAS"
+ href="s-blas2.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="3. The BLAS Interface"
+ href="node14.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="4. The LAPACK Interface"
+ href="node19.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
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+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="s-blas2.html">3.3 Level 2 BLAS</A>
+<b class="navlabel">Up:</b>
+<a class="sectref" rel="parent" href="node14.html">3. The BLAS Interface</A>
+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="node19.html">4. The LAPACK Interface</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
+
+</BODY>
+</HTML>
diff --git a/doc/cvxopt/s-builtinfuncs.html b/doc/cvxopt/s-builtinfuncs.html
new file mode 100644
index 0000000..22f6eea
--- /dev/null
+++ b/doc/cvxopt/s-builtinfuncs.html
@@ -0,0 +1,219 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
+<link rel="next" href="s-otherfuncs.html" />
+<link rel="prev" href="s-indexing.html" />
+<link rel="parent" href="node4.html" />
+<link rel="next" href="s-otherfuncs.html" />
+<meta name='aesop' content='information' />
+<title>2.5 Built-in Functions</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="2.4 Indexing and Slicing"
+ href="s-indexing.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="2. Dense Matrices (cvxopt.base)"
+ href="node4.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="2.6 Other Matrix Functions"
+ href="s-otherfuncs.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="s-indexing.html">2.4 Indexing and Slicing</A>
+<b class="navlabel">Up:</b>
+<a class="sectref" rel="parent" href="node4.html">2. Dense Matrices (cvxopt.base)</A>
+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="s-otherfuncs.html">2.6 Other Matrix Functions</A>
+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION004500000000000000000"></A> <A NAME="s-builtinfuncs"></A>
+<BR>
+2.5 Built-in Functions
+</H1>
+Many Python built-in functions and operations can be used with matrix
+arguments. We list some useful examples.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-11' xml:id='l2h-11' class="function">len</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+Returns the product of the number of rows and the number of columns.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-12' xml:id='l2h-12' class="function">bool</tt></b>(</nobr></td>
+ <td><var></var><big>[</big><var>x</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Returns <code>False</code> if <var>x</var> is empty (<EM>i.e.</EM>, <code>len(<var>x</var>)</code> is zero)
+and <code>True</code> otherwise.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-13' xml:id='l2h-13' class="function">max</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+Returns the maximum element of <var>x</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-14' xml:id='l2h-14' class="function">min</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+Returns the minimum element of <var>x</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-15' xml:id='l2h-15' class="function">abs</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+Returns a matrix with the absolute values of the elements of <var>x</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-16' xml:id='l2h-16' class="function">sum</tt></b>(</nobr></td>
+ <td><var>x</var><big>[</big><var>, start=0.0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Returns the sum of <var>start</var> and the elements of <var>x</var>.
+</dl>
+
+<P>
+Matrices can be used as arguments to the <tt class="function">list()</tt>,
+<tt class="function">tuple()</tt>, <tt class="function">zip()</tt>, <tt class="function">map()</tt>, and
+<tt class="function">filter()</tt> functions described in section 2.1 of the Python
+Library Reference. <code>list(<var>A</var>)</code> and <code>tuple(<var>A</var>)</code>
+construct a list, respectively a tuple, from the elements of <var>A</var>.
+<code>zip(<var>A</var>,<var>B</var>,...)</code> returns a list of tuples,
+with the <I>i</I>th tuple containing the <I>i</I>th elements of <var>A</var>,
+<var>B</var>, ....
+
+<P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> A = matrix([[-11., -5., -20.], [-6., -0., 7.]])
+>>> B = matrix(range(6), (3,2))
+>>> list(A)
+[-11.0, -5.0, -20.0, -6.0, 0.0, 7.0]
+>>> tuple(B)
+(0, 1, 2, 3, 4, 5)
+>>> zip(A,B)
+[(-11.0, 0), (-5.0, 1), (-20.0, 2), (-6.0, 3), (0.0, 4), (7.0, 5)]
+</pre></div>
+
+<P>
+<code>map(<var>f</var>,<var>A</var>)</code>, where <var>f</var> is a function and <var>A</var>
+is a matrix, returns a list constructed by applying <var>f</var> to each
+element of <var>A</var>. Multiple arguments can be provided, for example,
+as in <code>map(<var>f</var>,<var>A</var>,<var>B</var>)</code>, if <var>f</var> is a function
+with two arguments.
+<div class="verbatim"><pre>
+>>> A = matrix([[5, -4, 10, -7], [-1, -5, -6, 2], [6, 1, 5, 2], [-1, 2, -3, -7]])
+>>> B = matrix([[4,-15, 9, -14], [-4, -12, 1, -22], [-10, -9, 9, 12], [-9, -7,-11, -6]])
+>>> print matrix(map(max, A, B), (4,4)) # takes componentwise maximum
+ 5 -1 6 -1
+ -4 -5 1 2
+ 10 1 9 -3
+ -7 2 12 -6
+</pre></div>
+
+<P>
+<code>filter(<var>f</var>,<var>A</var>)</code>, where <var>f</var> is a function and
+<var>A</var> is a matrix, returns a list containing the elements of <var>A</var>
+for which <var>f</var> is true.
+<div class="verbatim"><pre>
+>>> print filter(lambda x: x%2, A) # list of odd elements in A
+[5, -7, -1, -5, 1, 5, -1, -3, -7]
+>>> print filter(lambda x: -2 < x < 3, A) # list of elements between -2 and 3
+[-1, 2, 1, 2, -1, 2]
+</pre></div>
+
+<P>
+It is also possible to iterate over matrix elements, as illustrated in
+the following example.
+<div class="verbatim"><pre>
+>>> A = matrix([[5, -3], [9, 11]])
+>>> for x in A: print max(x,0)
+...
+5
+0
+9
+11
+>>> [max(x,0) for x in A]
+[5, 0, 9, 11]
+</pre></div>
+
+<P>
+The expression "<tt class="samp"><var>x</var> in <var>A</var></tt>" returns <code>True</code> if an element
+of <var>A</var> is equal to <var>x</var> and <code>False</code> otherwise.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="2.4 Indexing and Slicing"
+ href="s-indexing.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="2. Dense Matrices (cvxopt.base)"
+ href="node4.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="2.6 Other Matrix Functions"
+ href="s-otherfuncs.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
+ border='0' height='32' alt='' width='32' /></td>
+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
+ border='0' height='32' alt='Index' width='32' /></A></td>
+</tr></table>
+<div class='online-navigation'>
+<b class="navlabel">Previous:</b>
+<a class="sectref" rel="prev" href="s-indexing.html">2.4 Indexing and Slicing</A>
+<b class="navlabel">Up:</b>
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+<b class="navlabel">Next:</b>
+<a class="sectref" rel="next" href="s-otherfuncs.html">2.6 Other Matrix Functions</A>
+</div>
+</div>
+<hr />
+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
+<!--End of Navigation Panel-->
+
+</BODY>
+</HTML>
diff --git a/doc/cvxopt/s-cholmod.html b/doc/cvxopt/s-cholmod.html
new file mode 100644
index 0000000..2980c4a
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+++ b/doc/cvxopt/s-cholmod.html
@@ -0,0 +1,514 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
+<link rel="next" href="e-covsel.html" />
+<link rel="prev" href="s-umfpack.html" />
+<link rel="parent" href="c-spsolvers.html" />
+<link rel="next" href="e-covsel.html" />
+<meta name='aesop' content='information' />
+<title>7.3 Positive Definite Linear Equations (cvxopt.cholmod)</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="7.2 General Linear Equations"
+ href="s-umfpack.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
+<td class='online-navigation'><a rel="parent" title="7. Sparse Linear Equation"
+ href="c-spsolvers.html"><img src='up.gif'
+ border='0' height='32' alt='Up One Level' width='32' /></A></td>
+<td class='online-navigation'><a rel="next" title="7.4 Example: Covariance Selection"
+ href="e-covsel.html"><img src='next.gif'
+ border='0' height='32' alt='Next Page' width='32' /></A></td>
+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
+<td class='online-navigation'><a rel="contents" title="Table of Contents"
+ href="contents.html"><img src='contents.gif'
+ border='0' height='32' alt='Contents' width='32' /></A></td>
+<td class='online-navigation'><img src='blank.gif'
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+<td class='online-navigation'><a rel="index" title="Index"
+ href="genindex.html"><img src='index.gif'
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+
+<H1><A NAME="SECTION009300000000000000000"></A>
+<A NAME="s-cholmod"></A>
+<BR>
+7.3 Positive Definite Linear Equations (<tt class="module">cvxopt.cholmod</tt>)
+</H1>
+
+<P>
+<tt class="module">cvxopt.cholmod</tt> is an interface to the Cholesky factorization
+routines of the CHOLMOD package.
+It includes functions for Cholesky factorization of sparse positive
+definite matrices, and for solving sparse sets of linear equations with
+positive definite matrices.
+The routines can also be used for computing LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img40.gif"
+ ALT="$\mathrm{{}^T}$"></SPAN>
+(or LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img89.gif"
+ ALT="$\mathrm{{}^H}$"></SPAN>) factorizations of symmetric indefinite matrices
+(with L unit lower-triangular and D diagonal and nonsingular) if
+such a factorization exists.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://www.cise.ufl.edu/research/sparse/cholmod'
+ >CHOLMOD code, documentation, copyright and license.</a></dt>
+ <dd></dd>
+ </dl>
+</div>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-138' xml:id='l2h-138' class="function">linsolve</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, p=<code>None</code></var><big>[</big><var>,
+uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX = B
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="60" HEIGHT="24" BORDER="0"
+ SRC="img47.gif"
+ ALT="\begin{displaymath}
+AX=B
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+with <I>A</I> sparse and real symmetric or complex Hermitian.
+<var>B</var> is a dense matrix of the same type as <var>A</var>. On exit it
+is overwritten with the solution.
+The argument <var>p</var> is an integer matrix with length equal to the
+order of <var>A</var>, and specifies an optional reordering of <var>A</var>.
+If <var>p</var> is not specified, CHOLMOD used a reordering from the
+AMD library.
+Raises an <code>ArithmeticError</code> if the factorization does not exist.
+</dl>
+
+<P>
+As an example, we solve
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+\left[ \begin{array}{rrrr}
+ 10 & 0 & 3 & 0 \\
+ 0 & 5 & 0 & -2 \\
+ 3 & 0 & 5 & 0 \\
+ 0 & -2 & 0 & 2
+ \end{array}\right] X = \left[ \begin{array}{cc}
+ 0 & 4 \\1 & 5 \\2 & 6 \\3 & 7\end{array} \right].
+\end{equation}
+ -->
+<A NAME="e-A-pd"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-A-pd"></A><IMG
+ WIDTH="258" HEIGHT="83" BORDER="0"
+ SRC="img90.gif"
+ ALT="\begin{displaymath}
+\left[ \begin{array}{rrrr}
+10 & 0 & 3 & 0 \\
+0 & 5 & 0 & ...
+...ray}{cc}
+0 & 4 \\ 1 & 5 \\ 2 & 6 \\ 3 & 7\end{array} \right].
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(7.2)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix, spmatrix
+>>> from cvxopt import cholmod
+>>> A = spmatrix([10,3, 5,-2, 5, 2], [0,2, 1,3, 2, 3], [0,0, 1,1, 2, 3])
+>>> X = matrix(range(8), (4,2), 'd')
+>>> cholmod.linsolve(A,X)
+>>> print X
+-1.4634e-01 4.8780e-02
+ 1.3333e+00 4.0000e+00
+ 4.8780e-01 1.1707e+00
+ 2.8333e+00 7.5000e+00
+</pre></div>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-139' xml:id='l2h-139' class="function">splinsolve</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, p=<code>None</code></var><big>[</big><var>,
+uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Similar to <tt class="function">linsolve()</tt> except that <var>B</var> is a sparse
+matrix and that the solution is returned as an output
+argument (as a new sparse matrix). <var>B</var> is not modified.
+</dl>
+
+<P>
+The following code computes the inverse of the coefficient matrix
+in (<A HREF="#e-A-pd">7.2</A>) as a sparse matrix.
+<div class="verbatim"><pre>
+>>> X = cholmod.splinsolve(A, spmatrix(1.0,range(4),range(4)))
+>>> print X
+SIZE: (4,4)
+(0, 0) 1.2195e-01
+(2, 0) -7.3171e-02
+(1, 1) 3.3333e-01
+(3, 1) 3.3333e-01
+(0, 2) -7.3171e-02
+(2, 2) 2.4390e-01
+(1, 3) 3.3333e-01
+(3, 3) 8.3333e-01
+</pre></div>
+
+<P>
+The functions <tt class="function">linsolve()</tt> and <tt class="function">splinsolve()</tt> are
+equivalent to <tt class="function">symbolic()</tt> and <tt class="function">numeric()</tt> called in
+sequence, followed by <tt class="function">solve()</tt>, respectively,
+<tt class="function">spsolve()</tt>.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-140' xml:id='l2h-140' class="function">symbolic</tt></b>(</nobr></td>
+ <td><var>A</var><big>[</big><var>, p=<code>None</code></var><big>[</big><var>, uplo='L'</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Performs a symbolic analysis of a sparse real symmetric or
+complex Hermitian matrix <var>A</var> for one of the two factorizations:
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+PAP^T = LL^T, \qquad PAP^T = LL^H,
+\end{equation}
+ -->
+<A NAME="e-chol-ll"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-chol-ll"></A><IMG
+ WIDTH="244" HEIGHT="27" BORDER="0"
+ SRC="img91.gif"
+ ALT="\begin{displaymath}
+PAP^T = LL^T, \qquad PAP^T = LL^H,
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(7.3)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+and
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+PAP^T = LDL^T, \qquad PAP^T = LDL^H,
+\end{equation}
+ -->
+<A NAME="e-chol-ldl"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-chol-ldl"></A><IMG
+ WIDTH="272" HEIGHT="27" BORDER="0"
+ SRC="img92.gif"
+ ALT="\begin{displaymath}
+PAP^T = LDL^T, \qquad PAP^T = LDL^H,
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(7.4)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+where <I>P</I> is a permutation matrix, <I>L</I> is lower triangular
+(unit lower triangular in the second factorization), and
+<I>D</I> is nonsingular diagonal. The type of factorization depends
+on the value of <code>options['supernodal']</code>.
+
+<P>
+If <var>uplo</var> is <code>'L'</code>, only the lower triangular part of <var>A</var>
+is accessed and the upper triangular part is ignored.
+If <var>uplo</var> is <code>'U'</code>, only the upper triangular part of <var>A</var>
+is accessed and the lower triangular part is ignored.
+
+<P>
+The symbolic factorization is returned as an opaque C object that
+can be passed to <tt class="function">cholmod.numeric()</tt>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-141' xml:id='l2h-141' class="function">numeric</tt></b>(</nobr></td>
+ <td><var>A, F</var>)</td></tr></table></dt>
+<dd>
+Performs a numeric factorization of a sparse symmetric matrix
+as (<A HREF="#e-chol-ll">7.3</A>) or (<A HREF="#e-chol-ldl">7.4</A>).
+The argument <var>F</var> is the symbolic factorization
+computed by <tt class="function">cholmod.symbolic()</tt> applied to the matrix <var>A</var>,
+or to another sparse matrix with the same sparsity pattern and
+typecode, or by
+<tt class="function">cholmod.numeric()</tt> applied to a matrix with the same
+sparsity pattern and typecode as <var>A</var>.
+
+<P>
+If <var>F</var> was created by a <tt class="function">cholmod.symbolic</tt> with
+<var>uplo</var> equal to <code>'L'</code>, then only the lower triangular part
+of <var>A</var> is accessed and the upper triangular part is ignored.
+If it was created with <var>uplo</var> is <code>'U'</code>, then only the upper
+triangular part of <var>A</var> is accessed and the lower triangular part
+is ignored.
+
+<P>
+On successful exit, the factorization is stored in <var>F</var>.
+Raises an <code>ArithmeticError</code> if the factorization does not
+exist.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-142' xml:id='l2h-142' class="function">solve</tt></b>(</nobr></td>
+ <td><var>F, B</var><big>[</big><var>, sys=0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves one of the following linear equations where <var>B</var> is a dense
+matrix and <var>F</var> is the numeric
+factorization (<A HREF="#e-chol-ll">7.3</A>) or (<A HREF="#e-chol-ldl">7.4</A>) computed by
+<tt class="function">cholmod_numeric()</tt>.
+<var>sys</var> is an integer with values between 0 and 8.
+
+<P>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1">
+<TR><TD ALIGN="CENTER"><var>sys</var></TD>
+<TD ALIGN="CENTER">equation</TD>
+</TR>
+<TR><TD ALIGN="CENTER">0</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="64" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img93.gif"
+ ALT="$AX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">1</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="98" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img94.gif"
+ ALT="$LDL^TX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">2</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="88" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img95.gif"
+ ALT="$LDLX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">3</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="87" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img96.gif"
+ ALT="$DL^TX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">4</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="63" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img97.gif"
+ ALT="$LX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">5</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="73" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img98.gif"
+ ALT="$L^TX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">6</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="66" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img99.gif"
+ ALT="$DX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">7</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="75" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img100.gif"
+ ALT="$P^TX=B$"></SPAN></TD>
+</TR>
+<TR><TD ALIGN="CENTER">8</TD>
+<TD ALIGN="CENTER"><SPAN CLASS="MATH"><IMG
+ WIDTH="65" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img101.gif"
+ ALT="$PX=B$"></SPAN></TD>
+</TR>
+</TABLE>
+</DIV>
+
+<P>
+(If <var>F</var> is a Cholesky factorization of the form (<A HREF="#e-chol-ll">7.3</A>),
+<I>D</I> is an identity matrix in this table.
+If <var>A</var> is complex, <SPAN CLASS="MATH"><IMG
+ WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img102.gif"
+ ALT="$L^T$"></SPAN> should be replaced by <SPAN CLASS="MATH"><IMG
+ WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
+ SRC="img103.gif"
+ ALT="$L^H$"></SPAN>.)
+
+<P>
+The matrix <var>B</var> is a dense <code>'d'</code> or <code>'z'</code> matrix, with the same type
+as <var>A</var>. On exit it is overwritten by the solution.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-143' xml:id='l2h-143' class="function">spsolve</tt></b>(</nobr></td>
+ <td><var>F, B</var><big>[</big><var>, sys=0</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Similar to <tt class="function">solve()</tt>, except that <var>B</var> is a
+sparse matrix, and the solution is returned as an output argument
+(as a sparse matrix). <var>B</var> must have the same typecode as <var>A</var>.
+</dl>
+
+<P>
+For the same example as above:
+<div class="verbatim"><pre>
+>>> X = matrix(range(8), (4,2), 'd')
+>>> F = cholmod.symbolic(A)
+>>> cholmod.numeric(A,F)
+>>> cholmod.solve(F,X)
+>>> print X
+-1.4634e-01 4.8780e-02
+ 1.3333e+00 4.0000e+00
+ 4.8780e-01 1.1707e+00
+ 2.8333e+00 7.5000e+00
+</pre></div>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-144' xml:id='l2h-144' class="function">diag</tt></b>(</nobr></td>
+ <td><var>F</var>)</td></tr></table></dt>
+<dd>
+Returns the diagonal elements of the Cholesky factor <I>L</I>
+in (<A HREF="#e-chol-ll">7.3</A>), as a dense matrix of the same type as <var>A</var>.
+Note that this only applies to Cholesky factorizations.
+The matrix <I>D</I> in an LDL<SPAN CLASS="MATH"><IMG
+ WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img40.gif"
+ ALT="$\mathrm{{}^T}$"></SPAN> factorization can be
+retrieved via <tt class="function">cholmod.solve()</tt> with <var>sys</var> equal to 6.
+</dl>
+
+<P>
+In the functions listed above, the default values of the control
+parameters described in the CHOLMOD user guide are used, except for
+<tt class="ctype">Common->print</tt> which is set to 0 instead of 3
+and
+<tt class="ctype">Common->supernodal</tt> which is set to 2 instead of 1.
+These parameters (and a few others) can be modified by making an
+entry in the dictionary <tt class="member">cholmod.options</tt>.
+The meaning of these parameters is as follows.
+<DL>
+<DT><STRONG><code>options['supernodal']</code></STRONG></DT>
+<DD>If equal to 0, a
+factorization (<A HREF="#e-chol-ldl">7.4</A>) is computed using a simplicial
+algorithm.
+If equal to 2, a factorization (<A HREF="#e-chol-ll">7.3</A>) is
+computed using a supernodal algorithm.
+If equal to 1, the most efficient of the two factorizations is
+selected, based on the sparsity pattern. Default: 2.
+
+<P>
+</DD>
+<DT><STRONG><code>options['print']</code></STRONG></DT>
+<DD>A nonnegative integer that controls the
+amount of output printed to the screen.
+Default: 0 (no output).
+</DD>
+</DL>
+
+<P>
+As an example that illustrates <tt class="function">diag()</tt> and the use of
+<tt class="member">cholmod.options</tt>, we compute the logarithm of the determinant
+of the coefficient matrix in (<A HREF="#e-A-pd">7.2</A>) by two methods.
+<div class="verbatim"><pre>
+>>> import math
+>>> from cvxopt.cholmod import options
+>>> from cvxopt.base import log
+>>> options['supernodal'] = 2
+>>> F = cholmod.symbolic(A)
+>>> cholmod.numeric(A,F)
+>>> print 2.0 * sum(log(cholmod.diag(F)))
+5.50533153593
+</pre></div>
+<div class="verbatim"><pre>
+>>> options['supernodal'] = 0
+>>> F = cholmod.symbolic(A)
+>>> cholmod.numeric(A,F)
+>>> Di = matrix(1.0, (4,1))
+>>> cholmod.solve(F,Di,sys=6)
+>>> print -sum(log(Di))
+5.50533153593
+</pre></div>
+
+<P>
+
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+
+<H1><A NAME="SECTION005100000000000000000"></A> <A NAME="s-conventions"></A>
+<BR>
+3.1 Matrix Classes
+</H1>
+
+<P>
+The BLAS exploit several types of matrix structure: symmetric,
+Hermitian, triangular, and banded. We represent all these matrix
+classes by dense real or complex <tt class="class">matrix</tt> objects, with additional
+arguments that specify the structure.
+
+<P>
+<DL>
+<DT><STRONG>Vector</STRONG></DT>
+<DD>A real or complex <I>n</I>-vector is represented by a <tt class="class">matrix</tt> of type
+<code>'d'</code> or <code>'z'</code> and length <I>n</I>, with the entries of the vector
+stored in column-major order.
+
+<P>
+</DD>
+<DT><STRONG>General matrix</STRONG></DT>
+<DD>A general real or complex <I>m</I> by <I>n</I> matrix is represented by
+a real or complex <tt class="class">matrix</tt> of size (<I>m</I>, <I>n</I>).
+
+<P>
+</DD>
+<DT><STRONG>Symmetric matrix</STRONG></DT>
+<DD>A real or complex symmetric matrix of order <I>n</I> is represented
+by a real or complex <tt class="class">matrix</tt> of size (<I>n</I>, <I>n</I>), and a character
+argument <var>uplo</var> with two possible values:
+<code>'L'</code> and <code>'U'</code>.
+If <var>uplo</var> is <code>'L'</code>, the lower triangular part of the
+symmetric matrix is stored; if <var>uplo</var> is <code>'U'</code>, the upper
+triangular part is stored. A square <tt class="class">matrix</tt> <var>X</var> of size
+(<I>n</I>, <I>n</I>) can therefore be used to represent the symmetric
+matrices
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+& \left[\begin{array}{ccccc}
+X[0,0] & X[1,0] & X[2,0] & \cdots & X[n-1,0] \\
+X[1,0] & X[1,1] & X[2,1] & \cdots & X[n-1,1] \\
+X[2,0] & X[2,1] & X[2,2] & \cdots & X[n-1,2] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+& \left[\begin{array}{ccccc}
+X[0,0] & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+X[0,1] & X[1,1] & X[1,2] & \cdots & X[1,n-1] \\
+X[0,2] & X[1,2] & X[2,2] & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[0,n-1] & X[1,n-1] & X[2,n-1] & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = U'}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="542" HEIGHT="225" BORDER="0"
+ SRC="img1.gif"
+ ALT="\begin{eqnarray*}
+& \left[\begin{array}{ccccc}
+X[0,0] & X[1,0] & X[2,0] & \cdots...
+...& \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = U'}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+</DD>
+<DT><STRONG>Complex Hermitian matrix</STRONG></DT>
+<DD>A complex Hermitian matrix of order <I>n</I> is represented
+by a <tt class="class">matrix</tt> of type <code>'z'</code> and size (<I>n</I>, <I>n</I>), and
+a character argument <var>uplo</var> with the ame meaning as for symmetric
+matrices.
+A complex <tt class="class">matrix</tt> <var>X</var> of size (<I>n</I>, <I>n</I>) can
+represent the Hermitian matrices
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+&
+\left[\begin{array}{ccccc}
+\Re X[0,0] & \bar X[1,0] & \bar X[2,0] & \cdots & \bar X[n-1,0] \\
+X[1,0] & \Re X[1,1] & \bar X[2,1] & \cdots & \bar X[n-1,1] \\
+X[2,0] & X[2,1] & \Re X[2,2] & \cdots & \bar X[n-1,2] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & \Re X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+& \left[\begin{array}{ccccc}
+\Re X[0,0] & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+\bar X[0,1] & \Re X[1,1] & X[1,2] & \cdots & X[1,n-1] \\
+\bar X[0,2] & \bar X[1,2] & \Re X[2,2] & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+\bar X[0,n-1] & \bar X[1,n-1] & \bar X[2,n-1] & \cdots & \Re X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'U'}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="556" HEIGHT="225" BORDER="0"
+ SRC="img2.gif"
+ ALT="\begin{eqnarray*}
+&
+\left[\begin{array}{ccccc}
+\Re X[0,0] & \bar X[1,0] & \bar X...
+...dots & \Re X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'U'}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+</DD>
+<DT><STRONG>Triangular matrix</STRONG></DT>
+<DD>A real or complex triangular matrix of order <I>n</I> is represented
+by a real or complex <tt class="class">matrix</tt> of size (<I>n</I>, <I>n</I>), and two
+character arguments: an argument <var>uplo</var> with possible values
+<code>'L'</code> and <code>'U'</code> to distinguish between lower and upper
+triangular matrices, and an argument <var>diag</var> with possible values
+<code>'U'</code> and <code>'N'</code> to distinguish between unit and non-unit
+triangular matrices. A square <tt class="class">matrix</tt> <var>X</var> of size
+(<I>n</I>, <I>n</I>) can represent the triangular matrices
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+& \left[\begin{array}{ccccc}
+X[0,0] & 0 & 0 & \cdots & 0 \\
+X[1,0] & X[1,1] & 0 & \cdots & 0 \\
+X[2,0] & X[2,1] & X[2,2] & \cdots & 0 \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'N'}, \\
+& \left[\begin{array}{ccccc}
+1 & 0 & 0 & \cdots & 0 \\
+X[1,0] & 1 & 0 & \cdots & 0 \\
+X[2,0] & X[2,1] & 1 & \cdots & 0 \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+X[n-1,0] & X[n-1,1] & X[n-1,2] & \cdots & 1
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'U'}, \\
+& \left[\begin{array}{ccccc}
+X[0,0] & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+0 & X[1,1] & X[1,2] & \cdots & X[1,n-1] \\
+0 & 0 & X[2,2] & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+0 & 0 & 0 & \cdots & X[n-1,n-1]
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'N'}, \\
+& \left[\begin{array}{ccccc}
+1 & X[0,1] & X[0,2] & \cdots & X[0,n-1] \\
+0 & 1 & X[1,2] & \cdots & X[1,n-1] \\
+0 & 0 & 1 & \cdots & X[2,n-1] \\
+\vdots & \vdots & \vdots & \ddots & \vdots \\
+0 & 0 & 0 & \cdots & 1
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'U'}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="643" HEIGHT="450" BORDER="0"
+ SRC="img3.gif"
+ ALT="\begin{eqnarray*}
+& \left[\begin{array}{ccccc}
+X[0,0] & 0 & 0 & \cdots & 0 \\
+X...
+...ts & 1
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'U'}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+</DD>
+<DT><STRONG>General band matrix</STRONG></DT>
+<DD>A general real or complex <I>m</I> by <I>n</I> band matrix with <I>kl</I>
+subdiagonals and <I>ku</I> superdiagonals is represented by a real or
+complex <tt class="class">matrix</tt> <var>X</var> of size (<I>kl+ku+1</I>, <I>n</I>), and the two
+integers <I>m</I> and <I>kl</I>.
+The diagonals of the band matrix are stored in the rows of <var>X</var>,
+starting at the top diagonal, and shifted horizontally so that the
+entries of the
+<I>k</I>th column of the band matrix are stored in column <I>k</I> of
+<var>X</var>. A <tt class="class">matrix</tt> <var>X</var> of size (<I>kl+ku+1</I>, <I>n</I>) therefore
+represents the <I>m</I> by <I>n</I> band matrix
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\left[ \begin{array}{ccccccc}
+X[k_u,0] & X[k_u-1,1] & X[k_u-2,2] & \cdots & X[0,k_u] & 0 & \cdots \\
+X[k_u+1,0] & X[k_u,1] & X[k_u-1,2] & \cdots & X[1,k_u] & X[0,k_u+1] & \cdots \\
+X[k_u+2,0] & X[k_u+1,1] & X[k_u,2] & \cdots & X[2,k_u] & X[1,k_u+1] & \cdots \\
+ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[k_u+k_l,0] & X[k_u+k_l-1,1] & X[k_u+k_l-2,2] & \cdots & & & \\
+0 & X[k_u+k_l,1] & X[k_u+k_l-1,2] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right].
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="624" HEIGHT="161" BORDER="0"
+ SRC="img4.gif"
+ ALT="\begin{displaymath}
+\left[ \begin{array}{ccccccc}
+X[k_u,0] & X[k_u-1,1] & X[k_u-...
+...
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right].
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG>Symmetric band matrix</STRONG></DT>
+<DD>A real or complex symmetric band matrix of order <I>n</I> with <I>k</I>
+subdiagonals, is represented by a real or complex matrix <var>X</var> of
+size (<I>k</I>+1, <I>n</I>), and an argument <I>uplo</I> to indicate
+whether the subdiagonals (<I>uplo</I> is <code>'L'</code>) or superdiagonals
+(<I>uplo</I> is <code>'U'</code>) are stored.
+The <I>k</I>+1 diagonals are stored as rows of <var>X</var>, starting at the top
+diagonal (<EM>i.e.</EM>, the main diagonal if <I>uplo</I> is <code>'L'</code>, or
+the <I>k</I>th superdiagonal if <I>uplo</I> is <code>'U'</code>) and shifted
+horizontally so that the entries of the
+<I>k</I>th column of the band matrix are stored in column <I>k</I> of
+<var>X</var>. A <tt class="class">matrix</tt> <I>X</I> of size (<I>k</I>+1, <I>n</I>) can therefore
+represent the band matrices
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+& \left[ \begin{array}{ccccccc}
+X[0,0] & X[1,0] & X[2,0] & \cdots & X[k,0] & 0 & \cdots \\
+X[1,0] & X[0,1] & X[1,1] & \cdots & X[k-1,1] & X[k,1] & \cdots \\
+X[2,0] & X[1,1] & X[0,2] & \cdots & X[k-2,2] & X[k-1,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & & & \\
+0 & X[k,1] & X[k-1,2] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+&
+\left[ \begin{array}{ccccccc}
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & X[0,k] & 0 & \cdots \\
+X[k-1,1] & X[k,1] & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+X[k-2,2] & X[k-1,2] & X[k,2] & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[0,k] & X[1,k] & X[2,k] & \cdots & & & \\
+0 & X[0,k+1] & X[1,k+1] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo='U'}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="608" HEIGHT="322" BORDER="0"
+ SRC="img5.gif"
+ ALT="\begin{eqnarray*}
+& \left[ \begin{array}{ccccccc}
+X[0,0] & X[1,0] & X[2,0] & \cd...
+... \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo='U'}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+</DD>
+<DT><STRONG>Hermitian band matrix</STRONG></DT>
+<DD>A complex Hermitian band matrix of order <I>n</I> with <I>k</I>
+subdiagonals is represented by a complex matrix of size
+(<I>k+1</I>, <I>n</I>) and an argument <var>uplo</var>.
+A <tt class="class">matrix</tt> <I>X</I> of size (<I>k</I>+1, <I>n</I>) can represent the band
+matrices
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+& \left[ \begin{array}{ccccccc}
+\Re X[0,0] & \bar X[1,0] & \bar X[2,0] & \cdots & \bar X[k,0] & 0 & \cdots \\
+X[1,0] & \Re X[0,1] & \bar X[1,1] & \cdots & \bar X[k-1,1] & \bar X[k,1] & \cdots \\
+X[2,0] & X[1,1] & \Re X[0,2] & \cdots & \bar X[k-2,2] & \bar X[k-1,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & & & \\
+0 & X[k,1] & X[k-1,2] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo = 'L'}, \\
+&
+\left[ \begin{array}{ccccccc}
+\Re X[k,0] & X[k-1,1] & X[k-2,2] & \cdots & X[0,k] & 0 & \cdots \\
+\bar X[k-1,1] & \Re X[k,1] & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+\bar X[k-2,2] & \bar X[k-1,2] & \Re X[k,2] & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots \\
+\bar X[0,k] & \bar X[1,k] & \bar X[2,k] & \cdots & & & \\
+0 & \bar X[0,k+1] & \bar X[1,k+1] & \cdots & & & \\
+\vdots & \vdots & \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo='U'}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="619" HEIGHT="322" BORDER="0"
+ SRC="img6.gif"
+ ALT="\begin{eqnarray*}
+& \left[ \begin{array}{ccccccc}
+\Re X[0,0] & \bar X[1,0] & \ba...
+... \vdots & \ddots & & &
+\end{array}\right] & \mbox{if uplo='U'}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+</DD>
+<DT><STRONG>Triangular band matrix</STRONG></DT>
+<DD>A triangular band matrix of order <I>n</I> with <I>k</I> subdiagonals or
+superdiagonals is represented by a real complex matrix of size
+(<I>k+1</I>, <I>n</I>) and two character arguments <var>uplo</var> and
+<var>diag</var>.
+A <tt class="class">matrix</tt> <I>X</I> of size (<I>k</I>+1, <I>n</I>) can represent the band
+matrices
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+& \left[ \begin{array}{cccc}
+X[0,0] & 0 & 0 & \cdots \\
+X[1,0] & X[0,1] & 0 & \cdots \\
+X[2,0] & X[1,1] & X[0,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots \\
+0 & X[k,1] & X[k-1,1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'N'}, \\
+& \left[ \begin{array}{cccc}
+1 & 0 & 0 & \cdots \\
+X[1,0] & 1 & 0 & \cdots \\
+X[2,0] & X[1,1] & 1 & \cdots \\
+\vdots & \vdots & \vdots & \ddots \\
+X[k,0] & X[k-1,1] & X[k-2,2] & \cdots \\
+0 & X[k,1] & X[k-1,2] & \cdots \\
+\vdots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'L' and diag = 'U'}, \\
+& \left[ \begin{array}{ccccccc}
+X[k,0] & X[k-1,1] & X[k-2,3] & \cdots & X[0,k] & 0 & \cdots\\
+0 & X[k,1] & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+0 & 0 & X[k,2] & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'N'}, \\
+& \left[ \begin{array}{ccccccc}
+1 & X[k-1,1] & X[k-2,3] & \cdots & X[0,k] & 0 & \cdots\\
+0 & 1 & X[k-1,2] & \cdots & X[1,k] & X[0,k+1] & \cdots \\
+0 & 0 & 1 & \cdots & X[2,k] & X[1,k+1] & \cdots \\
+\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'U'}.
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="681" HEIGHT="509" BORDER="0"
+ SRC="img7.gif"
+ ALT="\begin{eqnarray*}
+& \left[ \begin{array}{cccc}
+X[0,0] & 0 & 0 & \cdots \\
+X[1,0...
+...ddots
+\end{array}\right] & \mbox{if uplo = 'U' and diag = 'U'}.
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+</DD>
+</DL>
+
+<P>
+When discussing BLAS functions in the following sections we will
+omit several less important optional arguments that can
+be used to select submatrices for in-place operations.
+The complete specification is documented in the docstrings of the
+source code and the <b class="program">pydoc</b> help program.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="3. The BLAS Interface"
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
+</DIV>
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+<H1><A NAME="SECTION004100000000000000000"></A><A NAME="s-creating-matrices"></A>
+<BR>
+2.1 Creating Matrices
+</H1>
+A <tt class="class">matrix</tt> object is created by calling the function <tt class="function">matrix()</tt>.
+The arguments specify the values of the coefficients, the
+dimensions, and the type (integer, double or complex) of the matrix.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-1' xml:id='l2h-1' class="function">matrix</tt></b>(</nobr></td>
+ <td><var>x</var><big>[</big><var>, size</var><big>[</big><var>, tc</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+<var>size</var> is a tuple of length two with the matrix dimensions.
+The number of rows and/or the number of columns can be zero.
+
+<P>
+<var>tc</var> stands for typecode. The possible values are <code>'i'</code>, <code>'d'</code> and
+<code>'z'</code>, for integer, real (double) and complex matrices, respectively.
+
+<P>
+<var>x</var> can be a number, a sequence of numbers, a dense or sparse
+matrix, a two-dimensional <tt class="module">numarray</tt> array, or a list of
+lists of matrices and numbers.
+
+<UL>
+<LI>If <var>x</var> is a number (Python integer, float or complex), a matrix
+is created with the dimensions specified by <var>size</var> and with all the
+coefficients equal to <var>x</var>.
+The default value of <var>size</var> is (1,1), and the default value
+of <var>tc</var> is the type of <var>x</var>.
+If necessary, the type of <var>x</var> is converted (from integer to double
+when used to create a matrix of type <code>'d'</code>, and from integer or
+double to complex when used to create a matrix of type <code>'z'</code>).
+
+<P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> A = matrix(1, (1,4))
+>>> print A
+ 1 1 1 1
+>>> A = matrix(1.0, (1,4))
+>>> print A
+ 1.0000e+00 1.0000e+00 1.0000e+00 1.0000e+00
+>>> A = matrix(1+1j)
+>>> print A
+ 1.0000e+00+j1.0000e+00
+</pre></div>
+
+<P>
+</LI>
+<LI>If <var>x</var> is a sequence of numbers (list, tuple, <tt class="module">array</tt>
+array, xrange object, one-dimensional <tt class="module">numarray</tt> array, ...),
+then the numbers are interpreted as the coefficients of a matrix in
+column-major order. The length of <var>x</var> must be equal to the product
+of <var>size</var>[0] and <var>size</var>[1].
+If <var>size</var> is not specified, a matrix with one column is created.
+If <var>tc</var> is not specified, it is determined from the elements of
+<var>x</var> (and if that is impossible, for example because <var>x</var> is
+an empty list, a value <code>'i'</code> is used).
+Type conversion takes place as for scalar <var>x</var>.
+
+<P>
+The following example shows several ways to define the same integer
+matrix.
+<div class="verbatim"><pre>
+>>> A = matrix([0, 1, 2, 3], (2,2))
+>>> A = matrix((0, 1, 2, 3), (2,2))
+>>> A = matrix(xrange(4), (2,2))
+>>> from array import array
+>>> A = matrix(array('i', [0,1,2,3]), (2,2))
+>>> print A
+ 0 2
+ 1 3
+</pre></div>
+
+<P>
+</LI>
+<LI>If <var>x</var> is a dense or sparse matrix (a <tt class="class">matrix</tt> or a <tt class="class">spmatrix</tt>
+object), or a two-dimensional <tt class="module">numarray</tt> array of type <code>'i'</code>,
+<code>'d'</code> or <code>'z'</code>, then the coefficients of <var>x</var> are copied, in
+column-major order, to a new matrix of the given size.
+The total number of elements in the new matrix (the product of
+<var>size</var>[0] and <var>size</var>[1]) must be the same as the product of
+the dimensions of <var>x</var>. If <var>size</var> is not specified, the
+dimensions of <var>x</var> are used.
+The default value of <var>tc</var> is the type of <var>x</var>.
+Type conversion takes place when the type of <var>x</var> differs from
+<var>tc</var>, in a similar way as for scalar <var>x</var>.
+
+<P>
+<div class="verbatim"><pre>
+>>> A = matrix([1., 2., 3., 4., 5., 6.], (2,3))
+>>> print A
+ 1.0000e+00 3.0000e+00 5.0000e+00
+ 2.0000e+00 4.0000e+00 6.0000e+00
+>>> B = matrix(A, (3,2))
+>>> print B
+ 1.0000e+00 4.0000e+00
+ 2.0000e+00 5.0000e+00
+ 3.0000e+00 6.0000e+00
+>>> C = matrix(B, tc='z')
+>>> print C
+ 1.0000e+00-j0.0000e+00 4.0000e+00-j0.0000e+00
+ 2.0000e+00-j0.0000e+00 5.0000e+00-j0.0000e+00
+ 3.0000e+00-j0.0000e+00 6.0000e+00-j0.0000e+00
+>>> from numarray import array
+>>> x = array([1., 2., 3., 4., 5., 6.], shape=(2,3))
+>>> print x
+[[ 1. 2. 3.]
+ [ 4. 5. 6.]]
+>>> y = matrix(x)
+>>> print y
+ 1.0000e+00 2.0000e+00 3.0000e+00
+ 4.0000e+00 5.0000e+00 6.0000e+00
+</pre></div>
+
+<P>
+</LI>
+<LI>If <var>x</var> is a list of lists of matrices
+(<tt class="class">matrix</tt> or <tt class="class">spmatrix</tt> objects) or numbers (Python integer, float or
+complex), then each element of <var>x</var> is interpreted as a
+block-column stored in column-major order.
+If <var>size</var> is not specified, the block-columns are juxtaposed
+to obtain a matrix with <code>len(<var>x</var>)</code> block-columns.
+If <var>size</var> is specified, then the matrix with <code>len(<var>x</var>)</code>
+block-columns is resized by copying its elements in column-major order
+into a matrix of the dimensions given by <var>size</var>.
+If <var>tc</var> is not specified, it is determined from the elements of
+<var>x</var> (and if that is impossible, for example because <var>x</var> is
+a list of empty lists, a value <code>'i'</code> is used).
+The same rules for type conversion apply as for scalar <var>x</var>.
+
+<P>
+<div class="verbatim"><pre>
+>>> A = matrix([[1., 2.], [3., 4.], [5., 6.]])
+>>> print A
+ 1.0000e+00 3.0000e+00 5.0000e+00
+ 2.0000e+00 4.0000e+00 6.0000e+00
+>>> A1 = matrix([1, 2], (2,1))
+>>> B1 = matrix([6, 7, 8, 9, 10, 11], (2,3))
+>>> B2 = matrix([12, 13, 14, 15, 16, 17], (2,3))
+>>> B3 = matrix([18, 19, 20], (1,3))
+>>> print matrix([[A1, 3.0, 4.0, 5.0], [B1, B2, B3]])
+ 1.0000e+00 6.0000e+00 8.0000e+00 1.0000e+01
+ 2.0000e+00 7.0000e+00 9.0000e+00 1.1000e+01
+ 3.0000e+00 1.2000e+01 1.4000e+01 1.6000e+01
+ 4.0000e+00 1.3000e+01 1.5000e+01 1.7000e+01
+ 5.0000e+00 1.8000e+01 1.9000e+01 2.0000e+01
+</pre></div>
+
+<P>
+A matrix with a single block-column can be represented by a single
+list (<EM>i.e.</EM>, when the length of <var>x</var> is one, it can be replaced with
+<code><var>x</var>[0]</code>).
+<div class="verbatim"><pre>
+>>> print matrix([B1, B2, B3])
+ 6 8 10
+ 7 9 11
+ 12 14 16
+ 13 15 17
+ 18 19 20
+</pre></div>
+</LI>
+</UL>
+</dl>
+
+<P>
+
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+
+<H1><A NAME="SECTION008100000000000000000"></A> <A NAME="s-creating-spmatrix"></A>
+<BR>
+6.1 Creating Sparse Matrices
+</H1>
+A general <tt class="class">spmatrix</tt> object can be thought of as a <em>triplet
+description</em> of a sparse matrix, <EM>i.e.</EM>, a list of entries of the matrix,
+with for each entry the value, row index, and column index.
+Entries that are not included in the list are assumed to be zero.
+For example, the sparse matrix
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+A = \left[ \begin{array}{rrrrr}
+ 0 & 2 & 0 & 0 & 3 \\
+ 2 & 0 & 0 & 0 & 0 \\
+ -1 & -2 & 0 & 4 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \end{array} \right]
+\end{equation}
+ -->
+<A NAME="e-sparse-A"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-sparse-A"></A><IMG
+ WIDTH="193" HEIGHT="83" BORDER="0"
+ SRC="img78.gif"
+ ALT="\begin{displaymath}
+A = \left[ \begin{array}{rrrrr}
+0 & 2 & 0 & 0 & 3 \\
+2 &...
+...-1 & -2 & 0 & 4 & 0 \\
+0 & 0 & 1 & 0 & 0 \end{array} \right]
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(6.1)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+has the triplet description
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+(2,1,0), \qquad (-1,2,0), \qquad (2,0,1), \qquad (-2,2,1), \qquad
+(1,3,2), \qquad (4,2,3), \qquad (3,0,4).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="611" HEIGHT="28" BORDER="0"
+ SRC="img79.gif"
+ ALT="\begin{displaymath}
+(2,1,0), \qquad (-1,2,0), \qquad (2,0,1), \qquad (-2,2,1), \qquad
+(1,3,2), \qquad (4,2,3), \qquad (3,0,4).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The list may include entries with a zero value, so triplet
+descriptions are not necessarily unique.
+The list
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+(2,1,0), \qquad (-1,2,0), \qquad (0,3,0), \qquad (2,0,1), \qquad
+ (-2,2,1), \qquad (1,3,2), \qquad (4,2,3), \qquad (3,0,4)
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="696" HEIGHT="28" BORDER="0"
+ SRC="img80.gif"
+ ALT="\begin{displaymath}
+(2,1,0), \qquad (-1,2,0), \qquad (0,3,0), \qquad (2,0,1), \qquad
+(-2,2,1), \qquad (1,3,2), \qquad (4,2,3), \qquad (3,0,4)
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+is another triplet description of the same matrix.
+
+<P>
+An <tt class="class">spmatrix</tt> object corresponds to a particular triplet
+description of a sparse matrix. We will refer to the entries in
+the triplet description as the <em>nonzero entries</em> of the object,
+even though they may have a numerical value zero.
+
+<P>
+Two functions are provided to create sparse matrices.
+The first, <tt class="function">spmatrix()</tt>, constructs a sparse matrix from
+a triplet description.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-115' xml:id='l2h-115' class="function">spmatrix</tt></b>(</nobr></td>
+ <td><var>x, I, J</var><big>[</big><var>, size</var><big>[</big><var>, tc</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+
+<P>
+<var>I</var> and <var>J</var> are sequences of integers (lists, tuples,
+<tt class="module">array</tt> arrays, xrange objects, ...) or integer matrices
+(<tt class="class">matrix</tt> objects with typecode <code>'i'</code>), containing the row and column
+indices of the nonzero entries.
+The lengths of <var>I</var> and <var>J</var> must be equal. If they
+are matrices, they are treated as lists of indices stored in
+column-major order, <EM>i.e.</EM>, as lists <code>list(<var>I</var>)</code>, respectively,
+<code>list(<var>J</var>)</code>.
+
+<P>
+<var>size</var> is a tuple of nonnegative integers with the row and column
+dimensions of the matrix.
+The <var>size</var> argument is only needed when creating a matrix with
+a zero last row or last column. If <var>size</var> is not specified, it
+is determined from <var>I</var> and <var>J</var>:
+the default value for <code><var>size</var>[0]</code> is <code>max(<var>I</var>)+1</code>
+if <var>I</var> is nonempty and zero otherwise.
+The default value for <code><var>size</var>[1]</code> is
+<code>max(<var>J</var>)+1</code> if <var>J</var> is nonempty and zero otherwise.
+
+<P>
+<var>tc</var> is the typecode, <code>'d'</code> or <code>'z'</code>, for double and complex
+matrices, respectively. Integer sparse matrices are not implemented.
+
+<P>
+<var>x</var> can be a number, a sequence of numbers, or a dense matrix.
+This argument specifies the numerical values of the nonzero entries.
+
+<UL>
+<LI>If <var>x</var> is a number (Python integer, float or complex),
+a matrix is created with the sparsity pattern defined by <var>I</var> and
+<var>J</var>, and nonzero entries initialized to the value of <var>x</var>.
+The default value of <var>tc</var> is <code>'d'</code> if <var>x</var> is integer or float,
+and <code>'z'</code> if <var>x</var> is complex.
+
+<P>
+The following code creates a 4 by 4 sparse identity matrix.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix
+>>> A = spmatrix(1.0, range(4), range(4))
+>>> print A
+SIZE: (4,4)
+(0, 0) 1.0000e+00
+(1, 1) 1.0000e+00
+(2, 2) 1.0000e+00
+(3, 3) 1.0000e+00
+</pre></div>
+
+<P>
+</LI>
+<LI>If <var>x</var> is a sequence of numbers, a sparse matrix is created
+with the entries of <var>x</var> copied to the entries indexed by <var>I</var>
+and <var>J</var>. The list <var>x</var> must have the same length as <var>I</var> and
+<var>J</var>.
+The default value of <var>tc</var> is determined from the elements of
+<var>x</var>:
+<code>'d'</code> if <var>x</var> contains integers and floating-point numbers or
+if <var>x</var> is an empty list,
+and <code>'z'</code> if <var>x</var> contains at least one complex number.
+
+<P>
+As an example, the matrix (<A HREF="#e-sparse-A">6.1</A>) can be created as follows.
+<div class="verbatim"><pre>
+>>> A = spmatrix([2,-1,2,-2,1,4,3], [1,2,0,2,3,2,0], [0,0,1,1,2,3,4])
+>>> print A
+SIZE: (4,5)
+(1, 0) 2.0000e+00
+(2, 0) -1.0000e+00
+(0, 1) 2.0000e+00
+(2, 1) -2.0000e+00
+(3, 2) 1.0000e+00
+(2, 3) 4.0000e+00
+(0, 4) 3.0000e+00
+</pre></div>
+
+<P>
+</LI>
+<LI>If <var>x</var> is a dense matrix, a sparse matrix is created with
+all the entries of <var>x</var> copied, in column-major order, to the
+entries indexed by <var>I</var> and <var>J</var>.
+The matrix <var>x</var> must have the same length as <var>I</var> and <var>J</var>.
+The default value of <var>tc</var> is <code>'d'</code> if <var>x</var> is an <code>'i'</code> or <code>'d'</code> matrix, and <code>'z'</code> otherwise.
+</LI>
+</UL>
+
+<P>
+If <var>I</var> and <var>J</var> contain repeated entries, the corresponding
+values of the coefficients are added.
+</dl>
+
+<P>
+The function <tt class="function">sparse()</tt> constructs a sparse matrix from
+a block-matrix description.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-116' xml:id='l2h-116' class="function">sparse</tt></b>(</nobr></td>
+ <td><var>x</var><big>[</big><var>, tc</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+<var>tc</var> is the typecode, <code>'d'</code> or <code>'z'</code>, for double and complex
+matrices, respectively.
+
+<P>
+<var>x</var> can be a <tt class="class">matrix</tt>, <tt class="class">spmatrix</tt>, or a list of lists of matrices
+(<tt class="class">matrix</tt> or <tt class="class">spmatrix</tt> objects) and numbers (Python integer, float or
+complex).
+
+<UL>
+<LI>If <var>x</var> is a <tt class="class">matrix</tt> or <tt class="class">spmatrix</tt> object, then a sparse matrix
+of the same size and the same numerical value is created.
+Numerical zeros in <var>x</var> are treated as structural zeros and removed
+from the triplet description of the new sparse matrix.
+
+<P>
+</LI>
+<LI>If <var>x</var> is a list of lists of matrices (<tt class="class">matrix</tt> or <tt class="class">spmatrix</tt>)
+and numbers (Python integer, float or complex) then each element of
+<var>x</var> is interpreted as a (block-)column matrix stored in
+colum-major order, and a block-matrix is constructed by juxtaposing
+the <code>len(<var>x</var>)</code> block-columns
+(as in <tt class="function">matrix()</tt>, see section <A href="s-creating-matrices.html#s-creating-matrices">2.1</A>).
+Numerical zeros are removed from the triplet description of the new
+matrix.
+
+<P>
+The following example shows how to construct a sparse block-matrix.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix, spmatrix, sparse
+>>> A = matrix([[1, 2, 0], [2, 1, 2], [0, 2, 1]])
+>>> B = spmatrix([], [], [], (3,3))
+>>> C = spmatrix([3, 4, 5], [0, 1, 2], [0, 1, 2])
+>>> print sparse([[A, B], [B, C]])
+SIZE: (6,6)
+(0, 0) 1.0000e+00
+(1, 0) 2.0000e+00
+(0, 1) 2.0000e+00
+(1, 1) 1.0000e+00
+(2, 1) 2.0000e+00
+(1, 2) 2.0000e+00
+(2, 2) 1.0000e+00
+(3, 3) 3.0000e+00
+(4, 4) 4.0000e+00
+(5, 5) 5.0000e+00
+</pre></div>
+
+<P>
+A matrix with a single block-column can be represented by a single
+list.
+<div class="verbatim"><pre>
+>>> print sparse([A, C])
+SIZE: (6,3)
+(0, 0) 1.0000e+00
+(1, 0) 2.0000e+00
+(3, 0) 3.0000e+00
+(0, 1) 2.0000e+00
+(1, 1) 1.0000e+00
+(2, 1) 2.0000e+00
+(4, 1) 4.0000e+00
+(1, 2) 2.0000e+00
+(2, 2) 1.0000e+00
+(5, 2) 5.0000e+00
+</pre></div>
+</LI>
+</UL>
+
+<P>
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+</head>
+<body>
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+
+<H1><A NAME="SECTION0010800000000000000000"></A> <A NAME="s-external"></A>
+<BR>
+8.8 Optional Solvers
+</H1>
+CVXOPT includes optional interfaces to several other optimization
+libraries.
+
+<P>
+<DL>
+<DT><STRONG>GLPK</STRONG></DT>
+<DD><tt class="function">lp()</tt> with the <code>solver='glpk'</code> option uses
+the the simplex algorithm in
+<a class="ulink" href="http://www.gnu.org/software/glpk/glpk.html"
+ >GLPK (GNU Linear Programming Kit)</a>.
+
+<P>
+</DD>
+<DT><STRONG>MOSEK</STRONG></DT>
+<DD><tt class="function">lp()</tt> and <tt class="function">qp()</tt> with the
+<code>solver='mosek'</code> option call routines from
+<a class="ulink" href="http://www.mosek.com"
+ >MOSEK</a> version 4.
+
+<P>
+</DD>
+<DT><STRONG>DSDP</STRONG></DT>
+<DD><tt class="function">sdp()</tt> with the <code>solver='dsdp'</code> option uses
+the
+<a class="ulink" href="http://www-unix.mcs.anl.gov/DSDP"
+ >DSDP5.8</a> solver.
+</DD>
+</DL>
+GLPK, MOSEK and DSDP are not included in the CVXOPT distribution and
+need to be installed separately.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel="parent" href="node55.html" />
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+<meta name='aesop' content='information' />
+<title>9.2 Functions</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="9.1 Variables"
+ href="s-variables.html"><img src='previous.gif'
+ border='0' height='32' alt='Previous Page' width='32' /></A></td>
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+ href="node55.html"><img src='up.gif'
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+<td class='online-navigation'><a rel="next" title="9.3 Constraints"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+<a class="sectref" rel="next" href="node58.html">9.3 Constraints</A>
+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0011200000000000000000"></A> <A NAME="s-functions"></A>
+<BR>
+9.2 Functions
+</H1>
+Objective and constraint functions can be defined via overloaded
+operations on variables and other functions. A function <var>f</var> is
+interpreted as a column vector, with length <code>len(<var>f</var>)</code>
+and with a value that depends on the values of its variables.
+Functions have two public attributes.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-155' xml:id='l2h-155' class="method">variables</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns a copy of the list of variables of the function.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-156' xml:id='l2h-156' class="method">value</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+The function value. If any of the variables of <var>f</var> has value
+<code>None</code>, then <var>f</var>.<tt class="method">value()</tt> returns <code>None</code>.
+Otherwise, it returns a dense <code>'d'</code> matrix of size
+(<code>len(<var>f</var>)</code>,1) with the function value computed from the
+<tt class="member">value</tt> attributes of the variables of <var>f</var>.
+</dl>
+
+<P>
+Three types of functions are supported: affine, convex
+piecewise-linear and concave piecewise-linear.
+
+<P>
+<b>Affine functions</b> represent vector valued functions of the form
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+f(x_1,\ldots,x_n) = A_1 x_1 + \cdots + A_n x_n + b.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="272" HEIGHT="28" BORDER="0"
+ SRC="img169.gif"
+ ALT="\begin{displaymath}
+f(x_1,\ldots,x_n) = A_1 x_1 + \cdots + A_n x_n + b.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The coefficients can be scalars or dense or sparse matrices. The
+constant term is a scalar or a column vector.
+
+<P>
+Affine functions result from the following operations.
+<DL>
+<DT><STRONG>Unary operations</STRONG></DT>
+<DD>For a variable <var>x</var>, the unary operation <code>+<var>x</var></code> results in
+an affine function with <var>x</var> as variable, coefficient 1.0, and
+constant term 0.0. The unary operation <code>-<var>x</var></code> returns an
+affine function with <var>x</var> as variable, coefficient -1.0, and
+constant term 0.0. For an affine function <var>f</var>, <code>+<var>f</var></code> is
+a copy of <var>f</var>, and <code>-<var>f</var></code> is a copy of <var>f</var> with the
+signs of its coefficients and constant term reversed.
+
+<P>
+</DD>
+<DT><STRONG>Addition and subtraction</STRONG></DT>
+<DD>Sums and differences of affine functions, variables and constants
+result in new affine functions.
+The constant terms in the sum can be of type integer or float, or
+dense or sparse <code>'d'</code> matrices with one column.
+
+<P>
+The rules for addition and subtraction follow the conventions for
+matrix addition and subtraction in sections <A href="s-arithmetic.html#s-arithmetic">2.3</A>
+and <A href="s-spmatrix-arith.html#s-spmatrix-arith">6.3</A>, with variables and affine functions
+interpreted as dense <code>'d'</code> matrices with one column.
+In particular, a scalar term (integer, float, 1 by 1 dense <code>'d'</code> matrix,
+variable of length 1, or affine function of length 1) can be added
+to an affine function or variable of length greater than 1.
+
+<P>
+</DD>
+<DT><STRONG>Multiplication</STRONG></DT>
+<DD>Suppose <var>v</var> is an affine function or a variable, and <var>a</var> is
+an integer, float, sparse or dense <code>'d'</code> matrix. The products
+<code><var>a</var>*<var>v</var></code> and <code><var>v</var>*<var>a</var></code> are
+valid affine functions whenever the product is allowed under the rules
+for matrix and scalar multiplication of sections <A href="s-arithmetic.html#s-arithmetic">2.3</A>
+and <A href="s-spmatrix-arith.html#s-spmatrix-arith">6.3</A>, with <var>v</var> interpreted as a <code>'d'</code> matrix
+with one column.
+In particular, the product <code><var>a</var>*<var>v</var></code> is defined if
+<var>a</var> is a scalar (integer, float or 1 by 1 dense <code>'d'</code> matrix),
+or a matrix (dense or sparse) with
+<code><var>a</var>.<tt class="member">size</tt>[1] = len(<var>v</var>)</code>.
+The operation <code><var>v</var>*<var>a</var></code> is defined if <var>a</var> is scalar,
+or if <code>len(<var>v</var>)</code> = 1 and <var>a</var> is a matrix with one
+column.
+
+<P>
+</DD>
+<DT><STRONG>Inner products</STRONG></DT>
+<DD>The following two functions return scalar affine functions defined
+as inner products of a constant vector with a variable or affine
+function.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-157' xml:id='l2h-157' class="function">sum</tt></b>(</nobr></td>
+ <td><var>v</var>)</td></tr></table></dt>
+<dd>
+The argument is an affine function or a variable. The result is an
+affine function of length 1, with the sum of the components of the
+argument <var>v</var>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-158' xml:id='l2h-158' class="function">dot</tt></b>(</nobr></td>
+ <td><var>u,v</var>)</td></tr></table></dt>
+<dd>
+If <var>v</var> is a variable or affine function and <var>u</var> is a <code>'d'</code> matrix of size (<code>len(<var>v</var>)</code>,1), then
+<code>dot(<var>u</var>,<var>v</var>)</code> and <code>dot(<var>v</var>,<var>u</var>)</code> are
+equivalent to <code><var>u</var>.<tt class="method">trans()</tt>*<var>v</var></code>.
+
+<P>
+If <var>u</var> and <var>v</var> are dense matrices, then
+<code>dot(<var>u</var>,<var>v</var>)</code>
+is equivalent to the function <code>blas.dot(<var>u</var>,<var>v</var>)</code>
+defined in section <A href="s-blas1.html#s-blas1">3.2</A>, <EM>i.e.</EM>, it returns the inner product of
+the two matrices.
+</dl>
+</DD>
+</DL>
+
+<P>
+In the following example, the variable <var>x</var> has length 1 and
+<var>y</var> has length 2.
+The functions <var>f</var> and <var>g</var> are given by
+<P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{eqnarray*}
+f(x,y) & = & \left[ \begin{array}{c} 2 \\2 \end{array}\right] x
+ + y + \left[ \begin{array}{c} 3 \\3 \end{array}\right], \\
+ g(x,y) & = &
+ \left[ \begin{array}{cc} 1 & 3 \\2 & 4 \end{array}\right] f(x,y)
+ + \left[ \begin{array}{cc} 1 & 1 \\1 & 1 \end{array} \right] y +
+ \left[ \begin{array}{c} 1 \\-1 \end{array} \right] \\
+ & = & \left[ \begin{array}{c} 8 \\12 \end{array}\right] x
+ + \left[ \begin{array}{cc} 2 & 4 \\3 & 5 \end{array}\right] y
+ + \left[ \begin{array}{c} 13 \\17\end{array}\right].
+\end{eqnarray*}
+ -->
+<IMG
+ WIDTH="366" HEIGHT="134" BORDER="0"
+ SRC="img170.gif"
+ ALT="\begin{eqnarray*}
+f(x,y) & = & \left[ \begin{array}{c} 2 \\ 2 \end{array}\right...
+...\right] y
++ \left[ \begin{array}{c} 13 \\ 17\end{array}\right].
+\end{eqnarray*}"></DIV>
+<BR CLEAR="ALL"><P></P>
+<BR CLEAR="ALL"><P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.modeling import variable
+>>> x = variable(1,'x')
+>>> y = variable(2,'y')
+>>> f = 2*x + y + 3
+>>> A = matrix([[1., 2.], [3.,4.]])
+>>> b = matrix([1.,-1.])
+>>> g = A*f + sum(y) + b
+>>> print g
+affine function of length 2
+constant term:
+ 1.3000e+01
+ 1.7000e+01
+linear term: linear function of length 2
+coefficient of variable(2,'y'):
+ 2.0000e+00 4.0000e+00
+ 3.0000e+00 5.0000e+00
+coefficient of variable(1,'x'):
+ 8.0000e+00
+ 1.2000e+01
+</pre></div>
+
+<P>
+<DL>
+<DT><STRONG>In-place operations</STRONG></DT>
+<DD>For an affine function <var>f</var> the operations <code><var>f</var> += <var>u</var></code>
+and <code><var>f</var> -= <var>u</var></code>, with <var>u</var> a constant, a variable or
+an affine function, are allowed if they do not change the length of
+<var>f</var>, <EM>i.e.</EM>, if <var>u</var> has length <code>len(<var>f</var>)</code> or length 1.
+In-place multiplication <code><var>f</var> *= <var>u</var></code> and division
+<code><var>f</var> /= <var>u</var></code> are allowed if <var>u</var> is an integer, float, or
+1 by 1 matrix.
+</DD>
+</DL>
+
+<P>
+<DL>
+<DT><STRONG>Indexing and slicing</STRONG></DT>
+<DD>Variables and affine functions admit
+single-argument indexing of the four types described in
+section <A href="s-indexing.html#s-indexing">2.4</A>. The result of an indexing or slicing
+operation is an affine function.
+</DD>
+</DL>
+
+<P>
+<div class="verbatim"><pre>
+>>> x = variable(4,'x')
+>>> f = x[::2]
+>>> print f
+>>> linear function of length 2
+linear term: linear function of length 2
+coefficient of variable(4,'x'):
+TYPE: general
+SIZE: (2,4)
+(0, 0) 1.0000e+00
+(1, 2) 1.0000e+00
+>>> y = variable(3,'x')
+>>> g = matrix(range(12),(3,4),'d')*x - 3*y + 1
+>>> print g[0] + g[2]
+affine function of length 1
+constant term:
+ 2.0000e+00
+linear term: linear function of length 1
+coefficient of variable(4,'x'):
+ 2.0000e+00 8.0000e+00 1.4000e+01 2.0000e+01
+coefficient of variable(3,'y'):
+TYPE: general
+SIZE: (1,3)
+(0, 0) -3.0000e+00
+(0, 2) -3.0000e+00
+</pre></div>
+
+<P>
+The general expression of a <b>convex piecewise-linear</b> function is
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
+ \sum_{k=1}^K \max (y_1, y_2, \ldots, y_{m_k}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="458" HEIGHT="56" BORDER="0"
+ SRC="img171.gif"
+ ALT="\begin{displaymath}
+f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
+\sum_{k=1}^K \max (y_1, y_2, \ldots, y_{m_k}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The maximum in this expression is a componentwise maximum of its
+vector arguments, which can be constant vectors, variables, affine
+functions or convex piecewise-linear functions.
+The general expression for a <b>concave piecewise-linear</b> function
+is
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
+ \sum_{k=1}^K \min (y_1, y_2, \ldots, y_{m_k}).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="456" HEIGHT="56" BORDER="0"
+ SRC="img172.gif"
+ ALT="\begin{displaymath}
+f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
+\sum_{k=1}^K \min (y_1, y_2, \ldots, y_{m_k}).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+Here the arguments of the <tt class="function">min()</tt> can be constants, variables,
+affine functions or concave piecewise-linear functions.
+
+<P>
+Piecewise-linear functions can be created using the following
+operations.
+<DL>
+<DT><STRONG><tt class="function">max</tt></STRONG></DT>
+<DD>If the arguments in
+<code><var>f</var> = max(<var>y1</var>,<var>y2</var>, ...)</code>
+do not include any variables or functions, then the Python built-in
+<tt class="function">max()</tt> is evaluated.
+
+<P>
+If one or more of the arguments are variables or functions,
+<tt class="function">max()</tt> returns a piecewise-linear function defined as the
+elementwise maximum of its arguments.
+In other words, <var>f</var>[<var>k</var>] =
+<code>max(<var>y1</var>[<var>k</var>],<var>y2</var>[<var>k</var>], ...)</code>
+for <var>k</var>=0, ..., <code>len(<var>f</var>)</code>-1.
+The length of <var>f</var> is equal to the maximum of the lengths of the
+arguments. Each argument must have length equal to
+<code>len(<var>f</var>)</code> or length one.
+Arguments with length one are interpreted as vectors of
+length <code>len(<var>f</var>)</code> with identical entries.
+
+<P>
+The arguments can be scalars of type integer or float,
+dense <code>'d'</code> matrices with one column, variables, affine functions or
+convex piecewise-linear functions.
+
+<P>
+With one argument, <code><var>f</var> = max(<var>u</var>)</code> is interpreted as
+<code><var>f</var> = max(<var>u</var>[0],<var>u</var>[1],...,
+<var>u</var>[<tt class="function">len</tt>(<var>u</var>)-1])</code>.
+
+<P>
+</DD>
+<DT><STRONG><tt class="function">min</tt></STRONG></DT>
+<DD>Similar to <tt class="function">max()</tt> but returns a concave
+piecewise-linear function. The arguments can be scalars of type
+integer or float, dense <code>'d'</code> matrices with one column,
+variables, affine functions or concave piecewise-linear functions.
+
+<P>
+</DD>
+<DT><STRONG><tt class="function">abs</tt></STRONG></DT>
+<DD>If <var>u</var> is a variable or affine function then
+<code><var>f</var> = abs(<var>u</var>)</code> returns the convex piecewise-linear
+function <code>max(<var>u</var>,-<var>u</var>)</code>.
+
+<P>
+</DD>
+<DT><STRONG>Unary plus and minus</STRONG></DT>
+<DD><code>+<var>f</var></code> creates a copy of <var>f</var>.
+<code>-<var>f</var></code> is a concave piecewise-linear function if <var>f</var> is
+convex and a convex piecewise-linear function if <var>f</var> is concave.
+
+<P>
+</DD>
+<DT><STRONG>Addition and subtraction</STRONG></DT>
+<DD>Sums and differences involving
+piecewise-linear functions are allowed if they result in convex
+or concave functions. For example, one can add two convex or two
+concave functions, but not a convex and a concave function.
+The command <code>sum(<var>f</var>)</code> is equivalent
+to <code><var>f</var>[0] + <var>f</var>[1] + ...+ <var>f</var>[len(<var>f</var>)-1]</code>.
+
+<P>
+</DD>
+<DT><STRONG>Multiplication</STRONG></DT>
+<DD>Scalar multiplication <code><var>a</var>*<var>f</var></code> of a
+piecewise-linear function <var>f</var> is defined if <var>a</var>
+is an integer, float, 1 by 1 <code>'d'</code> matrix.
+Matrix-matrix multiplications <code><var>a</var>*<var>f</var></code> or
+<code><var>f</var>*<var>a</var></code> are only defined if <var>a</var> is a dense or
+sparse 1 by 1 matrix.
+
+<P>
+</DD>
+<DT><STRONG>Indexing and slicing</STRONG></DT>
+<DD>Piecewise-linear functions admit
+single-argument indexing of the four types described in
+section <A href="s-indexing.html#s-indexing">2.4</A>. The result of an indexing or slicing
+operation is a new piecewise-linear function.
+</DD>
+</DL>
+
+<P>
+In the following example, <var>f</var> is the 1-norm of a vector
+variable <var>x</var> of length 10, <var>g</var> is its infinity-norm and
+<var>h</var> is the function
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+h(x) = \sum_k \phi(x[k]),\qquad
+ \phi(u) = \left\{\begin{array}{ll}
+ 0 & |u| \leq 1 \\
+ |u|-1 & 1 \leq |u| \leq 2 \\
+ 2|u|-3 & |u| \geq 2. \end{array}\right.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="383" HEIGHT="64" BORDER="0"
+ SRC="img173.gif"
+ ALT="\begin{displaymath}
+h(x) = \sum_k \phi(x[k]),\qquad
+\phi(u) = \left\{\begin{ar...
+...\\
+2\vert u\vert-3 & \vert u\vert \geq 2. \end{array}\right.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> f = sum(abs(x))
+>>> g = max(abs(x))
+>>> h = sum(max(0, abs(x)-1, 2*abs(x)-3))
+</pre></div>
+
+<P>
+<DL>
+<DT><STRONG>In-place operations</STRONG></DT>
+<DD>If <var>f</var> is piecewise-linear then the in-place operations
+<code><var>f</var> += <var>u</var></code>, <code><var>f</var> -= <var>u</var></code>,
+<code><var>f</var> *= <var>u</var></code>, <code><var>f</var> /= <var>u</var></code> are defined if the
+corresponding expanded operations <code><var>f</var> = <var>f</var>+<var>u</var></code>,
+<code><var>f</var> = <var>f</var>-<var>u</var></code>, <code><var>f</var> = <var>f</var>*<var>u</var></code>
+and <code><var>f</var> = <var>f</var>/<var>u</var></code> are defined and if they do not
+change the length of <var>f</var>.
+</DD>
+</DL>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="9.1 Variables"
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@@ -0,0 +1,263 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+
+<H1><A NAME="SECTION004400000000000000000"></A> <A NAME="s-indexing"></A>
+<BR>
+2.4 Indexing and Slicing
+</H1>
+
+<P>
+Matrices can be indexed using one or two arguments. In single-argument
+indexing of a matrix <var>A</var>, the index runs from
+<code>-len(<var>A</var>)</code> to <code>len(<var>A</var>)-1</code>, and is interpreted as an
+index in the one-dimensional array of coefficients of <var>A</var>
+in column-major order. Negative indices have the standard Python
+interpretation: for negative <var>k</var>, <code><var>A</var>[<var>k</var>]</code> is the
+same element as <code><var>A</var>[len(<var>A</var>)+<var>k</var>]</code>.
+
+<P>
+Four different types of one-argument indexing are implemented.
+
+<OL>
+<LI>The index can be a single integer. This returns a
+number, <EM>e.g.</EM>, <code><var>A</var>[0]</code> is the first element of <var>A</var>.
+
+<P>
+</LI>
+<LI>The index can be an integer matrix. This returns a
+column matrix: the command "<tt class="samp">A[matrix([0,1,2,3])]</tt>"
+returns the 4 by 1 matrix consisting of the first four elements of
+<var>A</var>. The size of the index matrix is ignored:
+"<tt class="samp">A[matrix([0,1,2,3], (2,2))]</tt>" returns the same 4 by 1 matrix.
+
+<P>
+</LI>
+<LI>The index can be a list of integers. This returns a column
+matrix, <EM>e.g.</EM>, <code><var>A</var>[[0,1,2,3]]</code> is the 4 by 1 matrix consisting
+of elements 0, 1, 2, 3 of <var>A</var>.
+
+<P>
+</LI>
+<LI>The index can be a Python slice. This returns a matrix with one
+column (possibly 0 by 1, or 1 by 1). For example, <code><var>A</var>[::2]</code>
+is the column matrix defined by taking every other element of <var>A</var>,
+stored in column-major order.
+<code><var>A</var>[0:0]</code> is a matrix with size (0,1).
+</LI>
+</OL>
+Thus, single-argument indexing returns a scalar (if the index is an
+integer), or a matrix with one column. This is consistent with the
+interpretation that single-argument indexing accesses the matrix in
+column-major order.
+
+<P>
+Note that an index list or an index matrix are equivalent,
+but they are both useful, especially when we perform operations on
+index sets. For example, if <var>I</var> and <var>J</var> are lists then
+<code><var>I</var>+<var>J</var></code> is the concatenated list, and <code>2*<var>I</var></code>
+is <var>I</var> repeated twice. If they are matrices, these operations are
+interpreted as arithmetic operations.
+For large index sets, indexing with integer matrices is also faster
+than indexing with lists.
+
+<P>
+The following example illustrates one-argument indexing.
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> A = matrix(range(16), (4,4), 'd')
+>>> print A
+ 0.0000e+00 4.0000e+00 8.0000e+00 1.2000e+01
+ 1.0000e+00 5.0000e+00 9.0000e+00 1.3000e+01
+ 2.0000e+00 6.0000e+00 1.0000e+01 1.4000e+01
+ 3.0000e+00 7.0000e+00 1.1000e+01 1.5000e+01
+>>> A[4]
+4.0
+>>> I = matrix([0, 5, 10, 15])
+>>> print A[I] # the diagonal
+ 0.0000e+00
+ 5.0000e+00
+ 1.0000e+01
+ 1.5000e+01
+>>> I = [0,2]; J = [1,3]
+>>> print A[2*I+J] # duplicate I and append J
+ 0.0000e+00
+ 2.0000e+00
+ 0.0000e+00
+ 2.0000e+00
+ 1.0000e+00
+ 3.0000e+00
+>>> I = matrix([0, 2]); J = matrix([1, 3])
+>>> print A[2*I+J] # multiply I by 2 and add J
+ 1.0000e+00
+ 7.0000e+00
+>>> print A[4::4] # get every fourth element skipping the first four
+ 4.0000e+00
+ 8.0000e+00
+ 1.2000e+01
+</pre></div>
+
+<P>
+In two-argument indexing the arguments can be any combinations of the
+four types listed above. The first argument indexes the rows of
+the matrix and the second argument indexes the columns. If both
+indices are scalars, then a scalar is returned. In all other cases,
+a matrix is returned. We continue the example.
+<div class="verbatim"><pre>
+>>> print A[:,1]
+ 4.0000e+00
+ 5.0000e+00
+ 6.0000e+00
+ 7.0000e+00
+>>> J = matrix([0, 2])
+>>> print A[J,J]
+ 0.0000e+00 8.0000e+00
+ 2.0000e+00 1.0000e+01
+>>> print A[:2, -2:]
+ 8.0000e+00 1.2000e+01
+ 9.0000e+00 1.3000e+01
+</pre></div>
+
+<P>
+Expressions of the form <code><var>A</var>[<var>I</var>]</code> or
+<code><var>A</var>[<var>I</var>,<var>J</var>]</code> can also appear on the lefthand side
+of an assignment.
+The righthand side must be a scalar (<EM>i.e.</EM>, a number or a 1 by 1 dense
+matrix), a sequence of numbers, or a dense or sparse matrix.
+If the righthand side is a scalar, it is interpreted as a
+matrix with identical entries and the dimensions of the lefthand side.
+If the righthand side is a sequence of numbers (list, tuple,
+<tt class="module">array</tt> array, xrange object, ...) its values are
+interpreted as the coefficients of the lefthand side in column-major
+order. If the righthand side is a matrix (<tt class="class">matrix</tt> or <tt class="class">spmatrix</tt>), it must
+have the same size as the lefthand side. Sparse matrices are
+converted to dense in the assignment.
+
+<P>
+Indexed assignments are only allowed if they do not change the type of
+the matrix. For example, if <var>A</var> is a matrix with type <code>'d'</code>, then
+<code><var>A</var>[<var>I</var>] = <var>B</var></code> is only permitted if <var>B</var> is
+an integer, a float, or a matrix of type <code>'i'</code> or <code>'d'</code>.
+If <var>A</var> is an integer matrix, then <code><var>A</var>[<var>I</var>] = <var>B</var></code>
+is only permitted if <var>B</var> is an integer or an integer matrix.
+
+<P>
+The following example illlustrates indexed assignment.
+<div class="verbatim"><pre>
+>>> A = matrix(range(16), (4,4))
+>>> A[::2,::2] = matrix([[-1, -2], [-3, -4]])
+>>> print A
+ -1 4 -3 12
+ 1 5 9 13
+ -2 6 -4 14
+ 3 7 11 15
+>>> A[::5] += 1
+>>> print A
+ 0 4 -3 12
+ 1 6 9 13
+ -2 6 -3 14
+ 3 7 11 16
+>>> A[0,:] = -1, 1, -1, 1
+>>> print A
+ -1 1 -1 1
+ 1 6 9 13
+ -2 6 -3 14
+ 3 7 11 16
+>>> A[2:,2:] = xrange(4)
+>>> print A
+ -1 1 -1 1
+ 1 6 9 13
+ -2 6 0 2
+ 3 7 1 3
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<title>9.4 Optimization Problems</title>
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+</DIV>
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+
+<H1><A NAME="SECTION0011400000000000000000"></A> <A NAME="s-lp"></A>
+<BR>
+9.4 Optimization Problems
+</H1>
+
+<P>
+Optimization problems are be constructed by calling the following
+function.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><span class="typelabel">class</span> <tt id='l2h-163' xml:id='l2h-163' class="class">op</tt></b>(</nobr></td>
+ <td><var></var><big>[</big><var>objective</var><big>[</big><var>, constraints</var><big>[</big><var>, name</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+The first argument specifies the objective function to be minimized.
+It can be an affine or convex piecewise-linear function with length 1,
+a variable with length 1, or a scalar constant
+(integer, float or 1 by 1 dense <code>'d'</code> matrix). The default value is
+<code>0.0</code>.
+
+<P>
+The second argument is a single constraint, or a list of
+constraint objects. The default value is an empty list.
+
+<P>
+The third argument is a string with a name for the problem.
+The default value is the empty string.
+</dl>
+
+<P>
+The following attributes and methods are useful for examining
+and modifying optimization problems.
+
+<P>
+<dl><dt><b><tt id='l2h-164' xml:id='l2h-164' class="member">objective</tt></b></dt>
+<dd>
+The objective or cost function. One can write to this
+attribute to change the objective of an existing problem.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-165' xml:id='l2h-165' class="method">variables</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns a list of the variables of the problem.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-166' xml:id='l2h-166' class="method">constraints</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns a list of the constraints.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-167' xml:id='l2h-167' class="method">inequalities</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns a list of the inequality constraints.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-168' xml:id='l2h-168' class="method">equalities</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns a list of the equality constraints.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-169' xml:id='l2h-169' class="method">delconstraint</tt></b>(</nobr></td>
+ <td><var>c</var>)</td></tr></table></dt>
+<dd>
+Deletes constraint <TT>c</TT> from the problem.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-170' xml:id='l2h-170' class="method">addconstraint</tt></b>(</nobr></td>
+ <td><var>c</var>)</td></tr></table></dt>
+<dd>
+Adds constraint <TT>c</TT> to the problem.
+</dl>
+
+<P>
+An optimization problem with convex piecewise-linear objective and
+constraints can be solved by calling the method <tt class="function">solve()</tt>.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-171' xml:id='l2h-171' class="method">solve</tt></b>(</nobr></td>
+ <td><var></var><big>[</big><var>format</var><big>[</big><var>, solver</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+This function converts the optimization problem to a linear program
+in matrix form and then solves it using the solver described in
+section <A href="s-lpsolver.html#s-lpsolver">8.1</A>.
+
+<P>
+The first argument is either <code>'dense'</code> or <code>'sparse'</code>, and
+denotes the matrix types used in the matrix representation of the LP.
+The default value is <code>'dense'</code>.
+
+<P>
+The second argument is either <code>None</code>. <code>'glpk'</code> or <code>'mosek'</code>,
+and selects one of three available LP solvers: a default solver
+written in Python, the GLPK solver (if installed) or the
+MOSEK LP solver (if installed); see section <A href="s-lpsolver.html#s-lpsolver">8.1</A>.
+The default value is <code>None</code>.
+
+<P>
+The solver reports the outcome of optimization by setting
+the attribute <var>self</var>.<tt class="member">status</tt> and by modifying
+the <tt class="member">value</tt> attributes of the variables and the constraint
+multipliers of the problem.
+
+<UL>
+<LI>If the problem is solved to optimality,
+<var>self</var>.<tt class="member">status</tt> is set to <code>'optimal'</code>.
+The <tt class="member">value</tt> attributes of the variables in the problem are set
+to their computed solutions, and the <tt class="member">value</tt> attributes of the
+multipliers of the constraints of the problem are set to the computed
+dual optimal solution.
+
+<P>
+</LI>
+<LI>If it is determined that the problem is infeasible,
+<var>self</var>.<tt class="member">status</tt> is set to <code>'primal infeasible'</code>.
+The <tt class="member">value</tt> attributes of the variables are set to <code>None</code>.
+The <tt class="member">value</tt> attributes of the
+multipliers of the constraints of the problem are set to a certificate
+of primal infeasibility.
+With the <code>'glpk'</code> option, <tt class="function">solve()</tt>
+does not provide certificates of infeasibility.
+
+<P>
+</LI>
+<LI>If it is determined that the problem is dual infeasible,
+<var>self</var>.<tt class="member">status</tt> is set to <code>'dual infeasible'</code>.
+The <tt class="member">value</tt> attributes of the multipliers of the constraints of
+the problem are set to <code>None</code>.
+The <tt class="member">value</tt> attributes of the
+variables are set to a certificate of dual infeasibility.
+With the <code>'glpk'</code> option, <tt class="function">solve()</tt> does not provide
+certificates of infeasibility.
+
+<P>
+</LI>
+<LI>If the problem was not solved successfully,
+<var>self</var>.<tt class="member">status</tt> is set to <code>'unknown'</code>.
+The <tt class="member">value</tt> attributes of the variables and the constraint
+multipliers are set to <code>None</code>.
+</LI>
+</UL>
+</dl>
+We refer to section <A href="s-lpsolver.html#s-lpsolver">8.1</A> for details on the algorithms and
+the different solver options.
+
+<P>
+As an example we solve the LP
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+ \mbox{minimize} & -4x - 5y \\
+ \mbox{subject to} & 2x +y \leq 3 \\
+ & x +2y \leq 3 \\
+ & x \geq 0, \quad y \geq 0.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="179" HEIGHT="83" BORDER="0"
+ SRC="img177.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & -4x - 5y \\
+\mbox{su...
+...
+& x +2y \leq 3 \\
+& x \geq 0, \quad y \geq 0.
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> x = variable()
+>>> y = variable()
+>>> c1 = ( 2*x+y <= 3 )
+>>> c2 = ( x+2*y <= 3 )
+>>> c3 = ( x >= 0 )
+>>> c4 = ( y >= 0 )
+>>> lp1 = op(-4*x-5*y, [c1,c2,c3,c4])
+>>> lp1.solve()
+>>> print lp1.status
+optimal
+>>> print lp1.objective.value()
+-9.0000e+00
+>>> print x.value
+ 1.0000e-00
+>>> print y.value
+ 1.0000e-00
+>>> print c1.multiplier.value
+ 1.0000e-00
+>>> print c2.multiplier.value
+ 2.0000e-00
+>>> print c3.multiplier.value
+ 8.8912e-09
+>>> print c4.multiplier.value
+ 9.8567e-09
+</pre></div>
+
+<P>
+We can solve the same LP in matrix form as follows.
+<div class="verbatim"><pre>
+>>> x = variable(2)
+>>> A = matrix([[2.,1.,-1.,0.], [1.,2.,0.,-1.]])
+>>> b = matrix([3.,3.,0.,0.])
+>>> c = matrix([-4.,-5.])
+>>> ineq = ( A*x <= b )
+>>> lp2 = op(dot(c,x), ineq)
+>>> lp2.solve()
+>>> print lp2.objective.value()
+-9.0000e+00
+>>> print x.value
+ 1.0000e-00
+ 1.0000e-00
+>>> print ineq.multiplier.value
+ 1.0000e+00
+ 2.0000e+00
+ 8.8912e-09
+ 9.8567e-09
+</pre></div>
+
+<P>
+The op class also includes two methods for writing and reading
+files in
+<a class="ulink" href="http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/linearprog/mps.html"
+ >MPS format</a>.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-172' xml:id='l2h-172' class="method">tofile</tt></b>(</nobr></td>
+ <td><var>filename</var>)</td></tr></table></dt>
+<dd>
+If the problem is an LP, writes it to the file <code>'filename'</code> using
+the MPS format. Row and column labels are assigned based on the
+variable and constraint names in the LP.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-173' xml:id='l2h-173' class="method">fromfile</tt></b>(</nobr></td>
+ <td><var>filename</var>)</td></tr></table></dt>
+<dd>
+Reads the LP from the file <code>'filename'</code>. The file must be
+a fixed-format MPS file. Some features of the MPS format are not
+supported: comments beginning with dollar signs,
+the row types 'DE', 'DL', 'DG', and 'DN', and the capability of
+reading multiple righthand side, bound or range vectors.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="9.3 Constraints"
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<link rel='index' href='genindex.html' title='Index' />
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+<title>8.1 Linear Programming</title>
+</head>
+<body>
+<DIV CLASS="navigation">
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+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td class='online-navigation'><a rel="next" title="8.2 Quadratic Programming"
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+<td align="center" width="100%">CVXOPT: A Python Package for Convex Optimization</td>
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+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0010100000000000000000"></A> <A NAME="s-lpsolver"></A>
+<BR>
+8.1 Linear Programming
+</H1>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-145' xml:id='l2h-145' class="function">lp</tt></b>(</nobr></td>
+ <td><var>c, G, h</var><big>[</big><var>, A, b</var><big>[</big><var>,
+solver</var><big>[</big><var>, primalstart</var><big>[</big><var>, dualstart</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves the pair of primal and dual LPs
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+\mbox{Primal:}\quad \begin{array}[t]{ll}
+\mbox{minimize} & c^Tx \\
+\mbox{subject to} & Gx + s = h \\& Ax=b \\& s \succeq 0
+\end{array} \qquad\qquad
+\mbox{Dual:}\quad
+\begin{array}[t]{ll}
+\mbox{maximize} & -h^T z - b^T y \\
+\mbox{subject to} & G^Tz + A^T y + c = 0 \\& z \succeq 0.
+\end{array}
+\end{equation}
+ -->
+<A NAME="e-lp"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-lp"></A><IMG
+ WIDTH="571" HEIGHT="87" BORDER="0"
+ SRC="img111.gif"
+ ALT="\begin{displaymath}
+\mbox{Primal:}\quad \begin{array}[t]{ll}
+\mbox{minimize} & c...
+...ubject to} & G^Tz + A^T y + c = 0 \\ & z \succeq 0.
+\end{array}\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(8.1)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+<var>c</var>, <var>h</var> and <var>b</var> are real single-column dense matrices.
+<var>G</var> and <var>A</var> are real dense or sparse matrices.
+The default values for <var>A</var> and <var>b</var> are sparse matrices with
+zero rows, meaning that there are no equality constraints.
+
+<P>
+The <var>solver</var> argument is used to choose among three solvers.
+When it is omitted or <code>None</code>, the default CVXOPT solver is used.
+The external solvers GLPK and MOSEK (if installed) can be selected by
+setting <code><var>solver</var>='glpk'</code> or
+<code><var>solver</var>='mosek'</code>; see section <A href="s-external.html#s-external">8.8</A>.
+
+<P>
+The optional arguments <var>primalstart</var> and <var>dualstart</var> are only
+referenced by the default solver.
+<var>primalstart</var> is a dictionary with keys <code>'x'</code> and <code>'s'</code>,
+used as an optional primal starting point.
+<var>dualstart</var> is a dictionary with keys <code>'y'</code> and <code>'z'</code>,
+used as an optional dual starting point.
+
+<P>
+<tt class="function">lp()</tt> returns a dictionary with keys <code>'status'</code>,
+<code>'x'</code>, <code>'s'</code>, <code>'y'</code>, <code>'z'</code>.
+The possible values of the <code>'status'</code> item are as follows.
+<DL>
+<DT><STRONG><code>'optimal'.</code></STRONG></DT>
+<DD>In this case the <code>'x'</code>, <code>'s'</code>,
+<code>'y'</code> and <code>'z'</code> entries contain the primal and dual solutions,
+which approximately satisfy
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+Gx + s = h, \qquad Ax=b, \qquad G^T z + A^T y + c = 0, \qquad
+ s \succeq 0, \qquad z \succeq 0, \qquad s^T z =0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="567" HEIGHT="27" BORDER="0"
+ SRC="img112.gif"
+ ALT="\begin{displaymath}
+Gx + s = h, \qquad Ax=b, \qquad G^T z + A^T y + c = 0, \qquad
+s \succeq 0, \qquad z \succeq 0, \qquad s^T z =0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'primal infeasible'.</code></STRONG></DT>
+<DD>The <code>'x'</code> and <code>'s'</code> entries are <code>None</code>, and the <code>'y'</code>,
+<code>'z'</code> entries provide an approximate certificate of
+infeasibility, <EM>i.e.</EM>, vectors that approximately satisfy
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+G^T z + A^T y = 0, \qquad h^T z + b^T y = -1, \qquad z \succeq 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="340" HEIGHT="27" BORDER="0"
+ SRC="img113.gif"
+ ALT="\begin{displaymath}
+G^T z + A^T y = 0, \qquad h^T z + b^T y = -1, \qquad z \succeq 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+With the <code>'glpk'</code> option, no proof of infeasibility is returned
+(all entries of the dictionary are <code>None</code>).
+
+<P>
+</DD>
+<DT><STRONG><code>'dual infeasible'.</code></STRONG></DT>
+<DD>The LP is dual infeasible.
+The <code>'y'</code> and <code>'z'</code> entries are <code>None</code>, and the <code>'x'</code>
+and <code>'s'</code> entries contain an approximate certificate of dual
+infeasibility
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+Gx + s = 0, \qquad Ax=0, \qquad c^T x = -1, \qquad s \succeq 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="350" HEIGHT="27" BORDER="0"
+ SRC="img114.gif"
+ ALT="\begin{displaymath}
+Gx + s = 0, \qquad Ax=0, \qquad c^T x = -1, \qquad s \succeq 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+With the <code>'glpk'</code> option, no proof of dual infeasibility is
+returned.
+
+<P>
+</DD>
+<DT><STRONG><code>'unknown'</code>.</STRONG></DT>
+<DD>The <code>'x'</code>, <code>'s'</code>, <code>'y'</code>,
+<code>'z'</code> entries are <code>None</code>.
+</DD>
+</DL>
+
+<P>
+</dl>
+
+<P>
+As a simple example we solve the LP
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}[t]{ll}
+ \mbox{minimize} & -4x_1 - 5x_2 \\
+ \mbox{subject to} & 2x_1 + x_2 \leq 3 \\
+ & x_1 + 2x_2 \leq 3 \\
+ & x_1 \geq 0, \quad x_2 \geq 0.
+ \end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="195" HEIGHT="87" BORDER="0"
+ SRC="img115.gif"
+ ALT="\begin{displaymath}
+\begin{array}[t]{ll}
+\mbox{minimize} & -4x_1 - 5x_2 \\
+\...
+...2x_2 \leq 3 \\
+& x_1 \geq 0, \quad x_2 \geq 0.
+\end{array}
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt import solvers
+>>> c = matrix([-4., -5.])
+>>> G = matrix([[2., 1., -1., 0.], [1., 2., 0., -1.]])
+>>> h = matrix([3., 3., 0., 0.])
+>>> sol = solvers.lp(c,G,h)
+>>> print sol['x']
+ 1.0000e-00
+ 1.0000e-00
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
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+<p></p><hr />
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diff --git a/doc/cvxopt/s-orderings.html b/doc/cvxopt/s-orderings.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+</head>
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+
+<H1><A NAME="SECTION009100000000000000000"></A> <A NAME="s-orderings"></A>
+<BR>
+7.1 Matrix Orderings (<tt class="module">cvxopt.amd</tt>)
+</H1>
+
+<P>
+CVXOPT includes an interface to the AMD library for computing
+approximate minimum degree orderings of sparse matrices.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://www.cise.ufl.edu/research/sparse/amd'
+ >AMD code,
+documentation, copyright and license.</a></dt>
+ <dd></dd>
+ </dl>
+<div class="seetext"><p>P. R. Amestoy, T. A. Davis, I. S. Duff,
+Algorithm 837: AMD, An Approximate Minimum Degree Ordering Algorithm,
+ACM Transactions on Mathematical Software, 30(3), 381-388, 2004.</p></div>
+</div>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-133' xml:id='l2h-133' class="function">order</tt></b>(</nobr></td>
+ <td><var>A</var><big>[</big><var>, uplo='L'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Computes the approximate mimimum degree ordering of a symmetric sparse
+matrix <I>A</I>.
+The ordering is returned as an integer dense matrix with length equal
+to the order of <var>A</var>. Its entries specify a permutation that
+reduces fill-in during the Cholesky factorization.
+More precisely, if <code><var>p</var> = order(<var>A</var>)</code>, then
+<code><var>A</var>[<var>p</var>,<var>p</var>]</code> has sparser Cholesky factors
+than <code><var>A</var></code>.
+</dl>
+
+<P>
+As an example we consider the matrix
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\left[ \begin{array}{rrrr}
+ 10 & 0 & 3 & 0 \\
+ 0 & 5 & 0 & -2 \\
+ 3 & 0 & 5 & 0 \\
+ 0 & -2 & 0 & 2
+\end{array}\right].
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="150" HEIGHT="83" BORDER="0"
+ SRC="img85.gif"
+ ALT="\begin{displaymath}
+\left[ \begin{array}{rrrr}
+10 & 0 & 3 & 0 \\
+0 & 5 & 0 & -2 \\
+3 & 0 & 5 & 0 \\
+0 & -2 & 0 & 2
+\end{array}\right].
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix
+>>> from cvxopt import amd
+>>> A = spmatrix([10,3,5,-2,5,2], [0,2,1,2,2,3], [0,0,1,1,2,3])
+>>> P = amd.order(A)
+>>> print P
+ 1
+ 0
+ 2
+ 3
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+<title>2.6 Other Matrix Functions</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td class='online-navigation'><a rel="next" title="2.7 Randomly Generated Matrices"
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+<td class='online-navigation'><a rel="index" title="Index"
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+ border='0' height='32' alt='Index' width='32' /></A></td>
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+
+<H1><A NAME="SECTION004600000000000000000"></A> <A NAME="s-otherfuncs"></A>
+<BR>
+2.6 Other Matrix Functions
+</H1>
+The following functions of dense matrices can be imported from
+<tt class="module">cvxopt.base</tt>.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-17' xml:id='l2h-17' class="function">sqrt</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+The elementwise square root of <var>x</var>. The result is returned
+as a real matrix if <var>x</var> is an integer or real matrix and
+as a complex matrix if <var>x</var> is a complex matrix. Raises an
+exception when <var>x</var> is an integer or real matrix with negative
+elements.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-18' xml:id='l2h-18' class="function">sin</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+The sine function applied elementwise to <var>x</var>.
+The result is returned as a real matrix if <var>x</var> is an integer
+or real matrix and as a complex matrix otherwise.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-19' xml:id='l2h-19' class="function">cos</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+The cosine function applied elementwise to <var>x</var>.
+The result is returned as a real matrix if <var>x</var> is an integer
+or real matrix and as a complex matrix otherwise.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-20' xml:id='l2h-20' class="function">exp</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+The exponential function applied elementwise to <var>x</var>.
+The result is returned as a real matrix if <var>x</var> is an integer
+or real matrix and as a complex matrix otherwise.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-21' xml:id='l2h-21' class="function">log</tt></b>(</nobr></td>
+ <td><var>x</var>)</td></tr></table></dt>
+<dd>
+The natural logarithm applied elementwise to <var>x</var>.
+The result is returned as a real matrix if <var>x</var> is an integer
+or real matrix and as a complex matrix otherwise.
+Raises an exception when <var>x</var> is an integer or real matrix with
+nonnegative elements, or a complex matrix with zero elements.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-22' xml:id='l2h-22' class="function">mul</tt></b>(</nobr></td>
+ <td><var>x, y</var>)</td></tr></table></dt>
+<dd>
+The elementwise product of <var>x</var> and <var>y</var>.
+The two matrices must have the same size and type.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-23' xml:id='l2h-23' class="function">div</tt></b>(</nobr></td>
+ <td><var>x, y</var>)</td></tr></table></dt>
+<dd>
+The elementwise division of <var>x</var> by <var>y</var>.
+The two matrices must have the same size and type.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
+<td class='online-navigation'><a rel="prev" title="2.5 Built-in Functions"
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+
+<H1><A NAME="SECTION0010900000000000000000"></A> <A NAME="s-parameters"></A>
+<BR>
+8.9 Algorithm Parameters
+</H1>
+In this section we list some algorithm control parameters that can
+be modified without editing the source code.
+These control parameters are accessible via the dictionary
+<tt class="member">solvers.options</tt>. By default the dictionary
+is empty and the default values of the parameters are used.
+
+<P>
+One can change the parameters in the <b>default</b> solvers by
+adding entries with the following key values.
+<DL>
+<DT><STRONG><code>'show_progress'</code></STRONG></DT>
+<DD><code>True</code> or <code>False</code>; turns the output to the screen on or off
+(default: <code>True</code>).
+</DD>
+<DT><STRONG><code>'maxiters'</code></STRONG></DT>
+<DD>maximum number of iterations (default: 100).
+</DD>
+<DT><STRONG><code>'abstol'</code></STRONG></DT>
+<DD>absolute accuracy (default: <code>1e-7</code>).
+</DD>
+<DT><STRONG><code>'reltol'</code></STRONG></DT>
+<DD>relative accuracy (default: <code>1e-7</code>).
+</DD>
+<DT><STRONG><code>'feastol'</code></STRONG></DT>
+<DD>tolerance for feasibility conditions (default:
+<code>1e-7</code>).
+</DD>
+<DT><STRONG><code>'refinement'</code></STRONG></DT>
+<DD><code>True</code> or <code>False</code>. If <code>True</code>,
+one step of iterative refinement is applied after solving KKT equations
+in <tt class="function">conelp()</tt>, <tt class="function">lp()</tt>, and <tt class="function">sdp()</tt>
+(default: <code>True</code>).
+</DD>
+</DL>
+For example the command
+<div class="verbatim"><pre>
+>>> from cvxopt import solvers
+>>> solvers.options['show_progress'] = False
+</pre></div>
+turns off the screen output during calls to the solvers.
+The tolerances <var>abstol</var>, <var>reltol</var> and <var>feastol</var> have the
+following meaning. <tt class="function">conelp()</tt> terminates with
+status <code>'optimal'</code>, if
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0,
+\qquad
+ \frac{\|G_\mathrm{l}x+s_\mathrm{l}-h_\mathrm{l}\|_2}
+ {\max\{1,\|h_\mathrm{l}\|_2\}} \leq \epsilon_\mathrm{feas},
+\qquad
+\frac{\|G_\mathrm{s}(x)+S_\mathrm{s}-H_\mathrm{s}\|_F}
+{\max\{1,\|H_\mathrm{s}\|_F\}} \leq \epsilon_\mathrm{feas},
+\qquad
+\frac{\|Ax-b\|_2}{\max\{1,\|b\|_2\}} \leq \epsilon_\mathrm{feas},
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="748" HEIGHT="44" BORDER="0"
+ SRC="img161.gif"
+ ALT="\begin{displaymath}
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0,
+\qqu...
+...t _2}{\max\{1,\Vert b\Vert _2\}} \leq \epsilon_\mathrm{feas},
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0, \qquad
+\frac{\|G_\mathrm{l}^Tz_\mathrm{l}+
+G_\mathrm{s}^T(Z_\mathrm{s}) + A^Ty+c\|_2}{\max\{1,\|c\|_2\}}
+\leq \epsilon_\mathrm{feas},
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="426" HEIGHT="45" BORDER="0"
+ SRC="img162.gif"
+ ALT="\begin{displaymath}
+z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0, \qqua...
+... _2}{\max\{1,\Vert c\Vert _2\}}
+\leq \epsilon_\mathrm{feas},
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+and
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+s_\mathrm{l}^T z_\mathrm{l} + \mathop{\bf tr}(S_\mathrm{s}Z_\mathrm{s}) \leq
+ \epsilon_\mathrm{abs} \qquad \mbox{or} \qquad
+\left( \min\left\{c^Tx,
+ h_\mathrm{l}^T z_\mathrm{l} + \mathop{\bf tr}(H_\mathrm{s} Z_\mathrm{s})
+ + b^Ty \right\} < 0, \quad
+ \frac{s_\mathrm{l}^Tz_\mathrm{l} + \mathop{\bf tr}(S_\mathrm{s}Z_\mathrm{s})}
+ {-\min\{c^Tx, h_\mathrm{l}^Tz_\mathrm{l} +
+ \mathop{\bf tr}(H_\mathrm{s} Z_\mathrm{s}) + b^T y\}} \leq \epsilon_\mathrm{rel}
+\right).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="842" HEIGHT="47" BORDER="0"
+ SRC="img163.gif"
+ ALT="\begin{displaymath}
+s_\mathrm{l}^T z_\mathrm{l} + \mathop{\bf tr}(S_\mathrm{s}Z...
+...} Z_\mathrm{s}) + b^T y\}} \leq \epsilon_\mathrm{rel}
+\right).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+It returns with status <code>'primal infeasible'</code> if
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+z_\mathrm{l} \succeq 0, \qquad
+Z_\mathrm{s} \succeq 0, \qquad
+\qquad \|G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s})
+ +A^Ty\|_2 \leq \epsilon_\mathrm{feas},
+ \qquad h_\mathrm{l}^Tz_\mathrm{l} + \mathop{\bf tr}(H_\mathrm{s} Z_\mathrm{s})
+ +b^Ty = -1.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="637" HEIGHT="28" BORDER="0"
+ SRC="img164.gif"
+ ALT="\begin{displaymath}
+z_\mathrm{l} \succeq 0, \qquad
+Z_\mathrm{s} \succeq 0, \qqua...
+...{l} + \mathop{\bf tr}(H_\mathrm{s} Z_\mathrm{s})
++b^Ty = -1.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+It returns with status <code>'dual infeasible'</code> if
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+s_\mathrm{l} \succeq 0, \qquad
+S_\mathrm{s} \succeq 0, \qquad
+\qquad
+\|G_\mathrm{l}x+s_\mathrm{l}\|_2 \leq \epsilon_\mathrm{feas}, \qquad
+\|G_\mathrm{s}(x)+S_\mathrm{s}\|_F \leq \epsilon_\mathrm{feas}, \qquad
+\|Ax\|_2 \leq \epsilon_\mathrm{feas}, \qquad
+c^Tx = -1.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="742" HEIGHT="28" BORDER="0"
+ SRC="img165.gif"
+ ALT="\begin{displaymath}
+s_\mathrm{l} \succeq 0, \qquad
+S_\mathrm{s} \succeq 0, \qqua...
+...Vert Ax\Vert _2 \leq \epsilon_\mathrm{feas}, \qquad
+c^Tx = -1.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The functions <tt class="function">lp()</tt> and <tt class="function">sdp()</tt> call
+<tt class="function">conelp()</tt> and hence use the same stopping criteria.
+
+<P>
+<tt class="function">nlcp()</tt> returns with status <code>'optimal'</code> if
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\frac{\| \nabla f_0(x) + D\tilde f(x)^Tz_\mathrm{nl} +
+ G^Tz_\mathrm{l} + A^T y \|_2 }
+{\max\{ 1,
+\| \nabla f_0(x_0) + D\tilde f(x_0)^T{\bf 1}+ G^T{\bf 1}\|_2 \}}
+\leq \epsilon_\mathrm{feas}, \qquad
+\frac{\| ( \tilde f(x) + s_{\mathrm{nl}}, Gx + s_\mathrm{l} - h,
+ Ax-b ) \|_2}
+{\max\{1, \| ( \tilde f(x_0) + {\bf 1},
+Gx_0 + {\bf 1}-h, Ax_0-b) \|_2 \}} \leq \epsilon_\mathrm{feas}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="742" HEIGHT="49" BORDER="0"
+ SRC="img166.gif"
+ ALT="\begin{displaymath}
+\frac{\Vert \nabla f_0(x) + D\tilde f(x)^Tz_\mathrm{nl} +
+...
+...+ {\bf 1}-h, Ax_0-b) \Vert _2 \}} \leq \epsilon_\mathrm{feas}
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <I>x0</I> is the point returned by <code>F()</code>, and
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\mathrm{gap} \leq \epsilon_\mathrm{abs}
+\qquad \mbox{or} \qquad \left( f_0(x) < 0, \quad
+\frac{\mathrm{gap}} {-f_0(x)} \leq \epsilon_\mathrm{rel} \right)
+\qquad \mbox{or} \qquad
+\left( L(x,y,z) > 0, \quad \frac{\mathrm{gap}}
+{L(x,y,z)} \leq \epsilon_\mathrm{rel} \right)
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="684" HEIGHT="45" BORDER="0"
+ SRC="img167.gif"
+ ALT="\begin{displaymath}
+\mathrm{gap} \leq \epsilon_\mathrm{abs}
+\qquad \mbox{or} \qq...
+...ac{\mathrm{gap}}
+{L(x,y,z)} \leq \epsilon_\mathrm{rel} \right)
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\mathrm{gap} =
+\left[\begin{array}{c} s_\mathrm{nl} \\s_\mathrm{l}
+\end{array}\right]^T
+\left[\begin{array}{c} z_\mathrm{nl} \\z_\mathrm{l}
+\end{array}\right],
+\qquad
+L(x,y,z) = f_0(x) + z_\mathrm{nl}^T \tilde f(x) +
+ z_\mathrm{l}^T (Gx-h) + y^T(Ax-b).
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="558" HEIGHT="48" BORDER="0"
+ SRC="img168.gif"
+ ALT="\begin{displaymath}
+\mathrm{gap} =
+\left[\begin{array}{c} s_\mathrm{nl} \\ s_\...
+...athrm{nl}^T \tilde f(x) +
+z_\mathrm{l}^T (Gx-h) + y^T(Ax-b).
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+The functions <tt class="function">qp()</tt>, <tt class="function">gp()</tt> and <tt class="function">cp()</tt>
+call <tt class="function">nlcp()</tt> and hence use the same stopping criteria
+(with <I>x0</I>=0 for <tt class="function">qp()</tt> and <tt class="function">gp()</tt>).
+
+<P>
+The control parameters listed in the <b>GLPK</b> documentation are
+set to their default values and can also be customized by making
+an entry in <tt class="member">solvers.options</tt>.
+The keys in the dictionary are strings with the name of the GLPK
+parameter. The command
+<div class="verbatim"><pre>
+>>> from cvxopt import solvers
+>>> solvers.options['LPX_K_MSGLEV'] = 0
+</pre></div>
+turns off the screen output subsequent calls <tt class="function">lp()</tt> with
+the <code>'glpk'</code> option.
+
+<P>
+The <b>MOSEK</b> <a class="ulink" href="http://www.mosek.com/products/3/tools/doc/html/tools/node22.html"
+ >control parameters</a>
+are set to their default values.
+The corresponding keys in <code>solvers.options</code> are strings with the
+name of the MOSEK parameter. For example the command
+<div class="verbatim"><pre>
+>>> from cvxopt import solvers
+>>> solvers.options['MSK_IPAR_LOG'] = 0
+</pre></div>
+turns off the screen output during calls of <tt class="function">lp()</tt>
+and <tt class="function">qp()</tt> with the <code>'mosek'</code> option.
+
+<P>
+The following control parameters affect the <b>DSDP</b> algorithm:
+<DL>
+<DT><STRONG><code>'DSDP_Monitor'</code></STRONG></DT>
+<DD>the interval (in number of iterations)
+ at which output is printed to the screen
+(default: 0).
+</DD>
+<DT><STRONG><code>'DSDP_MaxIts'</code></STRONG></DT>
+<DD>maximum number of iterations.
+</DD>
+<DT><STRONG><code>'DSDP_GapTolerance'</code></STRONG></DT>
+<DD>relative accuracy (default:
+<code>1e-5</code>).
+</DD>
+</DL>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
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+
+<H1><A NAME="SECTION004700000000000000000"></A> <A NAME="s-random"></A>
+<BR>
+2.7 Randomly Generated Matrices
+</H1>
+The module <tt class="module">cvxopt.random</tt> provides functions for generating
+random matrices. Two types of random matrices are defined:
+matrices with normally distributed entries and matrices with uniformly
+distributed entries.
+
+<P>
+The pseudo-random number generators used to
+generate the random matrices are from the package described in the
+references below.
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://www.cs.wm.edu/~va/software/park/park.html'
+ >S. Park, Random Number Generators.</a></dt>
+ <dd></dd>
+ </dl>
+
+<P>
+S. Park, D. Geyer, Random Number Generators: Good Ones Are
+Hard To Find,
+Communications of the ACM, October 1988.
+</div>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-24' xml:id='l2h-24' class="function">normal</tt></b>(</nobr></td>
+ <td><var>nrows</var><big>[</big><var>, ncols</var><big>[</big><var>,
+ mean</var><big>[</big><var>, std</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Returns a type <code>'d'</code> matrix of size <var>nrows</var> by
+<var>ncols</var> with random elements chosen from a normal distribution
+with mean <var>mean</var> and standard deviation <var>std</var>.
+The default values for the optional arguments are
+<var>ncols</var>=1, <var>mean</var>=0.0, <var>std</var>=1.0.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-25' xml:id='l2h-25' class="function">uniform</tt></b>(</nobr></td>
+ <td><var>nrows</var><big>[</big><var>, ncols</var><big>[</big><var>,
+ a</var><big>[</big><var>, b</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Returns a type <code>'d'</code> matrix of size <var>nrows</var> by
+<var>ncols</var> matrix with random elements, uniformly distributed
+between <var>a</var> and <var>b</var>.
+The default values for the optional arguments are
+<var>ncols</var>=1, <var>a</var>=0.0, <var>b</var>=1.0.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-26' xml:id='l2h-26' class="function">getseed</tt></b>(</nobr></td>
+ <td><var></var>)</td></tr></table></dt>
+<dd>
+Returns the current seed value (the state of the random number
+generator).
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-27' xml:id='l2h-27' class="function">setseed</tt></b>(</nobr></td>
+ <td><var></var><big>[</big><var>value</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Sets the seed value. <var>value</var> must be a nonnegative integer.
+If <var>value</var> is absent or equal to zero, the seed value is taken
+from the system clock.
+</dl>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<td class='online-navigation'><a rel="prev" title="2.6 Other Matrix Functions"
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+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+
+<H1><A NAME="SECTION0010400000000000000000"></A> <A NAME="s-sdpsolver"></A>
+<BR>
+8.4 Semidefinite Programming
+</H1>
+We use the following notation for a pair of primal and dual
+semidefinite programs (SDPs):
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+\mbox{Primal:}\quad \begin{array}[t]{ll}
+\mbox{minimize} & c^Tx \\
+\mbox{subject to} & G_\mathrm{l}x + s_\mathrm{l} = h_\mathrm{l} \\
+ & G_\mathrm{s}(x) + S_\mathrm{s} = H_\mathrm{s} \\
+ & Ax=b \\& s_\mathrm{l} \succeq 0, \quad S_\mathrm{s} \succeq 0
+\end{array} \qquad\qquad
+\mbox{Dual:}\quad
+\begin{array}[t]{ll}
+\mbox{maximize} & -h_\mathrm{l}^T z_\mathrm{l} -
+ \mathop{\bf tr}(H_\mathrm{s} Z_\mathrm{s}) - b^T y \\
+\mbox{subject to} & G_\mathrm{l}^Tz_\mathrm{l} +
+ G_\mathrm{s}^T(Z_\mathrm{s}) + A^T y + c = 0 \\
+ & z_\mathrm{l} \succeq 0, \quad Z_\mathrm{s} \succeq 0.
+\end{array}
+\end{equation}
+ -->
+<A NAME="e-sdp"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-sdp"></A><IMG
+ WIDTH="682" HEIGHT="106" BORDER="0"
+ SRC="img127.gif"
+ ALT="\begin{displaymath}
+\mbox{Primal:}\quad \begin{array}[t]{ll}
+\mbox{minimize} & c...
+...\mathrm{l} \succeq 0, \quad Z_\mathrm{s} \succeq 0.
+\end{array}\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(8.2)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+The dimensions of the primal and dual variables are
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x\in {\mbox{\bf R}}^n, \qquad s_\mathrm{l} \in {\mbox{\bf R}}^m,
+\qquad S_\mathrm{s} \in {\mbox{\bf S}}^{m_0} \times \cdots \times
+{\mbox{\bf S}}^{m_{N-1}}, \qquad
+ y \in{\mbox{\bf R}}^p, \qquad z_\mathrm{l}\in {\mbox{\bf R}}^m,
+\qquad Z_\mathrm{s} \in {\mbox{\bf S}}^{m_0} \times \cdots \times
+{\mbox{\bf S}}^{m_{N-1}},
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="705" HEIGHT="27" BORDER="0"
+ SRC="img128.gif"
+ ALT="\begin{displaymath}
+x\in {\mbox{\bf R}}^n, \qquad s_\mathrm{l} \in {\mbox{\bf R...
+...{\bf S}}^{m_0} \times \cdots \times
+{\mbox{\bf S}}^{m_{N-1}},
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <!-- MATH
+ ${\mbox{\bf S}}^n$
+ -->
+<SPAN CLASS="MATH"><IMG
+ WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ SRC="img129.gif"
+ ALT="${\mbox{\bf S}}^n$"></SPAN> is the set of real symmetric matrices
+of order <I>n</I>. The problem data are the matrices
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+c\in{\mbox{\bf R}}^n, \qquad G_\mathrm{l} \in{\mbox{\bf R}}^{m\times n},
+\qquad h_\mathrm{l} \in {\mbox{\bf R}}^{m}, \qquad
+ H_\mathrm{s} \in {\mbox{\bf S}}^{m_0} \times \cdots \times {\mbox{\bf S}}^{m_{N-1}},
+\qquad
+A \in {\mbox{\bf R}}^{p\times n}, \qquad b \in {\mbox{\bf R}}^{p},
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="645" HEIGHT="27" BORDER="0"
+ SRC="img130.gif"
+ ALT="\begin{displaymath}
+c\in{\mbox{\bf R}}^n, \qquad G_\mathrm{l} \in{\mbox{\bf R}}^...
+... {\mbox{\bf R}}^{p\times n}, \qquad b \in {\mbox{\bf R}}^{p},
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+and the linear mapping
+<!-- MATH
+ $G_\mathrm{s} : {\mbox{\bf R}}^n \rightarrow {\mbox{\bf S}}^{m_1} \times \cdots \times
+{\mbox{\bf S}}^{m_N}$
+ -->
+<SPAN CLASS="MATH"><IMG
+ WIDTH="196" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ SRC="img131.gif"
+ ALT="$G_\mathrm{s} : {\mbox{\bf R}}^n \rightarrow {\mbox{\bf S}}^{m_1} \times \cdots \times
+{\mbox{\bf S}}^{m_N}$"></SPAN> and its adjoint <!-- MATH
+ $G_\mathrm{s}^T$
+ -->
+<SPAN CLASS="MATH"><IMG
+ WIDTH="26" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
+ SRC="img132.gif"
+ ALT="$G_\mathrm{s}^T$"></SPAN>.
+As for LPs we store vector variables as dense real matrices with one
+column.
+Block-diagonal symmetric matrices are stored as lists of square
+dense real matrices, with the lower triangular part of each matrix
+representing the lower triangular part of a diagonal block. Entries
+above the diagonal are not referenced.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-148' xml:id='l2h-148' class="function">sdp</tt></b>(</nobr></td>
+ <td><var>c</var><big>[</big><var>, Gl, hl</var><big>[</big><var>,
+ Gs, hs</var><big>[</big><var>, A, b</var><big>[</big><var>, solver</var><big>[</big><var>,
+ primalstart</var><big>[</big><var>, dualstart</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+
+<P>
+Solves the pair of primal and dual SDPs (<A HREF="#e-sdp">8.2</A>).
+
+<P>
+<var>c</var> is a dense real matrix with one column.
+<var>Gl</var> and <var>A</var> are dense or sparse real matrices.
+<var>hl</var> and <var>b</var> are dense real matrices with one column.
+The default values for <var>Gl</var>, <var>hl</var>, <var>A</var> and <var>b</var> are
+empty matrices, <EM>i.e.</EM>, matrices with zero rows.
+
+<P>
+<var>Gs</var> and <var>hs</var> are lists of length <I>N</I> that specify the
+linear matrix inequality constraints.
+<var>hs</var> is a list of square dense real matrices <code><var>hs</var>[k]</code> of
+order <I>m_k</I>.
+<var>Gs</var> is a list of dense or sparse real matrices
+<code><var>Gs</var>[k]</code> with <I>m_k</I>*<I>m_k</I> rows and <I>n</I> columns,
+such that the product <code><var>Gs</var>[k]*<var>x</var></code>
+is the <I>k</I>th diagonal block of <I>Gs</I>(<var>x</var>), stored
+columnwise.
+
+<P>
+The <var>solver</var> argument is used to choose between two
+solvers: the default solver (used when <var>solver</var> is absent or
+equal to <code>None</code>) and the external solver DSDP5
+(<code><var>solver</var>='dsdp'</code>); see section <A href="s-external.html#s-external">8.8</A>.
+With the <code>'dsdp'</code> option the code does not accept problems with
+equality constraints.
+
+<P>
+The optional argument <var>primalstart</var> is a dictionary with keys
+<code>'x'</code>, <code>'sl'</code>, and <code>'ss'</code>, used as an optional primal
+starting point.
+<var>dualstart</var> is a dictionary with keys <code>'y'</code>, <code>'zl'</code>,
+<code>'zs'</code>, used as an optional dual starting point.
+These two arguments are ignored when the DSDP solver is used.
+
+<P>
+<tt class="function">sdp()</tt> returns a dictionary with keys <code>'status'</code>,
+<code>'x'</code>, <code>'sl'</code>, <code>'ss'</code>, <code>'y'</code>, <code>'zl'</code>,
+<code>'ss'</code>.
+The possible values of the <code>'status'</code> item are as follows.
+<DL>
+<DT><STRONG><code>'optimal'.</code></STRONG></DT>
+<DD>In this case the <code>'x'</code>, <code>'sl'</code>,
+<code>'ss'</code>, <code>'y'</code>, <code>'zl'</code>, <code>'zs'</code> entries contain
+primal and dual optimal solutions, which approximately satisfy
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+G_\mathrm{l}x+s_\mathrm{l} = h_\mathrm{l},
+\qquad
+G_\mathrm{s}(x)+S_\mathrm{s} = H_\mathrm{s},
+\qquad
+Ax=b, \qquad
+G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s}) + A^Ty+c = 0
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="553" HEIGHT="28" BORDER="0"
+ SRC="img133.gif"
+ ALT="\begin{displaymath}
+G_\mathrm{l}x+s_\mathrm{l} = h_\mathrm{l},
+\qquad
+G_\mathr...
+...m{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s}) + A^Ty+c = 0
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+and
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0, \qquad
+ z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0, \qquad
+ s_\mathrm{l}^T z_\mathrm{l} + \mathop{\bf tr}(S_\mathrm{s}Z_\mathrm{s}) = 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="469" HEIGHT="28" BORDER="0"
+ SRC="img134.gif"
+ ALT="\begin{displaymath}
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0, \qqu...
+... z_\mathrm{l} + \mathop{\bf tr}(S_\mathrm{s}Z_\mathrm{s}) = 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'primal infeasible'.</code></STRONG></DT>
+<DD>The <code>'x'</code>, <code>'sl'</code> and <code>'ss'</code> entries are <code>None</code>,
+and the <code>'y'</code>, <code>'zl'</code>, <code>'zs'</code> entries provide an
+approximate certificate of infeasibility:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s}) +A^Ty = 0
+\qquad h_\mathrm{l}^Tz_\mathrm{l} + \mathop{\bf tr}(H_\mathrm{s} Z_\mathrm{s})
+ +b^Ty = -1, \qquad
+z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="553" HEIGHT="28" BORDER="0"
+ SRC="img135.gif"
+ ALT="\begin{displaymath}
+G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s}) +A...
+...\qquad
+z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'dual infeasible'.</code></STRONG></DT>
+<DD>The SDP is dual infeasible.
+The <code>'y'</code>, <code>'zl'</code> and <code>'zs'</code> entries are <code>None</code>,
+and the <code>'x'</code>, <code>'sl'</code>, <code>'ss'</code> entries contain an
+approximate certificate of dual infeasibility:
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+G_\mathrm{l}x+s_\mathrm{l} = 0, \qquad
+G_\mathrm{s}(x)+S_\mathrm{s} = 0, \qquad
+Ax = 0, \qquad c^Tx = -1, \qquad
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="576" HEIGHT="28" BORDER="0"
+ SRC="img136.gif"
+ ALT="\begin{displaymath}
+G_\mathrm{l}x+s_\mathrm{l} = 0, \qquad
+G_\mathrm{s}(x)+S_\ma...
+...\qquad
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+
+<P>
+</DD>
+<DT><STRONG><code>'unknown'</code>.</STRONG></DT>
+<DD>The <code>'x'</code>, <code>'sl'</code>, <code>'ss'</code>,
+<code>'y'</code>, <code>'zl'</code> and <code>'zs'</code> entries are <code>None</code>.
+</DD>
+</DL>
+</dl>
+
+<P>
+We illustrate the calling sequence with a small example.
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & x_1 - x_2 + x_3 \\
+\mbox{subject to} &
+ x_1 \left[ \begin{array}{cc} -7 & -11 \\-11 & 3
+ \end{array}\right] +
+ x_2 \left[ \begin{array}{cc}
+ 7 & -18 \\-18 & 8 \end{array}\right] +
+ x_3 \left[ \begin{array}{cc}
+ -2 & -8 \\-8 & 1
+ \end{array}\right] \preceq
+ \left[ \begin{array}{cc}
+ 33 & -9 \\-9 & 26 \end{array}\right] \\*[1ex]
+& x_1 \left[ \begin{array}{ccc}
+ -21 & -11 & 0 \\-11 & 10 & 8 \\0 & 8 & 5
+ \end{array}\right] +
+ x_2 \left[ \begin{array}{ccc}
+ 0 & 10 & 16 \\
+10 & -10 & -10 \\
+16 & -10 & 3
+ \end{array}\right] +
+ x_3 \left[ \begin{array}{ccc}
+ -5 & 2 & -17 \\
+ 2 & -6 & -7 \\
+ -17 & 8 & 6
+ \end{array}\right]
+\preceq \left[ \begin{array}{ccc}
+ 14 & 9 & 40 \\
+ 9 & 91 & 10 \\
+ 40 & 10 & 15
+\end{array} \right]
+\end{array}
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="726" HEIGHT="121" BORDER="0"
+ SRC="img137.gif"
+ ALT="\begin{displaymath}
+\begin{array}{ll}
+\mbox{minimize} & x_1 - x_2 + x_3 \\
+\mbo...
+...
+9 & 91 & 10 \\
+40 & 10 & 15
+\end{array} \right]
+\end{array}\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt import solvers
+>>> c = matrix([1.,-1.,1.])
+>>> G = [ matrix([[-7., -11., -11., 3.],
+ [ 7., -18., -18., 8.],
+ [-2., -8., -8., 1.]]) ]
+>>> G += [ matrix([[-21., -11., 0., -11., 10., 8., 0., 8., 5.],
+ [ 0., 10., 16., 10., -10., -10., 16., -10., 3.],
+ [ -5., 2., -17., 2., -6., 8., -17., -7., 6.]]) ]
+>>> h = [ matrix([[33., -9.], [-9., 26.]]) ]
+>>> h += [ matrix([[14., 9., 40.], [9., 91., 10.], [40., 10., 15.]]) ]
+>>> sol = solvers.sdp(c, Gs=G, hs=h)
+>>> print sol['x']
+ -3.6775e-01
+ 1.8983e+00
+ -8.8747e-01
+>>> print sol['zs'][0]
+ 3.9613e-03 0.0000e+00
+ -4.3390e-03 4.7526e-03
+>>> print sol['zs'][1]
+ 5.5803e-02 0.0000e+00 0.0000e+00
+ -2.4103e-03 1.0411e-04 0.0000e+00
+ 2.4214e-02 -1.0459e-03 1.0507e-02
+</pre></div>
+Note that only the lower triangular parts of the dual variables are
+returned (in the example the returned values of the upper triangular
+elements happen to be zero, but this is not necessarily the case).
+
+<P>
+Only the entries in <var>Gs</var> and <var>hs</var> that correspond to lower
+triangular entries need to be provided, so in the example <var>h</var> and
+<var>G</var> can also be defined as follows.
+<div class="verbatim"><pre>
+>>> G = [ matrix([[-7., -11., 0., 3.],
+ [ 7., -18., 0., 8.],
+ [-2., -8., 0., 1.]]) ]
+>>> G += [ matrix([[-21., -11., 0., 0., 10., 8., 0., 0., 5.],
+ [ 0., 10., 16., 0., -10., -10., 0., 0., 3.],
+ [ -5., 2., -17., 0., -6., 8., 0., 0., 6.]]) ]
+>>> h = [ matrix([[33., -9.], [0., 26.]]) ]
+>>> h += [ matrix([[14., 9., 40.], [0., 91., 10.], [0., 0., 15.]]) ]
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
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+
+<H1><A NAME="SECTION008300000000000000000"></A> <A NAME="s-spmatrix-arith"></A>
+<BR>
+6.3 Arithmetic Operations
+</H1>
+Most of the operations defined for dense <code>'d'</code> and <code>'z'</code> matrices
+(section <A href="s-arithmetic.html#s-arithmetic">2.3</A>) are also defined for sparse matrices.
+In the following table, <var>A</var> is a sparse matrix,
+<var>B</var> is sparse or dense, and <var>c</var> is a scalar, defined as a
+Python number or a 1 by 1 dense matrix.
+
+<P>
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1">
+<TR><TD ALIGN="LEFT">Unary plus/minus</TD>
+<TD ALIGN="LEFT"><code>+<var>A</var></code>, <code>-<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Addition</TD>
+<TD ALIGN="LEFT"><code><var>A</var>+<var>B</var></code>, <code><var>B</var>+<var>A</var></code>,
+ <code><var>A</var>+<var>c</var></code>, <code><var>c</var>+<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Subtraction</TD>
+<TD ALIGN="LEFT"><code><var>A</var>-<var>B</var></code>, <code><var>B</var>-<var>A</var></code>,
+ <code><var>A</var>-<var>c</var></code>, <code><var>c</var>-<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Matrix multiplication</TD>
+<TD ALIGN="LEFT"><code><var>A</var>*<var>B</var></code>,
+ <code><var>B</var>*<var>A</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">Scalar multiplication and division</TD>
+<TD ALIGN="LEFT"><code><var>c</var>*<var>A</var></code>,
+ <code><var>A</var>*<var>c</var></code>, <code><var>A</var>/<var>c</var></code></TD>
+</TR>
+</TABLE>
+</DIV>
+
+<P>
+If <var>B</var> is a dense matrix, then the result of
+<code><var>A</var>+<var>B</var></code>, <code><var>B</var>+<var>A</var></code>, <code><var>A</var>-<var>B</var></code>,
+<code><var>B</var>-<var>A</var></code> is a dense matrix.
+The typecode of the result is <code>'d'</code> if <var>A</var> has typcode <code>'d'</code> and
+<var>B</var> has typecode <code>'i'</code> or <code>'d'</code>,
+and it is <code>'z'</code> if <var>A</var> and/or <var>B</var> have typecode <code>'z'</code>.
+
+<P>
+If <var>B</var> is a sparse matrix, then the result of
+<code><var>A</var>+<var>B</var></code>, <code><var>B</var>+<var>A</var></code>,
+<code><var>A</var>-<var>B</var></code>, <code><var>B</var>-<var>A</var></code> is a sparse
+matrix. The typecode of the result is <code>'d'</code> if <var>A</var> and <var>B</var>
+have typecode <code>'d'</code>, and <code>'z'</code> otherwise.
+
+<P>
+If <var>c</var> in <code><var>A</var>+<var>c</var></code>, <code><var>A</var>-<var>c</var></code>,
+<code><var>c</var>+<var>A</var></code>, <code><var>c</var>-<var>A</var></code> is a number,
+then it is interpreted as a dense matrix with the same size as
+<var>A</var>, typecode given by the type of <var>c</var>, and all entries equal
+to <var>c</var>.
+If <var>c</var> is a 1 by 1 dense matrix and the size of <var>A</var> is not 1
+by 1, then <var>c</var>
+is interpreted as a dense matrix of the same size as <var>A</var>,
+typecode given by the typecode of <var>c</var>, and all entries equal to
+<code><var>c</var>[0]</code>.
+
+<P>
+The result of a matrix-matrix product <code><var>A</var>*<var>B</var></code> or
+<code><var>B</var>*<var>A</var></code> is a dense matrix if <var>B</var> is dense, and sparse
+if <var>B</var> is sparse. The matrix-matrix product is not allowed if
+<var>B</var> is a dense <code>'i'</code> matrix.
+
+<P>
+If <var>c</var> is a number (Python integer float or complex), then the
+operations <code><var>c</var>*<var>A</var></code> and <code><var>A</var>*<var>c</var></code> define
+scalar multiplication and return a sparse matrix.
+
+<P>
+If <var>c</var> is a 1 by 1 dense matrix, then, if possible, the products
+<code><var>c</var>*<var>A</var></code> and <code><var>A</var>*<var>c</var></code> are interpreted as
+matrix-matrix products and a dense matrix is returned.
+If the product cannot be interpreted as a matrix-matrix product
+(either because the dimensions of <var>A</var> are incompatible or because
+<var>c</var> has typecode <code>'i'</code>), then the product is interpreted as the
+scalar multiplication with <code><var>c</var>[0]</code> and a sparse matrix is
+returned.
+
+<P>
+The division <code><var>A</var>/<var>c</var></code> is interpreted as scalar
+multiplication with <code>1.0/<var>c</var></code> if <var>c</var> is a number,
+or with <code>1.0/<var>c</var>[0]</code> if <var>c</var> is a 1 by 1 dense matrix.
+
+<P>
+The following in-place operations are defined for a sparse matrix
+<var>A</var> if they do not change the dimensions or type of <var>A</var>.
+<DIV ALIGN="CENTER">
+<TABLE CELLPADDING=3 BORDER="1">
+<TR><TD ALIGN="LEFT">In-place addition</TD>
+<TD ALIGN="LEFT"><code><var>A</var>+=<var>B</var></code>,
+ <code><var>A</var>+=<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">In-place subtraction</TD>
+<TD ALIGN="LEFT"><code><var>A</var>-=<var>B</var></code>,
+ <code><var>A</var>-=<var>c</var></code></TD>
+</TR>
+<TR><TD ALIGN="LEFT">In-place scalar multiplication and division</TD>
+<TD ALIGN="LEFT"><code><var>A</var>*=<var>c</var></code>, <code><var>A</var>/=<var>c</var></code></TD>
+</TR>
+</TABLE>
+</DIV>
+
+<P>
+For example, "<tt class="samp"><var>A</var> += 1.0</tt>" is not allowed because the
+operation "<tt class="samp"><var>A</var> = <var>A</var> + 1.0</tt>" results in a dense matrix,
+so it cannot be assigned to <var>A</var> without changing its type.
+
+<P>
+In-place matrix-matrix products are not allowed. (Except when
+<var>c</var> is a 1 by 1 dense matrix, in which case <code><var>A</var>*=<var>c</var></code>
+is interpreted as a scalar product <code><var>A</var>*=<var>c</var>[0]</code>.)
+
+<P>
+As for dense operations, the in-place sparse operations do not return
+a new matrix but modify the existing object <var>A</var>.
+The restrictions on in-place operations follow the principle that once
+a sparse matrix is created, its size and type cannot be modified.
+The only attributes that can be modified are the sparsity pattern and
+the numerical values of the nonzero elements.
+These attributes can be modified by in-place operations or by indexed
+assignments.
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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diff --git a/doc/cvxopt/s-umfpack.html b/doc/cvxopt/s-umfpack.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
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+</head>
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+
+<H1><A NAME="SECTION009200000000000000000"></A>
+<A NAME="s-umfpack"></A>
+<BR>
+7.2 General Linear Equations (<tt class="module">cvxopt.umfpack</tt>)
+</H1>
+The module <tt class="module">cvxopt.umfpack</tt> includes four functions for solving
+sparse non-symmetric sets of linear equations.
+They call routines from the UMFPACK library, with all control options
+set to the default values described in the UMFPACK user guide.
+
+<P>
+<div class="seealso">
+ <p class="heading">See Also:</p>
+
+<dl compact="compact" class="seeurl">
+ <dt><a href='http://www.cise.ufl.edu/research/sparse/umfpack'
+ >UMFPACK code, documentation, copyright and license.</a></dt>
+ <dd></dd>
+ </dl>
+<div class="seetext"><p>T. A. Davis,
+Algorithm 832: UMFPACK - an unsymmetric-pattern multifrontal method
+with a column pre-ordering strategy,
+ACM Transactions on Mathematical Software, 30(2), 196-199, 2004.</p></div>
+</div>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-134' xml:id='l2h-134' class="function">linsolve</tt></b>(</nobr></td>
+ <td><var>A, B</var><big>[</big><var>, trans='N'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a sparse set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX = B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX = B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX = B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <var>A</var> is a sparse matrix and <var>B</var> is a dense matrix of
+the same type (<code>'d'</code> or <code>'z'</code>) as <var>A</var>. On exit <var>B</var> contains
+the solution.
+Raises an <code>ArithmeticError</code> exception if the coefficient matrix
+is singular.
+</dl>
+In the following example we solve an equation with
+coefficient matrix
+<BR>
+<DIV ALIGN="RIGHT" CLASS="mathdisplay">
+
+<!-- MATH
+ \begin{equation}
+A = \left[\begin{array}{rrrrr}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 &-1 &-3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1
+ \end{array}\right].
+\end{equation}
+ -->
+<A NAME="e-sp-Adef"></A>
+<TABLE WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE"><TD></TD><TD ALIGN="CENTER" NOWRAP><A NAME="e-sp-Adef"></A><IMG
+ WIDTH="205" HEIGHT="102" BORDER="0"
+ SRC="img86.gif"
+ ALT="\begin{displaymath}
+A = \left[\begin{array}{rrrrr}
+2 & 3 & 0 & 0 & 0 \\
+3 & 0...
+...0 & 0 & 1 & 0 & 0 \\
+0 & 4 & 2 & 0 & 1
+\end{array}\right].
+\end{displaymath}"></TD>
+<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
+(7.1)</TD></TR>
+</TABLE>
+<BR CLEAR="ALL"></DIV><P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix, matrix
+>>> from cvxopt import umfpack
+>>> V = [2,3, 3,-1,4, 4,-3,1,2, 2, 6,1]
+>>> I = [0,1, 0, 2,4, 1, 2,3,4, 2, 1,4]
+>>> J = [0,0, 1, 1,1, 2, 2,2,2, 3, 4,4]
+>>> A = spmatrix(V,I,J)
+>>> B = matrix(1.0, (5,1))
+>>> umfpack.linsolve(A,B)
+>>> print B
+ 5.7895e-01
+-5.2632e-02
+ 1.0000e+00
+ 1.9737e+00
+-7.8947e-01
+</pre></div>
+The function <tt class="function">umfpack.linsolve()</tt> is equivalent to the
+following three functions called in sequence.
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-135' xml:id='l2h-135' class="function">symbolic</tt></b>(</nobr></td>
+ <td><var>A</var>)</td></tr></table></dt>
+<dd>
+Reorders the columns of <var>A</var> to reduce fill-in and performs a
+symbolic LU factorization. <var>A</var> is a sparse, possibly rectangular,
+matrix.
+Returns the symbolic factorization as an opaque C object that can be
+passed on to <tt class="function">umfpack.numeric()</tt>.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-136' xml:id='l2h-136' class="function">numeric</tt></b>(</nobr></td>
+ <td><var>A, F</var>)</td></tr></table></dt>
+<dd>
+Performs a numeric LU factorization of a sparse, possibly rectangular,
+matrix <var>A</var>. The argument <var>F</var> is the symbolic factorization
+computed by <tt class="function">umfpack.symbolic()</tt> applied to the matrix <var>A</var>,
+or another sparse matrix with the same sparsity pattern, dimensions,
+and type. The numeric factorization is returned as an opaque C object
+that that can be passed on to <tt class="function">umfpack.solve()</tt>. Raises an
+<code>ArithmeticError</code> if the matrix is singular.
+</dl>
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><tt id='l2h-137' xml:id='l2h-137' class="function">solve</tt></b>(</nobr></td>
+ <td><var>A, F, B</var><big>[</big><var>, trans='N'</var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+Solves a set of linear equations
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+AX = B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX = B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX = B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="601" HEIGHT="28" BORDER="0"
+ SRC="img43.gif"
+ ALT="\begin{displaymath}
+AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+A^TX=B ...
+...'T'}), \qquad
+A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+where <var>A</var> is a sparse matrix and <var>B</var> is a dense matrix of
+the same type as <var>A</var>.
+The argument <var>F</var> is a numeric factorization computed by
+<tt class="function">umfpack.numeric()</tt>.
+On exit <var>B</var> is overwritten by the solution.
+</dl>
+These separate functions are useful for solving several sets
+of linear equations with the same coefficient matrix and different
+righthand sides, or with coefficient matrices that share the same
+sparsity pattern.
+The symbolic factorization depends only on the sparsity pattern of
+the matrix, and not on the numerical values of the nonzero
+coefficients.
+The numerical factorization on the other hand depends on the sparsity
+pattern of the matrix and on its the numerical values.
+
+<P>
+As an example, suppose <I>A</I> is the matrix (<A HREF="#e-sp-Adef">7.1</A>) and
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+B = \left[\begin{array}{rrrrr}
+ 4 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 &-1 &-3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 2
+ \end{array}\right],
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="206" HEIGHT="102" BORDER="0"
+ SRC="img87.gif"
+ ALT="\begin{displaymath}
+B = \left[\begin{array}{rrrrr}
+4 & 3 & 0 & 0 & 0 \\
+3 & 0...
+...0 & 0 & 1 & 0 & 0 \\
+0 & 4 & 2 & 0 & 2
+\end{array}\right],
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+which differs from <I>A</I> in its first and last entries.
+The following code computes
+<BR><P></P>
+<DIV ALIGN="CENTER" CLASS="mathdisplay">
+<!-- MATH
+ \begin{displaymath}
+x = A^{-T}B^{-1}A^{-1}{\bf 1}.
+\end{displaymath}
+ -->
+
+<IMG
+ WIDTH="132" HEIGHT="24" BORDER="0"
+ SRC="img88.gif"
+ ALT="\begin{displaymath}
+x = A^{-T}B^{-1}A^{-1}{\bf 1}.
+\end{displaymath}">
+</DIV>
+<BR CLEAR="ALL">
+<P></P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import spmatrix, matrix
+>>> from cvxopt import umfpack
+>>> VA = [2,3, 3,-1,4, 4,-3,1,2, 2, 6,1]
+>>> VB = [4,3, 3,-1,4, 4,-3,1,2, 2, 6,2]
+>>> I = [0,1, 0, 2,4, 1, 2,3,4, 2, 1,4]
+>>> J = [0,0, 1, 1,1, 2, 2,2,2, 3, 4,4]
+>>> A = spmatrix(VA, I, J)
+>>> B = spmatrix(VB, I, J)
+>>> x = matrix(1.0, (5,1))
+>>> Fs = umfpack.symbolic(A)
+>>> FA = umfpack.numeric(A, Fs)
+>>> FB = umfpack.numeric(B, Fs)
+>>> umfpack.solve(A, FA, x)
+>>> umfpack.solve(B, FB, x)
+>>> umfpack.solve(A, FA, x, trans='T')
+>>> print x
+ 5.8065e-01
+-2.3660e-01
+ 1.6280e+00
+ 8.0656e+00
+-1.3075e-01
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
+<tr>
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
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diff --git a/doc/cvxopt/s-variables.html b/doc/cvxopt/s-variables.html
new file mode 100644
index 0000000..7063350
--- /dev/null
+++ b/doc/cvxopt/s-variables.html
@@ -0,0 +1,162 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+<head>
+<link rel="STYLESHEET" href="cvxopt.css" type='text/css' />
+<link rel="first" href="cvxopt.html" title='CVXOPT: A Python Package for Convex Optimization' />
+<link rel='contents' href='contents.html' title="Contents" />
+<link rel='index' href='genindex.html' title='Index' />
+<link rel='last' href='about.html' title='About this document...' />
+<link rel='help' href='about.html' title='About this document...' />
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+<meta name='aesop' content='information' />
+<title>9.1 Variables</title>
+</head>
+<body>
+<DIV CLASS="navigation">
+<div id='top-navigation-panel' xml:id='top-navigation-panel'>
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+</div>
+<hr /></div>
+</DIV>
+<!--End of Navigation Panel-->
+
+<H1><A NAME="SECTION0011100000000000000000"></A> <A NAME="s-variables"></A>
+<BR>
+9.1 Variables
+</H1>
+Optimization variables are represented by variable objects.
+
+<P>
+<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
+ <td><nobr><b><span class="typelabel">class</span> <tt id='l2h-152' xml:id='l2h-152' class="class">variable</tt></b>(</nobr></td>
+ <td><var></var><big>[</big><var>size</var><big>[</big><var>, name</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
+<dd>
+A vector variable. The first argument is the dimension of the
+vector (a positive integer with default value 1).
+The second argument is a string with a name for the variable.
+The name is optional and has default value <code>""</code>. It is only used
+when displaying variables (or objects that depend on variables, such
+as functions or constraints)
+using <tt class="function">print</tt> statements, when calling the built-in functions
+<tt class="function">repr()</tt> or <tt class="function">str()</tt>, or when writing linear programs
+to MPS files.
+</dl>
+The function <tt class="function">len()</tt> returns the length of a
+variable. A variable <var>x</var> has two attributes.
+<dl><dt><b><tt id='l2h-153' xml:id='l2h-153' class="member">name</tt></b></dt>
+<dd>
+The name of the variable.
+</dl>
+
+<P>
+<dl><dt><b><tt id='l2h-154' xml:id='l2h-154' class="member">value</tt></b></dt>
+<dd>
+Either <code>None</code> or a dense <code>'d'</code> matrix of size <code>len(<var>x</var>)</code> by 1.
+
+<P>
+The attribute <var>x</var>.<tt class="member">value</tt> is set to <code>None</code> when the
+variable <var>x</var> is created. It can be given a numerical value later,
+typically by solving an LP that has <var>x</var> as one of its variables.
+One can also make an explicit assignment
+<code><var>x</var>.<tt class="member">value</tt> = <var>y</var></code>. The
+assigned value <var>y</var> must be an integer or float, or a
+dense <code>'d'</code> matrix of size (<code>len(<var>x</var>)</code>,1).
+If <var>y</var> is an integer or float all the elements of
+<var>x</var>.<tt class="member">value</tt> are set to the value of <var>y</var>.
+</dl>
+
+<P>
+<div class="verbatim"><pre>
+>>> from cvxopt.base import matrix
+>>> from cvxopt.modeling import variable
+>>> x = variable(3,'a')
+>>> len(x)
+3
+>>> print x.name
+a
+>>> print x.value
+None
+>>> x.value = matrix([1.,2.,3.])
+>>> print x.value
+ 1.0000e+00
+ 2.0000e+00
+ 3.0000e+00
+>>> x.value = 1
+>>> print x.value
+ 1.0000e+00
+ 1.0000e+00
+ 1.0000e+00
+</pre></div>
+
+<P>
+
+<DIV CLASS="navigation">
+<div class='online-navigation'>
+<p></p><hr />
+<table align="center" width="100%" cellpadding="0" cellspacing="2">
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+<span class="release-info">Release 0.8.2, documentation updated on February 6, 2007.</span>
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diff --git a/doc/cvxopt/up.gif b/doc/cvxopt/up.gif
new file mode 100644
index 0000000..a9d3e13
Binary files /dev/null and b/doc/cvxopt/up.gif differ
diff --git a/doc/fftw.tex b/doc/fftw.tex
new file mode 100644
index 0000000..c8e98ca
--- /dev/null
+++ b/doc/fftw.tex
@@ -0,0 +1,92 @@
+\chapter{Discrete Transforms (\module{cvxopt.fftw})} \label{c-fftw}
+
+The \module{cvxopt.fftw} module is an interface to the FFTW library
+and contains routines for discrete Fourier, cosine, and sine
+transforms. This module is optional, and only installed when
+the FFTW library is made available during the CVXOPT installation.
+
+\begin{seealso}
+\seelink{http://www.fftw.org}{FFTW3 code, documentation, copyright and
+license.}{}
+\end{seealso}
+
+\section{Discrete Fourier Transform}
+\begin{funcdesc}{dft}{X}
+Replaces the columns of a dense complex matrix with their discrete
+Fourier transforms: if \var{X} has {\it n} rows,
+\[
+ X[k,:] := \sum_{j=0}^{n-1} e^{-2\pi j k \sqrt{-1}/n} X[j,:],
+ \qquad k=0,\ldots,n-1.
+\]
+\end{funcdesc}
+
+\begin{funcdesc}{idft}{X}
+Replaces the columns of a dense complex matrix with their inverse
+discrete Fourier transforms: if \var{X} has {\it n} rows,
+\[
+ X[k,:] :=
+ \frac{1}{n} \sum_{j=0}^{n-1} e^{2\pi j k \sqrt{-1}/n} X[j,:],
+ \qquad k=0,\ldots,n-1.
+\]
+\end{funcdesc}
+
+\section{Discrete Cosine Transform}
+\begin{funcdesc}{dct}{X\optional{, type=2}}
+Replaces the columns of a dense real matrix with their discrete
+cosine transforms. The second argument, an integer between 1 and 4,
+denotes the type of transform (DCT-I, DCT-II, DCT-III, DCT-IV).
+The DCT-I transform requires that the row dimension of \var{X} is at
+least 2.
+These transforms are defined as follows
+(for a matrix with {\it n} rows).
+\BEAS
+\mbox{DCT-I:} \qquad
+ X[k,:] & := & X[0,:] + (-1)^k X[n-1,:] +
+ 2 \sum_{j=1}^{n-2} X[j,:] \cos(\pi j k /(n-1)),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DCT-II:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \cos(\pi(j+1/2)k/n),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DCT-III:} \qquad
+ X[k,:] & := & X[0,:] + 2 \sum_{j=1}^{n-1} X[j,:] \cos(\pi j(k+1/2)/n),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DCT-IV:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \cos(\pi (j+1/2)(k+1/2)/n),
+ \qquad k=0,\ldots,n-1.
+\EEAS
+\end{funcdesc}
+
+\begin{funcdesc}{idct}{X\optional{, type=2}}
+Replaces the columns of a dense real matrix with the inverses
+of the discrete cosine transforms defined above.
+\end{funcdesc}
+
+\section{Discrete Sine Transform}
+\begin{funcdesc}{dst}{X\optional{, type=1}}
+Replaces the columns of a dense real matrix with their discrete
+sine transforms. The second argument, an integer between 1 and 4,
+denotes the type of transform (DST-I, DST-II, DST-III, DST-IV).
+These transforms are defined as follows
+(for a matrix with {\it n} rows).
+\BEAS
+\mbox{DST-I:} \qquad
+ X[k,:] & := &
+ 2 \sum_{j=0}^{n-1} X[j,:] \sin(\pi(j+1)(k+1)/(n+1)),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DST-II:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \sin(\pi(j+1/2)(k+1)/n),
+ \qquad k=0,\ldots,n-1.\\
+\mbox{DST-III:} \qquad
+ X[k,:] & := & (-1)^k X[n-1,:] + 2 \sum_{j=0}^{n-2}
+ X[j,:] \sin(\pi(j+1)(k+1/2)/n),
+ \qquad k=0,\ldots,n-1. \\
+\mbox{DST-IV:} \qquad
+ X[k,:] & := & 2 \sum_{j=0}^{n-1} X[j,:] \sin(\pi (j+1/2)(k+1/2)/n),
+ \qquad k=0,\ldots,n-1.
+\EEAS
+\end{funcdesc}
+
+\begin{funcdesc}{idst}{X\optional{, type=1}}
+Replaces the columns of a dense real matrix with the inverses
+of the discrete sine transforms defined above.
+\end{funcdesc}
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diff --git a/doc/intro.tex b/doc/intro.tex
new file mode 100644
index 0000000..f9f510c
--- /dev/null
+++ b/doc/intro.tex
@@ -0,0 +1,56 @@
+\chapter{Introduction}\label{chap:intro}
+
+CVXOPT is a free software package for convex optimization based on
+the Python programming language.
+It can be used with the interactive Python interpreter,
+on the command line by executing Python scripts, or integrated in
+other software via Python extension modules.
+Its main purpose is to make the development of software for convex
+optimization applications straightforward by building on Python's
+extensive standard library and on the strengths of Python as a
+high-level programming language.
+
+Release 0.8.2 of CVXOPT includes routines for basic linear algebra
+calculations,
+interfaces to efficient libraries for solving dense and sparse linear
+equations,
+convex optimization solvers written in Python,
+interfaces to a few other optimization libraries,
+and a modeling tool for piecewise-linear convex optimization problems.
+These components are organized in different modules.
+\begin{description}
+\item[\module{cvxopt.base}] This module defines a Python type
+ \mtrx\ for storing and manipulating dense matrices,
+ a Python type \spmtrx\ for storing and manipulating sparse
+ matrices, and routines for sparse matrix-vector and matrix-matrix
+ multiplication (see chapters~\ref{chap:matrix}
+ and~\ref{chap:spmatrix}).
+\item[\module{cvxopt.random}] Routines for generating random matrices
+ with uniformly or normally distributed entries
+ (see section~\ref{s-random}).
+\item[\module{cvxopt.blas}] Interface to most of the double-precision
+ real and complex BLAS (chapter~\ref{chap:blas}).
+\item[\module{cvxopt.lapack}] Interface to the dense double-precision
+ real and complex linear equation solvers and eigenvalue routines
+ from LAPACK (chapter~\ref{chap:lapack}).
+\item[\module{cvxopt.fftw}] An optional interface to the
+ discrete transform routines from FFTW (section~\ref{c-fftw}).
+\item[\module{cvxopt.amd}] Interface to the approximate minimum degree
+ ordering routine from AMD (chapter~\ref{s-orderings}).
+\item[\module{cvxopt.umfpack}] Interface to the sparse LU solver
+ from UMFPACK (section~\ref{s-umfpack}).
+\item[\module{cvxopt.cholmod}] Interface to the sparse Cholesky
+ solver from CHOLMOD (section~\ref{s-cholmod}).
+\item[\module{cvxopt.solvers}] Convex optimization routines
+ and optional interfaces to solvers from GLPK, MOSEK and DSDP5
+ (chapter~\ref{chap:solvers}).
+\item[\module{cvxopt.modeling}] Routines for specifying and solving
+ linear programs and convex optimization problems with piecewise-linear
+ cost and constraint functions (chapter~\ref{chap:modeling}).
+\item[\module{cvxopt.info}] Defines a string \code{version} with
+ the version number of the CVXOPT installation and a function
+ \function{license()} that prints the CVXOPT license.
+\end{description}
+The modules are described in detail in this manual and in the
+on-line Python help facility \program{pydoc}. Several example scripts
+are included in the distribution.
diff --git a/doc/lapack.tex b/doc/lapack.tex
new file mode 100644
index 0000000..15f4433
--- /dev/null
+++ b/doc/lapack.tex
@@ -0,0 +1,1041 @@
+\chapter{The LAPACK Interface (\module{cvxopt.lapack})}
+\label{chap:lapack}
+
+The module \module{cvxopt.lapack} includes functions for
+solving dense sets of linear equations, for the corresponding matrix
+factorizations (LU, Cholesky, LDL$\mathrm{{}^T}$),
+for solving least-squares and least-norm problems, for QR
+factorization, for symmetric eigenvalue problems and for singular
+value decomposition.
+
+In this chapter we briefly describe the Python calling sequences.
+For further details on the underlying LAPACK functions we refer to the
+LAPACK Users' Guide and manual pages.
+
+The BLAS conventional storage scheme of section~\ref{s-conventions} is
+used. As in the previous chapter, we omit from the function definitions
+less important arguments that are useful for selecting submatrices.
+The complete definitions are documented in the docstrings in the
+source code.
+
+\begin{seealso}
+\seelink{http://www.netlib.org/lapack/lug/lapack_lug.html}{LAPACK
+Users' Guide, Third Edition, SIAM, 1999.}{}
+\end{seealso}
+
+
+\section{General Linear Equations}
+\begin{funcdesc}{gesv}{A, B\optional{, ipiv=None}}
+Solves
+\[
+ A X = B,
+\]
+where {\it A} and {\it B} are real or complex matrices, with {\it A}
+square and nonsingular. On exit, \var{B} is replaced by the solution.
+The arguments \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc).
+The optional argument \var{ipiv} is an integer matrix of length at
+least \var{n}.
+If \var{ipiv} is provided, then \function{gesv()} solves the system,
+replaces \var{A} with its triangular factors, and returns the
+permutation matrix in \var{ipiv}.
+If \var{ipiv} is not specified, then \function{gesv()} solves the
+system but does not return the LU factorization and does not
+modify \var{A}.
+For example,
+\begin{verbatim}
+>>> gesv(A, B)
+\end{verbatim}
+solves the system without modifying \var{A} and returns the solution
+in \var{B}.
+\begin{verbatim}
+>>> gesv(A, B, ipiv)
+\end{verbatim}
+returns the solution in \var{B} and also returns the details of the
+LU factorization in \var{A} and \var{ipiv}.
+
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{getrf}{A, ipiv}
+LU factorization of a general, possibly rectangular, real or
+complex matrix,
+\[
+ A = PLU
+\]
+where {\it A} is \var{m} by \var{n}.
+The argument \var{ipiv} is an integer matrix of length at least
+min\{\var{m}, \var{n}\}.
+On exit, the lower triangular part of \var{A} is replaced by {\it L},
+the upper triangular part by {\it U}, and the permutation matrix is
+returned in \var{ipiv}.
+Raises an \code{ArithmeticError} if the matrix is not full rank.
+\end{funcdesc}
+
+\begin{funcdesc}{getrs}{A, ipiv, B\optional{, trans='N'}}
+Solves a general set of linear equations
+\[
+ AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+given the LU factorization computed by \function{gesv()} or
+\function{getrf()}.
+On entry, \var{A} and \var{ipiv} must contain the factorization
+as computed by \function{gesv()} or \function{getrf()}.
+On exit, \var{B} is overwritten with the solution.
+\var{B} must have the same type as \var{A}.
+\end{funcdesc}
+
+\begin{funcdesc}{getri}{A, ipiv}
+Computes the inverse of a matrix.
+On entry, \var{A} and \var{ipiv} must contain the factorization
+as computed by \function{gesv()} or \function{getrf()}. On exit,
+\var{A} contains the inverse.
+\end{funcdesc}
+
+In the following example we compute
+\[
+ x = (A^{-1} + A^{-T})b
+\]
+for randomly generated problem data, factoring the coefficient matrix
+once.
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt.random import normal
+>>> from cvxopt.lapack import gesv, getrs
+>>> n = 10
+>>> A = normal(n,n)
+>>> b = normal(n)
+>>> ipiv = matrix(0, (n,1))
+>>> x = +b
+>>> gesv(A, x, ipiv) # x = A^{-1}*b
+>>> x2 = +b
+>>> getrs(A, ipiv, x2, trans='T') # x2 = A^{-T}*b
+>>> x += x2
+\end{verbatim}
+
+Separate functions are provided for equations with band matrices.
+\begin{funcdesc}{gbsv}{A, kl, B\optional{, ipiv=None}}
+Solves
+\[
+ A X = B,
+\]
+where {\it A} and {\it B} are real or complex matrices, with {\it A}
+{\it n} by {\it n} and banded with \var{kl} subdiagonals.
+The arguments \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc).
+
+The optional argument \var{ipiv} is an integer matrix of length at least
+{\it n}.
+If \var{ipiv} is provided, then \var{A} must have
+2\var{kl} + \var{ku} + 1 rows. On entry the diagonals of {\it A} are
+stored in rows \var{kl} + 1 to 2\var{kl} + \var{ku} +1 of the \var{A}, using
+the BLAS format for general band matrices (see section~\ref{s-conventions}).
+On exit, the factorization is returned in {\var A} and \var{ipiv}.
+
+If \var{ipiv} is not provided, then \var{A} must have \var{kl} + \var{ku} +
+1 rows. On entry the diagonals of {\it A} are stored in the rows of
+\var{A}, following the standard format for general band matrices.
+In this case, \function{gbsv()} does not modify \var{A} on exit and does
+not return the factorization.
+
+On exit, \var{B} is replaced by the solution {\it X}.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{gbtrf}{A, m, kl, ipiv}
+LU factorization of a general {\it m} by {\it n} real or complex band
+matrix with \var{kl} subdiagonals.
+The matrix is stored using the BLAS format for general band matrices
+(see section~\ref{s-conventions}), by providing the
+diagonals (stored as rows of a \var{ku} + \var{kl} + 1 by {\it n} matrix),
+the number of rows \var{m}, and the number of subdiagonals \var{kl}.
+The argument \var{ipiv} is an integer matrix of length at least
+min\{{\it m}, {\it n}\}.
+On exit, \var{A} and \var{ipiv} contain the details of the factorization.
+Raises an \code{ArithmeticError} if the matrix is not full rank.
+\end{funcdesc}
+
+\begin{funcdesc}{gbtrs}{A, kl, ipiv, B\optional{, trans='N'}}
+Solves a set of linear equations
+\[
+ AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+with {\it A} a general band matrix with \var{kl} subdiagonals, given the
+LU factorization computed by \function{gbsv()} or \function{gbtrf()}.
+On entry, \var{A} and \var{ipiv} must contain the factorization
+as computed by \function{gbsv()} or \function{gbtrf()}.
+On exit, \var{B} is overwritten with the solution.
+\var{B} must have the same type as \var{A}.
+\end{funcdesc}
+
+As an example, we solve a linear equation with
+\[
+ A = \left[ \begin{array}{cccc}
+ 1 & 2 & 0 & 0 \\
+ 3 & 4 & 5 & 0 \\
+ 6 & 7 & 8 & 9 \\
+ 0 & 10 & 11 & 12
+ \end{array}\right], \qquad x = \left[\begin{array}{c} 1 \\ 1 \\ 1 \\ 1
+ \end{array}\right].
+\]
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt.lapack import gbsv, gbtrf, gbtrs
+>>> n, kl, ku = 4, 2, 1
+>>> A = matrix([[0., 1., 3., 6.], [2., 4., 7., 10.], [5., 8., 11., 0.], [9., 12., 0., 0.]])
+>>> x = matrix(1.0, (4,1))
+>>> gbsv(A, kl, x)
+>>> print x
+ 7.1429e-02
+ 4.6429e-01
+ -2.1429e-01
+ -1.0714e-01
+\end{verbatim}
+The code below illustrates how one can reuse the factorization returned
+by \function{gbsv()}.
+\begin{verbatim}
+>>> Ac = matrix(0.0, (2*kl+ku+1,n))
+>>> Ac[kl:,:] = A
+>>> ipiv = matrix(0, (n,1))
+>>> x = matrix(1.0, (4,1))
+>>> gbsv(Ac, kl, x, ipiv) # solves A*x = 1
+>>> print x
+ 7.1429e-02
+ 4.6429e-01
+ -2.1429e-01
+ -1.0714e-01
+>>> x = matrix(1.0, (4,1))
+>>> gbtrs(Ac, kl, ipiv, x, trans='T') # solve A^T*x = 1
+>>> print x
+ 7.1429e-02
+ 2.3810e-02
+ 1.4286e-01
+ -2.3810e-02
+\end{verbatim}
+An alternative method uses \function{getrf()} for the factorization.
+\begin{verbatim}
+>>> Ac[kl:,:] = A
+>>> gbtrf(Ac, n, kl, ipiv)
+>>> x = matrix(1.0, (4,1))
+>>> gbtrs(Ac, kl, ipiv, x) # solve A^T*x = 1
+>>> print x
+ 7.1429e-02
+ 4.6429e-01
+ -2.1429e-01
+ -1.0714e-01
+>>> x = matrix(1.0, (4,1))
+>>> gbtrs(Ac, kl, ipiv, x, trans='T') # solve A^T*x = 1
+>>> print x
+ 7.1429e-02
+ 2.3810e-02
+ 1.4286e-01
+ -2.3810e-02
+\end{verbatim}
+
+The following functions can be used for tridiagonal matrices They use a
+simpler matrix format, that stores the diagonals in three separate
+vectors.
+
+\begin{funcdesc}{gtsv}{dl, d, du, B)}
+Solves
+\[
+ A X = B,
+\]
+where {\it A} is an {\it n} by {\it n} tridiagonal matrix,
+with subdiagonal \var{dl} (a matrix of length {\it n}-1),
+diagonal \var{d} (a matrix of length {\it n}), and superdiagonal
+\var{du} (a matrix of length {\it n}-1).
+The four arguments must have the same type (\dtc\ or \ztc).
+On exit \var{dl}, \var{d}, \var{du} are overwritten with the details of
+the LU factorization of {\it A}, and \var{B} is overwritten with the
+solution {\it X}.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{gttrf}{dl, d, du, du2, ipiv}
+LU factorization of an {\it n} by {\it n} tridiagonal matrix with
+subdiagonal \var{dl}, diagonal \var{d} and superdiagonal \var{du}.
+\var{dl}, \var{d} and \var{du} must have the same type.
+\var{du2} is a matrix of length {\it n}-2, and of the same type as
+\var{dl}.
+\var{ipiv} is an \itc\ matrix of length {\it n}.
+On exit, the five arguments contain the details of the factorization.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{pttrs}{dl, d, du, du2, ipiv, B\optional{, trans='N'}}
+Solves a set of linear equations
+\[
+ AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is an {\it n} by {\it n} tridiagonal matrix.
+The arguments \var{dl}, \var{d}, \var{du}, \var{du2} and \var{ipiv}
+contain the details of the LU factorization as returned by
+\function{gttrf()}.
+On exit, \var{B} is overwritten with the solution {\it X}.
+\var{B} must have the same type as \var{dl}.
+\end{funcdesc}
+
+
+\section{Positive Definite Linear Equations}
+\begin{funcdesc}{posv}{A, B\optional{, uplo='L'}}
+Solves
+\[
+ A X = B,
+\]
+where {\it A} is a real symmetric or complex Hermitian positive
+definite matrix.
+On exit, \var{B} is replaced by the solution, and \var{A} is
+overwritten with the Cholesky factor.
+The matrices \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc).
+Raises an \code{ArithmeticError} if the matrix is not positive definite.
+\end{funcdesc}
+
+\begin{funcdesc}{potrf}{A\optional{, uplo='L'}}
+Cholesky factorization
+\[
+ A = LL^T \qquad \mbox{or} \qquad A = LL^H
+\]
+of a positive definite real symmetric or complex Hermitian matrix
+{\it A}. On exit, the lower triangular part of \var{A}
+(if \var{uplo} is \code{'L'}) or the upper triangular part
+(if \var{uplo} is \code{'U'}) is overwritten with the Cholesky factor
+or its (conjugate) transpose.
+Raises an \code{ArithmeticError} if the matrix is not positive definite.
+\end{funcdesc}
+
+\begin{funcdesc}{potrs}{A, B\optional{, uplo='L'}}
+Solves a set of linear equations
+\[
+ AX=B
+\]
+with a positive
+definite real symmetric or complex Hermitian matrix,
+given the Cholesky factorization computed by
+\function{posv()} or \function{potrf()}.
+On entry, \var{A} contains the triangular factor, as computed by
+\function{posv()} or \function{potrf()}. On exit, \var{B} is replaced
+by the solution.
+\var{B} must have the same type as \var{A}.
+\end{funcdesc}
+
+\begin{funcdesc}{potri}{A\optional{, uplo='L'}}
+Computes the inverse of a positive definite matrix.
+On entry, \var{A} contains the Cholesky factorization computed
+by \function{potrf()} or \function{posv()}. On exit, it contains
+the inverse.
+\end{funcdesc}
+
+As an example, we use \function{posv()} to solve the linear system
+\BEQ \label{e-kkt-example}
+ \left[ \begin{array}{cc}
+ -\diag(d)^2 & A \\
+ A^T & 0 \end{array} \right]
+ \left[ \begin{array}{c} x_1 \\ x_2 \end{array} \right]
+ = \left[ \begin{array}{c} b_1 \\ b_2 \end{array} \right]
+\EEQ
+by block-elimination.
+We first pick a random problem.
+\begin{verbatim}
+>>> from cvxopt.base import matrix, div
+>>> from cvxopt.random import normal, uniform
+>>> from cvxopt.blas import syrk, gemv
+>>> from cvxopt.lapack import posv
+>>> m, n = 100, 50
+>>> A = normal(m,n)
+>>> b1, b2 = normal(m), normal(n)
+>>> d = uniform(m)
+\end{verbatim}
+We then solve the equations
+\[
+ A^T \diag(d)^{-2}A x_2 = b_2 + A^T \diag(d)^{-2} b_1, \qquad
+ \diag(d)^2 x_1 = Ax_2 - b_1.
+\]
+\begin{verbatim}
+>>> Asc = div(A, d[:, n*[0]]) # Asc := diag(d)^{-1}*A
+>>> B = matrix(0.0, (n,n))
+>>> syrk(Asc, B, trans='T') # B := Asc^T * Asc = A^T * diag(d)^{-2} * A
+>>> x1 = div(b1, d) # x1 := diag(d)^{-1}*b1
+>>> x2 = +b2
+>>> gemv(Asc, x1, x2, trans='T', beta=1.0) # x2 := x2 + Asc^T*x1 = b2 + A^T*diag(d)^{-2}*b1
+>>> posv(B, x2) # x2 := B^{-1}*x2 = B^{-1}*(b2 + A^T*diag(d)^{-2}*b1)
+>>> gemv(Asc, x2, x1, beta=-1.0) # x1 := Asc*x2 - x1 = diag(d)^{-1} * (A*x2 - b1)
+>>> x1 = div(x1, d) # x1 := diag(d)^{-1}*x1 = diag(d)^{-2} * (A*x2 - b1)
+\end{verbatim}
+
+
+There are separate routines for equations with positive definite band
+matrices.
+\begin{funcdesc}{pbsv}{A, B\optional{, uplo='L'}}
+Solves
+\[
+ AX=B
+\]
+where {\it A} is a real symmetric or complex Hermitian positive definite
+band matrix. On entry, the diagonals of {\it A} are stored in \var{A},
+using the BLAS format for symmetric or Hermitian band matrices
+(see section~\ref{s-conventions}). On exit, \var{B} is replaced by the
+solution, and \var{A} is overwritten with the Cholesky factor (in the
+BLAS format for triangular band matrices). The matrices \var{A} and
+\var{B} must have the same type (\dtc\ or \ztc).
+Raises an \code{ArithmeticError} if the matrix is not positive definite.
+\end{funcdesc}
+
+\begin{funcdesc}{pbtrf}{A\optional{, uplo='L'}}
+Cholesky factorization
+\[
+ A = LL^T \qquad \mbox{or} \qquad A = LL^H
+\]
+of a positive definite real symmetric or complex Hermitian band matrix
+{\it A}. On entry, the diagonals of {\it A} are stored in \var{A},
+using the BLAS format for symmetric or Hermitian band matrices.
+On exit, \var{A} contains the Cholesky factor, in the BLAS format
+for triangular band matrices.
+Raises an \code{ArithmeticError} if the matrix is not positive definite.
+\end{funcdesc}
+
+\begin{funcdesc}{pbtrs}{A, B\optional{, uplo='L'}}
+Solves a set of linear equations
+\[
+ AX=B
+\]
+with a positive definite real symmetric or complex Hermitian band matrix,
+given the Cholesky factorization computed by \function{pbsv()} or
+\function{pbtrf()}.
+On entry, \var{A} contains the triangular factor, as computed by
+\function{pbsv()} or \function{pbtrf()}. On exit, \var{B} is replaced
+by the solution. \var{B} must have the same type as \var{A}.
+\end{funcdesc}
+
+The following functions are useful for tridiagonal systems.
+
+\begin{funcdesc}{ptsv}{d, e, B}
+Solves
+\[
+ A X = B,
+\]
+where {\it A} is an {\it n} by {\it n} real symmetric or complex
+Hermitian tridiagonal matrix, with diagonal \var{d} (a \dtc\ matrix of
+length {\it n}) and subdiagonal \var{e} (a \dtc\ or \ztc\ matrix of length
+{\it n}-1).
+The arguments \var{e} and \var{B} must have the same type.
+On exit \var{d} contains the diagonal elements of {\it D} in
+the LDL${}\mathrm{^T}$ or LDL${}\mathrm{^H}$ factorization
+of {\it A}, and \var{e} contains the subdiagonal elements of the unit
+lower bidiagonal matrix {\it L}.
+\var{B} is overwritten with the solution {\it X}.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{pttrf}{d, e}
+LDL${}\mathrm{^T}$ or LDL${}\mathrm{^H}$ factorization of an {\it n} by
+{\it n} real symmetric or complex Hermitian tridiagonal matrix {\it A}.
+On entry, the argument \var{d} is a \dtc\ matrix with the diagonal elements
+of {\it A}. The argument \var{e} is \dtc\ or \ztc\ matrix with
+the subdiagonal elements of {\it A}.
+On exit \var{d} contains the diagonal elements of {\it D}, and \var{e}
+contains the subdiagonal elements of the unit lower bidiagonal matrix
+{\it L}. Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{gttrs}{d, e, B\optional{, uplo='L'}}
+Solves a set of linear equations
+\[
+ AX=B
+\]
+where {\it A} is an {\it n} by {\it n} real symmetric or complex
+Hermitian tridiagonal matrix, given its LDL${}\mathrm{^T}$ or
+LDL${}\mathrm{^H}$ factorization.
+The argument \var{d} is the diagonal of the diagonal matrix {\it D}.
+The argument \var{uplo} only matters for complex matrices.
+If \var{uplo} is \code{'L'}, then \var{e} contains the subdiagonal
+elements of the unit bidiagonal matrix {\it L}.
+If \var{uplo} is \code{'U'}, then \var{e} contains the complex
+conjugates of the elements of the unit bidiagonal matrix {\it L}.
+On exit, \var{B} is overwritten with the solution {\it X}.
+\var{B} must have the same type as \var{e}.
+\end{funcdesc}
+
+
+\section{Symmetric and Hermitian Linear Equations}
+\begin{funcdesc}{sysv}{A, B\optional{, ipiv=None\optional{, uplo='L'}}}
+Solves
+\[
+ AX=B
+\]
+where {\it A} is a real or complex symmetric matrix of order {\it n}.
+On exit, \var{B} is replaced by the solution.
+The matrices \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc).
+The optional argument \var{ipiv} is an integer matrix of length at
+least equal to {\it n}.
+If \var{ipiv} is provided, \function{sysv()} solves the system and
+returns the factorization in \var{A} and \var{ipiv}.
+If \var{ipiv} is not specified, \function{sysv()} solves the
+system but does not return the factorization and does not modify
+\var{A}.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{sytrf}{A, ipiv\optional{, uplo='L'}}
+LDL${}\mathrm{^T}$ factorization
+\[
+ PAP^T = LDL^T
+\]
+of a real or complex symmetric matrix $A$ of order {\it n}.
+\var{ipiv} is an \itc\ matrix of length at least {\it n}.
+On exit, \var{A} and \var{ipiv} contain the factorization.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{sytrs}{A, ipiv, B\optional{, uplo='L'}}
+Solves
+\[
+ A X = B
+\]
+given the LDL${}\mathrm{^T}$ factorization computed by
+\function{sytrf()} or \function{sysv()}. \var{B} must have the same
+type as \var{A}.
+\end{funcdesc}
+
+\begin{funcdesc}{sytri}{A, ipiv\optional{, uplo='L'}}
+Computes the inverse of a real or complex symmetric matrix.
+On entry, \var{A} and \var{ipiv} contain the LDL${}\mathrm{^T}$
+factorization computed by \function{sytrf()} or \function{sysv()}.
+On exit, \var{A} contains the inverse.
+\end{funcdesc}
+
+\begin{funcdesc}{hesv}{A, B\optional{, ipiv=\None\optional{, uplo='L'}}}
+Solves
+\[
+ A X = B
+\]
+where {\it A} is a real symmetric or complex Hermitian of order {\it n}.
+On exit, \var{B} is replaced by the solution.
+The matrices \var{A} and \var{B} must have the same type (\dtc\ or
+\ztc).
+The optional argument \var{ipiv} is an integer matrix of length at
+least \var{n}.
+If \var{ipiv} is provided, then \function{hesv()} solves the system and
+returns the factorization in \var{A} and \var{ipiv}.
+If \var{ipiv} is not specified, then \function{hesv()} solves the
+system but does not return the factorization and does not modify
+\var{A}.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{hetrf}{A, ipiv\optional{, uplo='L'}}
+LDL${}\mathrm{^H}$ factorization
+\[
+ PAP^T = LDL^H
+\]
+of a real symmetric or complex Hermitian matrix of order {\it n}.
+\var{ipiv} is an \itc\ matrix of length at least \var{n}.
+On exit, \var{A} and \var{ipiv} contain the factorization.
+Raises an \code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{hetrs}{A, ipiv, B\optional{, uplo='L'}}
+Solves
+\[
+ A X = B
+\]
+given the LDL${}\mathrm{^H}$ factorization computed by
+\function{hetrf()} or \function{hesv()}.
+\end{funcdesc}
+
+\begin{funcdesc}{hetri}{A, ipiv\optional{, uplo='L'}}
+Computes the inverse of a real symmetric or complex Hermitian matrix.
+On entry, \var{A} and \var{ipiv} contain the LDL${}\mathrm{^H}$
+factorization computed by \function{hetrf()} or \function{hesv()}.
+On exit, \var{A} contains the inverse.
+\end{funcdesc}
+
+As an example we solve the KKT system~(\ref{e-kkt-example}).
+\begin{verbatim}
+>>> from cvxopt.lapack import sysv
+>>> K = matrix(0.0, (m+n,m+n))
+>>> K[: (m+n)*m : m+n+1] = -d**2
+>>> K[:m, m:] = A
+>>> x = matrix(0.0, (m+n,1))
+>>> x[:m], x[m:] = b1, b2
+>>> sysv(K, x, uplo='U')
+\end{verbatim}
+
+\section{Triangular Linear Equations}
+
+\begin{funcdesc}{trtrs}{A, B\optional{, uplo='L'\optional{,
+trans='N'\optional{, diag='N'}}}}
+Solves a triangular set of equations
+\[
+ AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is real or complex and triangular of order {\it n},
+and \var{B} is a matrix with {\it n} rows.
+\var{A} and \var{B} are matrices with the same type (\dtc\ or \ztc).
+\function{trtrs()} is similar to \function{blas.trsm()}, except
+that it raises an \code{ArithmeticError} if a diagonal element of
+\var{A} is zero (whereas \function{blas.trsm()} returns \code{inf}
+values).
+\end{funcdesc}
+
+\begin{funcdesc}{trtri}{A\optional{, uplo='L'\optional{, diag='N'}}}
+Computes the inverse of a real or complex triangular matrix {\it A}.
+On exit, \var{A} contains the inverse.
+\end{funcdesc}
+
+\begin{funcdesc}{tbtrs}{A, B\optional{, uplo='L'\optional{,
+trans='T'\optional{,diag='N'}}}}
+Solves a triangular set of equations
+\[
+ AX=B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX=B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX=B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\it A} is real or complex triangular band matrix of order {\it n},
+and \var{B} is a matrix with {\it n} rows.
+The diagonals of {\it A} are stored in \var{A} using the BLAS conventions
+for triangular band matrices.
+\var{A} and \var{B} are matrices with the same type (\dtc\ or \ztc).
+On exit, \var{B} is replaced by the solution {\it X}.
+\end{funcdesc}
+
+\section{Least-Squares and Least-Norm Problems}
+\begin{funcdesc}{gels}{A, B\optional{, trans='N'}}
+Solves least-squares and least-norm problems with a full rank
+{\it m} by {\it n} matrix {\it A}.
+
+\begin{enumerate}
+\item \var{trans} is \code{'N'}. If {\it m} is greater than or equal
+to {\it n}, \function{gels()} solves the least-squares problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|AX-B\|_F.
+ \end{array}
+\]
+If {\it m} is less than or equal to {\it n}, \function{gels()} solves
+the least-norm problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|X\|_F \\
+ \mbox{subject to} & AX = B.
+ \end{array}
+\]
+
+\item \var{trans} is \code{'T'} or \code{'C'} and \var{A} and \var{B}
+are real. If {\it m} is greater than or equal to {\it n},
+\function{gels()} solves the least-norm problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|X\|_F \\
+ \mbox{subject to} & A^TX=B.
+ \end{array}
+\]
+If {\it m} is less than or equal to {\it n}, \function{gels()} solves
+the least-squares problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|A^TX-B\|_F.
+ \end{array}
+\]
+
+\item \var{trans} is \code{'C'} and \var{A} and \var{B}
+are complex. If {\it m} is greater than or equal to {\it n},
+\function{gels()} solves the least-norm problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|X\|_F \\
+ \mbox{subject to} & A^HX=B.
+ \end{array}
+\]
+If {\it m} is less than or equal to {\it n}, \function{gels()} solves
+the least-squares problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|A^HX-B\|_F.
+ \end{array}
+\]
+\end{enumerate}
+\var{A} and \var{B} must have the same typecode (\dtc\ or \ztc).
+\var{trans} = \code{'T'} is not allowed if \var{A} is complex.
+On exit, the solution {\it X} is stored as the leading submatrix
+of \var{B}.
+The array \var{A} is overwritten with details of the QR or the LQ
+factorization of {\it A}.
+Note that \function{gels()} does not check whether $A$ is full rank.
+\end{funcdesc}
+
+\begin{funcdesc}{geqrf}{A, tau}
+QR factorization of a real or complex matrix \var{A}:
+\[
+ A = Q R.
+\]
+If \var{A} is {\it m} by {\it n}, then {\it Q} is {\it m} by {\it m}
+and orthogonal/unitary, and \var{R} is {\it m} by {\it n}
+and upper triangular (if \var{m} is greater than or equal to \var{n}),
+or upper trapezoidal (if \var{m} is less than or equal to \var{n}).
+\var{tau} is a matrix of the same type as {\var A} and of length at
+least min\{\var{m}, \var{n}\}.
+On exit, {\it R} is stored in the upper triangular part of \var{A}.
+The matrix {\it Q} is stored as a product of min\{\var{m}, \var{n}\}
+elementary reflectors in the first min\{\var{m}, \var{n}\} columns
+of \var{A} and in \var{tau}.
+\end{funcdesc}
+
+\begin{funcdesc}{ormqr}{A, tau, C\optional{, side='L'\optional{,
+trans='N'}}}
+Product with a real orthogonal matrix:
+\[
+ C := \op(Q)C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := C\op(Q) \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \op(Q) = \left\{ \begin{array}{ll}
+ Q & \mathrm{trans} = \mathrm{'N'} \\
+ Q^T & \mathrm{trans} = \mathrm{'T'},
+\end{array}\right.
+\]
+where {\it Q} is square and orthogonal.
+{\it Q} is stored in \var{A} and \var{tau} as a product
+of min\{\var{A}.\member{size}[0], \var{A}.\member{size}[1]\}
+elementary reflectors, as computed by \function{geqrf()}.
+\end{funcdesc}
+
+\begin{funcdesc}{unmqr}{A, tau, C\optional{, side='L'\optional{,
+trans='N'}}}
+Product with a real orthogonal or complex unitary matrix:
+\[
+ C := \op(Q)C \quad (\mathrm{side} = \mathrm{'L'}), \qquad
+ C := C\op(Q) \quad (\mathrm{side} = \mathrm{'R'}), \qquad
+ \op(Q) = \left\{ \begin{array}{ll}
+ Q & \mathrm{trans} = \mathrm{'N'} \\
+ Q^T & \mathrm{trans} = \mathrm{'T'} \\
+ Q^H & \mathrm{trans} = \mathrm{'C'},
+\end{array}\right.
+\]
+{\it Q} is square and orthogonal or unitary.
+{\it Q} is stored in \var{A} and \var{tau} as a product of
+min\{\var{A}.\member{size}[0], \var{A}.\member{size}[1]\}
+elementary reflectors, as computed by \function{geqrf()}.
+The arrays \var{A}, \var{tau} and \var{C} must have the same type.
+\code{\var{trans} = 'T'} is only allowed if the typecode is \dtc.
+\end{funcdesc}
+
+
+In the following example, we solve a least-squares problem
+by a direct call to \function{gels()}, and by separate calls to
+\function{geqrf()}, \function{ormqr()}, and \function{trtrs()}.
+\begin{verbatim}
+>>> from cvxopt import random, blas, lapack
+>>> from cvxopt.base import matrix
+>>> m, n = 10, 5
+>>> A, b = random.normal(m,n), random.normal(m,1)
+>>> x1 = +b
+>>> lapack.gels(+A, x1) # x1[:n] minimizes ||A*x1[:n] - b||_2
+>>> tau = matrix(0.0, (n,1))
+>>> lapack.geqrf(A, tau) # A = [Q1, Q2] * [R1; 0]
+>>> x2 = +b
+>>> lapack.ormqr(A, tau, x2, trans='T') # x2 := [Q1, Q2]' * b
+>>> lapack.trtrs(A[:n,:], x2, uplo='U') # x2[:n] := R1^{-1}*x2[:n]
+>>> blas.nrm2(x1[:n] - x2[:n])
+3.0050798580569307e-16
+\end{verbatim}
+
+
+\section{Symmetric and Hermitian Eigenvalue Decomposition}
+The first four routines compute all or selected eigenvalues and
+eigenvectors of a real symmetric matrix $A$:
+\[
+ A = V\diag(\lambda)V^T,\qquad V^TV = I.
+\]
+
+\begin{funcdesc}{syev}{A, W\optional{, jobz='N'\optional{, uplo='L'}}}
+Eigenvalue decomposition of a real symmetric matrix of order {\it n}.
+\var{W} is a real matrix of length at least {\it n}.
+On exit, \var{W} contains the eigenvalues in ascending order.
+If \var{jobz} is \code{'V'}, the eigenvectors are also computed
+and returned in \var{A}.
+If \var{jobz} is \code{'N'}, the eigenvectors are not returned and the
+contents of \var{A} are destroyed.
+Raises an \code{ArithmeticError} if the eigenvalue decomposition fails.
+\end{funcdesc}
+
+\begin{funcdesc}{syevd}{A, W\optional{, jobz='N'\optional{, uplo='L'}}}
+This is an alternative to \function{syev()}, based on a different
+algorithm. It is faster on large problems, but also uses more memory.
+\end{funcdesc}
+
+\begin{funcdesc}{syevx}{A, W\optional{, jobz='N'\optional{,
+range='A'\optional{, uplo='L'\optional{, vl=0.0, vu=0.0\optional{,
+il=1, iu=1\optional{, Z=\None}}}}}}}
+Computes selected eigenvalues and eigenvectors of a real symmetric
+matrix \var{A} of order {\it n}.
+
+\var{W} is a real matrix of length at least \var{n}.
+On exit, \var{W} contains the eigenvalues in ascending order.
+If \var{range} is \code{'A'}, all the eigenvalues are computed.
+If \var{range} is \code{'I'}, eigenvalues \var{il} through \var{iu}
+are computed, where \var{1} \code{<=} \var{il} \code{<=} \var{iu}
+\code{<=} \var{n}.
+If \var{range} is \code{'V'}, the eigenvalues in the interval
+\code{(\var{vl},\var{vu}]} are computed.
+
+If \var{jobz} is \code{'V'}, the (normalized) eigenvectors are
+computed, and returned in \var{Z}. If \var{jobz} is \code{'N'}, the
+eigenvectors are not computed. In both cases, the contents of \var{A}
+are destroyed on exit.
+\var{Z} is optional (and not referenced) if \var{jobz} is \code{'N'}.
+It is required if \var{jobz} is \code{'V'} and must have at least
+\var{n} columns if \var{range} is \code{'A'} or \code{'V'} and at
+least \code{\var{iu}-\var{il}+1} columns if \var{range} is \code{'I'}.
+
+\function{syevx()} returns the number of computed eigenvalues.
+\end{funcdesc}
+
+\begin{funcdesc}{syevr}{A, W\optional{, jobz='N'\optional{,
+range='A'\optional{, uplo='L'\optional{, vl=0.0, vu=0.0\optional{,
+il=1, iu=n\optional{, Z=\None}}}}}}}
+This is an alternative to \function{syevx()}.
+\function{syevr()} is the most recent LAPACK routine for symmetric
+eigenvalue problems, and expected to supersede the three other
+routines in future releases.
+\end{funcdesc}
+
+The next four routines can be used to compute eigenvalues and
+eigenvectors for complex Hermitian matrices:
+\[
+ A = V\diag(\lambda)V^H,\qquad V^HV = I.
+\]
+For real symmetric matrices they are identical to the corresponding
+\function{syev\_()} routines.
+
+\begin{funcdesc}{heev}{A, W\optional{, jobz='N'\optional{, uplo='L'}}}
+Eigenvalue decomposition of a real symmetric or complex Hermitian
+matrix of order {\it n}.
+The calling sequence is identical to \function{syev()}, except that
+\var{A} can be real or complex.
+\end{funcdesc}
+
+\begin{funcdesc}{heevd}{A, W\optional{, jobz='N'\optional{, uplo='L'}}}
+This is an alternative to \function{heev()}.
+\end{funcdesc}
+
+\begin{funcdesc}{heevx}{A, W\optional{, jobz='N'\optional{,
+range='A'\optional{, uplo='L'\optional{, vl=0.0, vu=0.0 \optional{,
+il=1, iu=n\optional{, Z=\None}}}}}}}
+Computes selected eigenvalues and eigenvectors of a real symmetric
+or complex Hermitian matrix of order {\it n}.
+The calling sequence is identical to \function{syevx()},
+except that \var{A} can be real or complex.
+\var{Z} must have the same type as \var{A}.
+\end{funcdesc}
+
+\begin{funcdesc}{heevr}{A, W\optional{, jobz='N'\optional{,
+range='A'\optional{, uplo='L'\optional{, vl=0.0, vu=0.0\optional{,
+il=1, iu=n\optional{, Z=\None}}}}}}}
+This is an alternative to \function{heevx()}.
+\end{funcdesc}
+
+\section{Generalized Symmetric Definite Eigenproblems}
+Three types of generalized eigenvalue problems can be solved:
+\BEQ \label{e-gevd}
+ AZ = BZ\diag(\lambda)\quad \mbox{(type 1)}, \qquad
+ ABZ = Z\diag(\lambda) \quad \mbox{(type 2)}, \qquad
+ BAZ = Z\diag(\lambda) \quad \mbox{(type 3)},
+\EEQ
+with $A$ and $B$ real symmetric or complex Hermitian, and $B$ positive
+definite.
+The matrix of eigenvectors is normalized as follows:
+\[
+ Z^H BZ = I \quad \mbox{(types 1 and 2)}, \qquad
+ Z^H B^{-1}Z = I \quad \mbox{(type 3)}.
+\]
+
+\begin{funcdesc}{sygv}{A, B, W\optional{, itype=1\optional{,
+jobz='N'\optional{, uplo='L'}}}}
+Solves the generalized eigenproblem~(\ref{e-gevd}) for real symmetric
+matrices of order {\it n}, stored in real matrices \var{A} and \var{B}.
+\var{itype} is an integer with possible values 1, 2, 3, and specifies
+the type of eigenproblem.
+\var{W} is a real matrix of length at least {\it n}.
+On exit, it contains the eigenvalues in ascending order.
+On exit, \var{B} contains the Cholesky factor of {\it B}.
+If \var{jobz} is \code{'V'}, the eigenvectors are computed
+and returned in \var{A}.
+If \var{jobz} is \code{'N'}, the eigenvectors are not returned and the
+contents of \var{A} are destroyed.
+\end{funcdesc}
+
+\begin{funcdesc}{hegv}{A, B, W\optional{, itype=1\optional{,
+jobz='N'\optional{, uplo='L'}}}}
+Generalized eigenvalue problem~(\ref{e-gevd}) of real symmetric or
+complex Hermitian matrix of order \var{n}.
+The calling sequence is identical to \function{sygv()},
+except that \var{A} and \var{B} can be real or complex.
+\end{funcdesc}
+
+
+\section{Singular Value Decomposition}
+
+\begin{funcdesc}{gesvd}{A, S\optional{, jobu='N'\optional{,
+jobvt='N'\optional{, U=\None\optional{, Vt=\None}}}}}
+Singular value decomposition
+\[
+ A = U \Sigma V^T, \qquad A = U \Sigma V^H
+\]
+of a real or complex {\it m} by {\it n} matrix \var{A}.
+
+\var{S} is a real matrix of length at least min\{{\it m}, {\it n}\}.
+On exit, its first min\{{\it m}, {\it n}\} elements are the
+singular values in descending order.
+
+The argument \var{jobu} controls how many left singular vectors are
+computed. The possible values are \code{'N'}, \code{'A'}, \code{'S'}
+and \code{'O'}.
+If \var{jobu} is \code{'N'}, no left singular vectors are
+computed.
+If \var{jobu} is \code{'A'}, all left singular vectors are computed
+and returned as columns of \var{U}.
+If \var{jobu} is \code{'S'}, the first min\{{\it m},{\it n}\} left
+singular vectors are computed and returned as columns of \var{U}.
+If \var{jobu} is \code{'O'}, the first min\{{\it m},{\it n}\} left
+singular vectors are computed and returned as columns of \var{A}.
+The argument \var{U} is \None\ (if \var{jobu} is \code{'N'}
+or \code{'A'}) or a matrix of the same type as \var{A}.
+
+The argument \var{jobvt} controls how many right singular vectors are
+computed. The possible values are \code{'N'}, \code{'A'}, \code{'S'}
+and \code{'O'}.
+If \var{jobvt} is \code{'N'}, no right singular vectors are
+computed. If \var{jobvt} is \code{'A'}, all right singular vectors
+are computed and returned as rows of \var{Vt}.
+If \var{jobvt} is \code{'S'}, the first min\{{\it m},{\it n}\} right
+singular vectors are computed and their (conjugate) transposes are
+returned as rows of \var{Vt}.
+If \var{jobvt} is \code{'O'}, the first min\{{\it m}, {\it n}\} right
+singular vectors are computed and their (conjugate) transposes
+are returned as rows of \var{A}.
+Note that the (conjugate) transposes of the right singular vectors
+(\ie, the matrix $V^H$) are returned in \var{Vt} or \var{A}.
+The argument \var{Vt} can be \None\ (if \var{jobvt} is \code{'N'}
+or \code{'A'}) or a matrix of the same type as \var{A}.
+
+On exit, the contents of \var{A} are destroyed.
+\end{funcdesc}
+
+\begin{funcdesc}{gesdd}{A, S\optional{, jobz='N'\optional{,
+U=\None\optional{, Vt=\None}}}}
+Singular value decomposition of a real or complex {\it m} by {\it n}
+matrix \var{A}. This function is based on a divide-and-conquer
+algorithm and is faster than \function{gesvd()}.
+
+\var{S} is a real matrix of length at least min\{{\it m}, {\it n}\}.
+On exit, its first min\{{\it m}, {\it n}\} elements are the
+singular values in descending order.
+
+The argument \var{jobz} controls how many singular vectors are
+computed. The possible values are \code{'N'}, \code{'A'}, \code{'S'}
+and \code{'O'}.
+If \var{jobz} is \code{'N'}, no singular vectors are computed.
+If \var{jobz} is \code{'A'}, all {\it m} left singular vectors are
+computed and returned as columns of \var{U} and all {\it n} right
+singular vectors are computed and returned as rows of \var{Vt}.
+If \var{jobz} is \code{'S'}, the first min\{{\it m}, {\it n}\} left
+and right singular vectors are computed and returned as columns of
+\var{U} and rows of \var{Vt}.
+If \var{jobz} is \code{'O'} and {\it m} is greater than or equal
+to {\it n}, the first {\it n} left singular vectors are returned as
+columns of \var{A} and the {\it n} right singular vectors are returned
+as rows of \var{Vt}. If \var{jobz} is \code{'O'} and {\it m} is less
+than {\it n}, the {\it m} left singular vectors are returned as columns
+of \var{U} and the first {\it m} right singular vectors are returned
+as rows of \var{A}.
+Note that the (conjugate) transposes of the right singular vectors
+are returned in \var{Vt} or \var{A}.
+
+The argument \var{U} can be \None\ (if \var{jobz} is \code{'N'}
+or \code{'A'} of \var{jobz} is \code{'O'} and {\it m} is greater than
+or equal to {\it n}) or a matrix of the same type as \var{A}.
+The argument \var{Vt} can be \None\ (if \var{jobz} is \code{'N'}
+or \code{'A'} or \var{jobz} is \code{'O'} and {\it m} is less than
+{\it n}) or a matrix of the same type as \var{A}.
+
+On exit, the contents of \var{A} are destroyed.
+\end{funcdesc}
+
+\section{Example: Analytic Centering}
+The analytic centering problem is defined as
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & -\sum_{i=1}^m \log(b_i-a_i^Tx).
+ \end{array}
+\]
+In the code below we solve the problem using Newton's method.
+At each iteration the Newton direction is computed by solving
+a positive definite set of linear equations
+\[
+ A^T \diag(b-Ax)^{-2} A v = -\diag(b-Ax)^{-1}\ones
+\]
+(where {\it A} has rows $a_i^T$), and a suitable step size is determined
+by a backtracking line search.
+
+We use the level-3 BLAS function \function{syrk()} to form the Hessian
+matrix and the LAPACK function \function{posv()} to solving the Newton
+system. The code can be further optimized by replacing the
+matrix-vector products with the level-2 BLAS function \function{gemv()}.
+
+\begin{verbatim}
+from cvxopt.base import matrix, log, mul, div
+from cvxopt import blas, lapack, random
+from math import sqrt
+
+def acent(A,b):
+ """
+ Returns the analytic center of A*x <= b.
+ We assume that b > 0 and the feasible set is bounded.
+ """
+
+ MAXITERS = 100
+ ALPHA = 0.01
+ BETA = 0.5
+ TOL = 1e-8
+
+ m, n = A.size
+ x = matrix(0.0, (n,1))
+ H = matrix(0.0, (n,n))
+ g = matrix(0.0, (n,1))
+
+ for iter in xrange(MAXITERS):
+
+ # Gradient is g = A^T * (1./(b-A*x)).
+ d = (b-A*x)**-1
+ g = A.T * d
+
+ # Hessian is H = A^T * diag(d)^2 * A.
+ Asc = mul( d[:,n*[0]], A )
+ blas.syrk(Asc, H, trans='T')
+
+ # Newton step is v = -H^-1 * g.
+ v = -g
+ lapack.posv(H, v)
+
+ # Terminate if Newton decrement is less than TOL.
+ lam = blas.dot(g, v)
+ if sqrt(-lam) < TOL: return x
+
+ # Backtracking line search.
+ y = mul(A*v, d)
+ step = 1.0
+ while 1-step*max(y) < 0: step *= BETA
+ while True:
+ if -sum(log(1-step*y)) < ALPHA*step*lam: break
+ step *= BETA
+ x += step*v
+\end{verbatim}
diff --git a/doc/modeling.tex b/doc/modeling.tex
new file mode 100644
index 0000000..e380dd5
--- /dev/null
+++ b/doc/modeling.tex
@@ -0,0 +1,747 @@
+\chapter{Modeling (\module{cvxopt.modeling})}
+\label{chap:modeling}
+The module \module{cvxopt.modeling} can be used to specify and solve
+optimization problems with convex piecewise-linear objective and
+constraint functions.
+
+To specify an optimization problem one first defines
+the optimization variables (see section~\ref{s-variables}),
+and then defines the objective and constraint functions
+using linear operations (vector addition and subtraction,
+matrix-vector multiplication, indexing and slicing)
+and nested evaluations of \function{max()}, \function{min()},
+\function{abs()} and \function{sum()} (see section~\ref{s-functions}).
+
+\section{Variables} \label{s-variables}
+Optimization variables are represented by \pytype{variable} objects.
+
+\begin{classdesc}{variable}{\optional{size\optional{, name}}}
+A vector variable. The first argument is the dimension of the
+vector (a positive integer with default value 1).
+The second argument is a string with a name for the variable.
+The name is optional and has default value \code{""}. It is only used
+when displaying variables (or objects that depend on variables, such
+as functions or constraints)
+using \function{print} statements, when calling the built-in functions
+\function{repr()} or \function{str()}, or when writing linear programs
+to MPS files.
+\end{classdesc}
+The function \function{len()} returns the length of a
+\pytype{variable}. A \pytype{variable} \var{x} has two attributes.
+\begin{memberdesc}[variable]{name}
+The name of the variable.
+\end{memberdesc}
+
+\begin{memberdesc}[variable]{value}
+Either \None\ or a dense \dtc\ matrix of size \code{len(\var{x})} by 1.
+
+The attribute \var{x}.\member{value} is set to \None\ when the
+variable \var{x} is created. It can be given a numerical value later,
+typically by solving an LP that has \var{x} as one of its variables.
+One can also make an explicit assignment
+\code{\var{x}.\member{value} = \var{y}}. The
+assigned value \var{y} must be an \intgr\ or \flt, or a
+dense \dtc\ matrix of size (\code{len(\var{x})},1).
+If \var{y} is an \intgr\ or \flt\, all the elements of
+\var{x}.\member{value} are set to the value of \var{y}.
+\end{memberdesc}
+
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt.modeling import variable
+>>> x = variable(3,'a')
+>>> len(x)
+3
+>>> print x.name
+a
+>>> print x.value
+None
+>>> x.value = matrix([1.,2.,3.])
+>>> print x.value
+ 1.0000e+00
+ 2.0000e+00
+ 3.0000e+00
+>>> x.value = 1
+>>> print x.value
+ 1.0000e+00
+ 1.0000e+00
+ 1.0000e+00
+\end{verbatim}
+
+
+\section{Functions} \label{s-functions}
+Objective and constraint functions can be defined via overloaded
+operations on variables and other functions. A function \var{f} is
+interpreted as a column vector, with length \code{len(\var{f})}
+and with a value that depends on the values of its variables.
+Functions have two public attributes.
+\begin{methoddesc}{variables}{}
+Returns a copy of the list of variables of the function.
+\end{methoddesc}
+
+\begin{methoddesc}{value}{}
+The function value. If any of the variables of \var{f} has value
+\None, then \var{f}.\method{value()} returns \None.
+Otherwise, it returns a dense \dtc\ matrix of size
+(\code{len(\var{f})},1) with the function value computed from the
+\member{value} attributes of the variables of \var{f}.
+\end{methoddesc}
+
+Three types of functions are supported: affine, convex
+piecewise-linear and concave piecewise-linear.
+
+\textbf{Affine functions} represent vector valued functions of the form
+\[
+ f(x_1,\ldots,x_n) = A_1 x_1 + \cdots + A_n x_n + b.
+\]
+The coefficients can be scalars or dense or sparse matrices. The
+constant term is a scalar or a column vector.
+
+Affine functions result from the following operations.
+\begin{description}
+\item[Unary operations]
+For a variable \var{x}, the unary operation \code{+\var{x}} results in
+an affine function with \var{x} as variable, coefficient 1.0, and
+constant term 0.0. The unary operation \code{-\var{x}} returns an
+affine function with \var{x} as variable, coefficient -1.0, and
+constant term 0.0. For an affine function \var{f}, \code{+\var{f}} is
+a copy of \var{f}, and \code{-\var{f}} is a copy of \var{f} with the
+signs of its coefficients and constant term reversed.
+
+\item[Addition and subtraction]
+Sums and differences of affine functions, variables and constants
+result in new affine functions.
+The constant terms in the sum can be of type \intgr\ or \flt, or
+dense or sparse \dtc\ matrices with one column.
+
+The rules for addition and subtraction follow the conventions for
+matrix addition and subtraction in sections~\ref{s-arithmetic}
+and~\ref{s-spmatrix-arith}, with variables and affine functions
+interpreted as dense \dtc\ matrices with one column.
+In particular, a scalar term (\intgr, \flt, 1 by 1 dense \dtc\ matrix,
+variable of length 1, or affine function of length 1) can be added
+to an affine function or variable of length greater than 1.
+
+\item[Multiplication]
+Suppose \var{v} is an affine function or a variable, and \var{a} is
+an \intgr, \flt, sparse or dense \dtc\ matrix. The products
+\code{\var{a}*\var{v}} and \code{\var{v}*\var{a}} are
+valid affine functions whenever the product is allowed under the rules
+for matrix and scalar multiplication of sections~\ref{s-arithmetic}
+and~\ref{s-spmatrix-arith}, with \var{v} interpreted as a \dtc\ matrix
+with one column.
+In particular, the product \code{\var{a}*\var{v}} is defined if
+\var{a} is a scalar (\intgr, \flt\ or 1 by 1 dense \dtc\ matrix),
+or a matrix (dense or sparse) with
+\code{\var{a}.\member{size}[1] = len(\var{v})}.
+The operation \code{\var{v}*\var{a}} is defined if \var{a} is scalar,
+or if \code{len(\var{v})} = 1 and \var{a} is a matrix with one
+column.
+
+\item[Inner products]
+The following two functions return scalar affine functions defined
+as inner products of a constant vector with a variable or affine
+function.
+\begin{funcdesc}{sum}{v}
+The argument is an affine function or a variable. The result is an
+affine function of length 1, with the sum of the components of the
+argument \var{v}.
+\end{funcdesc}
+
+\begin{funcdesc}{dot}{u,v}
+If \var{v} is a variable or affine function and \var{u} is a \dtc\
+matrix of size (\code{len(\var{v})},1), then
+\code{dot(\var{u},\var{v})} and \code{dot(\var{v},\var{u})} are
+equivalent to \code{\var{u}.\method{trans()}*\var{v}}.
+
+If \var{u} and \var{v} are dense matrices, then
+\code{dot(\var{u},\var{v})}
+is equivalent to the function \code{blas.dot(\var{u},\var{v})}
+defined in section~\ref{s-blas1}, \ie, it returns the inner product of
+the two matrices.
+\end{funcdesc}
+\end{description}
+
+In the following example, the variable \var{x} has length 1 and
+\var{y} has length 2.
+The functions \var{f} and \var{g} are given by
+\BEAS
+ f(x,y) & = & \left[ \begin{array}{c} 2 \\ 2 \end{array}\right] x
+ + y + \left[ \begin{array}{c} 3 \\ 3 \end{array}\right], \\
+ g(x,y) & = &
+ \left[ \begin{array}{cc} 1 & 3 \\ 2 & 4 \end{array}\right] f(x,y)
+ + \left[ \begin{array}{cc} 1 & 1 \\ 1 & 1 \end{array} \right] y +
+ \left[ \begin{array}{c} 1 \\ -1 \end{array} \right] \\
+ & = & \left[ \begin{array}{c} 8 \\ 12 \end{array}\right] x
+ + \left[ \begin{array}{cc} 2 & 4 \\ 3 & 5 \end{array}\right] y
+ + \left[ \begin{array}{c} 13 \\ 17\end{array}\right].
+\EEAS
+\begin{verbatim}
+>>> from cvxopt.modeling import variable
+>>> x = variable(1,'x')
+>>> y = variable(2,'y')
+>>> f = 2*x + y + 3
+>>> A = matrix([[1., 2.], [3.,4.]])
+>>> b = matrix([1.,-1.])
+>>> g = A*f + sum(y) + b
+>>> print g
+affine function of length 2
+constant term:
+ 1.3000e+01
+ 1.7000e+01
+linear term: linear function of length 2
+coefficient of variable(2,'y'):
+ 2.0000e+00 4.0000e+00
+ 3.0000e+00 5.0000e+00
+coefficient of variable(1,'x'):
+ 8.0000e+00
+ 1.2000e+01
+\end{verbatim}
+
+\begin{description}
+\item[In-place operations]
+For an affine function \var{f} the operations \code{\var{f} += \var{u}}
+and \code{\var{f} -= \var{u}}, with \var{u} a constant, a variable or
+an affine function, are allowed if they do not change the length of
+\var{f}, \ie, if \var{u} has length \code{len(\var{f})} or length 1.
+In-place multiplication \code{\var{f} *= \var{u}} and division
+\code{\var{f} /= \var{u}} are allowed if \var{u} is an \intgr, \flt, or
+1 by 1 matrix.
+\end{description}
+
+\begin{description}
+\item[Indexing and slicing] Variables and affine functions admit
+single-argument indexing of the four types described in
+section~\ref{s-indexing}. The result of an indexing or slicing
+operation is an affine function.
+\end{description}
+
+\begin{verbatim}
+>>> x = variable(4,'x')
+>>> f = x[::2]
+>>> print f
+>>> linear function of length 2
+linear term: linear function of length 2
+coefficient of variable(4,'x'):
+TYPE: general
+SIZE: (2,4)
+(0, 0) 1.0000e+00
+(1, 2) 1.0000e+00
+>>> y = variable(3,'x')
+>>> g = matrix(range(12),(3,4),'d')*x - 3*y + 1
+>>> print g[0] + g[2]
+affine function of length 1
+constant term:
+ 2.0000e+00
+linear term: linear function of length 1
+coefficient of variable(4,'x'):
+ 2.0000e+00 8.0000e+00 1.4000e+01 2.0000e+01
+coefficient of variable(3,'y'):
+TYPE: general
+SIZE: (1,3)
+(0, 0) -3.0000e+00
+(0, 2) -3.0000e+00
+\end{verbatim}
+
+
+The general expression of a \textbf{convex piecewise-linear} function is
+\[
+ f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
+ \sum_{k=1}^K \max (y_1, y_2, \ldots, y_{m_k}).
+\]
+The maximum in this expression is a componentwise maximum of its
+vector arguments, which can be constant vectors, variables, affine
+functions or convex piecewise-linear functions.
+The general expression for a \textbf{concave piecewise-linear} function
+is
+\[
+ f(x_1,\ldots,x_n) = b + A_1 x_1 + \cdots + A_n x_n +
+ \sum_{k=1}^K \min (y_1, y_2, \ldots, y_{m_k}).
+\]
+Here the arguments of the \function{min()} can be constants, variables,
+affine functions or concave piecewise-linear functions.
+
+Piecewise-linear functions can be created using the following
+operations.
+\begin{description}
+\item[\function{max}] If the arguments in
+\code{\var{f} = max(\var{y1},\var{y2}, \ldots)}
+do not include any variables or functions, then the Python built-in
+\function{max()} is evaluated.
+
+If one or more of the arguments are variables or functions,
+\function{max()} returns a piecewise-linear function defined as the
+elementwise maximum of its arguments.
+In other words, \var{f}[\var{k}] =
+\code{max(\var{y1}[\var{k}],\var{y2}[\var{k}], \ldots)}
+for \var{k}=0, \ldots, \code{len(\var{f})}-1.
+The length of \var{f} is equal to the maximum of the lengths of the
+arguments. Each argument must have length equal to
+\code{len(\var{f})} or length one.
+Arguments with length one are interpreted as vectors of
+length \code{len(\var{f})} with identical entries.
+
+The arguments can be scalars of type \intgr\ or \flt,
+dense \dtc\ matrices with one column, variables, affine functions or
+convex piecewise-linear functions.
+
+With one argument, \code{\var{f} = max(\var{u})} is interpreted as
+\code{\var{f} = max(\var{u}[0],\var{u}[1],\ldots,
+\var{u}[\function{len}(\var{u})-1])}.
+
+\item[\function{min}] Similar to \function{max()} but returns a concave
+piecewise-linear function. The arguments can be scalars of type
+\intgr\ or \flt, dense \dtc\ matrices with one column,
+variables, affine functions or concave piecewise-linear functions.
+
+\item[\function{abs}]
+If \var{u} is a variable or affine function then
+\code{\var{f} = abs(\var{u})} returns the convex piecewise-linear
+function \code{max(\var{u},-\var{u})}.
+
+\item[Unary plus and minus] \code{+\var{f}}\ creates a copy of \var{f}.
+\code{-\var{f}}\ is a concave piecewise-linear function if \var{f} is
+convex and a convex piecewise-linear function if \var{f} is concave.
+
+\item[Addition and subtraction] Sums and differences involving
+piecewise-linear functions are allowed if they result in convex
+or concave functions. For example, one can add two convex or two
+concave functions, but not a convex and a concave function.
+The command \code{sum(\var{f})} is equivalent
+to \code{\var{f}[0] + \var{f}[1] + \ldots + \var{f}[len(\var{f})-1]}.
+
+\item[Multiplication] Scalar multiplication \code{\var{a}*\var{f}} of a
+piecewise-linear function \var{f} is defined if \var{a}
+is an \intgr, \flt, 1 by 1 \dtc\ matrix.
+Matrix-matrix multiplications \code{\var{a}*\var{f}} or
+\code{\var{f}*\var{a}} are only defined if \var{a} is a dense or
+sparse 1 by 1 matrix.
+
+\item[Indexing and slicing] Piecewise-linear functions admit
+single-argument indexing of the four types described in
+section~\ref{s-indexing}. The result of an indexing or slicing
+operation is a new piecewise-linear function.
+\end{description}
+
+In the following example, \var{f} is the 1-norm of a vector
+variable \var{x} of length 10, \var{g} is its infinity-norm and
+\var{h} is the function
+\[
+ h(x) = \sum_k \phi(x[k]),\qquad
+ \phi(u) = \left\{\begin{array}{ll}
+ 0 & |u| \leq 1 \\
+ |u|-1 & 1 \leq |u| \leq 2 \\
+ 2|u|-3 & |u| \geq 2. \end{array}\right.
+\]
+\begin{verbatim}
+>>> f = sum(abs(x))
+>>> g = max(abs(x))
+>>> h = sum(max(0, abs(x)-1, 2*abs(x)-3))
+\end{verbatim}
+
+\begin{description}
+\item[In-place operations]
+If \var{f} is piecewise-linear then the in-place operations
+\code{\var{f} += \var{u}}, \code{\var{f} -= \var{u}},
+\code{\var{f} *= \var{u}}, \code{\var{f} /= \var{u}} are defined if the
+corresponding expanded operations \code{\var{f} = \var{f}+\var{u}},
+\code{\var{f} = \var{f}-\var{u}}, \code{\var{f} = \var{f}*\var{u}}
+and \code{\var{f} = \var{f}/\var{u}} are defined and if they do not
+change the length of \var{f}.
+\end{description}
+
+\section{Constraints}
+Linear equality and inequality constraints of the form
+\[
+ f(x_1,\ldots,x_n) = 0, \qquad f(x_1,\ldots,x_n) \preceq 0,
+\]
+where $f$ is a convex function, are represented by \pytype{constraint}
+objects. Equality constraints are created by expressions of the form
+\begin{quote}
+\code{\var{f1} == \var{f2}}.
+\end{quote}
+Here \var{f1} and \var{f2} can be any objects for which the
+difference \code{\var{f1}-\var{f2}} yields an affine function.
+Inequality constraints are created by expressions of the form
+\begin{quote}
+\code{\var{f1} <= \var{f2}}, \qquad \code{\var{f2} >= \var{f1}},
+\end{quote}
+where \var{f1} and \var{f2} can be any objects for which the difference
+\code{\var{f1}-\var{f2}} yields a convex piecewise-linear function.
+The comparison operators first convert the expressions to
+\code{\var{f1}-\var{f2} == 0}, resp.\, \code{\var{f1}-\var{f2} <= 0},
+and then return a new \pytype{constraint}\ object with constraint
+function
+\code{\var{f1}-\var{f2}}.
+
+In the following example we create three constraints
+\[
+ 0 \preceq x \preceq \ones, \qquad \ones^T x = 2,
+\]
+for a variable of length 5.
+\begin{verbatim}
+>>> x = variable(5,'x')
+>>> c1 = (x <= 1)
+>>> c2 = (x >= 0)
+>>> c3 = (sum(x) == 2)
+\end{verbatim}
+
+The built-in fucntion \function{len()} returns the dimension of the
+constraint function.
+
+Constraints have four public attributes.
+\begin{methoddesc}[constraint]{type}{}
+Returns \code{'='} if the constraint is an equality constraint,
+and \code{'<'} if the constraint is an inequality constraint.
+\end{methoddesc}
+
+\begin{methoddesc}[constraint]{value}{}
+Returns the value of the constraint function.
+\end{methoddesc}
+
+\begin{memberdesc}[constraint]{multiplier}
+For a constraint \var{c}, \var{c}.\member{multiplier} is a
+\pytype{variable} object of dimension \code{len(\var{c})}.
+It is used to represent the Lagrange multiplier or dual variable
+associated with the constraint.
+Its value is initialized as \None, and can be modified
+by making an assignment to \var{c}.\member{multiplier}.\member{value}.
+\end{memberdesc}
+
+\begin{memberdesc}[constraint]{name}
+The name of the constraint. Changing the name of a constraint
+also changes the name of the multiplier of \var{c}.
+For example, the command \code{\var{c}.\member{name} = 'newname'} also
+changes
+\var{c}.\member{multiplier}.\member{name} to \code{'newname\_mul'}.
+\end{memberdesc}
+
+
+\section{Optimization Problems} \label{s-lp}
+
+Optimization problems are be constructed by calling the following
+function.
+\begin{classdesc}{op}{\optional{objective\optional{, constraints\optional{, name}}}}
+The first argument specifies the objective function to be minimized.
+It can be an affine or convex piecewise-linear function with length 1,
+a \pytype{variable} with length 1, or a scalar constant
+(\intgr, \flt\ or 1 by 1 dense \dtc\ matrix). The default value is
+\code{0.0}.
+
+The second argument is a single \pytype{constraint}, or a list of
+\pytype{constraint} objects. The default value is an empty list.
+
+The third argument is a string with a name for the problem.
+The default value is the empty string.
+\end{classdesc}
+
+The following attributes and methods are useful for examining
+and modifying optimization problems.
+
+\begin{memberdesc}[op]{objective}
+The objective or cost function. One can write to this
+attribute to change the objective of an existing problem.
+\end{memberdesc}
+
+\begin{methoddesc}[lp]{variables}{}
+Returns a list of the variables of the problem.
+\end{methoddesc}
+
+\begin{methoddesc}[lp]{constraints}{}
+Returns a list of the constraints.
+\end{methoddesc}
+
+\begin{methoddesc}[lp]{inequalities}{}
+Returns a list of the inequality constraints.
+\end{methoddesc}
+
+\begin{methoddesc}[lp]{equalities}{}
+Returns a list of the equality constraints.
+\end{methoddesc}
+
+\begin{methoddesc}[lp]{delconstraint}{c}
+Deletes constraint {\tt c} from the problem.
+\end{methoddesc}
+
+\begin{methoddesc}[lp]{addconstraint}{c}
+Adds constraint {\tt c} to the problem.
+\end{methoddesc}
+
+An optimization problem with convex piecewise-linear objective and
+constraints can be solved by calling the method \function{solve()}.
+
+\begin{methoddesc}[op]{solve}{\optional{format\optional{, solver}}}
+This function converts the optimization problem to a linear program
+in matrix form and then solves it using the solver described in
+section~\ref{s-lpsolver}.
+
+The first argument is either \code{'dense'} or \code{'sparse'}, and
+denotes the matrix types used in the matrix representation of the LP.
+The default value is \code{'dense'}.
+
+The second argument is either \None. \code{'glpk'} or \code{'mosek'},
+and selects one of three available LP solvers: a default solver
+written in Python, the GLPK solver (if installed) or the
+MOSEK LP solver (if installed); see section~\ref{s-lpsolver}.
+The default value is \None.
+
+The solver reports the outcome of optimization by setting
+the attribute \var{self}.\member{status} and by modifying
+the \member{value} attributes of the variables and the constraint
+multipliers of the problem.
+\BIT
+\item If the problem is solved to optimality,
+\var{self}.\member{status} is set to \code{'optimal'}.
+The \member{value} attributes of the variables in the problem are set
+to their computed solutions, and the \member{value} attributes of the
+multipliers of the constraints of the problem are set to the computed
+dual optimal solution.
+
+\item If it is determined that the problem is infeasible,
+\var{self}.\member{status} is set to \code{'primal infeasible'}.
+The \member{value} attributes of the variables are set to \None.
+The \member{value} attributes of the
+multipliers of the constraints of the problem are set to a certificate
+of primal infeasibility.
+With the \code{'glpk'} option, \function{solve()}
+does not provide certificates of infeasibility.
+
+\item If it is determined that the problem is dual infeasible,
+\var{self}.\member{status} is set to \code{'dual infeasible'}.
+The \member{value} attributes of the multipliers of the constraints of
+the problem are set to \None.
+The \member{value} attributes of the
+variables are set to a certificate of dual infeasibility.
+With the \code{'glpk'} option, \function{solve()} does not provide
+certificates of infeasibility.
+
+\item If the problem was not solved successfully,
+\var{self}.\member{status} is set to \code{'unknown'}.
+The \member{value} attributes of the variables and the constraint
+multipliers are set to \None.
+\EIT
+\end{methoddesc}
+We refer to section~\ref{s-lpsolver} for details on the algorithms and
+the different solver options.
+
+As an example we solve the LP
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & -4x - 5y \\
+ \mbox{subject to} & 2x +y \leq 3 \\
+ & x +2y \leq 3 \\
+ & x \geq 0, \quad y \geq 0.
+ \end{array}
+\]
+\begin{verbatim}
+>>> x = variable()
+>>> y = variable()
+>>> c1 = ( 2*x+y <= 3 )
+>>> c2 = ( x+2*y <= 3 )
+>>> c3 = ( x >= 0 )
+>>> c4 = ( y >= 0 )
+>>> lp1 = op(-4*x-5*y, [c1,c2,c3,c4])
+>>> lp1.solve()
+>>> print lp1.status
+optimal
+>>> print lp1.objective.value()
+-9.0000e+00
+>>> print x.value
+ 1.0000e-00
+>>> print y.value
+ 1.0000e-00
+>>> print c1.multiplier.value
+ 1.0000e-00
+>>> print c2.multiplier.value
+ 2.0000e-00
+>>> print c3.multiplier.value
+ 8.8912e-09
+>>> print c4.multiplier.value
+ 9.8567e-09
+\end{verbatim}
+
+We can solve the same LP in matrix form as follows.
+\begin{verbatim}
+>>> x = variable(2)
+>>> A = matrix([[2.,1.,-1.,0.], [1.,2.,0.,-1.]])
+>>> b = matrix([3.,3.,0.,0.])
+>>> c = matrix([-4.,-5.])
+>>> ineq = ( A*x <= b )
+>>> lp2 = op(dot(c,x), ineq)
+>>> lp2.solve()
+>>> print lp2.objective.value()
+-9.0000e+00
+>>> print x.value
+ 1.0000e-00
+ 1.0000e-00
+>>> print ineq.multiplier.value
+ 1.0000e+00
+ 2.0000e+00
+ 8.8912e-09
+ 9.8567e-09
+\end{verbatim}
+
+The \pytype{op} class also includes two methods for writing and reading
+files in
+\ulink{MPS format}{http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/linearprog/mps.html}.
+
+\begin{methoddesc}[op]{tofile}{filename}
+If the problem is an LP, writes it to the file \code{'filename'} using
+the MPS format. Row and column labels are assigned based on the
+variable and constraint names in the LP.
+\end{methoddesc}
+
+\begin{methoddesc}[lp]{fromfile}{filename}
+Reads the LP from the file \code{'filename'}. The file must be
+a fixed-format MPS file. Some features of the MPS format are not
+supported: comments beginning with dollar signs,
+the row types 'DE', 'DL', 'DG', and 'DN', and the capability of
+reading multiple righthand side, bound or range vectors.
+\end{methoddesc}
+
+
+\section{Examples}
+
+\begin{description}
+\item[Norm and Penalty Approximation]
+
+In the first example we solve the norm approximation problems
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|Ax - b\|_\infty,
+ \end{array} \qquad
+ \begin{array}{ll}
+ \mbox{minimize} & \|Ax - b\|_1
+ \end{array},
+\]
+and the penalty approximation problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \sum_k \phi((Ax-b)_k),
+ \end{array} \qquad
+ \phi(u) = \left\{\begin{array}{ll}
+ 0 & |u| \leq 3/4 \\
+ |u|-3/4 & 3/4 \leq |u| \leq 3/2 \\
+ 2|u|-9/4 & |u| \geq 3/2.\end{array}\right.
+\]
+We use randomly generated data.
+
+The code uses the \ulink{Matplotlib}{http://matplotlib.sourceforge.net}
+package for plotting the histograms of the residual vectors for the
+two solutions. It generates the figure shown below.
+
+\begin{verbatim}
+from cvxopt.random import normal
+from cvxopt.modeling import variable, op, max, sum
+import pylab
+
+m, n = 500, 100
+A = normal(m,n)
+b = normal(m)
+
+x1 = variable(n)
+op(max(abs(A*x1-b))).solve()
+
+x2 = variable(n)
+op(sum(abs(A*x2-b))).solve()
+
+x3 = variable(n)
+op(sum(max(0, abs(A*x3-b)-0.75, 2*abs(A*x3-b)-2.25))).solve()
+
+pylab.subplot(311)
+pylab.hist(A*x1.value-b, m/5)
+pylab.subplot(312)
+pylab.hist(A*x2.value-b, m/5)
+pylab.subplot(313)
+pylab.hist(A*x3.value-b, m/5)
+pylab.show()
+\end{verbatim}
+
+\begin{center}
+\includegraphics[width=\linewidth]{figures/normappr.eps}
+\end{center}
+
+Equivalently, we can formulate and solve the problems as LPs.
+\begin{verbatim}
+t = variable()
+x1 = variable(n)
+op(t, [-t <= A*x1-b, A*x1-b<=t]).solve()
+
+u = variable(m)
+x2 = variable(n)
+op(sum(u), [-u <= A*x2+b, A*x2+b <= u]).solve()
+
+v = variable(m)
+x3 = variable(n)
+op(sum(v), [v >= 0, v >= A*x3+b-0.75, v >= -(A*x3+b)-0.75, v >= 2*(A*x3-b)-2.25, v >= -2*(A*x3-b)-2.25]).solve()
+\end{verbatim}
+
+
+\item[Robust Linear Programming]
+The robust LP
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & c^T x \\
+ \mbox{subject to} & \sup_{\|v\|_\infty \leq 1}
+ (a_i+v)^T x \leq b_i, \qquad i=1,\ldots,m
+ \end{array}
+\]
+is equivalent to the problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & c^Tx \\
+ \mbox{subject to} & a_i^Tx + \|x\|_1 \leq b_i, \qquad i=1,\ldots,m.
+ \end{array}
+\]
+The following code computes the solution and the solution of
+the equivalent LP
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & c^Tx \\
+ \mbox{subject to} & a_i^Tx + \ones^Ty \leq b_i, \qquad i=1,\ldots,m \\
+& -y \preceq x \preceq y
+\end{array}
+\]
+for randomly generated data.
+
+\begin{verbatim}
+from cvxopt.random import normal, uniform
+from cvxopt.modeling import variable, dot, op, sum
+from cvxopt.blas import nrm2
+
+m, n = 500, 100
+A = normal(m,n)
+b = uniform(m)
+c = normal(n)
+
+x = variable(n)
+op(dot(c,x), A*x+sum(abs(x)) <= b).solve()
+
+x2 = variable(n)
+y = variable(n)
+op(dot(c,x2), [A*x2+sum(y) <= b, -y <= x2, x2 <= y]).solve()
+\end{verbatim}
+
+
+\item[1-Norm Support Vector Classifier]
+
+The following problem arises in classification:
+\[
+\begin{array}{ll}
+\mbox{minimize} & \|x\|_1 + \ones^Tu \\
+\mbox{subject to} & Ax \succeq \ones -u \\
+& u \succeq 0.
+\end{array}
+\]
+It can be solved as follows.
+\begin{verbatim}
+x = variable(A.size[1],'x')
+u = variable(A.size[0],'u')
+op(sum(abs(x)) + sum(u), [A*x >= 1-u, u >= 0]).solve()
+\end{verbatim}
+An equivalent unconstrained formulation is
+\begin{verbatim}
+x = variable(A.size[1],'x')
+op(sum(abs(x)) + sum(max(0,1-A*x))).solve()
+\end{verbatim}
+\end{description}
diff --git a/doc/python.sty b/doc/python.sty
new file mode 100644
index 0000000..3fdb8b7
--- /dev/null
+++ b/doc/python.sty
@@ -0,0 +1,1330 @@
+%
+% python.sty for the Python docummentation [works only with Latex2e]
+%
+
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesPackage{python}
+ [1998/01/11 LaTeX package (Python markup)]
+
+\RequirePackage{longtable}
+
+% Uncomment these two lines to ignore the paper size and make the page
+% size more like a typical published manual.
+%\renewcommand{\paperheight}{9in}
+%\renewcommand{\paperwidth}{8.5in} % typical squarish manual
+%\renewcommand{\paperwidth}{7in} % O'Reilly ``Programmming Python''
+
+% These packages can be used to add marginal annotations which indicate
+% index entries and labels; useful for reviewing this messy documentation!
+%
+%\RequirePackage{showkeys}
+%\RequirePackage{showidx}
+
+% If we ever want to indent paragraphs, this needs to be changed.
+% This is used inside the macros defined here instead of coding
+% \noindent directly.
+\let\py at parindent=\noindent
+
+% for PDF output, use maximal compression & a lot of other stuff
+% (test for PDF recommended by Tanmoy Bhattacharya <tanmoy at qcd.lanl.gov>)
+%
+\newif\ifpy at doing@page at targets
+\py at doing@page at targetsfalse
+
+\newif\ifpdf\pdffalse
+\ifx\pdfoutput\undefined\else\ifcase\pdfoutput
+\else
+ \pdftrue
+ \input{pdfcolor}
+ \let\py at LinkColor=\NavyBlue
+ \let\py at NormalColor=\Black
+ \pdfcompresslevel=9
+ \pdfpagewidth=\paperwidth % page width of PDF output
+ \pdfpageheight=\paperheight % page height of PDF output
+ %
+ % Pad the number with '0' to 3 digits wide so no page name is a prefix
+ % of any other.
+ %
+ \newcommand{\py at targetno}[1]{\ifnum#1<100 0\fi\ifnum#1<10 0\fi#1}
+ \newcommand{\py at pageno}{\py at targetno\thepage}
+ %
+ % This definition allows the entries in the page-view of the ToC to be
+ % active links. Some work, some don't.
+ %
+ \let\py at OldContentsline=\contentsline
+ %
+ % Backward compatibility hack: pdfTeX 0.13 defined \pdfannotlink,
+ % but it changed to \pdfstartlink in 0.14. This let's us use either
+ % version and still get useful behavior.
+ %
+ \@ifundefined{pdfstartlink}{
+ \let\pdfstartlink=\pdfannotlink
+ }{}
+ %
+ % The \py at parindent here is a hack -- we're forcing pdfTeX into
+ % horizontal mode since \pdfstartlink requires that.
+ \def\py at pdfstartlink{%
+ \ifvmode\py at parindent\fi%
+ \pdfstartlink%
+ }
+ %
+ % Macro that takes two args: the name to link to and the content of
+ % the link. This takes care of the PDF magic, getting the colors
+ % the same for each link, and avoids having lots of garbage all over
+ % this style file.
+ \newcommand{\py at linkToName}[2]{%
+ \py at pdfstartlink attr{/Border [0 0 0]} goto name{#1}%
+ \py at LinkColor#2\py at NormalColor%
+ \pdfendlink%
+ }
+ % Compute the padded page number separately since we end up with a pair of
+ % \relax tokens; this gets the right string computed and works.
+ \renewcommand{\contentsline}[3]{%
+ \def\my at pageno{\py at targetno{#3}}%
+ \py at OldContentsline{#1}{\py at linkToName{page\my at pageno}{#2}}{#3}%
+ }
+ \AtEndDocument{
+ \def\_{\string_}
+ \InputIfFileExists{\jobname.bkm}{\pdfcatalog{/PageMode /UseOutlines}}{}
+ }
+ \newcommand{\py at target}[1]{%
+ \ifpy at doing@page at targets%
+ {\pdfdest name{#1} xyz}%
+ \fi%
+ }
+ \let\py at OldLabel=\label
+ \renewcommand{\label}[1]{%
+ \py at OldLabel{#1}%
+ \py at target{label-#1}%
+ }
+ % This stuff adds a page# destination to every PDF page, where # is three
+ % digits wide, padded with leading zeros. This doesn't really help with
+ % the frontmatter, but does fine with the body.
+ %
+ % This is *heavily* based on the hyperref package.
+ %
+ \def\@begindvi{%
+ \unvbox \@begindvibox
+ \@hyperfixhead
+ }
+ \def\@hyperfixhead{%
+ \let\H at old@thehead\@thehead
+ \global\def\@foo{\py at target{page\py at pageno}}%
+ \expandafter\ifx\expandafter\@empty\H at old@thehead
+ \def\H at old@thehead{\hfil}\fi
+ \def\@thehead{\@foo\relax\H at old@thehead}%
+ }
+\fi\fi
+
+% Increase printable page size (copied from fullpage.sty)
+\topmargin 0pt
+\advance \topmargin by -\headheight
+\advance \topmargin by -\headsep
+
+% attempt to work a little better for A4 users
+\textheight \paperheight
+\advance\textheight by -2in
+
+\oddsidemargin 0pt
+\evensidemargin 0pt
+%\evensidemargin -.25in % for ``manual size'' documents
+\marginparwidth 0.5in
+
+\textwidth \paperwidth
+\advance\textwidth by -2in
+
+
+% Style parameters and macros used by most documents here
+\raggedbottom
+\sloppy
+\parindent = 0mm
+\parskip = 2mm
+\hbadness = 5000 % don't print trivial gripes
+
+\pagestyle{empty} % start this way; change for
+\pagenumbering{roman} % ToC & chapters
+
+% Use this to set the font family for headers and other decor:
+\newcommand{\py at HeaderFamily}{\sffamily}
+
+% Set up abstract ways to get the normal and smaller font sizes that
+% work even in footnote context.
+\newif\ifpy at infootnote \py at infootnotefalse
+\let\py at oldmakefntext\@makefntext
+\def\@makefntext#1{%
+ \bgroup%
+ \py at infootnotetrue
+ \py at oldmakefntext{#1}%
+ \egroup%
+}
+\def\py at defaultsize{%
+ \ifpy at infootnote\footnotesize\else\normalsize\fi%
+}
+\def\py at smallsize{%
+ \ifpy at infootnote\scriptsize\else\small\fi%
+}
+
+% Redefine the 'normal' header/footer style when using "fancyhdr" package:
+\@ifundefined{fancyhf}{}{
+ % Use \pagestyle{normal} as the primary pagestyle for text.
+ \fancypagestyle{normal}{
+ \fancyhf{}
+ \fancyfoot[LE,RO]{{\py at HeaderFamily\thepage}}
+ \fancyfoot[LO]{{\py at HeaderFamily\nouppercase{\rightmark}}}
+ \fancyfoot[RE]{{\py at HeaderFamily\nouppercase{\leftmark}}}
+ \renewcommand{\headrulewidth}{0pt}
+ \renewcommand{\footrulewidth}{0.4pt}
+ }
+ % Update the plain style so we get the page number & footer line,
+ % but not a chapter or section title. This is to keep the first
+ % page of a chapter and the blank page between chapters `clean.'
+ \fancypagestyle{plain}{
+ \fancyhf{}
+ \fancyfoot[LE,RO]{{\py at HeaderFamily\thepage}}
+ \renewcommand{\headrulewidth}{0pt}
+ \renewcommand{\footrulewidth}{0.4pt}
+ }
+ % Redefine \cleardoublepage so that the blank page between chapters
+ % gets the plain style and not the fancy style. This is described
+ % in the documentation for the fancyhdr package by Piet von Oostrum.
+ \@ifundefined{chapter}{}{
+ \renewcommand{\cleardoublepage}{
+ \clearpage\if at openright \ifodd\c at page\else
+ \hbox{}
+ \thispagestyle{plain}
+ \newpage
+ \if at twocolumn\hbox{}\newpage\fi\fi\fi
+ }
+ }
+}
+
+% This sets up the {verbatim} environment to be indented and a minipage,
+% and to have all the other mostly nice properties that we want for
+% code samples.
+
+\let\py at OldVerbatim=\verbatim
+\let\py at OldEndVerbatim=\endverbatim
+\RequirePackage{verbatim}
+\let\py at OldVerbatimInput=\verbatiminput
+
+% Variable used by begin code command
+\newlength{\py at codewidth}
+
+\renewcommand{\verbatim}{%
+ \setlength{\parindent}{1cm}%
+ % Calculate the text width for the minipage:
+ \setlength{\py at codewidth}{\linewidth}%
+ \addtolength{\py at codewidth}{-\parindent}%
+ %
+ \par\indent%
+ \begin{minipage}[t]{\py at codewidth}%
+ \small%
+ \py at OldVerbatim%
+}
+\renewcommand{\endverbatim}{%
+ \py at OldEndVerbatim%
+ \end{minipage}%
+}
+\renewcommand{\verbatiminput}[1]{%
+ {\setlength{\parindent}{1cm}%
+ % Calculate the text width for the minipage:
+ \setlength{\py at codewidth}{\linewidth}%
+ \addtolength{\py at codewidth}{-\parindent}%
+ %
+ \small%
+ \begin{list}{}{\setlength{\leftmargin}{1cm}}
+ \item%
+ \py at OldVerbatimInput{#1}%
+ \end{list}
+ }%
+}
+
+% This does a similar thing for the {alltt} environment:
+\RequirePackage{alltt}
+\let\py at OldAllTT=\alltt
+\let\py at OldEndAllTT=\endalltt
+
+\renewcommand{\alltt}{%
+ \setlength{\parindent}{1cm}%
+ % Calculate the text width for the minipage:
+ \setlength{\py at codewidth}{\linewidth}%
+ \addtolength{\py at codewidth}{-\parindent}%
+ \let\e=\textbackslash%
+ %
+ \par\indent%
+ \begin{minipage}[t]{\py at codewidth}%
+ \small%
+ \py at OldAllTT%
+}
+\renewcommand{\endalltt}{%
+ \py at OldEndAllTT%
+ \end{minipage}%
+}
+
+
+\newcommand{\py at modulebadkey}{{--just-some-junk--}}
+
+
+%% Lots of index-entry generation support.
+
+% Command to wrap around stuff that refers to function / module /
+% attribute names in the index. Default behavior: like \code{}. To
+% just keep the index entries in the roman font, uncomment the second
+% definition; it matches O'Reilly style more.
+%
+\newcommand{\py at idxcode}[1]{\texttt{#1}}
+%\renewcommand{\py at idxcode}[1]{#1}
+
+% Command to generate two index entries (using subentries)
+\newcommand{\indexii}[2]{\index{#1!#2}\index{#2!#1}}
+
+% And three entries (using only one level of subentries)
+\newcommand{\indexiii}[3]{\index{#1!#2 #3}\index{#2!#3, #1}\index{#3!#1 #2}}
+
+% And four (again, using only one level of subentries)
+\newcommand{\indexiv}[4]{
+\index{#1!#2 #3 #4}
+\index{#2!#3 #4, #1}
+\index{#3!#4, #1 #2}
+\index{#4!#1 #2 #3}
+}
+
+% Command to generate a reference to a function, statement, keyword,
+% operator.
+\newcommand{\kwindex}[1]{\indexii{keyword}{#1@{\py at idxcode{#1}}}}
+\newcommand{\stindex}[1]{\indexii{statement}{#1@{\py at idxcode{#1}}}}
+\newcommand{\opindex}[1]{\indexii{operator}{#1@{\py at idxcode{#1}}}}
+\newcommand{\exindex}[1]{\indexii{exception}{#1@{\py at idxcode{#1}}}}
+\newcommand{\obindex}[1]{\indexii{object}{#1}}
+\newcommand{\bifuncindex}[1]{%
+ \index{#1@{\py at idxcode{#1()}} (built-in function)}}
+
+% Add an index entry for a module
+\newcommand{\py at refmodule}[2]{\index{#1@{\py at idxcode{#1}} (#2module)}}
+\newcommand{\refmodindex}[1]{\py at refmodule{#1}{}}
+\newcommand{\refbimodindex}[1]{\py at refmodule{#1}{built-in }}
+\newcommand{\refexmodindex}[1]{\py at refmodule{#1}{extension }}
+\newcommand{\refstmodindex}[1]{\py at refmodule{#1}{standard }}
+
+% Refer to a module's documentation using a hyperlink of the module's
+% name, at least if we're building PDF:
+\ifpdf
+ \newcommand{\refmodule}[2][\py at modulebadkey]{%
+ \ifx\py at modulebadkey#1\def\py at modulekey{#2}\else\def\py at modulekey{#1}\fi%
+ \py at linkToName{label-module-\py at modulekey}{\module{#2}}%
+ }
+\else
+ \newcommand{\refmodule}[2][\py at modulebadkey]{\module{#2}}
+\fi
+
+% support for the module index
+\newif\ifpy at UseModuleIndex
+\py at UseModuleIndexfalse
+
+\newcommand{\makemodindex}{
+ \newwrite\modindexfile
+ \openout\modindexfile=mod\jobname.idx
+ \py at UseModuleIndextrue
+}
+
+% Add the defining entry for a module
+\newcommand{\py at modindex}[2]{%
+ \renewcommand{\py at thismodule}{#1}
+ \setindexsubitem{(in module #1)}%
+ \index{#1@{\py at idxcode{#1}} (#2module)|textbf}%
+ \ifpy at UseModuleIndex%
+ \@ifundefined{py at modplat@\py at thismodulekey}{
+ \write\modindexfile{\protect\indexentry{#1@{\texttt{#1}}}{\thepage}}%
+ }{\write\modindexfile{\protect\indexentry{#1@{\texttt{#1} %
+ \emph{(\py at platformof[\py at thismodulekey]{})}}}{\thepage}}%
+ }
+ \fi%
+}
+
+% *** XXX *** THE NEXT FOUR MACROS ARE NOW OBSOLETE !!! ***
+
+% built-in & Python modules in the main distribution
+\newcommand{\bimodindex}[1]{\py at modindex{#1}{built-in }%
+ \typeout{*** MACRO bimodindex IS OBSOLETE -- USE declaremodule INSTEAD!}}
+\newcommand{\stmodindex}[1]{\py at modindex{#1}{standard }%
+ \typeout{*** MACRO stmodindex IS OBSOLETE -- USE declaremodule INSTEAD!}}
+
+% Python & extension modules outside the main distribution
+\newcommand{\modindex}[1]{\py at modindex{#1}{}%
+ \typeout{*** MACRO modindex IS OBSOLETE -- USE declaremodule INSTEAD!}}
+\newcommand{\exmodindex}[1]{\py at modindex{#1}{extension }%
+ \typeout{*** MACRO exmodindex IS OBSOLETE -- USE declaremodule INSTEAD!}}
+
+% Additional string for an index entry
+\newif\ifpy at usingsubitem\py at usingsubitemfalse
+\newcommand{\py at indexsubitem}{}
+\newcommand{\setindexsubitem}[1]{\renewcommand{\py at indexsubitem}{ #1}%
+ \py at usingsubitemtrue}
+\newcommand{\ttindex}[1]{%
+ \ifpy at usingsubitem
+ \index{#1@{\py at idxcode{#1}}\py at indexsubitem}%
+ \else%
+ \index{#1@{\py at idxcode{#1}}}%
+ \fi%
+}
+\newcommand{\withsubitem}[2]{%
+ \begingroup%
+ \def\ttindex##1{\index{##1@{\py at idxcode{##1}} #1}}%
+ #2%
+ \endgroup%
+}
+
+
+% Module synopsis processing -----------------------------------------------
+%
+\newcommand{\py at thisclass}{}
+\newcommand{\py at thismodule}{}
+\newcommand{\py at thismodulekey}{}
+\newcommand{\py at thismoduletype}{}
+
+\newcommand{\py at standardIndexModule}[1]{\py at modindex{#1}{standard }}
+\newcommand{\py at builtinIndexModule}[1]{\py at modindex{#1}{built-in }}
+\newcommand{\py at extensionIndexModule}[1]{\py at modindex{#1}{extension }}
+\newcommand{\py at IndexModule}[1]{\py at modindex{#1}{}}
+
+\newif\ifpy at HaveModSynopsis \py at HaveModSynopsisfalse
+\newif\ifpy at ModSynopsisFileIsOpen \py at ModSynopsisFileIsOpenfalse
+\newif\ifpy at HaveModPlatform \py at HaveModPlatformfalse
+
+% \declaremodule[key]{type}{name}
+\newcommand{\declaremodule}[3][\py at modulebadkey]{
+ \py at openModSynopsisFile
+ \renewcommand{\py at thismoduletype}{#2}
+ \ifx\py at modulebadkey#1
+ \renewcommand{\py at thismodulekey}{#3}
+ \else
+ \renewcommand{\py at thismodulekey}{#1}
+ \fi
+ \@ifundefined{py@#2IndexModule}{%
+ \typeout{*** MACRO declaremodule called with unknown module type: `#2'}
+ \py at IndexModule{#3}%
+ }{%
+ \csname py@#2IndexModule\endcsname{#3}%
+ }
+ \label{module-\py at thismodulekey}
+}
+\newif\ifpy at ModPlatformFileIsOpen \py at ModPlatformFileIsOpenfalse
+\newcommand{\py at ModPlatformFilename}{\jobname.pla}
+\newcommand{\platform}[1]{
+ \ifpy at ModPlatformFileIsOpen\else
+ \newwrite\py at ModPlatformFile
+ \openout\py at ModPlatformFile=\py at ModPlatformFilename
+ \py at ModPlatformFileIsOpentrue
+ \fi
+}
+\InputIfFileExists{\jobname.pla}{}{}
+\newcommand{\py at platformof}[2][\py at modulebadkey]{%
+ \ifx\py at modulebadkey#1 \def\py at key{#2}%
+ \else \def\py at key{#1}%
+ \fi%
+ \csname py at modplat@\py at key\endcsname%
+}
+\newcommand{\ignorePlatformAnnotation}[1]{}
+
+% \moduleauthor{name}{email}
+\newcommand{\moduleauthor}[2]{}
+
+% \sectionauthor{name}{email}
+\newcommand{\sectionauthor}[2]{}
+
+
+\newcommand{\py at defsynopsis}{Module has no synopsis.}
+\newcommand{\py at modulesynopsis}{\py at defsynopsis}
+\newcommand{\modulesynopsis}[1]{
+ \py at HaveModSynopsistrue
+ \renewcommand{\py at modulesynopsis}{#1}
+}
+
+% define the file
+\newwrite\py at ModSynopsisFile
+
+% hacked from \addtocontents from latex.ltx:
+\long\def\py at writeModSynopsisFile#1{%
+ \protected at write\py at ModSynopsisFile%
+ {\let\label\@gobble \let\index\@gobble \let\glossary\@gobble}%
+ {\string#1}%
+}
+\newcommand{\py at closeModSynopsisFile}{
+ \ifpy at ModSynopsisFileIsOpen
+ \closeout\py at ModSynopsisFile
+ \py at ModSynopsisFileIsOpenfalse
+ \fi
+}
+\newcommand{\py at openModSynopsisFile}{
+ \ifpy at ModSynopsisFileIsOpen\else
+ \openout\py at ModSynopsisFile=\py at ModSynopsisFilename
+ \py at ModSynopsisFileIsOpentrue
+ \fi
+}
+
+\newcommand{\py at ProcessModSynopsis}{
+ \ifpy at HaveModSynopsis
+ \py at writeModSynopsisFile{\modulesynopsis%
+ {\py at thismodulekey}{\py at thismodule}%
+ {\py at thismoduletype}{\py at modulesynopsis}}%
+ \py at HaveModSynopsisfalse
+ \fi
+ \renewcommand{\py at modulesynopsis}{\py at defsynopsis}
+}
+\AtEndDocument{\py at ProcessModSynopsis\py at closeModSynopsisFile}
+
+
+\long\def\py at writeModPlatformFile#1{%
+ \protected at write\py at ModPlatformFile%
+ {\let\label\@gobble \let\index\@gobble \let\glossary\@gobble}%
+ {\string#1}%
+}
+
+
+\newcommand{\localmoduletable}{
+ \IfFileExists{\py at ModSynopsisFilename}{
+ \begin{synopsistable}
+ \input{\py at ModSynopsisFilename}
+ \end{synopsistable}
+ }{}
+}
+
+\ifpdf
+ \newcommand{\py at ModSynopsisSummary}[4]{%
+ \py at linkToName{label-module-#1}{\bfcode{#2}} & #4\\
+ }
+\else
+ \newcommand{\py at ModSynopsisSummary}[4]{\bfcode{#2} & #4\\}
+\fi
+\newenvironment{synopsistable}{
+ % key, name, type, synopsis
+ \let\modulesynopsis=\py at ModSynopsisSummary
+ \begin{tabular}{ll}
+}{
+ \end{tabular}
+}
+%
+% --------------------------------------------------------------------------
+
+
+\newcommand{\py at reset}{
+ \py at usingsubitemfalse
+ \py at ProcessModSynopsis
+ \renewcommand{\py at thisclass}{}
+ \renewcommand{\py at thismodule}{}
+ \renewcommand{\py at thismodulekey}{}
+ \renewcommand{\py at thismoduletype}{}
+}
+
+% Augment the sectioning commands used to get our own font family in place,
+% and reset some internal data items:
+\renewcommand{\section}{\py at reset%
+ \@startsection{section}{1}{\z@}%
+ {-3.5ex \@plus -1ex \@minus -.2ex}%
+ {2.3ex \@plus.2ex}%
+ {\reset at font\Large\py at HeaderFamily}}
+\renewcommand{\subsection}{\@startsection{subsection}{2}{\z@}%
+ {-3.25ex\@plus -1ex \@minus -.2ex}%
+ {1.5ex \@plus .2ex}%
+ {\reset at font\large\py at HeaderFamily}}
+\renewcommand{\subsubsection}{\@startsection{subsubsection}{3}{\z@}%
+ {-3.25ex\@plus -1ex \@minus -.2ex}%
+ {1.5ex \@plus .2ex}%
+ {\reset at font\normalsize\py at HeaderFamily}}
+\renewcommand{\paragraph}{\@startsection{paragraph}{4}{\z@}%
+ {3.25ex \@plus1ex \@minus.2ex}%
+ {-1em}%
+ {\reset at font\normalsize\py at HeaderFamily}}
+\renewcommand{\subparagraph}{\@startsection{subparagraph}{5}{\parindent}%
+ {3.25ex \@plus1ex \@minus .2ex}%
+ {-1em}%
+ {\reset at font\normalsize\py at HeaderFamily}}
+
+
+% This gets the underscores closer to the right width; the only change
+% from standard LaTeX is the width specified.
+
+\DeclareTextCommandDefault{\textunderscore}{%
+ \leavevmode \kern.06em\vbox{\hrule\@width.55em}}
+
+% Underscore hack (only act like subscript operator if in math mode)
+%
+% The following is due to Mark Wooding (the old version didn't work with
+% Latex 2e.
+
+%%\DeclareRobustCommand\hackscore{%
+%% \ifmmode_\else\textunderscore\fi%
+%%}
+%%\begingroup
+%%\catcode`\_\active
+%%\def\next{%
+%% \AtBeginDocument{\catcode`\_\active\def_{\hackscore{}}}%
+%%}
+%%\expandafter\endgroup\next
+
+
+% Now for a lot of semantically-loaded environments that do a ton of magical
+% things to get the right formatting and index entries for the stuff in
+% Python modules and C API.
+
+
+% {fulllineitems} is used in one place in libregex.tex, but is really for
+% internal use in this file.
+%
+\newcommand{\py at itemnewline}[1]{%
+ \@tempdima\linewidth%
+ \advance\@tempdima \leftmargin\makebox[\@tempdima][l]{#1}%
+}
+
+\newenvironment{fulllineitems}{
+ \begin{list}{}{\labelwidth \leftmargin \labelsep 0pt
+ \rightmargin 0pt \topsep -\parskip \partopsep \parskip
+ \itemsep -\parsep
+ \let\makelabel=\py at itemnewline}
+}{\end{list}}
+
+% \optional is mostly for use in the arguments parameters to the various
+% {*desc} environments defined below, but may be used elsewhere. Known to
+% be used in the debugger chapter.
+%
+% Typical usage:
+%
+% \begin{funcdesc}{myfunc}{reqparm\optional{, optparm}}
+% ^^^ ^^^
+% No space here No space here
+%
+% When a function has multiple optional parameters, \optional should be
+% nested, not chained. This is right:
+%
+% \begin{funcdesc}{myfunc}{\optional{parm1\optional{, parm2}}}
+%
+\let\py at badkey=\@undefined
+
+\newcommand{\optional}[1]{%
+ {\textnormal{\Large[}}{#1}\hspace{0.5mm}{\textnormal{\Large]}}}
+
+% This can be used when a function or method accepts an varying number
+% of arguments, such as by using the *args syntax in the parameter list.
+\newcommand{\py at moreargs}{...}
+
+% This can be used when you don't want to document the parameters to a
+% function or method, but simply state that it's an alias for
+% something else.
+\newcommand{\py at unspecified}{...}
+
+
+\newlength{\py at argswidth}
+\newcommand{\py at sigparams}[1]{%
+ \parbox[t]{\py at argswidth}{\py at varvars{#1}\code{)}}}
+\newcommand{\py at sigline}[2]{%
+ \settowidth{\py at argswidth}{#1\code{(}}%
+ \addtolength{\py at argswidth}{-2\py at argswidth}%
+ \addtolength{\py at argswidth}{\textwidth}%
+ \item[#1\code{(}\py at sigparams{#2}]}
+
+% C functions ------------------------------------------------------------
+% \begin{cfuncdesc}[refcount]{type}{name}{arglist}
+% Note that the [refcount] slot should only be filled in by
+% tools/anno-api.py; it pulls the value from the refcounts database.
+\newcommand{\cfuncline}[3]{
+ \py at sigline{\code{#1 \bfcode{#2}}}{#3}%
+ \index{#2@{\py at idxcode{#2()}}}
+}
+\newenvironment{cfuncdesc}[4][\py at badkey]{
+ \begin{fulllineitems}
+ \cfuncline{#2}{#3}{#4}
+ \ifx#1\@undefined\else%
+ \emph{Return value: \textbf{#1}.}\\
+ \fi
+}{\end{fulllineitems}}
+
+% C variables ------------------------------------------------------------
+% \begin{cvardesc}{type}{name}
+\newenvironment{cvardesc}[2]{
+ \begin{fulllineitems}
+ \item[\code{#1 \bfcode{#2}}\index{#2@{\py at idxcode{#2}}}]
+}{\end{fulllineitems}}
+
+% C data types -----------------------------------------------------------
+% \begin{ctypedesc}[index name]{typedef name}
+\newenvironment{ctypedesc}[2][\py at badkey]{
+ \begin{fulllineitems}
+ \item[\bfcode{#2}%
+ \ifx#1\@undefined%
+ \index{#2@{\py at idxcode{#2}} (C type)}
+ \else%
+ \index{#2@{\py at idxcode{#1}} (C type)}
+ \fi]
+}{\end{fulllineitems}}
+
+% C type fields ----------------------------------------------------------
+% \begin{cmemberdesc}{container type}{ctype}{membername}
+\newcommand{\cmemberline}[3]{
+ \item[\code{#2 \bfcode{#3}}]
+ \index{#3@{\py at idxcode{#3}} (#1 member)}
+}
+\newenvironment{cmemberdesc}[3]{
+ \begin{fulllineitems}
+ \cmemberline{#1}{#2}{#3}
+}{\end{fulllineitems}}
+
+% Funky macros -----------------------------------------------------------
+% \begin{csimplemacrodesc}{name}
+% -- "simple" because it has no args; NOT for constant definitions!
+\newenvironment{csimplemacrodesc}[1]{
+ \begin{fulllineitems}
+ \item[\bfcode{#1}\index{#1@{\py at idxcode{#1}} (macro)}]
+}{\end{fulllineitems}}
+
+% simple functions (not methods) -----------------------------------------
+% \begin{funcdesc}{name}{args}
+\newcommand{\funcline}[2]{%
+ \funclineni{#1}{#2}%
+ \index{#1@{\py at idxcode{#1()}} (in module \py at thismodule)}}
+\newenvironment{funcdesc}[2]{
+ \begin{fulllineitems}
+ \funcline{#1}{#2}
+}{\end{fulllineitems}}
+
+% similar to {funcdesc}, but doesn't add to the index
+\newcommand{\funclineni}[2]{%
+ \py at sigline{\bfcode{#1}}{#2}}
+\newenvironment{funcdescni}[2]{
+ \begin{fulllineitems}
+ \funclineni{#1}{#2}
+}{\end{fulllineitems}}
+
+% classes ----------------------------------------------------------------
+% \begin{classdesc}{name}{constructor args}
+\newenvironment{classdesc}[2]{
+ % Using \renewcommand doesn't work for this, for unknown reasons:
+ \global\def\py at thisclass{#1}
+ \begin{fulllineitems}
+ \py at sigline{\strong{class }\bfcode{#1}}{#2}%
+ \index{#1@{\py at idxcode{#1}} (class in \py at thismodule)}
+}{\end{fulllineitems}}
+
+% \begin{classdesc*}{name}
+\newenvironment{classdesc*}[1]{
+ % Using \renewcommand doesn't work for this, for unknown reasons:
+ \global\def\py at thisclass{#1}
+ \begin{fulllineitems}
+ \item[\strong{class }\code{\bfcode{#1}}%
+ \index{#1@{\py at idxcode{#1}} (class in \py at thismodule)}]
+}{\end{fulllineitems}}
+
+% \begin{excclassdesc}{name}{constructor args}
+% but indexes as an exception
+\newenvironment{excclassdesc}[2]{
+ % Using \renewcommand doesn't work for this, for unknown reasons:
+ \global\def\py at thisclass{#1}
+ \begin{fulllineitems}
+ \py at sigline{\strong{exception }\bfcode{#1}}{#2}%
+ \index{#1@{\py at idxcode{#1}} (exception in \py at thismodule)}
+}{\end{fulllineitems}}
+
+% There is no corresponding {excclassdesc*} environment. To describe
+% a class exception without parameters, use the {excdesc} environment.
+
+
+\let\py at classbadkey=\@undefined
+
+% object method ----------------------------------------------------------
+% \begin{methoddesc}[classname]{methodname}{args}
+\newcommand{\methodline}[3][\@undefined]{
+ \methodlineni{#2}{#3}
+ \ifx#1\@undefined
+ \index{#2@{\py at idxcode{#2()}} (\py at thisclass\ method)}
+ \else
+ \index{#2@{\py at idxcode{#2()}} (#1 method)}
+ \fi
+}
+\newenvironment{methoddesc}[3][\@undefined]{
+ \begin{fulllineitems}
+ \ifx#1\@undefined
+ \methodline{#2}{#3}
+ \else
+ \def\py at thisclass{#1}
+ \methodline{#2}{#3}
+ \fi
+}{\end{fulllineitems}}
+
+% similar to {methoddesc}, but doesn't add to the index
+% (never actually uses the optional argument)
+\newcommand{\methodlineni}[3][\py at classbadkey]{%
+ \py at sigline{\bfcode{#2}}{#3}}
+\newenvironment{methoddescni}[3][\py at classbadkey]{
+ \begin{fulllineitems}
+ \methodlineni{#2}{#3}
+}{\end{fulllineitems}}
+
+% object data attribute --------------------------------------------------
+% \begin{memberdesc}[classname]{membername}
+\newcommand{\memberline}[2][\py at classbadkey]{%
+ \ifx#1\@undefined
+ \memberlineni{#2}
+ \index{#2@{\py at idxcode{#2}} (\py at thisclass\ attribute)}
+ \else
+ \memberlineni{#2}
+ \index{#2@{\py at idxcode{#2}} (#1 attribute)}
+ \fi
+}
+\newenvironment{memberdesc}[2][\py at classbadkey]{
+ \begin{fulllineitems}
+ \ifx#1\@undefined
+ \memberline{#2}
+ \else
+ \def\py at thisclass{#1}
+ \memberline{#2}
+ \fi
+}{\end{fulllineitems}}
+
+% similar to {memberdesc}, but doesn't add to the index
+% (never actually uses the optional argument)
+\newcommand{\memberlineni}[2][\py at classbadkey]{\item[\bfcode{#2}]}
+\newenvironment{memberdescni}[2][\py at classbadkey]{
+ \begin{fulllineitems}
+ \memberlineni{#2}
+}{\end{fulllineitems}}
+
+% For exceptions: --------------------------------------------------------
+% \begin{excdesc}{name}
+% -- for constructor information, use excclassdesc instead
+\newenvironment{excdesc}[1]{
+ \begin{fulllineitems}
+ \item[\strong{exception }\bfcode{#1}%
+ \index{#1@{\py at idxcode{#1}} (exception in \py at thismodule)}]
+}{\end{fulllineitems}}
+
+% Module data or constants: ----------------------------------------------
+% \begin{datadesc}{name}
+\newcommand{\dataline}[1]{%
+ \datalineni{#1}\index{#1@{\py at idxcode{#1}} (data in \py at thismodule)}}
+\newenvironment{datadesc}[1]{
+ \begin{fulllineitems}
+ \dataline{#1}
+}{\end{fulllineitems}}
+
+% similar to {datadesc}, but doesn't add to the index
+\newcommand{\datalineni}[1]{\item[\bfcode{#1}]\nopagebreak}
+\newenvironment{datadescni}[1]{
+ \begin{fulllineitems}
+ \datalineni{#1}
+}{\end{fulllineitems}}
+
+% bytecode instruction ---------------------------------------------------
+% \begin{opcodedesc}{name}{var}
+% -- {var} may be {}
+\newenvironment{opcodedesc}[2]{
+ \begin{fulllineitems}
+ \item[\bfcode{#1}\quad\var{#2}]
+}{\end{fulllineitems}}
+
+
+\newcommand{\nodename}[1]{\label{#1}}
+
+% For these commands, use \command{} to get the typography right, not
+% {\command}. This works better with the texinfo translation.
+\newcommand{\ABC}{{\sc abc}}
+\newcommand{\UNIX}{{\sc Unix}}
+\newcommand{\POSIX}{POSIX}
+\newcommand{\ASCII}{{\sc ascii}}
+\newcommand{\Cpp}{C\protect\raisebox{.18ex}{++}}
+\newcommand{\C}{C}
+\newcommand{\EOF}{{\sc eof}}
+\newcommand{\NULL}{\constant{NULL}}
+\newcommand{\infinity}{\ensuremath{\infty}}
+\newcommand{\plusminus}{\ensuremath{\pm}}
+
+% \guilabel{Start}
+\newcommand{\guilabel}[1]{\textsf{#1}}
+% \menuselection{Start \sub Programs \sub Python}
+\newcommand{\menuselection}[1]{\guilabel{{\def\sub{ \ensuremath{>} }#1}}}
+
+% Also for consistency: spell Python "Python", not "python"!
+
+% code is the most difficult one...
+\newcommand{\code}[1]{\textrm{\@vobeyspaces\@noligs\def\{{\char`\{}\def\}{\char`\}}\def\~{\char`\~}\def\^{\char`\^}\def\e{\char`\\}\def\${\char`\$}\def\#{\char`\#}\def\&{\char`\&}\def\%{\char`\%}%
+\texttt{#1}}}
+
+\newcommand{\bfcode}[1]{\code{\bfseries#1}} % bold-faced code font
+\newcommand{\csimplemacro}[1]{\code{#1}}
+\newcommand{\kbd}[1]{\code{#1}}
+\newcommand{\samp}[1]{`\code{#1}'}
+\newcommand{\var}[1]{%
+ \ifmmode%
+ \hbox{\py at defaultsize\textrm{\textit{#1\/}}}%
+ \else%
+ \py at defaultsize\textrm{\textit{#1\/}}%
+ \fi%
+}
+\renewcommand{\emph}[1]{{\em #1}}
+\newcommand{\dfn}[1]{\emph{#1}}
+\newcommand{\strong}[1]{{\bf #1}}
+% let's experiment with a new font:
+\newcommand{\file}[1]{`\filenq{#1}'}
+\newcommand{\filenq}[1]{{\py at smallsize\textsf{\let\e=\textbackslash#1}}}
+
+% Use this def/redef approach for \url{} since hyperref defined this already,
+% but only if we actually used hyperref:
+\ifpdf
+ \newcommand{\url}[1]{{%
+ \py at pdfstartlink attr{/Border [0 0 0]} user{/S /URI /URI (#1)}%
+ \py at LinkColor% color of the link text
+ \py at smallsize\sf #1%
+ \py at NormalColor% Turn it back off; these are declarative
+ \pdfendlink}% and don't appear bound to the current
+ }% formatting "box".
+\else
+ \newcommand{\url}[1]{\mbox{\py at smallsize\textsf{#1}}}
+\fi
+\newcommand{\email}[1]{{\py at smallsize\textsf{#1}}}
+\newcommand{\newsgroup}[1]{{\py at smallsize\textsf{#1}}}
+
+\newcommand{\py at varvars}[1]{{%
+ {\let\unspecified=\py at unspecified%
+ \let\moreargs=\py at moreargs%
+ \var{#1}}}}
+
+% I'd really like to get rid of this!
+\newif\iftexi\texifalse
+
+% This is used to get l2h to put the copyright and abstract on
+% a separate HTML page.
+\newif\ifhtml\htmlfalse
+
+
+% These should be used for all references to identifiers which are
+% used to refer to instances of specific language constructs. See the
+% names for specific semantic assignments.
+%
+% For now, don't do anything really fancy with them; just use them as
+% logical markup. This might change in the future.
+%
+\newcommand{\module}[1]{\texttt{#1}}
+\newcommand{\keyword}[1]{\texttt{#1}}
+\newcommand{\exception}[1]{\texttt{#1}}
+\newcommand{\class}[1]{\texttt{#1}}
+\newcommand{\function}[1]{\texttt{#1}}
+\newcommand{\member}[1]{\texttt{#1}}
+\newcommand{\method}[1]{\texttt{#1}}
+
+\newcommand{\pytype}[1]{#1} % built-in Python type
+
+\newcommand{\cfunction}[1]{\texttt{#1}}
+\newcommand{\ctype}[1]{\texttt{#1}} % C struct or typedef name
+\newcommand{\cdata}[1]{\texttt{#1}} % C variable, typically global
+
+\newcommand{\mailheader}[1]{{\py at smallsize\textsf{#1:}}}
+\newcommand{\mimetype}[1]{{\py at smallsize\textsf{#1}}}
+% The \! is a "negative thin space" in math mode.
+\newcommand{\regexp}[1]{%
+ {\tiny$^{^\lceil}\!\!$%
+ {\py at defaultsize\code{#1}}%
+ $\!\rfloor\!$%
+ }}
+\newcommand{\envvar}[1]{%
+ #1%
+ \index{#1}%
+ \index{environment variables!{#1}}%
+}
+\newcommand{\makevar}[1]{#1} % variable in a Makefile
+\newcommand{\character}[1]{\samp{#1}}
+
+% constants defined in Python modules or C headers, not language constants:
+\newcommand{\constant}[1]{\code{#1}} % manifest constant, not syntactic
+
+\newcommand{\manpage}[2]{{\emph{#1}(#2)}}
+\newcommand{\pep}[1]{PEP #1\index{Python Enhancement Proposals!PEP #1}}
+\newcommand{\rfc}[1]{RFC #1\index{RFC!RFC #1}}
+\newcommand{\program}[1]{\strong{#1}}
+\newcommand{\programopt}[1]{\strong{#1}}
+% Note that \longprogramopt provides the '--'!
+\newcommand{\longprogramopt}[1]{\strong{-{}-#1}}
+
+% \ulink{link text}{URL}
+\ifpdf
+ \newcommand{\ulink}[2]{{%
+ % For PDF, we *should* only generate a link when the URL is absolute.
+ \py at pdfstartlink attr{/Border [0 0 0]} user{/S /URI /URI (#2)}%
+ \py at LinkColor% color of the link text
+ #1%
+ \py at NormalColor% Turn it back off; these are declarative
+ \pdfendlink}% and don't appear bound to the current
+ }% formatting "box".
+\else
+ \newcommand{\ulink}[2]{#1}
+\fi
+
+% cited titles: \citetitle{Title of Work}
+% online: \citetitle[url-to-resource]{Title of Work}
+\ifpdf
+ \newcommand{\citetitle}[2][\py at modulebadkey]{%
+ \ifx\py at modulebadkey#1\emph{#2}\else\ulink{\emph{#2}}{#1}\fi%
+ }
+\else
+ \newcommand{\citetitle}[2][URL]{\emph{#2}}
+\fi
+
+
+
+% This version is being checked in for the historical record; it shows
+% how I've managed to get some aspects of this to work. It will not
+% be used in practice, so a subsequent revision will change things
+% again. This version has problems, but shows how to do something
+% that proved more tedious than I'd expected, so I don't want to lose
+% the example completely.
+%
+\newcommand{\grammartoken}[1]{\texttt{#1}}
+\newenvironment{productionlist}[1][\py at badkey]{
+ \def\optional##1{{\Large[}##1{\Large]}}
+ \def\production##1##2{\code{##1}&::=&\code{##2}\\}
+ \def\productioncont##1{& &\code{##1}\\}
+ \def\token##1{##1}
+ \let\grammartoken=\token
+ \parindent=2em
+ \indent
+ \begin{tabular}{lcl}
+}{%
+ \end{tabular}
+}
+
+\newlength{\py at noticelength}
+
+\newcommand{\py at heavybox}{
+ \setlength{\fboxrule}{2pt}
+ \setlength{\fboxsep}{7pt}
+ \setlength{\py at noticelength}{\linewidth}
+ \addtolength{\py at noticelength}{-2\fboxsep}
+ \addtolength{\py at noticelength}{-2\fboxrule}
+ \setlength{\shadowsize}{3pt}
+ \Sbox
+ \minipage{\py at noticelength}
+}
+\newcommand{\py at endheavybox}{
+ \endminipage
+ \endSbox
+ \fbox{\TheSbox}
+}
+
+% a 'note' is as plain as it gets:
+\newcommand{\py at noticelabel@note}{Note:}
+\newcommand{\py at noticestart@note}{}
+\newcommand{\py at noticeend@note}{}
+
+% a 'warning' gets more visible distinction:
+\newcommand{\py at noticelabel@warning}{Warning:}
+\newcommand{\py at noticestart@warning}{\py at heavybox}
+\newcommand{\py at noticeend@warning}{\py at endheavybox}
+
+\newenvironment{notice}[1][note]{
+ \def\py at noticetype{#1}
+ \csname py at noticestart@#1\endcsname
+ \par\strong{\csname py at noticelabel@#1\endcsname}
+}{\csname py at noticeend@\py at noticetype\endcsname}
+\newcommand{\note}[1]{\strong{\py at noticelabel@note} #1}
+\newcommand{\warning}[1]{\strong{\py at noticelabel@warning} #1}
+
+% Deprecation stuff.
+% Should be extended to allow an index / list of deprecated stuff. But
+% there's a lot of stuff that needs to be done to make that automatable.
+%
+% First parameter is the release number that deprecates the feature, the
+% second is the action the should be taken by users of the feature.
+%
+% Example:
+% \deprecated{1.5.1}{Use \method{frobnicate()} instead.}
+%
+\newcommand{\deprecated}[2]{%
+ \strong{Deprecated since release #1.} #2\par}
+
+% New stuff.
+% This should be used to mark things which have been added to the
+% development tree but that aren't in the release, but are documented.
+% This allows release of documentation that already includes updated
+% descriptions. Place at end of descriptor environment.
+%
+% Example:
+% \versionadded{1.5.2}
+% \versionchanged[short explanation]{2.0}
+%
+\newcommand{\versionadded}[2][\py at badkey]{%
+ \ifx#1\@undefined%
+ { New in version #2. }%
+ \else%
+ { New in version #2:\ #1. }%
+ \fi%
+}
+\newcommand{\versionchanged}[2][\py at badkey]{%
+ \ifx#1\@undefined%
+ { Changed in version #2. }%
+ \else%
+ { Changed in version #2:\ #1. }%
+ \fi%
+}
+
+
+% Tables.
+%
+\newenvironment{tableii}[4]{%
+ \begin{center}%
+ \def\lineii##1##2{\csname#2\endcsname{##1}&##2\\}%
+ \begin{tabular}{#1}\strong{#3}&\strong{#4} \\* \hline%
+}{%
+ \end{tabular}%
+ \end{center}%
+}
+
+\newenvironment{longtableii}[4]{%
+ \begin{center}%
+ \def\lineii##1##2{\csname#2\endcsname{##1}&##2\\}%
+ \begin{longtable}[c]{#1}\strong{#3}&\strong{#4} \\* \hline\endhead%
+}{%
+ \end{longtable}%
+ \end{center}%
+}
+
+\newenvironment{tableiii}[5]{%
+ \begin{center}%
+ \def\lineiii##1##2##3{\csname#2\endcsname{##1}&##2&##3\\}%
+ \begin{tabular}{#1}\strong{#3}&\strong{#4}&\strong{#5} \\%
+ \hline%
+}{%
+ \end{tabular}%
+ \end{center}%
+}
+
+\newenvironment{longtableiii}[5]{%
+ \begin{center}%
+ \def\lineiii##1##2##3{\csname#2\endcsname{##1}&##2&##3\\}%
+ \begin{longtable}[c]{#1}\strong{#3}&\strong{#4}&\strong{#5} \\%
+ \hline\endhead%
+}{%
+ \end{longtable}%
+ \end{center}%
+}
+
+\newenvironment{tableiv}[6]{%
+ \begin{center}%
+ \def\lineiv##1##2##3##4{\csname#2\endcsname{##1}&##2&##3&##4\\}%
+ \begin{tabular}{#1}\strong{#3}&\strong{#4}&\strong{#5}&\strong{#6} \\%
+ \hline%
+}{%
+ \end{tabular}%
+ \end{center}%
+}
+
+\newenvironment{longtableiv}[6]{%
+ \begin{center}%
+ \def\lineiv##1##2##3##4{\csname#2\endcsname{##1}&##2&##3&##4\\}%
+ \begin{longtable}[c]{#1}\strong{#3}&\strong{#4}&\strong{#5}&\strong{#6}%
+ \\%
+ \hline\endhead%
+}{%
+ \end{longtable}%
+ \end{center}%
+}
+
+\newenvironment{tablev}[7]{%
+ \begin{center}%
+ \def\linev##1##2##3##4##5{\csname#2\endcsname{##1}&##2&##3&##4&##5\\}%
+ \begin{tabular}{#1}\strong{#3}&\strong{#4}&\strong{#5}&\strong{#6}&\strong{#7} \\%
+ \hline%
+}{%
+ \end{tabular}%
+ \end{center}%
+}
+
+\newenvironment{longtablev}[7]{%
+ \begin{center}%
+ \def\linev##1##2##3##4##5{\csname#2\endcsname{##1}&##2&##3&##4&##5\\}%
+ \begin{longtable}[c]{#1}\strong{#3}&\strong{#4}&\strong{#5}&\strong{#6}&\strong{#7}%
+ \\%
+ \hline\endhead%
+}{%
+ \end{longtable}%
+ \end{center}%
+}
+
+% XXX Don't think we can use this yet, though it cleans up some
+% tedious markup. There's no equivalent for the HTML transform yet,
+% and that needs to exist. I don't know how to write it.
+%
+% This should really have something that makes it easier to bind a
+% table's ``Notes'' column and an associated tablenotes environment,
+% and generates the right magic for getting the numbers right in the
+% table.
+%
+% So this is quite incomplete.
+%
+\newcounter{py at tablenotescounter}
+\newenvironment{tablenotes}{%
+ \noindent Notes:
+ \par
+ \setcounter{py at tablenotescounter}{0}
+ \begin{list}{(\arabic{py at tablenotescounter})}%
+ {\usecounter{py at tablenotescounter}}
+}{\end{list}}
+
+
+% Cross-referencing (AMK, new impl. FLD)
+% Sample usage:
+% \begin{seealso}
+% \seemodule{rand}{Uniform random number generator.}; % Module xref
+% \seetext{\emph{Encyclopedia Britannica}}. % Ref to a book
+%
+% % A funky case: module name contains '_'; have to supply an optional key
+% \seemodule[copyreg]{copy_reg}{Interface constructor registration for
+% \module{pickle}.}
+% \end{seealso}
+%
+% Note that the last parameter for \seemodule and \seetext should be complete
+% sentences and be terminated with the proper punctuation.
+
+\ifpdf
+ \newcommand{\py at seemodule}[3][\py at modulebadkey]{%
+ \par%
+ \ifx\py at modulebadkey#1\def\py at modulekey{#2}\else\def\py at modulekey{#1}\fi%
+ \begin{fulllineitems}
+ \item[\py at linkToName{label-module-\py at modulekey}{Module \module{#2}}
+ (section \ref{module-\py at modulekey}):]
+ #3
+ \end{fulllineitems}
+ }
+\else
+ \newcommand{\py at seemodule}[3][\py at modulebadkey]{%
+ \par%
+ \ifx\py at modulebadkey#1\def\py at modulekey{#2}\else\def\py at modulekey{#1}\fi%
+ \begin{fulllineitems}
+ \item[Module \module{#2} (section \ref{module-\py at modulekey}):]
+ #3
+ \end{fulllineitems}
+ }
+\fi
+
+% \seelink{url}{link text}{why it's interesting}
+\newcommand{\py at seelink}[3]{%
+ \par
+ \begin{fulllineitems}
+ \item[\ulink{#2}{#1}]
+ #3
+ \end{fulllineitems}
+}
+% \seetitle[url]{title}{why it's interesting}
+\newcommand{\py at seetitle}[3][\py at modulebadkey]{%
+ \par
+ \begin{fulllineitems}
+ \item[\citetitle{#2}]
+ \ifx\py at modulebadkey#1\else
+ \item[{\small{(\url{#1})}}]
+ \fi
+ #3
+ \end{fulllineitems}
+}
+% \seepep{number}{title}{why it's interesting}
+\newcommand{\py at seepep}[3]{%
+ \par%
+ \begin{fulllineitems}
+ \item[\pep{#1}, ``\emph{#2}'']
+ #3
+ \end{fulllineitems}
+}
+% \seerfc{number}{title}{why it's interesting}
+\newcommand{\py at seerfc}[3]{%
+ \par%
+ \begin{fulllineitems}
+ \item[\rfc{#1}, ``\emph{#2}'']
+ #3
+ \end{fulllineitems}
+}
+% \seeurl{url}{why it's interesting}
+\newcommand{\py at seeurl}[2]{%
+ \par%
+ \begin{fulllineitems}
+ \item[\url{#1}]
+ #2
+ \end{fulllineitems}
+}
+
+\newenvironment{seealso*}{
+ \par
+ \def\seetext##1{\par{##1}}
+ \let\seemodule=\py at seemodule
+ \let\seepep=\py at seepep
+ \let\seerfc=\py at seerfc
+ \let\seetitle=\py at seetitle
+ \let\seeurl=\py at seeurl
+ \let\seelink=\py at seelink
+}{\par}
+\newenvironment{seealso}{
+ \par
+ \strong{See Also:}
+ \par
+ \def\seetext##1{\par{##1}}
+ \let\seemodule=\py at seemodule
+ \let\seepep=\py at seepep
+ \let\seerfc=\py at seerfc
+ \let\seetitle=\py at seetitle
+ \let\seeurl=\py at seeurl
+ \let\seelink=\py at seelink
+}{\par}
+
+% Allow the Python release number to be specified independently of the
+% \date{}. This allows the date to reflect the document's date and
+% release to specify the Python release that is documented.
+%
+\newcommand{\py at release}{}
+\newcommand{\version}{}
+\newcommand{\shortversion}{}
+\newcommand{\releaseinfo}{}
+\newcommand{\releasename}{Release}
+\newcommand{\release}[1]{%
+ \renewcommand{\py at release}{\releasename\space\version}%
+ \renewcommand{\version}{#1}}
+\newcommand{\setshortversion}[1]{%
+ \renewcommand{\shortversion}{#1}}
+\newcommand{\setreleaseinfo}[1]{%
+ \renewcommand{\releaseinfo}{#1}}
+
+% Allow specification of the author's address separately from the
+% author's name. This can be used to format them differently, which
+% is a good thing.
+%
+\newcommand{\py at authoraddress}{}
+\newcommand{\authoraddress}[1]{\renewcommand{\py at authoraddress}{#1}}
+\let\developersaddress=\authoraddress
+\let\developer=\author
+\let\developers=\author
+
+% This sets up the fancy chapter headings that make the documents look
+% at least a little better than the usual LaTeX output.
+%
+\@ifundefined{ChTitleVar}{}{
+ \ChNameVar{\raggedleft\normalsize\py at HeaderFamily}
+ \ChNumVar{\raggedleft \bfseries\Large\py at HeaderFamily}
+ \ChTitleVar{\raggedleft \rm\Huge\py at HeaderFamily}
+ % This creates chapter heads without the leading \vspace*{}:
+ \def\@makechapterhead#1{%
+ {\parindent \z@ \raggedright \normalfont
+ \ifnum \c at secnumdepth >\m at ne
+ \DOCH
+ \fi
+ \interlinepenalty\@M
+ \DOTI{#1}
+ }
+ }
+}
+
+
+% Definition lists; requested by AMK for HOWTO documents. Probably useful
+% elsewhere as well, so keep in in the general style support.
+%
+\newenvironment{definitions}{%
+ \begin{description}%
+ \def\term##1{\item[##1]\mbox{}\\*[0mm]}
+}{%
+ \end{description}%
+}
+
+% Tell TeX about pathological hyphenation cases:
+\hyphenation{Base-HTTP-Re-quest-Hand-ler}
diff --git a/doc/solvers.tex b/doc/solvers.tex
new file mode 100644
index 0000000..90c014f
--- /dev/null
+++ b/doc/solvers.tex
@@ -0,0 +1,1578 @@
+\chapter{Optimization Routines (\module{cvxopt.solvers})}
+\label{chap:solvers}
+
+\section{Linear Programming} \label{s-lpsolver}
+
+\begin{funcdesc}{lp}{c, G, h\optional{, A, b\optional{,
+solver\optional{, primalstart\optional{, dualstart}}}}}
+Solves the pair of primal and dual LPs
+\BEQ \label{e-lp}
+\mbox{Primal:}\quad \begin{array}[t]{ll}
+\mbox{minimize} & c^Tx \\
+\mbox{subject to} & Gx + s = h \\ & Ax=b \\ & s \succeq 0
+\end{array} \qquad\qquad
+\mbox{Dual:}\quad
+\begin{array}[t]{ll}
+\mbox{maximize} & -h^T z - b^T y \\
+\mbox{subject to} & G^Tz + A^T y + c = 0 \\ & z \succeq 0.
+\end{array}
+\EEQ
+\var{c}, \var{h} and \var{b} are real single-column dense matrices.
+\var{G} and \var{A} are real dense or sparse matrices.
+The default values for \var{A} and \var{b} are sparse matrices with
+zero rows, meaning that there are no equality constraints.
+
+The \var{solver} argument is used to choose among three solvers.
+When it is omitted or \None, the default CVXOPT solver is used.
+The external solvers GLPK and MOSEK (if installed) can be selected by
+setting \code{\var{solver}='glpk'} or
+\code{\var{solver}='mosek'}; see section~\ref{s-external}.
+
+The optional arguments \var{primalstart} and \var{dualstart} are only
+referenced by the default solver.
+\var{primalstart} is a dictionary with keys \code{'x'} and \code{'s'},
+used as an optional primal starting point.
+\var{dualstart} is a dictionary with keys \code{'y'} and \code{'z'},
+used as an optional dual starting point.
+
+\function{lp()} returns a dictionary with keys \code{'status'},
+\code{'x'}, \code{'s'}, \code{'y'}, \code{'z'}.
+The possible values of the \code{'status'} item are as follows.
+\begin{description}
+\item[\code{'optimal'.}] In this case the \code{'x'}, \code{'s'},
+\code{'y'} and \code{'z'} entries contain the primal and dual solutions,
+which approximately satisfy
+\[
+ Gx + s = h, \qquad Ax=b, \qquad G^T z + A^T y + c = 0, \qquad
+ s \succeq 0, \qquad z \succeq 0, \qquad s^T z =0.
+\]
+
+\item[\code{'primal infeasible'.}]
+The \code{'x'} and \code{'s'} entries are \None, and the \code{'y'},
+\code{'z'} entries provide an approximate certificate of
+infeasibility, \ie, vectors that approximately satisfy
+\[
+ G^T z + A^T y = 0, \qquad h^T z + b^T y = -1, \qquad z \succeq 0.
+\]
+With the \code{'glpk'} option, no proof of infeasibility is returned
+(all entries of the dictionary are \None).
+
+\item[\code{'dual infeasible'.}] The LP is dual infeasible.
+The \code{'y'} and \code{'z'} entries are \None, and the \code{'x'}
+and \code{'s'} entries contain an approximate certificate of dual
+infeasibility
+\[
+ Gx + s = 0, \qquad Ax=0, \qquad c^T x = -1, \qquad s \succeq 0.
+\]
+With the \code{'glpk'} option, no proof of dual infeasibility is
+returned.
+
+\item[\code{'unknown'}.] The \code{'x'}, \code{'s'}, \code{'y'},
+\code{'z'} entries are \None.
+\end{description}
+
+%The default solver requires that
+%\[
+% \Rank(A) = p, \qquad \Rank (\left[ \begin{array}{c} G \\ A\end{array}
+% \right]) = n
+%\]
+%where \var{p} is the number of equality constraints and \var{n}
+%is the number of primal variables (dimension of \var{x}).
+\end{funcdesc}
+
+As a simple example we solve the LP
+\[
+ \begin{array}[t]{ll}
+ \mbox{minimize} & -4x_1 - 5x_2 \\
+ \mbox{subject to} & 2x_1 + x_2 \leq 3 \\
+ & x_1 + 2x_2 \leq 3 \\
+ & x_1 \geq 0, \quad x_2 \geq 0.
+ \end{array}
+\]
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt import solvers
+>>> c = matrix([-4., -5.])
+>>> G = matrix([[2., 1., -1., 0.], [1., 2., 0., -1.]])
+>>> h = matrix([3., 3., 0., 0.])
+>>> sol = solvers.lp(c,G,h)
+>>> print sol['x']
+ 1.0000e-00
+ 1.0000e-00
+\end{verbatim}
+
+\section{Quadratic Programming}
+\begin{funcdesc}{qp}{P, q, \optional{, G, h \optional{, A, b\optional{,
+solver}}}}
+Solves a convex quadratic program
+\[
+\begin{array}{ll}
+\mbox{minimize} & (1/2) x^TPx + q^T x \\
+\mbox{subject to} & Gx \preceq h \\ & Ax = b.
+\end{array}
+\]
+
+\var{P} is a square dense or sparse real matrix, representing a
+symmetric matrix in \code{'L'} storage, \ie, only the lower
+triangular part of \var{P} is referenced.
+\var{G} and \var{A} are dense or sparse real matrices.
+Their default values are sparse matrices with zero columns.
+\var{q}, \var{h} and \var{b} are single-column real dense matrices.
+The default values of \var{h} and \var{b} are matrices of size (0,1).
+
+The default CVXOPT solver is used when the \var{solver} argument
+is absent or \None. The MOSEK solver (if installed) can be
+selected by setting \var{solver}=\code{'mosek'}.
+
+\function{qp()} returns a dictionary with keys
+\code{'status'}, \code{'x'}, \code{'s'}, \code{'y'}, \code{'z'}.
+The possible values of the \code{'status'} key are as follows.
+\begin{description}
+\item[\code{'optimal'}] In this case the
+\code{'x'} entry is the primal optimal solution,
+the \code{'s'} entry is the corresponding slack in the inequality
+constraints, the \code{'z'} and \code{'y'} entries are the optimal
+values of the dual variables associated with the linear inequality
+and linear equality constraints.
+These values (approximately) satisfy the optimality conditions
+\[
+ Px + q + G^T z + A^T y = 0, \qquad Gx + s = h, \qquad
+ Ax = b, \qquad s \succeq 0, \qquad z \succeq 0, \qquad s^T z = 0.
+\]
+
+\item [\code{'primal infeasible'}] This only applies when
+\var{solver} is \code{'mosek'}, and means that a certificate of
+primal infeasibility has been found. The \code{'x'} and \code{'s'}
+entries are \None, and the
+\code{'z'} and \code{'y'} entries are vectors that approximately satisfy
+\[
+ G^Tz + A^T y = 0, \qquad h^Tz + b^Ty = -1, \qquad z \succeq 0.
+\]
+
+\item [\code{'dual infeasible'}] This only applies when
+\var{solver} is \code{'mosek'}, and means that a certificate of
+dual infeasibility has been found. The \code{'z'} and \code{'y'}
+entries are \None, and the \code{'x'} and \code{'s'} entries are
+vectors that approximately satisfy
+\[
+ Px = 0, \qquad q^Tx = -1, \qquad Gx + s = 0, \qquad Ax=0, \qquad
+ s \succeq 0.
+\]
+
+\item[\code{'unknown'}] This means that the algorithm reached
+the maximum number of iterations before a solution was found.
+The \code{'x'}, \code{'s'}, \code{'y'}, \code{'z'} entries are \None.
+\end{description}
+\end{funcdesc}
+
+As an example we compute the trade-off curve on page 187
+of the book \citetitle[http://www.stanford.edu/\~{}boyd/cvxbook]{Convex
+Optimization}, by solving the quadratic program
+\[
+\begin{array}{ll}
+\mbox{minimize} & -\bar p^T x + \mu x^T S x \\
+\mbox{subject to} & \ones^T x = 1, \quad x \succeq 0
+\end{array}
+\]
+for a sequence of positive values of {\it mu}.
+The code below computes the trade-off curve and produces two figures
+using the \ulink{Matplotlib}{http://matplotlib.sourceforge.net} package.
+\begin{center}
+\includegraphics[width=10cm]{figures/portfolio1.eps}
+\hspace*{\fill}
+\includegraphics[width=10cm]{figures/portfolio2.eps}
+\end{center}
+
+\begin{verbatim}
+from math import sqrt
+from cvxopt.base import matrix
+from cvxopt.blas import dot
+from cvxopt.solvers import qp
+import pylab
+
+# Problem data.
+n = 4
+S = matrix([[ 4e-2, 6e-3, -4e-3, 0.0 ],
+ [ 6e-3, 1e-2, 0.0, 0.0 ],
+ [-4e-3, 0.0, 2.5e-3, 0.0 ],
+ [ 0.0, 0.0, 0.0, 0.0 ]])
+pbar = matrix([.12, .10, .07, .03])
+G = matrix(0.0, (n,n))
+G[::n+1] = -1.0
+h = matrix(0.0, (n,1))
+A = matrix(1.0, (1,n))
+b = matrix(1.0)
+
+# Compute trade-off.
+N = 100
+mus = [ 10**(5.0*t/N-1.0) for t in xrange(N) ]
+portfolios = [ qp(mu*S, -pbar, G, h, A, b)['x'] for mu in mus ]
+returns = [ dot(pbar,x) for x in portfolios ]
+risks = [ sqrt(dot(x, S*x)) for x in portfolios ]
+
+# Plot trade-off curve and optimal allocations.
+pylab.figure(1, facecolor='w')
+pylab.plot(risks, returns)
+pylab.xlabel('standard deviation')
+pylab.ylabel('expected return')
+pylab.axis([0, 0.2, 0, 0.15])
+pylab.title('Risk-return trade-off curve (fig 4.12)')
+pylab.yticks([0.00, 0.05, 0.10, 0.15])
+
+pylab.figure(2, facecolor='w')
+c1 = [ x[0] for x in portfolios ]
+c2 = [ x[0] + x[1] for x in portfolios ]
+c3 = [ x[0] + x[1] + x[2] for x in portfolios ]
+c4 = [ x[0] + x[1] + x[2] + x[3] for x in portfolios ]
+pylab.fill(risks + [.20], c1 + [0.0], '#F0F0F0')
+pylab.fill(risks[-1::-1] + risks, c2[-1::-1] + c1, '#D0D0D0')
+pylab.fill(risks[-1::-1] + risks, c3[-1::-1] + c2, '#F0F0F0')
+pylab.fill(risks[-1::-1] + risks, c4[-1::-1] + c3, '#D0D0D0')
+pylab.axis([0.0, 0.2, 0.0, 1.0])
+pylab.xlabel('standard deviation')
+pylab.ylabel('allocation')
+pylab.text(.15,.5,'x1')
+pylab.text(.10,.7,'x2')
+pylab.text(.05,.7,'x3')
+pylab.text(.01,.7,'x4')
+pylab.title('Optimal allocations (fig 4.12)')
+pylab.show()
+\end{verbatim}
+
+
+\section{Geometric Programming}
+\begin{funcdesc}{gp}{K, F, g \optional{, G, h \optional{, A, b}}}
+Solves a geometric program in convex form
+\[
+\begin{array}{ll}
+\mbox{minimize} & f_0(x) = \lse(F_0x+g_0) \\
+\mbox{subject to} & f_i(x) = \lse(F_ix+g_i) \leq 0,\quad i=1,\ldots,m \\
+ & Gx \preceq h \\
+ & Ax=b
+\end{array}
+\]
+where
+\[
+ \lse(u) = \log \sum_k \exp(u_k), \qquad
+ F = \left[ \begin{array}{cccc}
+ F_0^T & F_1^T & \cdots & F_m^T \end{array}\right]^T, \qquad
+ g = \left[ \begin{array}{cccc}
+ g_0^T & g_1^T & \cdots & g_m^T \end{array}\right]^T.
+\]
+\var{K} is a list of \var{m}+1 positive integers with
+\code{\var{K}[\var i]}
+equal to the number of rows in {\it Fi}.
+\var{F} is a dense or sparse real matrix of size
+\code{(sum(\var K),\var n)}.
+\var{g} is a dense real matrix of size \code{(sum(\var K),1)}.
+\var{G} and \var{A} are dense or sparse real matrices.
+Their default values are sparse matrices with zero rows.
+\var{h} and \var{b} are dense real matrices with one column.
+Their default values are matrices of size (0,1).
+
+\function{gp()} returns a dictionary with keys
+\code{'status'}, \code{'x'}, \code{'snl'}, \code{'sl'},
+\code{'y'}, \code{'znl'} and \code{'zl'}.
+The possible values of the \code{'status'} key are:
+\begin{description}
+\item[\code{'optimal'}] In this case the
+\code{'x'} entry is the primal optimal solution,
+the \code{'snl'} and \code{'sl'} entries are the corresponding slacks
+in the nonlinear and linear inequality constraints.
+The \code{'znl'}, \code{'zl'} and \code{'y'} entries are the optimal
+values of the dual variables associated with the nonlinear and linear
+inequality constraints and the linear equality constraints.
+These values approximately satisfy
+\[
+ \nabla f_0(x) + \sum_{k=1}^m z_{\mathrm{nl},k}
+ \nabla f_k(x) + G^T z_\mathrm{l} + A^T y = 0, \qquad
+ f_k(x) + s_{\mathrm{nl},k} = 0, \quad k=1,\ldots,m, \qquad
+ Gx + s_\mathrm{l} = h, \qquad Ax=b
+\]
+and
+\[
+s_\mathrm{nl}\succeq 0, \qquad s_\mathrm{l}\succeq 0, \qquad
+z_\mathrm{nl} \succeq 0, \qquad z_\mathrm{l} \succeq 0, \qquad
+s_\mathrm{nl}^T z_\mathrm{nl} + s_\mathrm{l}^T z_\mathrm{l} = 0.
+\]
+
+\item[\code{'unknown'}] This means that the algorithm reached
+the maximum number of iterations before a solution was found.
+The \code{'x'}, \code{'snl'}, \code{'sl'}, \code{'y'}, \code{'znl'}
+and \code{'zl'} entries are \None.
+\end{description}
+\end{funcdesc}
+
+As an example, we solve the small GP on page~8 of the paper
+\citetitle[http://www.stanford.edu/\~{}boyd/gp\_tutorial]{A Tutorial on Geometric Programming}.
+The posynomial form of the problem is
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & w^{-1} h^{-1} d^{-1} \\
+ \mbox{subject to}
+ & (2/A_\mathrm{wall}) hw + (2/A_\mathrm{wall})hd \leq 1 \\
+ & (1/A_\mathrm{flr}) wd \leq 1 \\
+ & \alpha wh^{-1} \leq 1 \\
+ & (1/\beta) hw^{-1} \leq 1 \\
+ & \gamma wd^{-1} \leq 1 \\
+ & (1/\delta)dw^{-1} \leq 1
+ \end{array}
+\]
+with variables {\it h}, {\it w}, {\it d}.
+
+\begin{verbatim}
+from cvxopt.base import matrix, log, exp
+from cvxopt import solvers
+
+Aflr = 1000.0
+Awall = 100.0
+alpha = 0.5
+beta = 2.0
+gamma = 0.5
+delta = 2.0
+
+F = matrix( [[-1., 1., 1., 0., -1., 1., 0., 0.],
+ [-1., 1., 0., 1., 1., -1., 1., -1.],
+ [-1., 0., 1., 1., 0., 0., -1., 1.]])
+g = log( matrix( [1.0, 2/Awall, 2/Awall, 1/Aflr, alpha, 1/beta, gamma, 1/delta]) )
+K = [1, 2, 1, 1, 1, 1, 1]
+h, w, d = exp( solvers.gp(K, F, g)['x'] )
+\end{verbatim}
+
+\section{Semidefinite Programming} \label{s-sdpsolver}
+We use the following notation for a pair of primal and dual
+semidefinite programs (SDPs):
+\BEQ \label{e-sdp}
+\mbox{Primal:}\quad \begin{array}[t]{ll}
+\mbox{minimize} & c^Tx \\
+\mbox{subject to} & G_\mathrm{l}x + s_\mathrm{l} = h_\mathrm{l} \\
+ & G_\mathrm{s}(x) + S_\mathrm{s} = H_\mathrm{s} \\
+ & Ax=b \\ & s_\mathrm{l} \succeq 0, \quad S_\mathrm{s} \succeq 0
+\end{array} \qquad\qquad
+\mbox{Dual:}\quad
+\begin{array}[t]{ll}
+\mbox{maximize} & -h_\mathrm{l}^T z_\mathrm{l} -
+ \Tr(H_\mathrm{s} Z_\mathrm{s}) - b^T y \\
+\mbox{subject to} & G_\mathrm{l}^Tz_\mathrm{l} +
+ G_\mathrm{s}^T(Z_\mathrm{s}) + A^T y + c = 0 \\
+ & z_\mathrm{l} \succeq 0, \quad Z_\mathrm{s} \succeq 0.
+\end{array}
+\EEQ
+The dimensions of the primal and dual variables are
+\[
+ x\in \reals^n, \qquad s_\mathrm{l} \in \reals^m,
+\qquad S_\mathrm{s} \in \symm^{m_0} \times \cdots \times
+\symm^{m_{N-1}}, \qquad
+ y \in\reals^p, \qquad z_\mathrm{l}\in \reals^m,
+\qquad Z_\mathrm{s} \in \symm^{m_0} \times \cdots \times
+\symm^{m_{N-1}},
+\]
+where $\symm^n$ is the set of real symmetric matrices
+of order {\it n}. The problem data are the matrices
+\[
+c\in\reals^n, \qquad G_\mathrm{l} \in\reals^{m\times n},
+\qquad h_\mathrm{l} \in \reals^{m}, \qquad
+ H_\mathrm{s} \in \symm^{m_0} \times \cdots \times \symm^{m_{N-1}},
+\qquad
+A \in \reals^{p\times n}, \qquad b \in \reals^{p},
+\]
+and the linear mapping
+$G_\mathrm{s} : \reals^n \rightarrow \symm^{m_1} \times \cdots \times
+\symm^{m_N}$ and its adjoint $G_\mathrm{s}^T$.
+As for LPs we store vector variables as dense real matrices with one
+column.
+Block-diagonal symmetric matrices are stored as lists of square
+dense real matrices, with the lower triangular part of each matrix
+representing the lower triangular part of a diagonal block. Entries
+above the diagonal are not referenced.
+
+\begin{funcdesc}{sdp}{c\optional{, Gl, hl\optional{,
+ Gs, hs\optional{, A, b\optional{, solver\optional{,
+ primalstart\optional{, dualstart}}}}}}}
+
+Solves the pair of primal and dual SDPs~(\ref{e-sdp}).
+
+\var{c} is a dense real matrix with one column.
+\var{Gl} and \var{A} are dense or sparse real matrices.
+\var{hl} and \var{b} are dense real matrices with one column.
+The default values for \var{Gl}, \var{hl}, \var{A} and \var{b} are
+empty matrices, \ie, matrices with zero rows.
+
+\var{Gs} and \var{hs} are lists of length {\it N} that specify the
+linear matrix inequality constraints.
+\var{hs} is a list of square dense real matrices \code{\var{hs}[k]} of
+order {\it m\_k}.
+\var{Gs} is a list of dense or sparse real matrices
+\code{\var{Gs}[k]} with {\it m\_k}*{\it m\_k} rows and {\it n} columns,
+such that the product \code{\var{Gs}[k]*\var{x}}
+is the {\it k}th diagonal block of {\it Gs}(\var{x}), stored
+columnwise.
+
+The \var{solver} argument is used to choose between two
+solvers: the default solver (used when \var{solver} is absent or
+equal to \None) and the external solver DSDP5
+(\code{\var{solver}='dsdp'}); see section~\ref{s-external}.
+With the \code{'dsdp'} option the code does not accept problems with
+equality constraints.
+
+The optional argument \var{primalstart} is a dictionary with keys
+\code{'x'}, \code{'sl'}, and \code{'ss'}, used as an optional primal
+starting point.
+\var{dualstart} is a dictionary with keys \code{'y'}, \code{'zl'},
+\code{'zs'}, used as an optional dual starting point.
+These two arguments are ignored when the DSDP solver is used.
+
+\function{sdp()} returns a dictionary with keys \code{'status'},
+\code{'x'}, \code{'sl'}, \code{'ss'}, \code{'y'}, \code{'zl'},
+\code{'ss'}.
+The possible values of the \code{'status'} item are as follows.
+\begin{description}
+\item[\code{'optimal'.}] In this case the \code{'x'}, \code{'sl'},
+\code{'ss'}, \code{'y'}, \code{'zl'}, \code{'zs'} entries contain
+primal and dual optimal solutions, which approximately satisfy
+\[
+ G_\mathrm{l}x+s_\mathrm{l} = h_\mathrm{l},
+\qquad
+G_\mathrm{s}(x)+S_\mathrm{s} = H_\mathrm{s},
+\qquad
+Ax=b, \qquad
+G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s}) + A^Ty+c = 0
+\]
+and
+\[
+ s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0, \qquad
+ z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0, \qquad
+ s_\mathrm{l}^T z_\mathrm{l} + \Tr(S_\mathrm{s}Z_\mathrm{s}) = 0.
+\]
+
+\item[\code{'primal infeasible'.}]
+The \code{'x'}, \code{'sl'} and \code{'ss'} entries are \None,
+and the \code{'y'}, \code{'zl'}, \code{'zs'} entries provide an
+approximate certificate of infeasibility:
+\[
+G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s}) +A^Ty = 0
+\qquad h_\mathrm{l}^Tz_\mathrm{l} + \Tr(H_\mathrm{s} Z_\mathrm{s})
+ +b^Ty = -1, \qquad
+z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0.
+\]
+
+\item[\code{'dual infeasible'.}] The SDP is dual infeasible.
+The \code{'y'}, \code{'zl'} and \code{'zs'} entries are \None,
+and the \code{'x'}, \code{'sl'}, \code{'ss'} entries contain an
+approximate certificate of dual infeasibility:
+\[
+G_\mathrm{l}x+s_\mathrm{l} = 0, \qquad
+G_\mathrm{s}(x)+S_\mathrm{s} = 0, \qquad
+Ax = 0, \qquad c^Tx = -1, \qquad
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0.
+\]
+
+\item[\code{'unknown'}.] The \code{'x'}, \code{'sl'}, \code{'ss'},
+\code{'y'}, \code{'zl'} and \code{'zs'} entries are \None.
+\end{description}
+\end{funcdesc}
+
+We illustrate the calling sequence with a small example.
+\[
+\begin{array}{ll}
+\mbox{minimize} & x_1 - x_2 + x_3 \\
+\mbox{subject to} &
+ x_1 \left[ \begin{array}{cc} -7 & -11 \\ -11 & 3
+ \end{array}\right] +
+ x_2 \left[ \begin{array}{cc}
+ 7 & -18 \\ -18 & 8 \end{array}\right] +
+ x_3 \left[ \begin{array}{cc}
+ -2 & -8 \\ -8 & 1
+ \end{array}\right] \preceq
+ \left[ \begin{array}{cc}
+ 33 & -9 \\ -9 & 26 \end{array}\right] \\*[1ex]
+& x_1 \left[ \begin{array}{ccc}
+ -21 & -11 & 0 \\ -11 & 10 & 8 \\ 0 & 8 & 5
+ \end{array}\right] +
+ x_2 \left[ \begin{array}{ccc}
+ 0 & 10 & 16 \\
+10 & -10 & -10 \\
+16 & -10 & 3
+ \end{array}\right] +
+ x_3 \left[ \begin{array}{ccc}
+ -5 & 2 & -17 \\
+ 2 & -6 & -7 \\
+ -17 & 8 & 6
+ \end{array}\right]
+\preceq \left[ \begin{array}{ccc}
+ 14 & 9 & 40 \\
+ 9 & 91 & 10 \\
+ 40 & 10 & 15
+\end{array} \right]
+\end{array}
+\]
+\begin{verbatim}
+>>> from cvxopt.base import matrix
+>>> from cvxopt import solvers
+>>> c = matrix([1.,-1.,1.])
+>>> G = [ matrix([[-7., -11., -11., 3.],
+ [ 7., -18., -18., 8.],
+ [-2., -8., -8., 1.]]) ]
+>>> G += [ matrix([[-21., -11., 0., -11., 10., 8., 0., 8., 5.],
+ [ 0., 10., 16., 10., -10., -10., 16., -10., 3.],
+ [ -5., 2., -17., 2., -6., 8., -17., -7., 6.]]) ]
+>>> h = [ matrix([[33., -9.], [-9., 26.]]) ]
+>>> h += [ matrix([[14., 9., 40.], [9., 91., 10.], [40., 10., 15.]]) ]
+>>> sol = solvers.sdp(c, Gs=G, hs=h)
+>>> print sol['x']
+ -3.6775e-01
+ 1.8983e+00
+ -8.8747e-01
+>>> print sol['zs'][0]
+ 3.9613e-03 0.0000e+00
+ -4.3390e-03 4.7526e-03
+>>> print sol['zs'][1]
+ 5.5803e-02 0.0000e+00 0.0000e+00
+ -2.4103e-03 1.0411e-04 0.0000e+00
+ 2.4214e-02 -1.0459e-03 1.0507e-02
+\end{verbatim}
+Note that only the lower triangular parts of the dual variables are
+returned (in the example the returned values of the upper triangular
+elements happen to be zero, but this is not necessarily the case).
+
+Only the entries in \var{Gs} and \var{hs} that correspond to lower
+triangular entries need to be provided, so in the example \var{h} and
+\var{G} can also be defined as follows.
+\begin{verbatim}
+>>> G = [ matrix([[-7., -11., 0., 3.],
+ [ 7., -18., 0., 8.],
+ [-2., -8., 0., 1.]]) ]
+>>> G += [ matrix([[-21., -11., 0., 0., 10., 8., 0., 0., 5.],
+ [ 0., 10., 16., 0., -10., -10., 0., 0., 3.],
+ [ -5., 2., -17., 0., -6., 8., 0., 0., 6.]]) ]
+>>> h = [ matrix([[33., -9.], [0., 26.]]) ]
+>>> h += [ matrix([[14., 9., 40.], [0., 91., 10.], [0., 0., 15.]]) ]
+\end{verbatim}
+
+
+\section{Nonlinear Convex Programming}
+\begin{funcdesc}{cp}{F\optional{, G, h\optional{, A, b}}}
+Solves an optimization problem
+\BEQ \label{e-nlcp}
+ \begin{array}{ll}
+ \mbox{minimize} & f_0(x) \\
+ \mbox{subject to} & f_k(x) \leq 0, \quad k=1,\ldots,m \\
+ & G x \preceq h \\
+ & A x = b,
+ \end{array}
+\EEQ
+with $f=(f_0,\ldots,f_m)$ convex and twice differentiable.
+
+\var{F} is a function that evaluates the objective and nonlinear
+constraint functions. It must handle the following calling sequences.
+
+\begin{itemize}
+\item \code{F()} returns a tuple (\var{m}, \var{x0}), where \var{m} is
+ the number of nonlinear constraints and \var{x0} is a point in the
+ domain of {\it f}. \var{x0} is a dense real matrix of size
+ (\var{n},1).
+
+\item \code{F(x)}, with \var{x} a dense real matrix of size
+ (\var{n},1), returns a tuple (\var{f}, \var{Df}).
+ \var{f} is a dense real matrix of size (\var{m}+1,1), with
+ \code{\var{f}[\var{k}]} equal to {\it f\_k(x)}.
+ (If {\it m} is zero, \var{f} can also be returned as a number.)
+ \var{Df} is a dense or sparse real matrix of size (\var{m}+1,\var{n})
+ with \code{\var{Df}[\var{k},:]} equal to the transpose of the gradient
+ of {\it f\_k} at {\it x}.
+ If \var{x} is not in the domain of {\it f}, \code{F(x)} returns
+ \None\ or a tuple (\None,\None).
+
+\item \code{F(x,z)}, with \var{x} a dense real matrix of size
+ (\var{n},1) and \var{z} a positive dense real matrix of size
+ (\var{m}+1,1) returns a tuple (\var{f}, \var{Df}, \var{H}).
+ \var{f} and \var{Df} are defined as above.
+ \var{H} is a square dense or sparse real matrix of size
+ ({\it n}, {\it n}), whose lower triangular part contains the lower
+ triangular part of
+ \[
+ z_0 \nabla^2f_0(x) + z_1 \nabla^2f_1(x) + \cdots + z_m \nabla^2f_m(x).
+ \]
+ If \var{F} is called with two arguments, it can be assumed that
+ \var{x} is in the domain of {\it f}.
+\end{itemize}
+
+\var{G} and \var{A} are dense or sparse real matrices with \var{n}
+columns. Their default values are matrices of size (0,\var{n}).
+\var{h} and \var{b} are dense real matrices with one column, and the
+same number of rows as \var{G} and \var A, respectively.
+Their default values are matrices of size (0,1).
+
+\function{cp()} returns a dictionary with keys \code{'status'},
+\code{'x'}, \code{'snl'}, \code{'sl'}, \code{'y'}, \code{'znl'},
+\code{'zl'}.
+The possible values of the \code{'status'} key are:
+\begin{description}
+\item[\code{'optimal'}] In this case the
+\code{'x'} entry of the dictionary is the primal optimal solution,
+ the \code{'snl'} and \code{'sl'} entries are the corresponding
+ slacks in the nonlinear and linear inequality constraints, and the
+\code{'znl'}, \code{'zl'} and \code{'y'} entries are the optimal
+values of the dual variables associated with the nonlinear
+inequalities, the linear inequalities, and the linear equality
+constraints. These vectors approximately satisfy the Karush-
+Kuhn-Tucker (KKT) conditions
+\[
+ \nabla f_0(x) + D\tilde f(x)^T z_\mathrm{nl} +
+ G^T z_\mathrm{l} + A^T y = 0, \qquad
+\tilde f(x) + s_\mathrm{nl} = 0, \quad k=1,\ldots,m, \qquad
+ Gx + s_\mathrm{l} = h, \qquad
+ Ax = b,
+\]
+where $\tilde f = (f_1,\ldots, f_m)$,
+\[
+s_\mathrm{nl}\succeq 0, \qquad s_\mathrm{l}\succeq 0, \qquad
+z_\mathrm{nl} \succeq 0, \qquad z_\mathrm{l} \succeq 0, \qquad
+s_\mathrm{nl}^T z_\mathrm{nl} + s_\mathrm{l}^T z_\mathrm{l} = 0.
+\]
+
+\item[\code{'unknown'}] This indicates that the algorithm reached
+the maximum number of iterations before a solution was found.
+The \code{'x'}, \code{'snl'}, \code{'sl'},
+\code{'y'}, \code{'znl'} and \code{'zl'} entries are \None.
+\end{description}
+
+%\function{cp()} requires that the problem is solvable and that the
+%Karush-Kuhn-Tucker matrix
+%\[
+%\left[\begin{array}{cccc}
+%\sum_{k=0}^m z_k \nabla^2 f_k(x) & D\tilde f(x)^T & G^T & A^T\\
+%D\tilde f(x) & -\diag(d_1) & 0 & 0 \\
+% G & 0 & -\diag(d_2) & 0 \\
+% A & 0 & 0 & 0 \end{array}\right]
+%%\]
+%is nonsingular for all {\it x}, all nonnegative {\it z}, and all
+%positive {\it d\_1}, {\it d\_2}.
+\end{funcdesc}
+
+
+\begin{description}
+\item[Example: equality constrained analytic centering]
+
+The equality constrained analytic centering problem is defined as
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & -\sum_{i=1}^m \log x_i \\
+ \mbox{subject to} & Ax = b.
+ \end{array}
+\]
+The function \function{acent()} defined below solves the problem,
+assumping it is solvable.
+
+\begin{verbatim}
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, log
+
+def acent(A, b):
+ m, n = A.size
+ def F(x=None, z=None):
+ if x is None: return 0, matrix(1.0, (n,1))
+ if min(x) <= 0.0: return None
+ f = -sum(log(x))
+ Df = -(x**-1).T
+ if z is None: return f, Df
+ H = z[0] * spmatrix(x**-2, range(n), range(n))
+ return f, Df, H
+ return solvers.cp(F, A=A, b=b)['x']
+\end{verbatim}
+
+\item[Example: robust least-squares]
+
+The function \function{robls()} defined below solves the unconstrained
+problem
+\[
+\begin{array}{ll}
+\mbox{minimize} & \sum_{k=1}^m \phi((Ax-b)_k),
+\end{array} \qquad \mbox{where} \quad A \in\reals^{m\times n}, \quad
+\phi(u) = \sqrt{\rho + u^2}.
+\]
+
+\begin{verbatim}
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, sqrt, div
+
+def robls(A, b, rho):
+ m, n = A.size
+ def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (n,1))
+ y = A*x-b
+ w = sqrt(rho + y**2)
+ f = sum(w)
+ Df = div(y, w).T * A
+ if z is None: return f, Df
+ H = A.T * spmatrix(z[0]*rho*(w**-3), range(m), range(m)) * A
+ return f, Df, H
+ return solvers.cp(F)['x']
+\end{verbatim}
+
+\item[Example: floor planning]
+
+This example is the floor planning problem of section 8.8.2 in the book
+\citetitle[http://www.stanford.edu/\~{}boyd/cvxbook]{Convex Optimization}:
+\[
+\begin{array}{ll}
+ \mbox{minimize} & W + H \\
+ \mbox{subject to} & A_{\mathrm{min}, k}/h_k - w_k \leq 0,
+ \quad k=1,\ldots, 5 \\
+ & x_1 \geq 0, \quad x_2 \geq 0, \quad x_4 \geq 0 \\
+ & x_1 + w_1 + \rho \leq x_3, \quad x_2 + w_2 + \rho \leq x_3, \quad
+ x_3 + w_3 + \rho \leq x_5, \quad x_4 + w_4 + \rho \leq x_5, \quad
+ x_5 + w_5 \leq W \\
+ & y_2 \geq 0, \quad y_3 \geq 0, \quad y_5 \geq 0 \\
+ & y_2 + h_2 + \rho \leq y_1, \quad y_1 + h_1 + \rho \leq y_4, \quad
+ y_3 + h_3 + \rho \leq y_4, \quad y_4 + h_4 \leq H, \quad
+ y_5 + h_5 \leq H \\
+ & h_k/\gamma \leq w_k \leq \gamma h_k, \quad k=1,\ldots,5.
+\end{array}
+\]
+This problem has 22 variables
+\[
+W, \qquad H, \qquad x\in\reals^5, \qquad y\in\reals^5, \qquad
+w\in\reals^5, \qquad h\in\reals^5,
+\]
+5 nonlinear inequality constraints, and 26 linear inequality
+constraints. The code belows defines a function
+\function{floorplan()} that solves the problem by calling
+\function{cp()}, then applies it to 4 instances, and creates
+a figure.
+
+\begin{verbatim}
+import pylab
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, mul, div
+
+def floorplan(Amin):
+
+ # minimize W+H
+ # subject to Amink / hk <= wk, k = 1,..., 5
+ # x1 >= 0, x2 >= 0, x4 >= 0
+ # x1 + w1 + rho <= x3
+ # x2 + w2 + rho <= x3
+ # x3 + w3 + rho <= x5
+ # x4 + w4 + rho <= x5
+ # x5 + w5 <= W
+ # y2 >= 0, y3 >= 0, y5 >= 0
+ # y2 + h2 + rho <= y1
+ # y1 + h1 + rho <= y4
+ # y3 + h3 + rho <= y4
+ # y4 + h4 <= H
+ # y5 + h5 <= H
+ # hk/gamma <= wk <= gamma*hk, k = 1, ..., 5
+ #
+ # 22 Variables W, H, x (5), y (5), w (5), h (5).
+ #
+ # W, H: scalars; bounding box width and height
+ # x, y: 5-vectors; coordinates of bottom left corners of blocks
+ # w, h: 5-vectors; widths and heigths of the 5 blocks
+
+ rho, gamma = 1.0, 5.0 # min spacing, min aspect ratio
+
+ # The objective is to minimize W + H. There are five nonlinear
+ # constraints
+ #
+ # -wk + Amink / hk <= 0, k = 1, ..., 5
+
+ def F(x=None, z=None):
+ if x is None: return 5, matrix(17*[0.0] + 5*[1.0])
+ if min(x[17:]) <= 0.0: return None
+ f = matrix(0.0, (6,1))
+ f[0] = x[0] + x[1]
+ f[1:] = -x[12:17] + div(Amin, x[17:])
+ Df = matrix(0.0, (6,22))
+ Df[0, [0,1]] = 1.0
+ Df[1:,12:17] = spmatrix(-1.0, range(5), range(5))
+ Df[1:,17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
+ if z is None: return f, Df
+ H = spmatrix( 2.0* mul(z[1:], div(Amin, x[17::]**3)), range(17,22), range(17,22) )
+ return f, Df, H
+
+ G = matrix(0.0, (26,22))
+ h = matrix(0.0, (26,1))
+ G[0,2] = -1.0 # -x1 <= 0
+ G[1,3] = -1.0 # -x2 <= 0
+ G[2,5] = -1.0 # -x4 <= 0
+ G[3, [2, 4, 12]], h[3] = [1.0, -1.0, 1.0], -rho # x1 - x3 + w1 <= -rho
+ G[4, [3, 4, 13]], h[4] = [1.0, -1.0, 1.0], -rho # x2 - x3 + w2 <= -rho
+ G[5, [4, 6, 14]], h[5] = [1.0, -1.0, 1.0], -rho # x3 - x5 + w3 <= -rho
+ G[6, [5, 6, 15]], h[6] = [1.0, -1.0, 1.0], -rho # x4 - x5 + w4 <= -rho
+ G[7, [0, 6, 16]] = -1.0, 1.0, 1.0 # -W + x5 + w5 <= 0
+ G[8,8] = -1.0 # -y2 <= 0
+ G[9,9] = -1.0 # -y3 <= 0
+ G[10,11] = -1.0 # -y5 <= 0
+ G[11, [7, 8, 18]], h[11] = [-1.0, 1.0, 1.0], -rho # -y1 + y2 + h2 <= -rho
+ G[12, [7, 10, 17]], h[12] = [1.0, -1.0, 1.0], -rho # y1 - y4 + h1 <= -rho
+ G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho # y3 - y4 + h3 <= -rho
+ G[14, [1, 10, 20]] = -1.0, 1.0, 1.0 # -H + y4 + h4 <= 0
+ G[15, [1, 11, 21]] = -1.0, 1.0, 1.0 # -H + y5 + h5 <= 0
+ G[16, [12, 17]] = -1.0, 1.0/gamma # -w1 + h1/gamma <= 0
+ G[17, [12, 17]] = 1.0, -gamma # w1 - gamma * h1 <= 0
+ G[18, [13, 18]] = -1.0, 1.0/gamma # -w2 + h2/gamma <= 0
+ G[19, [13, 18]] = 1.0, -gamma # w2 - gamma * h2 <= 0
+ G[20, [14, 18]] = -1.0, 1.0/gamma # -w3 + h3/gamma <= 0
+ G[21, [14, 19]] = 1.0, -gamma # w3 - gamma * h3 <= 0
+ G[22, [15, 19]] = -1.0, 1.0/gamma # -w4 + h4/gamma <= 0
+ G[23, [15, 20]] = 1.0, -gamma # w4 - gamma * h4 <= 0
+ G[24, [16, 21]] = -1.0, 1.0/gamma # -w5 + h5/gamma <= 0
+ G[25, [16, 21]] = 1.0, -gamma # w5 - gamma * h5 <= 0.0
+
+ # solve and return W, H, x, y, w, h
+ sol = solvers.cp(F, G, h)
+ return sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], sol['x'][12:17], sol['x'][17:]
+
+pylab.figure(facecolor='w')
+pylab.subplot(221)
+Amin = matrix([100., 100., 100., 100., 100.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]], '#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(222)
+Amin = matrix([20., 50., 80., 150., 200.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]], '#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(223)
+Amin = matrix([180., 80., 80., 80., 80.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]],'#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(224)
+Amin = matrix([20., 150., 20., 200., 110.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]],'#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.show()
+\end{verbatim}
+
+\begin{center}
+\includegraphics[width=15cm]{figures/floorplan.eps}
+\end{center}
+\end{description}
+
+\section{Exploiting Structure in LPs and SDPs}
+The solvers \function{lp()} and \function{sdp()} are interfaces to
+a common function \function{conelp()}, which can also be called
+directly. When calling \function{conelp()}, the user must provide
+functions for evaluating the constraint functions and for
+solving the linear equations (KKT equations) that are solved in
+each iteration of the algorithm.
+This is useful for LPs and SDPs that possess some interesting
+structure that makes it possible to solve the KKT equations fast.
+
+\begin{funcdesc}{conelp}{c, kktsolver\optional{, Gl, hl\optional{,
+Gs, hs\optional{, A, b\optional{, primalstart\optional{, dualstart}}}}}}
+Solves the pair of primal and dual SDPs~(\ref{e-sdp}).
+The arguments \var{c}, \var{hl}, \var{hs}, \var{b},
+\var{primalstart}, \var{dualstart} have the same meaning as in
+\function{sdp()}.
+The arguments \var{kktsolver}, \var{Gl}, \var{Gs}, \var{A} are
+functions that must handle the following calling sequences.
+
+\begin{itemize}
+\item \function{kktsolver}(\var{d}, \var{R}) with \var{d} a positive
+dense real matrix of size ({\it ml},{\it 1}), and
+\var{R} a list of {\it N} square dense real matrices
+\code{\var{R}[k]} of order {\it m\_k}, returns a function for
+solving the equation
+\BEAS
+ A^T u_y + G_\mathrm{l}^T u_{z_\mathrm{l}} +
+ G_\mathrm{s}^T(u_{z_\mathrm{s}}) & = & b_x \\
+ A u_x & = & b_y \\
+G_\mathrm{l}u_x - \diag(d)^{-2} u_{z_\mathrm{l}} & = &
+ b_{z_\mathrm{l}} \\
+G_\mathrm{s}(u_x) - R^{-T} R^{-1} u_{z_\mathrm{s}} R^{-T} R^{-1}
+ & = & b_{z_\mathrm{s}}.
+\EEAS
+The function created by \samp{f = kktsolver(d, R)} will be
+called as \samp{f(bx, by, bzl, bzs)}.
+On entry, \var{bx}, \var{by}, \var{bzl} and \var{bzs} contain the
+righthand side. On exit, they should contain the solution of the KKT
+system, with {\it uzl} and {\it uzs} scaled:
+\[
+ b_x := u_x, \qquad
+ b_y := u_y, \qquad
+ b_{z_\mathrm{l}} := \diag(d)^{-1} u_{z_\mathrm{l}}, \qquad
+ b_{z_\mathrm{s}} := R^{-1} u_{z_\mathrm{s}} R^{-T}.
+\]
+
+\item\function{Gl}(\var{x}, \var{y}\optional{,
+\var{alpha}=1.0\optional{, \var{beta}=0.0\optional{,
+\var{trans}=\code{'N'}}}}) evaluates the matrix-vector products
+\[
+y := \alpha G_\mathrm{l}x + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha G_\mathrm{l}^T x + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\]
+
+\item \function{Gs}(\var{x}, \var{y}\optional{,
+\var{alpha}=1.0\optional{, \var{beta}=0.0\optional{,
+\var{trans}=\code{'N'}}}})
+evaluates the linear mappings
+\[
+y := \alpha G_\mathrm{s}(x) + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha G_\mathrm{s}^T(x) + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\]
+
+\item \function{A}(\var{x}, \var{y}\optional{,
+\var{alpha}=1.0\optional{, \var{beta}=0.0\optional{,
+\var{trans}=\code{'N'}}}})
+evaluates the matrix vector products
+\[
+y := \alpha Ax + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha A^Tx + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\]
+\end{itemize}
+\end{funcdesc}
+
+\begin{description}
+\item[Example: 1-norm approximation]
+
+The optimization problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|Pu-q\|_1
+ \end{array}
+\]
+can be formulated as an LP
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \ones^T v \\
+ \mbox{subject to} & -v \preceq Pu - q \preceq v.
+ \end{array}
+\]
+By exploiting the structure in the inequalities, the cost of
+an iteration of an interior-point method can be reduced
+to the cost of least-squares problem of the same dimensions.
+(See section 11.8.2 in the book
+\citetitle[http://www.ee.ucla.edu/\~{}vandenbe/cvxbook]{Convex Optimization}.)
+The code belows taks advantage of this fact.
+
+\begin{verbatim}
+from cvxopt import base, blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, mul, div
+
+def l1(P, q):
+ """
+
+ Returns the solution u, w of the l1 approximation problem
+
+ (primal) minimize ||P*u - q||_1
+
+ (dual) maximize q'*w
+ subject to P'*w = 0
+ ||w||_infty <= 1.
+ """
+
+ m, n = P.size
+
+ # Solve equivalent LP
+ #
+ # minimize [0; 1]' * [u; v]
+ # subject to [P, -I; -P, -I] * [u; v] <= [q; -q]
+ #
+ # maximize -[q; -q]' * z
+ # subject to [P', -P']*z = 0
+ # [-I, -I]*z + 1 = 0
+ # z >= 0
+
+ c = matrix(n*[0.0] + m*[1.0])
+ h = matrix([q, -q])
+
+ def Fi(x, y, alpha=1.0, beta=0.0, trans='N'):
+ if trans=='N':
+ # y := alpha * [P, -I; -P, -I] * x + beta*y
+ u = P*x[:n]
+ y[:m] = alpha * ( u - x[n:]) + beta*y[:m]
+ y[m:] = alpha * (-u - x[n:]) + beta*y[m:]
+
+ else:
+ # y := alpha * [P', -P'; -I, -I] * x + beta*y
+ y[:n] = alpha * P.T * (x[:m] - x[m:]) + beta*y[:n]
+ y[n:] = -alpha * (x[:m] + x[m:]) + beta*y[n:]
+
+
+ def kktsolver(d, R):
+
+ # Returns a function f(x,y,zl,zs) that solves
+ #
+ # [ 0 0 P' -P' ] [ x[:n] ] [ bx[:n] ]
+ # [ 0 0 -I -I ] [ x[n:] ] [ bx[n:] ]
+ # [ P -I -D1^{-1} 0 ] [ zl[:m]] = [ bzl[:m] ]
+ # [-P -I 0 -D2^{-1} ] [ zl[m:]] [ bzl[m:] ]
+ #
+ # where D1 = diag(d[:m])^2, D2 = diag(d[m:])^2.
+ #
+ # On entry bx, bzl are stored in x, zl.
+ # On exit x, zl contain the solution, with zl scaled: zl./d is
+ # returned instead of zl.
+
+ # Factor A = 4*P'*D*P where D = d1.*d2 ./(d1+d2) and
+ # d1 = d[:m].^2, d2 = d[m:].^2.
+
+ d1, d2 = d[:m]**2, d[m:]**2
+ D = div( mul(d1,d2), d1+d2 )
+ A = P.T * spmatrix(4*D, range(m), range(m)) * P
+ lapack.potrf(A)
+
+ def f(x, y, zl, zs):
+
+ # Solve for x[:n]:
+ #
+ # A*x[:n] = bx[:n] + P' * ( ((D1-D2)*(D1+D2)^{-1})*bx[n:]
+ # + (2*D1*D2*(D1+D2)^{-1}) * (bzl[:m] - bzl[m:]) ).
+ x[:n] += P.T * ( mul(div(d1-d2, d1+d2), x[n:]) + mul(2*D, zl[:m]-zl[m:]) )
+ lapack.potrs(A, x)
+
+ # x[n:] := (D1+D2)^{-1} * (bx[n:] - D1*bzl[:m] - D2*bzl[m:] + (D1-D2)*P*x[:n])
+ u = P*x[:n]
+ x[n:] = div(x[n:] - mul(d1, zl[:m]) - mul(d2, zl[m:]) + mul(d1-d2, u), d1+d2)
+
+ # z[:m] := d1[:m] .* ( P*x[:n] - x[n:] - bzl[:m])
+ # z[m:] := d2[m:] .* (-P*x[:n] - x[n:] - bzl[m:])
+ zl[:m] = mul(d[:m], u-x[n:]-zl[:m])
+ zl[m:] = mul(d[m:], -u-x[n:]-zl[m:])
+
+ return f
+
+ sol = solvers.conelp(c, kktsolver, Gl=Fi, hl=h)
+ return sol['x'][:n], sol['zl'][m:] - sol['zl'][:m]
+\end{verbatim}
+
+\item[Example: SDP with diagonal linear term]
+
+The SDP
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \ones^T x \\
+ \mbox{subject to} & W + \diag(x) \succeq 0
+ \end{array}
+\]
+can be solved efficiently by exploiting properties of the diag operator.
+
+\begin{verbatim}
+from cvxopt import base, blas, lapack, solvers
+from cvxopt.base import matrix
+
+def mcsdp(w):
+ """
+ Returns solution x, z to
+
+ (primal) minimize sum(x)
+ subject to w + diag(x) >= 0
+
+ (dual) maximize -tr(w*z)
+ subject to diag(z) = 1
+ z >= 0.
+ """
+
+ n = w.size[0]
+
+ def Fs(x, y, alpha=1.0, beta=0.0, trans='N'):
+ """
+ y := alpha*(-diag(x)) + beta*y.
+ """
+ if trans=='N':
+ # x is a vector; y[0] is a matrix.
+ y[0] *= beta
+ y[0][::n+1] -= alpha * x
+ else:
+ # x[0] is a matrix; y is a vector.
+ y *= beta
+ y -= alpha * x[::n+1]
+
+
+ def cngrnc(r, x, alpha=1.0):
+ """
+ Congruence transformation
+
+ x := alpha * r'*x*r.
+
+ r and x are square 'd' matrices.
+ """
+
+ # Scale diagonal of x by 1/2.
+ x[::n+1] *= 0.5
+
+ # a := tril(x)*r
+ a = +r
+ blas.trmm(x, a, side='L')
+
+ # x := alpha*(a*r' + r*a')
+ blas.syr2k(r, a, x, trans='T', alpha=alpha)
+
+
+ def kktsolver(d, r):
+
+ # t = r*r' as a nonsymmetric matrix.
+ t = matrix(0.0, (n,n))
+ blas.gemm(r[0], r[0], t, transB='T')
+
+ # Cholesky factorization of tsq = t.*t.
+ tsq = t**2
+ lapack.potrf(tsq)
+
+ def f(x, y, zl, zs):
+ """
+ Solve
+ -diag(zs) = bx
+ -diag(x) - inv(r*r')*zs*inv(r*r') = bs.
+
+ On entry, x and zs contain bx and bs.
+ On exit, they contain the solution, with zs scaled
+ (inv(r)'*zs*inv(r) is returned instead of zs).
+
+ We solve
+
+ ((r*r') .* (r*r')) * x = bx - diag(t*bs*t)
+
+ and take zs = -r' * (diag(x) + bs) * r.
+ """
+
+ # tbst := t * zs * t = t * bs * t
+ tbst = +zs[0]
+ cngrnc(t, tbst)
+
+ # x := x - diag(tbst) = bx - diag(r*r' * bs * r*r')
+ x -= tbst[::n+1]
+
+ # x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
+ lapack.potrs(tsq, x)
+
+ # zs := zs + diag(x) = bs + diag(x)
+ zs[0][::n+1] += x
+
+ # zs := -r' * zs * r = -r' * (diag(x) + bs) * r
+ cngrnc(r[0], zs[0], alpha=-1.0)
+
+ return f
+
+ c = matrix(1.0, (n,1))
+ sol = solvers.conelp(c, kktsolver, Gs=Fs, hs=[w])
+ return sol['x'], sol['zs'][0]
+\end{verbatim}
+\end{description}
+
+
+\section{Exploiting Structure in Nonlinear Convex Programs}
+The solvers \function{gp()}, \function{gp()} and \function{cp()} are
+interfaces to \function{nlcp()}, which can also be called directly
+but requires user-provided functions for evaluating the constraint
+and for solving the KKT equations.
+
+\begin{funcdesc}{nlcp}{kktsolver, F\optional{, G, h\optional{, A, b}}}
+Solves the nonlinear convex optimization problem~(\ref{e-nlcp}).
+
+The meaning of the arguments \var{h} and \var{b} is the same
+as for \function{cp()}.
+The arguments \var{kktsolver}, \var{F}, \var{G} and \var{A} are
+functions that must handle the following calling sequences.
+\begin{itemize}
+\item \function{kktsolver}(\var{x}, \var{z}, \var{dnl}, \var{dl}),
+returns a function for solving KKT systems
+\BEAS
+ \sum_{k=0}^m z_k \nabla^2 f_k(x)u_x + A^T u_y +
+ D \tilde f(x)^T u_{z_\mathrm{nl}} +
+ G_\mathrm{l}^T u_{z_\mathrm{l}} & = & b_x \\
+ A x & = & b_y \\
+ D\tilde f(x) x - \diag(d_\mathrm{nl})^{-2} z_\mathrm{nl} & = &
+ b_{z_\mathrm{nl}} \\
+ G_\mathrm{l}x - \diag(d_\mathrm{l})^{-2} z_\mathrm{l} & = &
+ b_{z_\mathrm{l}}
+\EEAS
+where $\tilde f = (f_1, \ldots, f_m)$.
+The arguments are single-column real dense matrices. \var{x} is in the
+domain of the objective and constraint functions. \var{z}, \var{dnl}
+and \var{dl} are positive vectors.
+
+The function \var{f} created by
+\samp{f = kktsolver(bx, by, bznl, bzl)} will be
+called as \samp{f(bx, by, bznl, bzl)}.
+On entry, the arguments contain the righthand sides. On exit, they
+should be replaced by the solution.
+
+\item Called with no arguments, \code{\function{F}()} returns a tuple
+(\var{m}, \var{x0}), where \var{m} is the number of nonlinear
+inequality constraints) and \var{x0} is a point in the domain
+of {\it f}).
+
+Called with one argument, \function{F(\var{x})} returns a tuple
+(\var{f}, \var{Df}). \var{f} is a dense matrix of size ({\it m}+1,1)
+with the function values of the objective function and the
+nonlinear constraint functions at \var{x}.
+\var{Df} is a dense or sparse real matrix of size (\var{m}+1,\var{n})
+with \code{\var{Df}[\var{k},:]} equal to the transpose of the gradient
+of {\it f\_k} at {\it x}.
+Alternatively, \var{Df} can be given as a function. In that case
+the function call \function{Df}(\var{u},\var{v}),
+where \var{u} and \var{v} are dense column vectors, should evaluate
+\[
+ v := \sum_{k=0}^m u_k \nabla f_k(x) + v.
+\]
+
+If \var{x} is not in the domain of {\it f}, \function{F}(\var{x})
+returns \None\ or (\None,\None).
+
+\item
+\function{G}(\var{x}, \var{y}\optional{,
+\var{alpha}=1.0\optional{, \var{beta}=0.0\optional{,
+\var{trans}=\code{'N'}}}}) evaluates the matrix-vector products
+\[
+y := \alpha G x + \beta y \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha G^T x + \beta y \quad (\mathrm{trans} = \mathrm{'T'}).
+\]
+Alternatively, \var{G} can be specified as a real sparse or dense
+matrix.
+
+\item \function{A}(\var{x}, \var{y}\optional{,
+\var{alpha}=1.0\optional{, \var{beta}=0.0\optional{,
+\var{trans}=\code{'N'}}}}) evaluates the matrix vector products
+\[
+y := \alpha Ax + \beta y \quad
+ (\mathrm{trans} = \mathrm{'N'}), \qquad
+y := \alpha A^Tx + \beta y \quad
+ (\mathrm{trans} = \mathrm{'T'}).
+\]
+Alternatively, \var{A} can be specified as a real sparse or dense
+matrix.
+\end{itemize}
+\end{funcdesc}
+
+As an example, we consider the 1-norm regularized least-squares problem
+\[
+\begin{array}{ll}
+\mbox{minimize} & \|Ax - y\|_2^2 + \|x\|_1
+\end{array}
+\]
+with variable {\it x}. The problem is equivalent to the quadratic
+program
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & \|Ax - y\|_2^2 + \ones^T u \\
+ \mbox{subject to} & -u \preceq x \preceq u
+ \end{array}
+\]
+with variables {\it x} and {\it u}. The implementation below is
+efficient when {\it A} has many more columns than rows.
+
+\begin{verbatim}
+from cvxopt.base import matrix, spmatrix, mul, div
+from cvxopt import blas, lapack, solvers
+
+m, n = A.size
+def F(x=None):
+ """
+ Function and gradient evaluation of
+
+ f = || A*x[:n] - y ||_2^2 + sum(x[n:])
+ """
+
+ nvars = 2*n
+ if x is None: return 0, matrix(0.0, (nvars,1))
+ r = A*x[:n] - y
+ f = blas.nrm2(r)**2 + sum(x[n:])
+ gradf = matrix(1.0, (1,2*n))
+ blas.gemv(A, r, gradf, alpha=2.0, trans='T')
+ return f, +gradf
+
+
+def G(u, v, alpha=1.0, beta=0.0, trans='N'):
+ """
+ v := alpha*[I, -I; -I, -I] * u + beta * v (trans = 'N' or 'T')
+ """
+
+ v *= beta
+ v[:n] += alpha*(u[:n] - u[n:])
+ v[n:] += alpha*(-u[:n] - u[n:])
+
+h = matrix(0.0, (2*n,1))
+
+
+# Customized solver for the KKT system
+#
+# [ 2.0*z[0]*A'*A 0 I -I ] [x[:n] ] [bx[:n] ]
+# [ 0 0 -I -I ] [x[n:] ] = [bx[n:] ].
+# [ I -I -D1^-1 0 ] [zl[:n]] [bzl[:n]]
+# [ -I -I 0 -D2^-1 ] [zl[n:]] [bzl[n:]]
+#
+#
+# We first eliminate zl and x[n:]:
+#
+# ( 2*z[0]*A'*A + 4*D1*D2*(D1+D2)^-1 ) * x[:n] = bx[:n] - (D2-D1)*(D1+D2)^-1 * bx[n:]
+# + D1 * ( I + (D2-D1)*(D1+D2)^-1 ) * bzl[:n] - D2 * ( I - (D2-D1)*(D1+D2)^-1 ) * bzl[n:]
+#
+# x[n:] = (D1+D2)^-1 * ( bx[n:] - D1*bzl[:n] - D2*bzl[n:] ) - (D2-D1)*(D1+D2)^-1 * x[:n]
+# zl[:n] = D1 * ( x[:n] - x[n:] - bzl[:n] )
+# zl[n:] = D2 * (-x[:n] - x[n:] - bzl[n:] ).
+#
+# The first equation has the form
+#
+# (z[0]*A'*A + D)*x[:n] = rhs
+#
+# and is equivalent to
+#
+# [ D A' ] [ x:n] ] = [ rhs ]
+# [ A -1/z[0]*I ] [ v ] [ 0 ].
+#
+# It can be solved as
+#
+# ( A*D^-1*A' + 1/z[0]*I ) * v = A * D^-1 * rhs
+# x[:n] = D^-1 * ( rhs - A'*v ).
+
+S = matrix(0.0, (m,m))
+Asc = matrix(0.0, (m,n))
+v = matrix(0.0, (m,1))
+def kktsolver(x, z, dnl, dl):
+
+ # Factor
+ #
+ # S = A*D^-1*A' + 1/z[0]*I
+ #
+ # where D = 2*D1*D2*(D1+D2)^-1, D1 = dl[:n]**2, D2 = dl[n:]**2.
+
+ d1, d2 = dl[:n]**2, dl[n:]**2 # d1 = diag(D1), d2 = diag(D2)
+ # ds is square root of diagonal of D
+ ds = sqrt(2.0) * div( mul(dl[:n], dl[n:]), sqrt(d1+d2) )
+ d3 = div(d2 - d1, d1 + d2)
+
+ # Asc = A*diag(d)^-1/2
+ Asc = A * spmatrix( ds**-1, range(n), range(n))
+
+ # S = 1/z[0]*I + A * D^-1 * A'
+ blas.syrk(Asc, S)
+ S[::m+1] += 1.0 / z[0]
+ lapack.potrf(S)
+
+ def g(x, y, znl, zl):
+
+ x[:n] = 0.5 * ( x[:n] - mul(d3, x[n:]) + mul(d1, zl[:n] + mul(d3, zl[:n])) - mul(d2, zl[n:] - mul(d3, zl[n:])) )
+ x[:n] = div( x[:n], ds)
+
+ # Solve
+ #
+ # S * v = 0.5 * A * D^-1 * ( bx[:n] - (D2-D1)*(D1+D2)^-1 * bx[n:]
+ # + D1 * ( I + (D2-D1)*(D1+D2)^-1 ) * bzl[:n] - D2 * ( I - (D2-D1)*(D1+D2)^-1 ) * bzl[n:] )
+
+ blas.gemv(Asc, x, v)
+ lapack.potrs(S, v)
+
+ # x[:n] = D^-1 * ( rhs - A'*v ).
+ blas.gemv(Asc, v, x, alpha=-1.0, beta=1.0, trans='T')
+ x[:n] = div(x[:n], ds)
+
+ # x[n:] = (D1+D2)^-1 * ( bx[n:] - D1*bzl[:n] - D2*bzl[n:] ) - (D2-D1)*(D1+D2)^-1 * x[:n]
+ x[n:] = div( x[n:] - mul(d1, zl[:n]) - mul(d2, zl[n:]), d1+d2 ) - mul( d3, x[:n] )
+
+ # zl[:n] = D1 * ( x[:n] - x[n:] - bzl[:n] )
+ # zl[n:] = D2 * ( -x[:n] - x[n:] - bzl[n:] ).
+ zl[:n] = mul( d1, x[:n] - x[n:] - zl[:n] )
+ zl[n:] = mul( d2, -x[:n] - x[n:] - zl[n:] )
+
+ return g
+
+x = solvers.nlcp(kktsolver, F, G, h)['x'][:n]
+\end{verbatim}
+
+\section{Optional Solvers} \label{s-external}
+CVXOPT includes optional interfaces to several other optimization
+libraries.
+
+\begin{description}
+\item[GLPK] \function{lp()} with the \code{solver='glpk'} option uses
+the the simplex algorithm in
+\ulink{GLPK (GNU Linear Programming Kit)}{http://www.gnu.org/software/glpk/glpk.html}.
+
+\item[MOSEK] \function{lp()} and \function{qp()} with the
+\code{solver='mosek'} option call routines from
+\ulink{MOSEK}{http://www.mosek.com} version 4.
+
+\item[DSDP] \function{sdp()} with the \code{solver='dsdp'} option uses
+the
+\ulink{DSDP5.8}{http://www-unix.mcs.anl.gov/DSDP} solver.
+\end{description}
+GLPK, MOSEK and DSDP are not included in the CVXOPT distribution and
+need to be installed separately.
+
+\section{Algorithm Parameters} \label{s-parameters}
+In this section we list some algorithm control parameters that can
+be modified without editing the source code.
+These control parameters are accessible via the dictionary
+\member{solvers.options}. By default the dictionary
+is empty and the default values of the parameters are used.
+
+One can change the parameters in the \textbf{default} solvers by
+adding entries with the following key values.
+\begin{description}
+\item[\code{'show\_progress'}]
+\True\ or \False; turns the output to the screen on or off
+(default: \True).
+\item[\code{'maxiters'}] maximum number of iterations (default: 100).
+\item[\code{'abstol'}] absolute accuracy (default: \code{1e-7}).
+\item[\code{'reltol'}] relative accuracy (default: \code{1e-7}).
+\item[\code{'feastol'}] tolerance for feasibility conditions (default:
+\code{1e-7}).
+\item[\code{'refinement'}] \True\ or \False. If \True,
+one step of iterative refinement is applied after solving KKT equations
+in \function{conelp()}, \function{lp()}, and \function{sdp()}
+(default: \True).
+\end{description}
+For example the command
+\begin{verbatim}
+>>> from cvxopt import solvers
+>>> solvers.options['show_progress'] = False
+\end{verbatim}
+turns off the screen output during calls to the solvers.
+The tolerances \var{abstol}, \var{reltol} and \var{feastol} have the
+following meaning. \function{conelp()} terminates with
+status \code{'optimal'}, if
+\[
+s_\mathrm{l} \succeq 0, \qquad S_\mathrm{s} \succeq 0,
+\qquad
+ \frac{\|G_\mathrm{l}x+s_\mathrm{l}-h_\mathrm{l}\|_2}
+ {\max\{1,\|h_\mathrm{l}\|_2\}} \leq \epsilon_\mathrm{feas},
+\qquad
+\frac{\|G_\mathrm{s}(x)+S_\mathrm{s}-H_\mathrm{s}\|_F}
+{\max\{1,\|H_\mathrm{s}\|_F\}} \leq \epsilon_\mathrm{feas},
+\qquad
+\frac{\|Ax-b\|_2}{\max\{1,\|b\|_2\}} \leq \epsilon_\mathrm{feas},
+\]
+\[
+z_\mathrm{l} \succeq 0, \qquad Z_\mathrm{s} \succeq 0, \qquad
+\frac{\|G_\mathrm{l}^Tz_\mathrm{l}+
+G_\mathrm{s}^T(Z_\mathrm{s}) + A^Ty+c\|_2}{\max\{1,\|c\|_2\}}
+\leq \epsilon_\mathrm{feas},
+\]
+and
+\[
+ s_\mathrm{l}^T z_\mathrm{l} + \Tr(S_\mathrm{s}Z_\mathrm{s}) \leq
+ \epsilon_\mathrm{abs} \qquad \mbox{or} \qquad
+\left( \min\left\{c^Tx,
+ h_\mathrm{l}^T z_\mathrm{l} + \Tr(H_\mathrm{s} Z_\mathrm{s})
+ + b^Ty \right\} < 0, \quad
+ \frac{s_\mathrm{l}^Tz_\mathrm{l} + \Tr(S_\mathrm{s}Z_\mathrm{s})}
+ {-\min\{c^Tx, h_\mathrm{l}^Tz_\mathrm{l} +
+ \Tr(H_\mathrm{s} Z_\mathrm{s}) + b^T y\}} \leq \epsilon_\mathrm{rel}
+\right).
+\]
+It returns with status \code{'primal infeasible'} if
+\[
+z_\mathrm{l} \succeq 0, \qquad
+Z_\mathrm{s} \succeq 0, \qquad
+\qquad \|G_\mathrm{l}^Tz_\mathrm{l} + G_\mathrm{s}^T(Z_\mathrm{s})
+ +A^Ty\|_2 \leq \epsilon_\mathrm{feas},
+ \qquad h_\mathrm{l}^Tz_\mathrm{l} + \Tr(H_\mathrm{s} Z_\mathrm{s})
+ +b^Ty = -1.
+\]
+It returns with status \code{'dual infeasible'} if
+\[
+s_\mathrm{l} \succeq 0, \qquad
+S_\mathrm{s} \succeq 0, \qquad
+\qquad
+\|G_\mathrm{l}x+s_\mathrm{l}\|_2 \leq \epsilon_\mathrm{feas}, \qquad
+\|G_\mathrm{s}(x)+S_\mathrm{s}\|_F \leq \epsilon_\mathrm{feas}, \qquad
+\|Ax\|_2 \leq \epsilon_\mathrm{feas}, \qquad
+c^Tx = -1.
+\]
+The functions \function{lp()} and \function{sdp()} call
+\function{conelp()} and hence use the same stopping criteria.
+
+\function{nlcp()} returns with status \code{'optimal'} if
+\[
+\frac{\| \nabla f_0(x) + D\tilde f(x)^Tz_\mathrm{nl} +
+ G^Tz_\mathrm{l} + A^T y \|_2 }
+{\max\{ 1,
+\| \nabla f_0(x_0) + D\tilde f(x_0)^T\ones + G^T\ones \|_2 \}}
+\leq \epsilon_\mathrm{feas}, \qquad
+\frac{\| ( \tilde f(x) + s_{\mathrm{nl}}, Gx + s_\mathrm{l} - h,
+ Ax-b ) \|_2}
+{\max\{1, \| ( \tilde f(x_0) + \ones,
+Gx_0 + \ones-h, Ax_0-b) \|_2 \}} \leq \epsilon_\mathrm{feas}
+\]
+where {\it x0} is the point returned by \code{F()}, and
+\[
+\mathrm{gap} \leq \epsilon_\mathrm{abs}
+\qquad \mbox{or} \qquad \left( f_0(x) < 0, \quad
+\frac{\mathrm{gap}} {-f_0(x)} \leq \epsilon_\mathrm{rel} \right)
+\qquad \mbox{or} \qquad
+\left( L(x,y,z) > 0, \quad \frac{\mathrm{gap}}
+{L(x,y,z)} \leq \epsilon_\mathrm{rel} \right)
+\]
+where
+\[
+ \mathrm{gap} =
+\left[\begin{array}{c} s_\mathrm{nl} \\ s_\mathrm{l}
+\end{array}\right]^T
+\left[\begin{array}{c} z_\mathrm{nl} \\ z_\mathrm{l}
+\end{array}\right],
+\qquad
+L(x,y,z) = f_0(x) + z_\mathrm{nl}^T \tilde f(x) +
+ z_\mathrm{l}^T (Gx-h) + y^T(Ax-b).
+\]
+The functions \function{qp()}, \function{gp()} and \function{cp()}
+call \function{nlcp()} and hence use the same stopping criteria
+(with {\it x0}=0 for \function{qp()} and \function{gp()}).
+
+The control parameters listed in the \textbf{GLPK} documentation are
+set to their default values and can also be customized by making
+an entry in \member{solvers.options}.
+The keys in the dictionary are strings with the name of the GLPK
+parameter. The command
+\begin{verbatim}
+>>> from cvxopt import solvers
+>>> solvers.options['LPX_K_MSGLEV'] = 0
+\end{verbatim}
+turns off the screen output subsequent calls \function{lp()} with
+the \code{'glpk'} option.
+
+The \textbf{MOSEK} \ulink{control parameters}{http://www.mosek.com/products/3/tools/doc/html/tools/node22.html}
+are set to their default values.
+The corresponding keys in \code{solvers.options} are strings with the
+name of the MOSEK parameter. For example the command
+\begin{verbatim}
+>>> from cvxopt import solvers
+>>> solvers.options['MSK_IPAR_LOG'] = 0
+\end{verbatim}
+turns off the screen output during calls of \function{lp()}
+and \function{qp()} with the \code{'mosek'} option.
+
+The following control parameters affect the \textbf{DSDP} algorithm:
+\begin{description}
+\item[\code{'DSDP\_Monitor'}] the interval (in number of iterations)
+ at which output is printed to the screen
+(default: 0).
+\item[\code{'DSDP\_MaxIts'}] maximum number of iterations.
+\item[\code{'DSDP\_GapTolerance'}] relative accuracy (default:
+\code{1e-5}).
+\end{description}
diff --git a/doc/spsolvers.tex b/doc/spsolvers.tex
new file mode 100644
index 0000000..56b556f
--- /dev/null
+++ b/doc/spsolvers.tex
@@ -0,0 +1,566 @@
+\chapter{Sparse Linear Equation Solvers} \label{c-spsolvers}
+In this section we describe routines for solving sparse sets of linear
+equations.
+
+A real symmetric or complex Hermitian sparse matrix is stored as
+an \spmtrx\ object \var{X} of size ({\it n}, {\it n}) and an
+additional character argument \code{uplo} with possible values
+\code{'L'} and \code{'U'}.
+If \code{uplo} is \code{'L'}, the lower triangular part
+of \var{X} contains the lower triangular part of the
+symmetric or Hermitian matrix, and the upper triangular matrix
+of \var{X} is ignored.
+If \code{uplo} is \code{'U'}, the upper triangular part
+of \var{X} contains the upper triangular part of the
+matrix, and the lower triangular matrix of \var{X} is ignored.
+
+A general sparse square matrix of order {\it n} is represented by an
+\spmtrx\ object of size ({\it n}, {\it n}).
+
+Dense matrices, which appear as righthand sides of equations, are
+stored using the same conventions as in the BLAS and LAPACK modules.
+
+\section{Matrix Orderings (\module{cvxopt.amd})} \label{s-orderings}
+
+CVXOPT includes an interface to the AMD library for computing
+approximate minimum degree orderings of sparse matrices.
+
+\begin{seealso}
+\seelink{http://www.cise.ufl.edu/research/sparse/amd}{AMD code,
+documentation, copyright and license.}{}
+\seetext{P.\ R.\ Amestoy, T.\ A.\ Davis, I.\ S.\ Duff,
+Algorithm 837: AMD, An Approximate Minimum Degree Ordering Algorithm,
+ACM Transactions on Mathematical Software, 30(3), 381-388, 2004.}
+\end{seealso}
+
+\begin{funcdesc}{order}{A\optional{, uplo='L'}}
+Computes the approximate mimimum degree ordering of a symmetric sparse
+matrix {\it A}.
+The ordering is returned as an integer dense matrix with length equal
+to the order of \var{A}. Its entries specify a permutation that
+reduces fill-in during the Cholesky factorization.
+More precisely, if \code{\var{p} = order(\var{A})}, then
+\code{\var{A}[\var{p},\var{p}]} has sparser Cholesky factors
+than \code{\var{A}}.
+\end{funcdesc}
+
+As an example we consider the matrix
+\[
+\left[ \begin{array}{rrrr}
+ 10 & 0 & 3 & 0 \\
+ 0 & 5 & 0 & -2 \\
+ 3 & 0 & 5 & 0 \\
+ 0 & -2 & 0 & 2
+\end{array}\right].
+\]
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix
+>>> from cvxopt import amd
+>>> A = spmatrix([10,3,5,-2,5,2], [0,2,1,2,2,3], [0,0,1,1,2,3])
+>>> P = amd.order(A)
+>>> print P
+ 1
+ 0
+ 2
+ 3
+\end{verbatim}
+
+\section{General Linear Equations (\module{cvxopt.umfpack})}
+\label{s-umfpack}
+The module \module{cvxopt.umfpack} includes four functions for solving
+sparse non-symmetric sets of linear equations.
+They call routines from the UMFPACK library, with all control options
+set to the default values described in the UMFPACK user guide.
+
+\begin{seealso}
+\seelink{http://www.cise.ufl.edu/research/sparse/umfpack}{UMFPACK code, documentation, copyright and license.}{}
+\seetext{T.\ A.\ Davis,
+Algorithm 832: UMFPACK -- an unsymmetric-pattern multifrontal method
+with a column pre-ordering strategy,
+ACM Transactions on Mathematical Software, 30(2), 196-199, 2004.}
+\end{seealso}
+
+\begin{funcdesc}{linsolve}{A, B\optional{, trans='N'}}
+Solves a sparse set of linear equations
+\[
+ AX = B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX = B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX = B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\var A} is a sparse matrix and \var{B} is a dense matrix of
+the same type (\dtc\ or \ztc) as \var{A}. On exit \var{B} contains
+the solution.
+Raises an \code{ArithmeticError} exception if the coefficient matrix
+is singular.
+\end{funcdesc}
+In the following example we solve an equation with
+coefficient matrix
+\BEQ \label{e-sp-Adef}
+A = \left[\begin{array}{rrrrr}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 &-1 &-3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1
+ \end{array}\right].
+\EEQ
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix, matrix
+>>> from cvxopt import umfpack
+>>> V = [2,3, 3,-1,4, 4,-3,1,2, 2, 6,1]
+>>> I = [0,1, 0, 2,4, 1, 2,3,4, 2, 1,4]
+>>> J = [0,0, 1, 1,1, 2, 2,2,2, 3, 4,4]
+>>> A = spmatrix(V,I,J)
+>>> B = matrix(1.0, (5,1))
+>>> umfpack.linsolve(A,B)
+>>> print B
+ 5.7895e-01
+-5.2632e-02
+ 1.0000e+00
+ 1.9737e+00
+-7.8947e-01
+\end{verbatim}
+The function \function{umfpack.linsolve()} is equivalent to the
+following three functions called in sequence.
+\begin{funcdesc}{symbolic}{A}
+Reorders the columns of \var{A} to reduce fill-in and performs a
+symbolic LU factorization. \var{A} is a sparse, possibly rectangular,
+matrix.
+Returns the symbolic factorization as an opaque C object that can be
+passed on to \function{umfpack.numeric()}.
+\end{funcdesc}
+
+\begin{funcdesc}{numeric}{A, F}
+Performs a numeric LU factorization of a sparse, possibly rectangular,
+matrix \var{A}. The argument \var{F} is the symbolic factorization
+computed by \function{umfpack.symbolic()} applied to the matrix \var{A},
+or another sparse matrix with the same sparsity pattern, dimensions,
+and type. The numeric factorization is returned as an opaque C object
+that that can be passed on to \function{umfpack.solve()}. Raises an
+\code{ArithmeticError} if the matrix is singular.
+\end{funcdesc}
+
+\begin{funcdesc}{solve}{A, F, B\optional{, trans='N'}}
+Solves a set of linear equations
+\[
+ AX = B \quad (\mathrm{trans} = \mathrm{'N'}), \qquad
+ A^TX = B \quad (\mathrm{trans} = \mathrm{'T'}), \qquad
+ A^HX = B \quad (\mathrm{trans} = \mathrm{'C'}),
+\]
+where {\var A} is a sparse matrix and \var{B} is a dense matrix of
+the same type as \var{A}.
+The argument \var{F} is a numeric factorization computed by
+\function{umfpack.numeric()}.
+On exit \var{B} is overwritten by the solution.
+\end{funcdesc}
+These separate functions are useful for solving several sets
+of linear equations with the same coefficient matrix and different
+righthand sides, or with coefficient matrices that share the same
+sparsity pattern.
+The symbolic factorization depends only on the sparsity pattern of
+the matrix, and not on the numerical values of the nonzero
+coefficients.
+The numerical factorization on the other hand depends on the sparsity
+pattern of the matrix and on its the numerical values.
+
+As an example, suppose {\it A} is the matrix~(\ref{e-sp-Adef}) and
+\[
+B = \left[\begin{array}{rrrrr}
+ 4 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 &-1 &-3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 2
+ \end{array}\right],
+\]
+which differs from {\it A} in its first and last entries.
+The following code computes
+\[
+ x = A^{-T}B^{-1}A^{-1}\ones.
+\]
+\begin{verbatim}
+>>> from cvxopt.base import spmatrix, matrix
+>>> from cvxopt import umfpack
+>>> VA = [2,3, 3,-1,4, 4,-3,1,2, 2, 6,1]
+>>> VB = [4,3, 3,-1,4, 4,-3,1,2, 2, 6,2]
+>>> I = [0,1, 0, 2,4, 1, 2,3,4, 2, 1,4]
+>>> J = [0,0, 1, 1,1, 2, 2,2,2, 3, 4,4]
+>>> A = spmatrix(VA, I, J)
+>>> B = spmatrix(VB, I, J)
+>>> x = matrix(1.0, (5,1))
+>>> Fs = umfpack.symbolic(A)
+>>> FA = umfpack.numeric(A, Fs)
+>>> FB = umfpack.numeric(B, Fs)
+>>> umfpack.solve(A, FA, x)
+>>> umfpack.solve(B, FB, x)
+>>> umfpack.solve(A, FA, x, trans='T')
+>>> print x
+ 5.8065e-01
+-2.3660e-01
+ 1.6280e+00
+ 8.0656e+00
+-1.3075e-01
+\end{verbatim}
+
+\section{Positive Definite Linear Equations (\module{cvxopt.cholmod})}
+\label{s-cholmod}
+
+\module{cvxopt.cholmod} is an interface to the Cholesky factorization
+routines of the CHOLMOD package.
+It includes functions for Cholesky factorization of sparse positive
+definite matrices, and for solving sparse sets of linear equations with
+positive definite matrices.
+The routines can also be used for computing LDL$\mathrm{{}^T}$
+(or LDL$\mathrm{{}^H}$) factorizations of symmetric indefinite matrices
+(with L unit lower-triangular and D diagonal and nonsingular) if
+such a factorization exists.
+
+\begin{seealso}
+\seelink{http://www.cise.ufl.edu/research/sparse/cholmod}{CHOLMOD code, documentation, copyright and license.}{}
+\end{seealso}
+
+
+\begin{funcdesc}{linsolve}{A, B\optional{, p=\None\optional{,
+uplo='L'}}}
+Solves
+\[
+ AX = B
+\]
+with {\it A} sparse and real symmetric or complex Hermitian.
+\var{B} is a dense matrix of the same type as \var{A}. On exit it
+is overwritten with the solution.
+The argument \var{p} is an integer matrix with length equal to the
+order of \var{A}, and specifies an optional reordering of \var{A}.
+If \var{p} is not specified, CHOLMOD used a reordering from the
+AMD library.
+Raises an \code{ArithmeticError} if the factorization does not exist.
+\end{funcdesc}
+
+As an example, we solve
+\BEQ \label{e-A-pd}
+\left[ \begin{array}{rrrr}
+ 10 & 0 & 3 & 0 \\
+ 0 & 5 & 0 & -2 \\
+ 3 & 0 & 5 & 0 \\
+ 0 & -2 & 0 & 2
+ \end{array}\right] X = \left[ \begin{array}{cc}
+ 0 & 4 \\ 1 & 5 \\ 2 & 6 \\ 3 & 7\end{array} \right].
+\EEQ
+\begin{verbatim}
+>>> from cvxopt.base import matrix, spmatrix
+>>> from cvxopt import cholmod
+>>> A = spmatrix([10,3, 5,-2, 5, 2], [0,2, 1,3, 2, 3], [0,0, 1,1, 2, 3])
+>>> X = matrix(range(8), (4,2), 'd')
+>>> cholmod.linsolve(A,X)
+>>> print X
+-1.4634e-01 4.8780e-02
+ 1.3333e+00 4.0000e+00
+ 4.8780e-01 1.1707e+00
+ 2.8333e+00 7.5000e+00
+\end{verbatim}
+
+\begin{funcdesc}{splinsolve}{A, B\optional{, p=\None\optional{,
+uplo='L'}}}
+Similar to \function{linsolve()} except that \var{B} is a sparse
+matrix and that the solution is returned as an output
+argument (as a new sparse matrix). \var{B} is not modified.
+\end{funcdesc}
+
+The following code computes the inverse of the coefficient matrix
+in~(\ref{e-A-pd}) as a sparse matrix.
+\begin{verbatim}
+>>> X = cholmod.splinsolve(A, spmatrix(1.0,range(4),range(4)))
+>>> print X
+SIZE: (4,4)
+(0, 0) 1.2195e-01
+(2, 0) -7.3171e-02
+(1, 1) 3.3333e-01
+(3, 1) 3.3333e-01
+(0, 2) -7.3171e-02
+(2, 2) 2.4390e-01
+(1, 3) 3.3333e-01
+(3, 3) 8.3333e-01
+\end{verbatim}
+
+The functions \function{linsolve()} and \function{splinsolve()} are
+equivalent to \function{symbolic()} and \function{numeric()} called in
+sequence, followed by \function{solve()}, respectively,
+\function{spsolve()}.
+
+\begin{funcdesc}{symbolic}{A\optional{, p=\None\optional{, uplo='L'}}}
+Performs a symbolic analysis of a sparse real symmetric or
+complex Hermitian matrix \var{A} for one of the two factorizations:
+\BEQ \label{e-chol-ll}
+ PAP^T = LL^T, \qquad PAP^T = LL^H,
+\EEQ
+and
+\BEQ \label{e-chol-ldl}
+ PAP^T = LDL^T, \qquad PAP^T = LDL^H,
+\EEQ
+where {\it P} is a permutation matrix, {\it L} is lower triangular
+(unit lower triangular in the second factorization), and
+{\it D} is nonsingular diagonal. The type of factorization depends
+on the value of \code{options['supernodal']}.
+
+If \var{uplo} is \code{'L'}, only the lower triangular part of \var{A}
+is accessed and the upper triangular part is ignored.
+If \var{uplo} is \code{'U'}, only the upper triangular part of \var{A}
+is accessed and the lower triangular part is ignored.
+
+The symbolic factorization is returned as an opaque C object that
+can be passed to \function{cholmod.numeric()}.
+\end{funcdesc}
+
+\begin{funcdesc}{numeric}{A, F}
+Performs a numeric factorization of a sparse symmetric matrix
+as~(\ref{e-chol-ll}) or~(\ref{e-chol-ldl}).
+The argument \var{F} is the symbolic factorization
+computed by \function{cholmod.symbolic()} applied to the matrix \var{A},
+or to another sparse matrix with the same sparsity pattern and
+typecode, or by
+\function{cholmod.numeric()} applied to a matrix with the same
+sparsity pattern and typecode as \var{A}.
+
+If \var{F} was created by a \function{cholmod.symbolic} with
+\var{uplo} equal to \code{'L'}, then only the lower triangular part
+of \var{A} is accessed and the upper triangular part is ignored.
+If it was created with \var{uplo} is \code{'U'}, then only the upper
+triangular part of \var{A} is accessed and the lower triangular part
+is ignored.
+
+On successful exit, the factorization is stored in \var{F}.
+Raises an \code{ArithmeticError} if the factorization does not
+exist.
+\end{funcdesc}
+
+\begin{funcdesc}{solve}{F, B\optional{, sys=0}}
+Solves one of the following linear equations where \var{B} is a dense
+matrix and \var{F} is the numeric
+factorization~(\ref{e-chol-ll}) or~(\ref{e-chol-ldl}) computed by
+\function{cholmod\_numeric()}.
+\var{sys} is an integer with values between 0 and 8.
+
+\begin{center}
+\begin{tabular}{c|c|}
+ \var{sys} & equation \\ \hline
+ 0 & $AX=B$ \\ 1 & $LDL^TX=B$ \\ 2 & $LDLX=B$ \\
+ 3 & $DL^TX=B$ \\ 4 & $LX=B$ \\ 5 & $L^TX=B$ \\
+ 6 & $DX=B$ \\ 7 & $P^TX=B$ \\ 8 & $PX=B$
+\end{tabular}
+\end{center}
+
+(If \var{F} is a Cholesky factorization of the form~(\ref{e-chol-ll}),
+{\it D} is an identity matrix in this table.
+If \var{A} is complex, $L^T$ should be replaced by $L^H$.)
+
+The matrix \var{B} is a dense \dtc\ or \ztc\ matrix, with the same type
+as \var{A}. On exit it is overwritten by the solution.
+\end{funcdesc}
+
+\begin{funcdesc}{spsolve}{F, B\optional{, sys=0}}
+Similar to \function{solve()}, except that \var{B} is a
+sparse matrix, and the solution is returned as an output argument
+(as a sparse matrix). \var{B} must have the same typecode as \var{A}.
+\end{funcdesc}
+
+For the same example as above:
+\begin{verbatim}
+>>> X = matrix(range(8), (4,2), 'd')
+>>> F = cholmod.symbolic(A)
+>>> cholmod.numeric(A,F)
+>>> cholmod.solve(F,X)
+>>> print X
+-1.4634e-01 4.8780e-02
+ 1.3333e+00 4.0000e+00
+ 4.8780e-01 1.1707e+00
+ 2.8333e+00 7.5000e+00
+\end{verbatim}
+
+\begin{funcdesc}{diag}{F}
+Returns the diagonal elements of the Cholesky factor {\it L}
+in~(\ref{e-chol-ll}), as a dense matrix of the same type as \var{A}.
+Note that this only applies to Cholesky factorizations.
+The matrix {\it D} in an LDL$\mathrm{{}^T}$ factorization can be
+retrieved via \function{cholmod.solve()} with \var{sys} equal to 6.
+\end{funcdesc}
+
+In the functions listed above, the default values of the control
+parameters described in the CHOLMOD user guide are used, except for
+\ctype{Common->print} which is set to 0 instead of 3
+and
+\ctype{Common->supernodal} which is set to 2 instead of 1.
+These parameters (and a few others) can be modified by making an
+entry in the dictionary \member{cholmod.options}.
+The meaning of these parameters is as follows.
+\begin{description}
+\item[\code{options['supernodal']}] If equal to 0, a
+factorization~(\ref{e-chol-ldl}) is computed using a simplicial
+algorithm.
+If equal to 2, a factorization~(\ref{e-chol-ll}) is
+computed using a supernodal algorithm.
+If equal to 1, the most efficient of the two factorizations is
+selected, based on the sparsity pattern. Default: 2.
+
+\item[\code{options['print']}] A nonnegative integer that controls the
+amount of output printed to the screen.
+Default: 0 (no output).
+\end{description}
+
+As an example that illustrates \function{diag()} and the use of
+\member{cholmod.options}, we compute the logarithm of the determinant
+of the coefficient matrix in~(\ref{e-A-pd}) by two methods.
+\begin{verbatim}
+>>> import math
+>>> from cvxopt.cholmod import options
+>>> from cvxopt.base import log
+>>> options['supernodal'] = 2
+>>> F = cholmod.symbolic(A)
+>>> cholmod.numeric(A,F)
+>>> print 2.0 * sum(log(cholmod.diag(F)))
+5.50533153593
+\end{verbatim}
+\begin{verbatim}
+>>> options['supernodal'] = 0
+>>> F = cholmod.symbolic(A)
+>>> cholmod.numeric(A,F)
+>>> Di = matrix(1.0, (4,1))
+>>> cholmod.solve(F,Di,sys=6)
+>>> print -sum(log(Di))
+5.50533153593
+\end{verbatim}
+
+\section{Example: Covariance Selection}
+This example illustrates the use of the routines for sparse Cholesky
+factorization. We consider the problem
+\BEQ \label{e-covsel}
+ \begin{array}{ll}
+ \mbox{minimize} & -\log\det K + \Tr(KY)\\
+ \mbox{subject to} & K_{ij}=0,\quad (i,j) \not \in S.
+ \end{array}
+\EEQ
+The optimization variable is a symmetric matrix {\it K} of order {\it n}
+and the domain of the problem is the set of positive definite matrices.
+The matrix $Y$ and the index set $S$ are given. We assume that all
+the diagonal positions are included in $S$.
+This problem arises in maximum likelihood estimation of the covariance
+matrix of a zero-mean normal distribution, with constraints
+that specify that pairs of variables are conditionally independent.
+
+We can express {\it K} as
+\[
+ K(x) = E_1\diag(x)E_2^T+E_2\diag(x)E_1^T
+\]
+where {\it x} are the nonzero elements in the lower triangular part
+of {\it K}, with the diagonal elements scaled by 1/2,
+and
+\[
+ E_1 = \left[ \begin{array}{cccc}
+ e_{i_1} & e_{i_2} & \cdots & e_{i_q} \end{array}\right], \qquad
+ E_2 = \left[ \begin{array}{cccc}
+ e_{j_1} & e_{j_2} & \cdots & e_{j_q} \end{array}\right],
+\]
+where ({\it i\_k}, {\it j\_k}) are the positions of the nonzero
+entries in the lower-triangular part of {\it K}.
+With this notation, we can solve problem~(\ref{e-covsel}) by solving
+the unconstrained problem
+\[
+ \begin{array}{ll}
+ \mbox{minimize} & f(x) = -\log\det K(x) + \Tr(K(x)Y).
+ \end{array}
+\]
+The code below implements Newton's method with a backtracking line
+search. The gradient and Hessian of the objective function are given
+by
+\begin{eqnarray*}
+\nabla f(x)
+&=& 2 \diag( E_1^T (Y - K(x)^{-1}) E_2)) \\
+&=& 2\diag(Y_{IJ} - \left(K(x)^{-1}\right)_{IJ})\\
+\nabla^2 f(x) & = &
+ 2 (E_1^T K(x)^{-1} E_1) \circ (E_2^T K(x)^{-1} E_2)
+ + 2 (E_1^T K(x)^{-1} E_2) \circ (E_2^T K(x)^{-1} E_1) \\
+&=& 2 \left(K(x)^{-1}\right)_{II} \circ
+ \left(K(x)^{-1}\right)_{JJ}
+ +2 \left(K(x)^{-1}\right)_{IJ} \circ
+ \left(K(x)^{-1}\right)_{JI},
+\end{eqnarray*}
+where \code{o} denotes Hadamard product.
+
+\begin{verbatim}
+from cvxopt.base import matrix, spmatrix, log, mul
+from cvxopt import blas, lapack, amd, cholmod
+
+def covsel(Y):
+ """
+ Returns the solution of
+
+ minimize -logdet K + Tr(KY)
+ subject to K_{ij}=0, (i,j) not in indices listed in I,J.
+
+ Y is a symmetric sparse matrix with nonzero diagonal elements.
+ I = Y.I, J = Y.J.
+ """
+
+ I, J = Y.I, Y.J
+ n, m = Y.size[0], len(I)
+ N = I + J*n # non-zero positions for one-argument indexing
+ D = [k for k in xrange(m) if I[k]==J[k]] # position of diagonal elements
+
+ # starting point: symmetric identity with nonzero pattern I,J
+ K = spmatrix(0, I, J)
+ K[::n+1] = 1
+
+ # Kn is used in the line search
+ Kn = spmatrix(0, I, J)
+
+ # symbolic factorization of K
+ F = cholmod.symbolic(K)
+
+ # Kinv will be the inverse of K
+ Kinv = matrix(0.0, (n,n))
+
+ for iters in xrange(100):
+
+ # numeric factorization of K
+ cholmod.numeric(K, F)
+ d = cholmod.diag(F)
+
+ # compute Kinv by solving K*X = I
+ Kinv[:] = 0
+ Kinv[::n+1] = 1
+ cholmod.solve(F, Kinv)
+
+ # solve Newton system
+ grad = 2*(Y.V - Kinv[N])
+ hess = 2*(mul(Kinv[I,J],Kinv[J,I]) + mul(Kinv[I,I],Kinv[J,J]))
+ v = -grad
+ lapack.posv(hess,v)
+
+ # stopping criterion
+ sqntdecr = -blas.dot(grad,v)
+ print "Newton decrement squared:%- 7.5e" %sqntdecr
+ if (sqntdecr < 1e-12):
+ print "number of iterations: ", iters+1
+ break
+
+ # line search
+ dx = +v
+ dx[D] *= 2 # scale the diagonal elems
+ f = -2.0 * sum(log(d)) # f = -log det K
+ s = 1
+ for lsiter in xrange(50):
+ Kn.V = K.V + s*dx
+ try:
+ cholmod.numeric(Kn, F)
+ except ArithmeticError:
+ s *= 0.5
+ else:
+ d = cholmod.diag(F)
+ fn = -2.0 * sum(log(d)) + 2*s*blas.dot(v,Y.V)
+ if (fn < f - 0.01*s*sqntdecr):
+ break
+ s *= 0.5
+
+ K.V = Kn.V
+
+ return K
+\end{verbatim}
diff --git a/examples/book/README b/examples/book/README
new file mode 100644
index 0000000..6ca767c
--- /dev/null
+++ b/examples/book/README
@@ -0,0 +1,7 @@
+This directory contains examples from the book "Convex Optimization"
+by Boyd and Vandenberghe (Cambridge University Press, 2004, and
+www.stanford.edu/~boyd/cvxbook).
+
+The scripts require the plotting library Matplotlib, available at
+matplotlib.sourceforge.net. They were tested with Matplotlib
+version 0.83.2-2.
diff --git a/examples/book/chap4/portfolio b/examples/book/chap4/portfolio
new file mode 100755
index 0000000..7d0046d
--- /dev/null
+++ b/examples/book/chap4/portfolio
@@ -0,0 +1,57 @@
+#!/usr/bin/python
+
+# Figure 4.12, page 187.
+# Risk-return trade-off.
+
+from math import sqrt
+from cvxopt.base import matrix
+from cvxopt.blas import dot
+from cvxopt.solvers import qp, options
+import pylab
+
+n = 4
+S = matrix( [[ 4e-2, 6e-3, -4e-3, 0.0 ],
+ [ 6e-3, 1e-2, 0.0, 0.0 ],
+ [-4e-3, 0.0, 2.5e-3, 0.0 ],
+ [ 0.0, 0.0, 0.0, 0.0 ]] )
+pbar = matrix([.12, .10, .07, .03])
+
+G = matrix(0.0, (n,n))
+G[::n+1] = -1.0
+h = matrix(0.0, (n,1))
+A = matrix(1.0, (1,n))
+b = matrix(1.0)
+
+N = 100
+mus = [ 10**(5.0*t/N-1.0) for t in xrange(N) ]
+options['show_progress'] = False
+xs = [ qp(mu*S, -pbar, G, h, A, b)['x'] for mu in mus ]
+returns = [ dot(pbar,x) for x in xs ]
+risks = [ sqrt(dot(x, S*x)) for x in xs ]
+
+pylab.figure(1, facecolor='w')
+pylab.plot(risks, returns)
+pylab.xlabel('standard deviation')
+pylab.ylabel('expected return')
+pylab.axis([0, 0.2, 0, 0.15])
+pylab.title('Risk-return trade-off curve (fig 4.12)')
+pylab.yticks([0.00, 0.05, 0.10, 0.15])
+
+pylab.figure(2, facecolor='w')
+c1 = [ x[0] for x in xs ]
+c2 = [ x[0] + x[1] for x in xs ]
+c3 = [ x[0] + x[1] + x[2] for x in xs ]
+c4 = [ x[0] + x[1] + x[2] + x[3] for x in xs ]
+pylab.fill(risks + [.20], c1 + [0.0], '#F0F0F0')
+pylab.fill(risks[-1::-1] + risks, c2[-1::-1] + c1 , '#D0D0D0')
+pylab.fill(risks[-1::-1] + risks, c3[-1::-1] + c2, '#F0F0F0')
+pylab.fill(risks[-1::-1] + risks, c4[-1::-1] + c3, '#D0D0D0')
+pylab.axis([0.0, 0.2, 0.0, 1.0])
+pylab.xlabel('standard deviation')
+pylab.ylabel('allocation')
+pylab.text(.15,.5,'x1')
+pylab.text(.10,.7,'x2')
+pylab.text(.05,.7,'x3')
+pylab.text(.01,.7,'x4')
+pylab.title('Optimal allocations (fig 4.12)')
+pylab.show()
diff --git a/examples/book/chap4/rls b/examples/book/chap4/rls
new file mode 100755
index 0000000..50ddc05
--- /dev/null
+++ b/examples/book/chap4/rls
@@ -0,0 +1,79 @@
+#!/usr/bin/python
+
+# Figure 4.11, page 185.
+# Regularized least-squares.
+
+import pylab
+from pickle import load
+from cvxopt import blas, lapack
+from cvxopt.base import matrix
+from cvxopt import solvers
+solvers.options['show_progress'] = 0
+
+data = load(open("rls.pic",'r'))
+A, b = data['A'], data['b']
+m, n = A.size
+
+# LS solution
+xls = +b
+lapack.gels(+A, xls)
+xls = xls[:n]
+
+# We compute the optimal values of
+#
+# minimize/maximize || A*x - b ||_2^2
+# subject to x'*x = alpha
+#
+# via the duals.
+#
+# Lower bound:
+#
+# maximize -t - u*alpha
+# subject to [u*I, 0; 0, t] + [A, b]'*[A, b] >= 0
+#
+# Upper bound:
+#
+# minimize t + u*alpha
+# subject to [u*I, 0; 0, t] - [A, b]'*[A, b] >= 0.
+#
+# Two variables (t, u).
+
+G = matrix(0.0, ((n+1)**2, 2))
+G[-1, 0] = -1.0 # coefficient of t
+G[: (n+1)**2-1 : n+2, 1] = -1.0 # coefficient of u
+h = matrix( [ [ A.T * A, b.T * A ], [ A.T * b, b.T * b ] ] )
+c = matrix(1.0, (2,1))
+
+nopts = 40
+alpha1 = [ 2.0/(nopts/2-1) * alpha for alpha in xrange(nopts/2) ] + \
+ [ 2.0 + (15.0 - 2.0)/(nopts/2) * alpha for alpha in
+ xrange(1,nopts/2+1) ]
+lbnds = [ blas.nrm2(b)**2 ]
+for alpha in alpha1[1:]:
+ c[1:] = alpha
+ lbnds += [ -blas.dot(c, solvers.sdp(c, Gs=[G], hs=[h])['x']) ]
+
+nopts = 10
+alpha2 = [ 1.0/(nopts-1) * alpha for alpha in xrange(nopts) ]
+ubnds = [ blas.nrm2(b)**2 ]
+for alpha in alpha2[1:]:
+ c[1:] = alpha
+ ubnds += [ blas.dot(c, solvers.sdp(c, Gs=[G], hs=[-h])['x']) ]
+
+pylab.figure(1, facecolor='w')
+pylab.plot(lbnds, alpha1, '-', ubnds, alpha2, '-')
+kmax = max([ k for k in xrange(len(alpha1)) if alpha1[k] <
+ blas.nrm2(xls)**2 ])
+pylab.plot( [ blas.nrm2(b)**2 ] + lbnds[:kmax] +
+ [ blas.nrm2(A*xls-b)**2 ], [0.0] + alpha1[:kmax] +
+ [ blas.nrm2(xls)**2 ], '-', linewidth=2)
+pylab.plot([ blas.nrm2(b)**2, blas.nrm2(A*xls-b)**2 ],
+ [0.0, blas.nrm2(xls)**2], 'o')
+pylab.fill(lbnds[-1::-1] + ubnds + [ubnds[-1]],
+ alpha1[-1::-1] + alpha2+ [alpha1[-1]], '#D0D0D0')
+pylab.axis([0, 15, -1.0, 15])
+pylab.xlabel('||A*x-b||_2^2')
+pylab.ylabel('||x||_2^2')
+pylab.grid()
+pylab.title('Regularized least-squares (fig. 4.11)')
+pylab.show()
diff --git a/examples/book/chap4/rls.pic b/examples/book/chap4/rls.pic
new file mode 100644
index 0000000..c84e402
--- /dev/null
+++ b/examples/book/chap4/rls.pic
@@ -0,0 +1,1125 @@
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+F-0.16143195583510889
+aF-0.67768343369526307
+aF0.16084359462457573
+aF0.10428881011413052
+aF-0.2655660443561319
+aF0.35919523061889325
+aF0.16074025143663787
+aF-0.11421264589574148
+aF0.098575589230285338
+aF-0.021461162957776336
+aF1.2870291537691783
+aF0.22335913212959874
+aF-0.18518011941716028
+aF0.72719403274095085
+aF-0.054520392271940908
+aF0.055706624603291927
+aF0.37152784451573234
+aF-0.0026790126321343567
+aF-0.065305446670940251
+aF-0.28319748376470066
+aF0.12179419200875374
+aF-0.46190759357216132
+aF0.24532948045493169
+aF0.57741574009209129
+aF-0.20038800518743327
+aF0.28434957039940145
+aF0.41205424755274606
+aF-0.52413630165258562
+aF-0.43005085334118509
+aF0.21446375085140315
+aF-0.10612113952760373
+aF0.25388213127924197
+aF0.25844013670185351
+aF0.2311036000053617
+aF0.4426226427094434
+aF0.25002892502222307
+aF0.41806883402445871
+aF-0.41824718377434011
+aF-0.049830631694555358
+aF-0.090913971598374915
+aF-0.52843704660670243
+aF0.091982740793313131
+aF-0.34299336373036504
+aF0.51841960641550788
+aF-0.24989594994933934
+aF0.15668483679512873
+aF0.086065466792963577
+aF-0.30200799730645128
+aF-0.69916629701899902
+aF-0.035171689140503309
+aF-0.34615218824469418
+aF0.18552621575276762
+aF0.1765564681877021
+aF0.56172664224590207
+aF0.16514178827701431
+aF-0.26105954348224142
+aF0.13476505078644202
+aF-0.27374501099003851
+aF-0.017102093695764001
+aF-0.068996860348989178
+aF0.051640117356078631
+aF-0.12095289663013524
+aF0.40856213778679173
+aF-0.67228595777644418
+aF0.1363984331429296
+aF0.31097275492788917
+aF0.26695864898146232
+aF0.18710267994878738
+aF-0.0029622200880384877
+aF0.25177200926602317
+aF0.18701557903892782
+aF-0.10280763300825679
+aF-0.15555116047213355
+aF-0.089792732233990868
+aF-0.48911861854845107
+aF-0.12748333832274483
+aF0.071923350466736591
+aF0.11594797486324034
+aF0.48429640311993932
+aF-0.13201718008527658
+aF0.23117313315298862
+aF0.2262593150867224
+aF0.33708782380681585
+aF-0.32833055771415132
+aF0.054518808290491542
+aF0.063110698981614963
+aF-0.28119470239217825
+aF-0.24684768490375322
+aF0.30522250706068588
+aF0.008667421388934643
+aF0.15682379142847355
+aF0.037458202825196588
+aF-0.14092181857921926
+aF-0.17069068456403164
+aF0.14970644989506304
+aF-0.2752575961425312
+aF0.28359094471774626
+aF0.20607585138147697
+aF-0.24478992166892741
+aF-0.081555771076436148
+a(I100
+I1
+tp10
+g5
+tp11
+Rp12
+s.
\ No newline at end of file
diff --git a/examples/book/chap6/basispursuit b/examples/book/chap6/basispursuit
new file mode 100755
index 0000000..ee686ae
--- /dev/null
+++ b/examples/book/chap6/basispursuit
@@ -0,0 +1,249 @@
+#!/usr/bin/python
+
+# Figures 6.21-23, pages 335-337.
+# Basis pursuit.
+
+from cvxopt.base import matrix, mul, div, cos, sin, exp, sqrt
+from cvxopt import blas, lapack, solvers
+import pylab
+
+# Basis functions are Gabor pulses: for k = 0,...,K-1,
+#
+# exp(-(t - k * tau)^2/sigma^2 ) * cos (l*omega0*t), l = 0,...,L
+# exp(-(t - k * tau)^2/sigma^2 ) * sin (l*omega0*t), l = 1,...,L
+
+sigma = 0.05
+tau = 0.002
+omega0 = 5.0
+K = 501
+L = 30
+N = 501 # number of samples of each signal in [0,1]
+
+# Build dictionary matrix
+ts = (1.0/N) * matrix(range(N), tc='d')
+B = ts[:, K*[0]] - tau * matrix(range(K), (1,K), 'd')[N*[0],:]
+B = exp(-(B/sigma)**2)
+A = matrix(0.0, (N, K*(2*L+1)))
+
+# First K columns are DC pulses for k = 0,...,K-1
+A[:,:K] = B
+for l in xrange(L):
+
+ # Cosine pulses for omega = (l+1)*omega0 and k = 0,...,K-1.
+ A[:, K+l*(2*K) : K+l*(2*K)+K] = \
+ mul(B, cos((l+1)*omega0*ts)[:, K*[0]])
+
+ # Sine pulses for omega = (l+1)*omega0 and k = 0,...,K-1.
+ A[:, K+l*(2*K)+K : K+(l+1)*(2*K)] = \
+ mul(B, sin((l+1)*omega0*ts)[:,K*[0]])
+
+
+pylab.figure(1, facecolor='w')
+pylab.subplot(311)
+# DC pulse for k = 250 (tau = 0.5)
+pylab.plot(ts, A[:,250])
+pylab.ylabel('f(0.5, 0, c)')
+pylab.axis([0, 1, -1, 1])
+pylab.title('Three basis elements (fig. 6.21)')
+# Cosine pulse for k = 250 (tau = 0.5) and l = 15 (omega = 75)
+pylab.subplot(312)
+pylab.ylabel('f(0.5, 75, c)')
+pylab.plot(ts, A[:, K + 14*(2*K) + 250])
+pylab.axis([0, 1, -1, 1])
+pylab.subplot(313)
+# Cosine pulse for k = 250 (tau = 0.5) and l = 30 (omega = 150)
+pylab.plot(ts, A[:, K + 29*(2*K) + 250])
+pylab.ylabel('f(0.5, 150, c)')
+pylab.axis([0, 1, -1, 1])
+pylab.xlabel('t')
+
+# Signal.
+y = mul( 1.0 + 0.5 * sin(11*ts), sin(30 * sin(5*ts)))
+
+
+# Basis pursuit problem
+#
+# minimize ||A*x - y||_2^2 + ||x||_1
+#
+# minimize ||A*x - y||_2^2 + 1'*u
+# subject to -u <= x <= u
+#
+# Variables x (n), u (n).
+
+m, n = A.size
+r = matrix(0.0, (m,1))
+gradf = matrix(1.0, (1,2*n))
+
+def F(x=None):
+ """
+ Function and gradient evaluation of
+
+ f = || A*x[:n] - y ||_2^2 + sum(x[n:])
+ """
+
+ nvars = 2*n
+ if x is None: return 0, matrix(0.0, (nvars,1))
+ blas.copy(y, r)
+ blas.gemv(A, x, r, beta=-1.0) # r = A*x[:n] - y
+ f = blas.nrm2(r)**2 + blas.asum(x, offset=n)
+ blas.gemv(A, r, gradf, alpha=2.0, trans='T') #gradf = [2*A'*r; 1.0]
+ return f, +gradf
+
+
+def G(u, v, alpha=1.0, beta=0.0, trans='N'):
+ """
+ v := alpha*[I, -I; -I, -I] * u + beta * v (trans = 'N' or 'T')
+ """
+
+ blas.scal(beta, v)
+ blas.axpy(u, v, n=n)
+ blas.axpy(u, v, n=n, alpha=-1.0, offsetx=n)
+ blas.axpy(u, v, n=n, alpha=-1.0, offsety=n)
+ blas.axpy(u, v, n=n, alpha=-1.0, offsetx=n, offsety=n)
+
+h = matrix(0.0, (2*n,1))
+
+
+# Customized solver for the KKT system
+#
+# [ 2.0*z[0]*A'*A 0 I -I ] [x[:n] ] [bx[:n] ]
+# [ 0 0 -I -I ] [x[n:] ] = [bx[n:] ].
+# [ I -I -D1^-1 0 ] [zl[:n]] [bzl[:n]]
+# [ -I -I 0 -D2^-1 ] [zl[n:]] [bzl[n:]]
+#
+#
+# We first eliminate zl and x[n:]:
+#
+# ( 2*z[0]*A'*A + 4*D1*D2*(D1+D2)^-1 ) * x[:n] =
+# bx[:n] - (D2-D1)*(D1+D2)^-1 * bx[n:]
+# + D1 * ( I + (D2-D1)*(D1+D2)^-1 ) * bzl[:n]
+# - D2 * ( I - (D2-D1)*(D1+D2)^-1 ) * bzl[n:]
+#
+# x[n:] = (D1+D2)^-1 * ( bx[n:] - D1*bzl[:n] - D2*bzl[n:] )
+# - (D2-D1)*(D1+D2)^-1 * x[:n]
+#
+# zl[:n] = D1 * ( x[:n] - x[n:] - bzl[:n] )
+# zl[n:] = D2 * (-x[:n] - x[n:] - bzl[n:] ).
+#
+#
+# The first equation has the form
+#
+# (z[0]*A'*A + D)*x[:n] = rhs
+#
+# and is equivalent to
+#
+# [ D A' ] [ x:n] ] = [ rhs ]
+# [ A -1/z[0]*I ] [ v ] [ 0 ].
+#
+# It can be solved as
+#
+# ( A*D^-1*A' + 1/z[0]*I ) * v = A * D^-1 * rhs
+# x[:n] = D^-1 * ( rhs - A'*v ).
+
+S = matrix(0.0, (m,m))
+Asc = matrix(0.0, (m,n))
+v = matrix(0.0, (m,1))
+
+def kktsolver(x, z, dnl, dl):
+
+ # Factor
+ #
+ # S = A*D^-1*A' + 1/z[0]*I
+ #
+ # where D = 2*D1*D2*(D1+D2)^-1, D1 = dl[:n]**2, D2 = dl[n:]**2.
+
+ d1 = dl[:n]**2 # d1 = diag(D1)
+ d2 = dl[n:]**2 # d2 = diag(D2)
+ # ds is square root of diagonal of D
+ ds = sqrt(2.0) * div( mul(dl[:n], dl[n:]), sqrt(d1+d2) )
+ d3 = div(d2 - d1, d1 + d2)
+
+ # Asc = A*diag(d)^-1/2
+ blas.copy(A, Asc)
+ for k in xrange(m):
+ blas.tbsv(ds, Asc, n=n, k=0, ldA=1, incx=m, offsetx=k)
+
+ # S = 1/z[0]*I + A * D^-1 * A'
+ blas.syrk(Asc, S)
+ S[::m+1] += 1.0 / z[0]
+ lapack.potrf(S)
+
+ def g(x, y, znl, zl):
+
+ x[:n] = 0.5 * ( x[:n] - mul(d3, x[n:]) + \
+ mul(d1, zl[:n] + mul(d3, zl[:n])) - \
+ mul(d2, zl[n:] - mul(d3, zl[n:])) )
+ x[:n] = div( x[:n], ds)
+
+ # Solve
+ #
+ # S * v = 0.5 * A * D^-1 * ( bx[:n]
+ # - (D2-D1)*(D1+D2)^-1 * bx[n:]
+ # + D1 * ( I + (D2-D1)*(D1+D2)^-1 ) * bzl[:n]
+ # - D2 * ( I - (D2-D1)*(D1+D2)^-1 ) * bzl[n:] )
+
+ blas.gemv(Asc, x, v)
+ lapack.potrs(S, v)
+
+ # x[:n] = D^-1 * ( rhs - A'*v ).
+ blas.gemv(Asc, v, x, alpha=-1.0, beta=1.0, trans='T')
+ x[:n] = div(x[:n], ds)
+
+ # x[n:] = (D1+D2)^-1 * ( bx[n:] - D1*bzl[:n] - D2*bzl[n:] )
+ # - (D2-D1)*(D1+D2)^-1 * x[:n]
+ x[n:] = div( x[n:] - mul(d1, zl[:n]) - mul(d2, zl[n:]), d1+d2 )\
+ - mul( d3, x[:n] )
+
+ # zl[:n] = D1 * ( x[:n] - x[n:] - bzl[:n] )
+ # zl[n:] = D2 * ( -x[:n] - x[n:] - bzl[n:] ).
+ zl[:n] = mul( d1, x[:n] - x[n:] - zl[:n] )
+ zl[n:] = mul( d2, -x[:n] - x[n:] - zl[n:] )
+
+ return g
+
+x = solvers.nlcp(kktsolver, F, G, h)['x'][:n]
+
+I = [ k for k in xrange(n) if abs(x[k]) > 1e-2 ]
+xls = +y
+lapack.gels(A[:,I], xls)
+ybp = A[:,I]*xls[:len(I)]
+
+print "Sparse basis contains %d basis functions." %len(I)
+print "Relative RMS error = %.1e." %(blas.nrm2(ybp-y) / blas.nrm2(y))
+
+pylab.figure(2, facecolor='w')
+pylab.subplot(211)
+pylab.plot(ts, y, '-', ts, ybp, 'r--')
+pylab.xlabel('t')
+pylab.ylabel('y(t), yhat(t)')
+pylab.axis([0, 1, -1.5, 1.5])
+pylab.title('Signal and basis pursuit approximation (fig. 6.22)')
+pylab.subplot(212)
+pylab.plot(ts, y-ybp, '-')
+pylab.xlabel('t')
+pylab.ylabel('y(t)-yhat(t)')
+pylab.axis([0, 1, -0.05, 0.05])
+
+pylab.figure(3, facecolor='w')
+pylab.subplot(211)
+pylab.plot(ts, y, '-')
+pylab.xlabel('t')
+pylab.ylabel('y(t)')
+pylab.axis([0, 1, -1.5, 1.5])
+pylab.title('Signal and time-frequency plot (fig. 6.23)')
+pylab.subplot(212)
+omegas, taus = [], []
+for i in I:
+ if i < K:
+ omegas += [0.0]
+ taus += [i*tau]
+ else:
+ l = (i-K)/(2*K)+1
+ k = ((i-K)%(2*K)) %K
+ omegas += [l*omega0]
+ taus += [k*tau]
+pylab.plot(ts, 150*abs(cos(5.0*ts)), '-', taus, omegas, 'ro')
+pylab.xlabel('t')
+pylab.ylabel('omega(t)')
+pylab.axis([0, 1, -5, 155])
+pylab.show()
diff --git a/examples/book/chap6/consumerpref b/examples/book/chap6/consumerpref
new file mode 100755
index 0000000..fc404b4
--- /dev/null
+++ b/examples/book/chap6/consumerpref
@@ -0,0 +1,135 @@
+#!/usr/bin/python
+
+# Figures 6.25 and 6.26, page 342.
+# Consumer preference analysis.
+
+import pylab
+from cvxopt import solvers
+from cvxopt.base import matrix, sqrt
+from cvxopt.modeling import variable, op
+solvers.options['show_progress'] = 0
+
+def utility(x, y):
+ return (1.1 * sqrt(x) + 0.8 * sqrt(y)) / 1.9
+
+B = matrix([
+ 4.5e-01, 9.6e-01,
+ 2.1e-01, 3.4e-01,
+ 2.8e-01, 8.7e-01,
+ 9.6e-01, 3.0e-02,
+ 8.0e-02, 9.2e-01,
+ 2.0e-02, 2.2e-01,
+ 0.0e+00, 3.9e-01,
+ 2.6e-01, 6.4e-01,
+ 3.5e-01, 9.7e-01,
+ 9.1e-01, 7.8e-01,
+ 1.2e-01, 1.4e-01,
+ 5.8e-01, 8.4e-01,
+ 3.2e-01, 7.3e-01,
+ 4.9e-01, 2.7e-01,
+ 7.0e-02, 8.0e-01,
+ 9.3e-01, 8.7e-01,
+ 4.4e-01, 8.6e-01,
+ 3.3e-01, 4.2e-01,
+ 8.9e-01, 9.0e-01,
+ 4.9e-01, 7.0e-02,
+ 9.5e-01, 3.3e-01,
+ 6.6e-01, 2.6e-01,
+ 9.5e-01, 7.3e-01,
+ 4.2e-01, 9.1e-01,
+ 6.8e-01, 2.0e-01,
+ 8.7e-01, 1.7e-01,
+ 5.2e-01, 6.2e-01,
+ 7.7e-01, 6.3e-01,
+ 2.0e-02, 2.9e-01,
+ 9.8e-01, 2.0e-02,
+ 5.0e-02, 7.9e-01,
+ 7.9e-01, 1.9e-01,
+ 6.2e-01, 6.0e-02,
+ 6.9e-01, 1.0e-01,
+ 6.9e-01, 3.7e-01,
+ 0.0e+00, 7.2e-01,
+ 6.3e-01, 4.0e-02,
+ 4.0e-02, 4.6e-01,
+ 3.6e-01, 9.5e-01,
+ 8.2e-01, 6.7e-01 ], (2, 40))
+m = B.size[1]
+
+# Plot some contour lines.
+nopts = 200
+a = (1.0/nopts)*matrix(range(nopts), tc='d')
+X, Y = a[:,nopts*[0]].T, a[:,nopts*[0]]
+pylab.figure(1, facecolor='w')
+pylab.plot(B[0,:], B[1,:], 'wo', markeredgecolor='b')
+pylab.contour(pylab.array(X), pylab.array(Y), pylab.array(utility(X,Y)),
+ [.1*(k+1) for k in xrange(9)], colors='k')
+pylab.xlabel('x1')
+pylab.ylabel('x2')
+pylab.title('Goods baskets and utility function (fig. 6.25)')
+print "Close figure to start analysis."
+pylab.show()
+
+
+# P are basket indices in order of increasing preference
+l = zip(utility(B[0,:], B[1,:]), range(m))
+l.sort()
+P = [ e[1] for e in l ]
+
+# baskets with known preference relations
+u = variable(m)
+gx = variable(m)
+gy = variable(m)
+
+# comparison basket at (.5, .5) has utility 0
+gxc = variable(1)
+gyc = variable(1)
+
+monotonicity = [ gx >= 0, gy >= 0, gxc >= 0, gyc >= 0 ]
+preferences = [ u[P[j+1]] >= u[P[j]] + 1.0 for j in xrange(m-1) ]
+concavity = [ u[j] <= u[i] + gx[i] * ( B[0,j] - B[0,i] ) +
+ gy[i] * ( B[1,j] - B[1,i] ) for i in xrange(m) for j in
+ xrange(m) ]
+concavity += [ 0 <= u[i] + gx[i] * ( 0.5 - B[0,i] ) +
+ gy[i] * ( 0.5 - B[1,i] ) for i in xrange(m) ]
+concavity += [ u[j] <= gxc * ( B[0,j] - 0.5 ) +
+ gyc * ( B[1,j] - 0.5 ) for j in xrange(m) ]
+
+preferred, rejected, neutral = [], [], []
+for k in xrange(m):
+ p = op(-u[k], monotonicity + preferences + concavity)
+ p.solve()
+ if p.status == 'optimal' and p.objective.value()[0] > 0:
+ rejected += [k]
+ print "Basket (%1.2f, %1.2f) rejected." %(B[0,k],B[1,k])
+ else:
+ p = op(u[k], monotonicity + preferences + concavity)
+ p.solve()
+ if p.status == 'optimal' and p.objective.value()[0] > 0:
+ print "Basket (%1.2f, %1.2f) preferred." %(B[0,k],B[1,k])
+ preferred += [k]
+ else:
+ print "No conclusion about basket (%1.2f, %1.2f)." \
+ %(B[0,k],B[1,k])
+ neutral += [k]
+
+pylab.figure(1, facecolor='w')
+pylab.plot(B[0,:], B[1,:], 'wo', markeredgecolor='b')
+pylab.contour(pylab.array(X), pylab.array(Y), pylab.array(utility(X,Y)),
+ [.1*(k+1) for k in xrange(9)], colors='k')
+pylab.xlabel('x1')
+pylab.ylabel('x2')
+pylab.title('Goods baskets and utility function (fig. 6.25)')
+
+pylab.figure(2, facecolor='w')
+pylab.plot(B[0,preferred], B[1,preferred], 'go')
+pylab.plot(B[0,rejected], B[1,rejected], 'ro')
+pylab.plot(B[0,neutral], B[1,neutral], 'ys')
+pylab.plot([0.5], [0.5], '+')
+pylab.plot([0.5, 0.5], [0,1], ':', [0,1], [0.5,0.5], ':')
+pylab.axis([0,1,0,1])
+pylab.contour(pylab.array(X), pylab.array(Y), pylab.array(utility(X,Y)),
+ [utility(0.5,0.5)], colors='k')
+pylab.xlabel('x1')
+pylab.ylabel('x2')
+pylab.title('Result of preference analysis (fig. 6.26)')
+pylab.show()
diff --git a/examples/book/chap6/cvxfit b/examples/book/chap6/cvxfit
new file mode 100755
index 0000000..f649289
--- /dev/null
+++ b/examples/book/chap6/cvxfit
@@ -0,0 +1,58 @@
+#!/usr/bin/python
+
+# Figure 6.24, page 339.
+# Least-squares fit of a convex function.
+
+import pylab
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, mul
+from pickle import load
+solvers.options['show_progress'] = 0
+
+data = load(open('cvxfit.pic','r'))
+u, y = data['u'], data['y']
+m = len(u)
+
+# minimize (1/2) * || yhat - y ||_2^2
+# subject to yhat[j] >= yhat[i] + g[i]' * (u[j] - u[i]),
+# j, i = 0,...,m-1
+#
+# Variables yhat (m), g (m).
+
+nvars = 2*m
+P = spmatrix(1.0, range(m), range(m), (nvars, nvars))
+q = matrix(0.0, (nvars,1))
+q[:m] = -y
+
+# m blocks (i = 0,...,m-1) of linear inequalities
+#
+# yhat[i] + g[i]' * (u[j] - u[i]) <= yhat[j], j = 0,...,m-1.
+
+G = spmatrix([],[],[], (m**2, nvars))
+I = spmatrix(1.0, range(m), range(m))
+for i in xrange(m):
+ # coefficients of yhat[i]
+ G[range(i*m, (i+1)*m), i] = 1.0
+
+ # coefficients of g[i]
+ G[range(i*m, (i+1)*m), m+i] = u - u[i]
+
+ # coefficients of yhat[j]
+ G[range(i*m, (i+1)*m), range(m)] -= I
+
+h = matrix(0.0, (m**2,1))
+
+sol = solvers.qp(P, q, G, h)
+yhat = sol['x'][:m]
+g = sol['x'][m:]
+
+nopts = 1000
+ts = [ 2.2/nopts * t for t in xrange(1000) ]
+f = [ max(yhat + mul(g, t-u)) for t in ts ]
+pylab.figure(1, facecolor='w')
+pylab.plot(u, y, 'wo', markeredgecolor='b')
+pylab.plot(ts, f, '-g')
+pylab.axis([-0.1, 2.3, -1.1, 7.2])
+pylab.axis('off')
+pylab.title('Least-squares fit of convex function (fig. 6.24)')
+pylab.show()
diff --git a/examples/book/chap6/cvxfit.pic b/examples/book/chap6/cvxfit.pic
new file mode 100644
index 0000000..ca2be7e
--- /dev/null
+++ b/examples/book/chap6/cvxfit.pic
@@ -0,0 +1,127 @@
+(dp0
+S'y'
+p1
+ccvxopt.base
+matrix
+p2
+((lp3
+F5.2057354002832819
+aF5.168529540303874
+aF4.4693174707257226
+aF3.1676414922996394
+aF3.2186726818679299
+aF2.7558774192658637
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+aF4.9123027288568162
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+a(I51
+I1
+tp4
+S'd'
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+tp6
+Rp7
+sS'u'
+p8
+g2
+((lp9
+F0.0
+aF0.040000000000000001
+aF0.080000000000000002
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+aF0.16
+aF0.20000000000000001
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+aF0.80000000000000004
+aF0.83999999999999997
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+aF0.95999999999999996
+aF1.0
+aF1.04
+aF1.0800000000000001
+aF1.1200000000000001
+aF1.1600000000000001
+aF1.2
+aF1.24
+aF1.28
+aF1.3199999999999998
+aF1.3599999999999999
+aF1.3999999999999999
+aF1.4399999999999999
+aF1.48
+aF1.52
+aF1.5600000000000001
+aF1.6000000000000001
+aF1.6400000000000001
+aF1.6799999999999999
+aF1.72
+aF1.76
+aF1.8
+aF1.8400000000000001
+aF1.8799999999999999
+aF1.9199999999999999
+aF1.96
+aF2.0
+a(I51
+I1
+tp10
+g5
+tp11
+Rp12
+s.
\ No newline at end of file
diff --git a/examples/book/chap6/huber b/examples/book/chap6/huber
new file mode 100755
index 0000000..14d0b3b
--- /dev/null
+++ b/examples/book/chap6/huber
@@ -0,0 +1,83 @@
+#!/usr/bin/python
+
+# Figure 6.5, page 300.
+# Robust regression.
+
+from cvxopt import solvers, lapack
+from cvxopt.base import matrix, spmatrix
+import pylab
+from pickle import load
+solvers.options['show_progress'] = 0
+
+data = load(open('huber.pic','r'))
+u, v = data['u'], data['v']
+m, n = len(u), 2
+
+A = matrix( [m*[1.0], [u]] )
+b = +v
+
+# Least squares solution.
+xls = +b
+lapack.gels(+A, xls)
+xls = xls[:2]
+
+
+# Robust least squares.
+#
+# minimize sum( h( A*x-b ))
+#
+# where h(u) = u^2 if |u| <= 1.0
+# = 2*(|u| - 1.0) if |u| > 1.0.
+#
+# Solve as a QP (see exercise 4.5):
+#
+# minimize (1/2) * u'*u + 1'*v
+# subject to -u - v <= A*x-b <= u + v
+# 0 <= u <= 1
+# v >= 0
+#
+# Variables x (n), u (m), v(m)
+
+novars = n+2*m
+P = spmatrix([],[],[], (novars, novars))
+P[n:n+m,n:n+m] = spmatrix(1.0, range(m), range(m))
+q = matrix(0.0, (novars,1))
+q[-m:] = 1.0
+
+G = spmatrix([], [], [], (5*m, novars))
+h = matrix(0.0, (5*m,1))
+
+# A*x - b <= u+v
+G[:m,:n] = A
+G[:m,n:n+m] = spmatrix(-1.0, range(m), range(m))
+G[:m,n+m:] = spmatrix(-1.0, range(m), range(m))
+h[:m] = b
+
+# -u - v <= A*x - b
+G[m:2*m,:n] = -A
+G[m:2*m,n:n+m] = spmatrix(-1.0, range(m), range(m))
+G[m:2*m,n+m:] = spmatrix(-1.0, range(m), range(m))
+h[m:2*m] = -b
+
+# u >= 0
+G[2*m:3*m,n:n+m] = spmatrix(-1.0, range(m), range(m))
+
+# u <= 1
+G[3*m:4*m,n:n+m] = spmatrix(1.0, range(m), range(m))
+h[3*m:4*m] = 1.0
+
+# v >= 0
+G[4*m:,n+m:] = spmatrix(-1.0, range(m), range(m))
+
+xh = solvers.qp(P, q, G, h)['x'][:n]
+
+pylab.figure(1,facecolor='w')
+pylab.plot(u, v,'o',
+ [-11,11], [xh[0]-11*xh[1], xh[0]+11*xh[1]], '-g',
+ [-11,11], [xls[0]-11*xls[1], xls[0]+11*xls[1]], '--r',
+ markerfacecolor='w', markeredgecolor='b')
+pylab.axis([-11, 11, -20, 25])
+pylab.xlabel('t')
+pylab.ylabel('f(t)')
+pylab.title('Robust regression (fig. 6.5)')
+pylab.show()
diff --git a/examples/book/chap6/huber.pic b/examples/book/chap6/huber.pic
new file mode 100644
index 0000000..4b382a5
--- /dev/null
+++ b/examples/book/chap6/huber.pic
@@ -0,0 +1,109 @@
+(dp0
+S'u'
+p1
+ccvxopt.base
+matrix
+p2
+((lp3
+F0.2581787157143367
+aF-0.79032498914297911
+aF-2.9920925260484657
+aF-8.0990852965503386
+aF-1.3265791215591971
+aF4.184703954581499
+aF-7.6806353487449863
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+aF-2.6149418356897964
+aF-9.3274324384180041
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+aF-0.57280309059322043
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+aF-1.0793022769872564
+aF0.16663067516248198
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+aF1.457560328514111
+aF-2.7835586633456675
+aF-3.2704548506394282
+aF-6.5346746968732559
+aF-8.2776303488191356
+aF-2.1332726032162421
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+aF-9.7783862518977305
+aF-5.3377356451646127
+aF8.677011718357452
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+aF5.7189394048037663
+aF-1.7854234631105435
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+aF2.6874068997276055
+aF7.247763721853385
+aF-6.8351268101647156
+aF2.0237015616259075
+aF-7.6478537533655082
+aF2.5219671859042574
+aF6.7024934928410183
+aF-9.5
+aF9.0
+a(I42
+I1
+tp4
+S'd'
+p5
+tp6
+Rp7
+sS'v'
+p8
+g2
+((lp9
+F5.4936896400312936
+aF5.4274168025687288
+aF2.5957278032779536
+aF-2.7682391951102887
+aF4.4450599912428901
+aF8.8287508575062894
+aF-2.9443247093129354
+aF-3.5593049753212678
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+aF-2.1188068795744126
+aF4.9546317086933325
+aF-2.300988118339931
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+aF7.7935911147364498
+aF3.1937903207238514
+aF4.303236510004866
+aF4.9477606964246261
+aF5.0033964014225072
+aF6.0324219885427803
+aF2.4207250219709726
+aF1.0605990066305857
+aF-1.4556289000445948
+aF-3.0969998656187521
+aF2.6304308708244863
+aF11.358429048442082
+aF-5.143167335848978
+aF0.23615669383315208
+aF13.58831462050204
+aF0.094486689236513599
+aF10.53303094377349
+aF3.3789693568024424
+aF-1.8187583043782631
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+aF12.761815572041129
+aF-2.4380182798326717
+aF6.0830273125621552
+aF-2.2168483473403287
+aF7.387425622245142
+aF11.458313858767751
+aF20.0
+aF-15.0
+a(I42
+I1
+tp10
+g5
+tp11
+Rp12
+s.
\ No newline at end of file
diff --git a/examples/book/chap6/inputdesign b/examples/book/chap6/inputdesign
new file mode 100755
index 0000000..efe9f0f
--- /dev/null
+++ b/examples/book/chap6/inputdesign
@@ -0,0 +1,93 @@
+#!/usr/bin/python
+
+# Figure 6.6, page 309.
+# Input design.
+
+from math import cos, sqrt
+from cvxopt import lapack
+from cvxopt.base import matrix
+import pylab
+
+m, n = 201, 201
+
+# Jtrack = 1/n * ||H*u-ydes||_2^2.
+H = matrix(0.0, (m,m))
+for t in xrange(m):
+ H[t::m+1] = (1.0/9.0) * .9**t * (1.0 - 0.4 * cos(2*t))
+ydes = matrix( 40*[0.0] + 50*[1.0] + 50*[-1.0] + 61*[0.0] )
+
+# Jmag = 1/n * ||I*u||_2^2
+I = matrix(0.0, (n,n))
+I[::n+1] = 1.0
+
+# Jder = 1/(n-1) * ||D*u||_2^2
+D = matrix(0.0, (n-1,n))
+D[::n] = -1.0
+D[n-1::n] = 1.0
+
+AA = matrix(0.0, (m + 2*n - 1, n))
+bb = matrix(0.0, (m + 2*n - 1, 1))
+AA[:n,:] = H
+bb[:n] = ydes
+
+delta, eta = 0.0, 0.005
+AA[n:2*n,:] = sqrt(eta)*I
+AA[2*n:,:] = sqrt(delta)*D
+x = +bb
+lapack.gels(+AA, x)
+u1 = x[:n]
+
+pylab.figure(1, facecolor='w', figsize=(10,10))
+ts = matrix(range(n), tc='d')
+pylab.subplot(321)
+pylab.plot(ts, u1, '-')
+pylab.xlabel('t')
+pylab.ylabel('u(t)')
+pylab.axis([0, 200, -10, 5])
+pylab.title('Optimal input (fig. 6.6.)')
+pylab.subplot(322)
+pylab.plot(ts, H*u1, '-', ts, ydes, 'g--')
+pylab.xlabel('t')
+pylab.ylabel('y(t)')
+pylab.axis([0, 200, -1.1, 1.1])
+pylab.title('Output')
+
+
+delta, eta = 0.0, 0.05
+AA[n:2*n,:] = sqrt(eta)*I
+AA[2*n:,:] = sqrt(delta)*D
+x = +bb
+lapack.gels(+AA, x)
+u2 = x[:n]
+
+pylab.subplot(323)
+pylab.plot(ts, u2, '-')
+pylab.xlabel('t')
+pylab.ylabel('u(t)')
+pylab.axis([0, 200, -4, 4])
+pylab.subplot(324)
+pylab.plot(ts, H*u2, '-', ts, ydes, 'g--')
+pylab.ylabel('y(t)')
+pylab.xlabel('t')
+pylab.axis([0, 200, -1.1, 1.1])
+
+
+delta, eta = 0.3, 0.05
+AA[n:2*n,:] = sqrt(eta)*I
+AA[2*n:,:] = sqrt(delta)*D
+x = +bb
+lapack.gels(+AA, x)
+u3 = x[:n]
+
+pylab.subplot(325)
+pylab.plot(ts, u3, '-')
+pylab.xlabel('t')
+pylab.ylabel('u(t)')
+pylab.axis([0, 200, -4, 4])
+pylab.subplot(326)
+pylab.plot(ts, H*u3, '-', ts, ydes, 'g--')
+pylab.ylabel('y(t)')
+pylab.xlabel('t')
+pylab.axis([0, 200, -1.1, 1.1])
+
+pylab.show()
diff --git a/examples/book/chap6/penalties b/examples/book/chap6/penalties
new file mode 100755
index 0000000..98c45a4
--- /dev/null
+++ b/examples/book/chap6/penalties
@@ -0,0 +1,98 @@
+#!/usr/bin/python
+
+# Figure 6.2, page 297.
+# Penalty approximation.
+#
+# The problem data are not the same as in the book figure.
+
+import pylab
+from cvxopt import random, lapack, solvers
+from cvxopt.base import matrix, spmatrix, log, div
+from cvxopt.modeling import variable, op, max, sum
+solvers.options['show_progress'] = 0
+
+m, n = 100, 30
+A = random.normal(m,n)
+b = random.normal(m,1)
+b /= (1.1 * max(abs(b))) # Make x = 0 feasible for log barrier.
+
+
+# l1 approximation
+#
+# minimize || A*x + b ||_1
+
+x = variable(n)
+op(sum(abs(A*x+b))).solve()
+x1 = x.value
+
+pylab.figure(1, facecolor='w', figsize=(10,10))
+pylab.subplot(411)
+nbins = 100
+bins = [-1.5 + 3.0/(nbins-1)*k for k in xrange(nbins)]
+pylab.hist( A*x1+b , bins)
+nopts = 200
+xs = -1.5 + 3.0/(nopts-1) * matrix(range(nopts))
+pylab.plot(xs, (35.0/1.5) * abs(xs), 'g-')
+pylab.axis([-1.5, 1.5, 0, 40])
+pylab.ylabel('l1')
+pylab.title('Penalty function approximation (fig. 6.2)')
+
+
+
+# l2 approximation
+#
+# minimize || A*x + b ||_2
+
+x = matrix(0.0, (m,1))
+lapack.gels(+A, x)
+x2 = x[:n]
+
+pylab.subplot(412)
+pylab.hist( A*x2+b , bins)
+pylab.plot(xs, (8.0/1.5**2) * xs**2 , 'g-')
+pylab.ylabel('l2')
+pylab.axis([-1.5, 1.5, 0, 10])
+
+
+# Deadzone approximation
+#
+# minimize sum(max(abs(A*x+b)-0.5, 0.0))
+
+x = variable(n)
+op(sum(max(abs(A*x+b)-0.5, 0.0))).solve()
+xdz = x.value
+
+pylab.subplot(413)
+pylab.hist( A*xdz+b , bins)
+pylab.plot(xs, 15.0/1.0 * matrix([ max(abs(xk)-0.5, 0.0) for xk
+ in xs ]), 'g-')
+pylab.ylabel('Deadzone')
+pylab.axis([-1.5, 1.5, 0, 20])
+
+
+# Log barrier
+#
+# minimize -sum (log ( 1.0 - A*x+b)**2)
+
+def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (n,1))
+ y = A*x+b
+ if max(abs(y)) >= 1.0: return None
+ f = -sum(log(1.0 - y**2))
+ gradf = 2.0 * A.T * div(y, 1-y**2)
+ if z is None: return f, gradf.T
+ H = A.T * spmatrix(2.0 * div( 1.0+y**2, (1.0 - y**2)**2 ), range(m),
+ range(m)) * A
+ return f, gradf.T, z[0]*H
+xlb = solvers.cp(F)['x']
+
+pylab.subplot(414)
+pylab.hist( A*xlb+b , bins)
+nopts = 200
+pylab.plot(xs, (8.0/1.5**2) * xs**2, 'g--')
+xs2 = -0.99999 + (2*0.99999 /(nopts-1)) * matrix(range(nopts))
+pylab.plot(xs2, -3.0 * log(1.0 - abs(xs2)**2), 'g-')
+pylab.ylabel('Log barrier')
+pylab.xlabel('residual')
+pylab.axis([-1.5, 1.5, 0, 10])
+pylab.show()
diff --git a/examples/book/chap6/polapprox b/examples/book/chap6/polapprox
new file mode 100755
index 0000000..1d9524b
--- /dev/null
+++ b/examples/book/chap6/polapprox
@@ -0,0 +1,148 @@
+#!/usr/bin/python
+
+# Figures 6.19 and 6.20, page 332.
+# Polynomial and spline fitting.
+
+from cvxopt import lapack, solvers
+from cvxopt.base import matrix, mul
+from cvxopt.modeling import op, variable, max
+import pylab
+from pickle import load
+solvers.options['show_progress'] = 0
+
+data = load(open('polapprox.pic','r'))
+t, y = data['t'], data['y']
+m = len(t)
+
+# LS fit of 5th order polynomial
+#
+# minimize ||A*x - y ||_2
+
+n = 6
+A = matrix( [[t**k] for k in xrange(n)] )
+xls = +y
+lapack.gels(+A,xls)
+xls = xls[:n]
+
+# Chebyshev fit of 5th order polynomial
+#
+# minimize ||A*x - y ||_inf
+
+xinf = variable(n)
+op( max(abs(A*xinf - y)) ).solve()
+xinf = xinf.value
+
+pylab.figure(1, facecolor='w')
+pylab.plot(t, y, 'bo', mfc='w', mec='b')
+nopts = 1000
+ts = -1.1 + (1.1 - (-1.1))/nopts * matrix(range(nopts), tc='d')
+yls = sum( xls[k] * ts**k for k in xrange(n) )
+yinf = sum( xinf[k] * ts**k for k in xrange(n) )
+pylab.plot(ts,yls,'g-', ts, yinf, '--r')
+pylab.axis([-1.1, 1.1, -0.1, 0.25])
+pylab.xlabel('u')
+pylab.ylabel('p(u)')
+pylab.title('Polynomial fitting (fig. 6.19)')
+
+
+# Fit of cubic spline
+#
+# f(t) = p1(t) -1 <= t <= -1/3
+# = p2(t) -1/3 <= t <= 1/3
+# = p3(t) 1/3 <= t <= 1
+#
+# p1(t) = x0 + x1*t + x2*t^2 + x3*t^3 -1 <= t <= -1/3
+# p2(t) = x4 + x5*t + x6*t^2 + x7*t^3 -1/3 <= t <= 1/3
+# p3(t) = x8 + x9*t + x10*t^2 + x11*t^3 1/3 <= t <= 1
+#
+# with constraints
+#
+# p1(-1/3) = p2(-1/3),
+# p1'(-1/3) = p2'(-1/3)
+# p1''(-1/3) = p2''(-1/3)
+# p2(1/3) = p3(1/3),
+# p2'(1/3) = p3'(1/3)
+# p2''(1/3) = p3''(1/3)
+
+
+n = 12
+u1, u2 = -1.0/3, 1.0/3
+I1 = [ k for k in xrange(m) if -1.0 <= t[k] < u1 ]
+I2 = [ k for k in xrange(m) if u1 <= t[k] < u2 ]
+I3 = [ k for k in xrange(m) if u2 <= t[k] <= 1.0 ]
+m1, m2, m3 = len(I1), len(I2), len(I3)
+A = matrix(0.0, (m,n))
+for k in xrange(4):
+ A[I1,k] = t[I1]**k
+ A[I2,k+4] = t[I2]**k
+ A[I3,k+8] = t[I3]**k
+
+G = matrix(0.0, (6,n))
+
+# p1(u1) = p2(u1), p1(u2) = p2(u2)
+G[0, range(8)] = 1.0, u1, u1**2, u1**3, -1.0, -u1, -u1**2, -u1**3
+G[1, range(4,12)] = 1.0, u2, u2**2, u2**3, -1.0, -u2, -u2**2, -u2**3
+
+# p1'(u1) = p2'(u1), p1'(u2) = p2'(u2)
+G[2, [1,2,3,5,6,7]] = 1.0, 2*u1, 3*u1**2, -1.0, -2*u1, -3*u1**2
+G[3, [5,6,7,9,10,11]] = 1.0, 2*u2, 3*u2**2, -1.0, -2*u2, -3*u2**2
+
+# p1''(u1) = p2''(u1), p1''(u2) = p2''(u2)
+G[4, [2,3,6,7]] = 2, 6*u1, -2, -6*u1
+G[5, [6,7,10,11]] = 2, 6*u2, -2, -6*u2
+
+
+# LS fit
+#
+# minimize (1/2) * || A*x - y ||_2^2
+# subject to G*x = h
+#
+# Solve as a linear equation
+#
+# [ A'*A G' ] [ x ] [ A'*y ]
+# [ G 0 ] [ y ] = [ 0 ].
+
+K = matrix(0.0, (n+6,n+6))
+K[:n,:n] = A.T * A
+K[n:,:n] = G
+xls = matrix(0.0, (n+6,1))
+xls[:n] = A.T * y
+lapack.sysv(K, xls)
+xls = xls[:n]
+
+
+# Chebyshev fit
+#
+# minimize || A*x - y ||_inf
+# subject to G*x = h
+
+xcheb = variable(12)
+op( max(abs(A*xcheb - y)), [G*xcheb == 0]).solve()
+xcheb = xcheb.value
+
+pylab.figure(2, facecolor='w')
+nopts = 100
+ts = -1.0 + (1.0 - (-1.0))/nopts * matrix(range(nopts), tc='d')
+I1 = [ k for k in xrange(nopts) if -1.0 <= ts[k] < u1 ]
+I2 = [ k for k in xrange(nopts) if u1 <= ts[k] < u2 ]
+I3 = [ k for k in xrange(nopts) if u2 <= ts[k] <= 1.0 ]
+yls = matrix(0.0, (nopts,1))
+yls[I1] = sum( xls[k]*ts[I1]**k for k in xrange(4) )
+yls[I2] = sum( xls[k+4]*ts[I2]**k for k in xrange(4) )
+yls[I3] = sum( xls[k+8]*ts[I3]**k for k in xrange(4) )
+ycheb = matrix(0.0, (nopts,1))
+ycheb[I1] = sum( xcheb[k]*ts[I1]**k for k in xrange(4) )
+ycheb[I2] = sum( xcheb[k+4]*ts[I2]**k for k in xrange(4) )
+ycheb[I3] = sum( xcheb[k+8]*ts[I3]**k for k in xrange(4) )
+
+pylab.plot(t, y, 'bo', mfc='w', mec='b')
+pylab.plot([-1.0, -1.0], [-0.1, 0.25], 'k--',
+ [-1./3,-1./3], [-0.1, 0.25], 'k--',
+ [1./3,1./3], [-0.1, 0.25], 'k--', [1,1], [-0.1, 0.25], 'k--')
+pylab.plot(ts, yls, '-g', ts, ycheb, '--r')
+pylab.axis([-1.1, 1.1, -0.1, 0.25])
+pylab.xlabel('u')
+pylab.ylabel('p(u)')
+pylab.title('Cubic spline fitting (fig. 6.20)')
+
+pylab.show()
diff --git a/examples/book/chap6/polapprox.pic b/examples/book/chap6/polapprox.pic
new file mode 100644
index 0000000..7474e93
--- /dev/null
+++ b/examples/book/chap6/polapprox.pic
@@ -0,0 +1,105 @@
+(dp0
+S'y'
+p1
+ccvxopt.base
+matrix
+p2
+((lp3
+F-0.082103425893059981
+aF-0.077658017081031816
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+g5
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\ No newline at end of file
diff --git a/examples/book/chap6/regsel b/examples/book/chap6/regsel
new file mode 100755
index 0000000..d583672
--- /dev/null
+++ b/examples/book/chap6/regsel
@@ -0,0 +1,127 @@
+#!/usr/bin/python
+
+# Figure 6.7, page 311.
+# Sparse regressor selection.
+#
+# The problem data are different from the book.
+
+import pylab
+from cvxopt import blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, mul
+from pickle import load
+solvers.options['show_progress'] = 0
+
+data = load(open('regsel.pic','r'))
+A, b = data['A'], data['b']
+m, n = A.size
+
+# In the heuristic, set x[k] to zero if abs(x[k]) <= tol * max(abs(x)).
+tol = 1e-1
+
+# Data for QP
+#
+# minimize (1/2) ||A*x - b|_2^2
+# subject to -y <= x <= y
+# sum(y) <= alpha
+
+P = matrix(0.0, (2*n,2*n))
+P[:n,:n] = A.T*A
+q = matrix(0.0, (2*n,1))
+q[:n] = -A.T*b
+I = matrix(0.0, (n,n))
+I[::n+1] = 1.0
+G = matrix([[I, -I, matrix(0.0, (1,n))], [-I, -I, matrix(1.0, (1,n))]])
+h = matrix(0.0, (2*n+1,1))
+
+# Least-norm solution
+xln = matrix(0.0, (n,1))
+xln[:m] = b
+lapack.gels(+A, xln)
+
+nopts = 100
+res = [ blas.nrm2(b) ]
+card = [ 0 ]
+alphas = blas.asum(xln)/(nopts-1) * matrix(range(1,nopts), tc='d')
+for alpha in alphas:
+
+ # minimize ||A*x-b||_2
+ # subject to ||x||_1 <= alpha
+
+ h[-1] = alpha
+ x = solvers.qp(P, q, G, h)['x'][:n]
+ xmax = max(abs(x))
+ I = [ k for k in xrange(n) if abs(x[k]) > tol*xmax ]
+ if len(I) <= m:
+ xs = +b
+ lapack.gels(A[:,I], xs)
+ x[:] = 0.0
+ x[I] = xs[:len(I)]
+ res += [ blas.nrm2(A*x-b) ]
+ card += [ len(I) ]
+
+# Eliminate duplicate cardinalities and make staircase plot.
+res2, card2 = [], []
+for c in xrange(m+1):
+ r = [ res[k] for k in xrange(len(res)) if card[k] == c ]
+ if r:
+ res2 += [ min(r), min(r) ]
+ card2 += [ c, c+1 ]
+
+pylab.figure(1, facecolor='w')
+pylab.plot( res2[::2], card2[::2], 'o')
+pylab.plot( res2, card2, '-')
+pylab.xlabel('||A*x-b||_2')
+pylab.ylabel('card(x)')
+pylab.title('Sparse regressor selection (fig 6.7)')
+print "Close figure to start exhaustive search."
+pylab.show()
+
+
+# Exhaustive search.
+
+def patterns(k,n):
+ """
+ Generates all 0-1 sequences of length n with exactly k nonzeros.
+ """
+ if k==0:
+ yield n*[0]
+ else:
+ for x in patterns(k-1,n-1): yield [1] + x
+ if k <= n-1:
+ for x in patterns(k,n-1): yield [0] + x
+
+
+bestx = matrix(0.0, (n, m)) # best solution for each cardinality
+bestres = matrix(blas.nrm2(b), (1, m+1)) # best residual
+x = matrix(0.0, (n,1))
+for k in xrange(1,m):
+ for s in patterns(k,n):
+ I = [ i for i in xrange(n) if s[i] ]
+ s = [k] + s
+ print ("%d nonzeros: " + n*"%d") %tuple(s)
+ x = +b
+ lapack.gels(A[:,I], x)
+ res = blas.nrm2(b - A[:,I] * x[:k])
+ if res < bestres[k]:
+ bestres[k] = res
+ bestx[:,k][I] = x[:k]
+bestres[m] = 0.0
+
+pylab.figure(1, facecolor='w')
+
+# heuristic result
+pylab.plot( res2[::2], card2[::2], 'o' )
+pylab.plot( res2, card2, '-')
+
+# exhaustive result
+res2, card2 = [ bestres[0] ], [ 0 ]
+for k in xrange(1,m+1):
+ res2 += [bestres[k-1], bestres[k]]
+ card2 += [ k, k]
+pylab.plot( bestres, range(m+1), 'go')
+pylab.plot( res2, card2, 'g-')
+
+pylab.xlabel('||A*x-b||_2')
+pylab.ylabel('card(x)')
+pylab.title('Sparse regressor selection (fig 6.7)')
+pylab.show()
diff --git a/examples/book/chap6/regsel.pic b/examples/book/chap6/regsel.pic
new file mode 100644
index 0000000..20f6469
--- /dev/null
+++ b/examples/book/chap6/regsel.pic
@@ -0,0 +1,235 @@
+(dp0
+S'A'
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+a(I10
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+S'd'
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+s.
\ No newline at end of file
diff --git a/examples/book/chap6/robls b/examples/book/chap6/robls
new file mode 100755
index 0000000..6efcbf7
--- /dev/null
+++ b/examples/book/chap6/robls
@@ -0,0 +1,161 @@
+#!/usr/bin/python
+
+# Figures 6.15 and 6.16, pages 320 and 325.
+# Stochastic and worst-case robust approximation.
+
+from math import pi
+from cvxopt import random, blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, mul, cos, sin, sqrt
+import pylab
+from pickle import load
+solvers.options['show_progress'] = 0
+
+def wcls(A, Ap, b):
+ """
+ Solves the robust least squares problem
+
+ minimize sup_{||u||<= 1} || (A + sum_k u[k]*Ap[k])*x - b ||_2^2.
+
+ A is mxn. Ap is a list of mxn matrices. b is mx1.
+ """
+
+ (m, n), p = A.size, len(Ap)
+
+ # minimize t + v
+ # subject to [ I * * ]
+ # [ P(x)' v*I -* ] >= 0.
+ # [ (A*x-b)' 0 t ]
+ #
+ # where P(x) = [Ap[0]*x, Ap[1]*x, ..., Ap[p-1]*x].
+ #
+ # Variables x (n), v (1), t(1).
+
+ novars = n + 2
+ M = m + p + 1
+ c = matrix( n*[0.0] + 2*[1.0])
+ Fs = [spmatrix([],[],[], (M**2, novars))]
+ for k in xrange(n):
+ # coefficient of x[k]
+ S = spmatrix([], [], [], (M, M))
+ for j in xrange(p):
+ S[m+j, :m] = -Ap[j][:,k].T
+ S[-1, :m ] = -A[:,k].T
+ Fs[0][:,k] = S[:]
+ # coefficient of v
+ Fs[0][(M+1)*m : (M+1)*(m+p) : M+1, -2] = -1.0
+ # coefficient of t
+ Fs[0][-1, -1] = -1.0
+
+ hs = [matrix(0.0, (M, M))]
+ hs[0][:(M+1)*m:M+1] = 1.0
+ hs[0][-1, :m] = -b.T
+
+ return solvers.sdp(c, None, None, Fs, hs)['x'][:n]
+
+
+# Figure 6.15
+
+data = load(open('robls.pic','r'))['6.15']
+A, b, B = data['A'], data['b'], data['B']
+m, n = A.size
+
+# Nominal problem: minimize || A*x - b ||_2
+xnom = +b
+lapack.gels(+A, xnom)
+xnom = xnom[:n]
+
+
+# Stochastic problem.
+#
+# minimize E || (A+u*B) * x - b ||_2^2
+# = || A*x - b||_2^2 + x'*P*x
+#
+# with P = E(u^2) * B'*B = (1/3) * B'*B
+
+S = A.T * A + (1.0/3.0) * B.T * B
+xstoch = A.T * b
+lapack.posv(S, xstoch)
+
+
+# Worst case approximation.
+#
+# minimize max_{-1 <= u <= 1} ||A*u - b||_2^2.
+
+xwc = wcls(A, [B], b)
+
+pylab.figure(1, facecolor='w')
+nopts = 500
+us = -2.0 + (2.0 - (-2.0))/(nopts-1) * matrix(range(nopts),tc='d')
+rnom = [ blas.nrm2( (A+u*B)*xnom - b) for u in us ]
+rstoch = [ blas.nrm2( (A+u*B)*xstoch - b) for u in us ]
+rwc = [ blas.nrm2( (A+u*B)*xwc - b) for u in us ]
+pylab.plot(us, rnom, us, rstoch, us, rwc)
+pylab.plot([-1, -1], [0, 12], '--k', [1, 1], [0, 12], '--k')
+pylab.axis([-2.0, 2.0, 0.0, 12.0])
+pylab.xlabel('u')
+pylab.ylabel('r(u)')
+pylab.text(us[9], rnom[9], 'nominal')
+pylab.text(us[9], rstoch[9], 'stochastic')
+pylab.text(us[9], rwc[9], 'worst case')
+pylab.title('Robust least-squares (fig.6.15)')
+
+
+# Figure 6.16
+
+data = load(open('robls.pic','r'))['6.16']
+A, Ap, b = data['A0'], [data['A1'], data['A2']], data['b']
+(m, n), p = A.size, len(Ap)
+
+# least squares solution: minimize || A*x - b ||_2^2
+xls = +b
+lapack.gels(+A, xls)
+xls = xls[:n]
+
+# Tikhonov solution: minimize || A*x - b ||_2^2 + 0.1*||x||^2_2
+xtik = A.T*b
+S = A.T*A
+S[::n+1] += 0.1
+lapack.posv(S, xtik)
+
+# Worst case solution
+xwc = wcls(A, Ap, b)
+
+notrials = 100000
+r = sqrt(random.uniform(1,notrials))
+theta = 2.0 * pi * random.uniform(1,notrials)
+u = matrix(0.0, (2,notrials))
+u[0,:] = mul(r, cos(theta))
+u[1,:] = mul(r, sin(theta))
+
+# LS solution
+q = A*xls - b
+P = matrix(0.0, (m,2))
+P[:,0], P[:,1] = Ap[0]*xls, Ap[1]*xls
+r = P*u + q[:,notrials*[0]]
+resls = sqrt( matrix(1.0, (1,m)) * mul(r,r) )
+
+q = A*xtik - b
+P[:,0], P[:,1] = Ap[0]*xtik, Ap[1]*xtik
+r = P*u + q[:,notrials*[0]]
+restik = sqrt( matrix(1.0, (1,m)) * mul(r,r) )
+
+q = A*xwc - b
+P[:,0], P[:,1] = Ap[0]*xwc, Ap[1]*xwc
+r = P*u + q[:,notrials*[0]]
+reswc = sqrt( matrix(1.0, (1,m)) * mul(r,r) )
+
+pylab.figure(2, facecolor='w')
+pylab.hist(resls, [0.1*k for k in xrange(50)], fc='w',
+ normed=True)
+pylab.text(4.4, 0.4, 'least-squares')
+pylab.hist(restik, [0.1*k for k in xrange(50)], fc='#D0D0D0',
+ normed=True)
+pylab.text(2.9, 0.75, 'Tikhonov')
+pylab.hist(reswc, [0.1*k for k in xrange(50)], fc='#B0B0B0',
+ normed=True)
+pylab.text(2.5, 2.0, 'robust least-squares')
+pylab.xlabel('residual')
+pylab.ylabel('frequency/binwidth')
+pylab.axis([0, 5, 0, 2.5])
+pylab.title('LS, Tikhonov and robust LS solutions (fig. 6.16)')
+pylab.show()
diff --git a/examples/book/chap6/robls.pic b/examples/book/chap6/robls.pic
new file mode 100644
index 0000000..d7dc67c
--- /dev/null
+++ b/examples/book/chap6/robls.pic
@@ -0,0 +1,3551 @@
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\ No newline at end of file
diff --git a/examples/book/chap6/smoothrec b/examples/book/chap6/smoothrec
new file mode 100755
index 0000000..ddca231
--- /dev/null
+++ b/examples/book/chap6/smoothrec
@@ -0,0 +1,84 @@
+#!/usr/bin/python
+
+# Figures 6.8-10, pages 313-314
+# Quadratic smoothing.
+
+from math import pi
+from cvxopt import random, blas, lapack
+from cvxopt.base import matrix, spmatrix, sin, mul
+import pylab
+
+n = 4000
+t = matrix(range(n), tc='d')
+ex = 0.5 * mul( sin(2*pi/n * t), sin(0.01 * t))
+corr = ex + 0.05 * random.normal(n,1)
+
+pylab.figure(1, facecolor='w', figsize=(8,5))
+pylab.subplot(211)
+pylab.plot(t, ex)
+pylab.ylabel('x[i]')
+pylab.xlabel('i')
+pylab.title('Original and corrupted signal (fig. 6.8)')
+pylab.subplot(212)
+pylab.plot(t, corr)
+pylab.ylabel('xcor[i]')
+pylab.xlabel('i')
+
+
+# A = D'*D is an n by n tridiagonal matrix with -1.0 on the
+# upper/lower diagonal and 1, 2, 2, ..., 2, 2, 1 on the diagonal.
+Ad = matrix([1.0] + (n-2)*[2.0] + [1.0])
+As = matrix(-1.0, (n-1,1))
+
+nopts = 50
+deltas = -10.0 + 20.0/(nopts-1) * matrix(range(nopts))
+cost1, cost2 = [], []
+for delta in deltas:
+ xr = +corr
+ lapack.ptsv(1.0 + 10**delta * Ad, 10**delta *As, xr)
+ cost1 += [blas.nrm2(xr - corr)]
+ cost2 += [blas.nrm2(xr[1:] - xr[:-1])]
+
+# Find solutions with ||xhat - xcorr || roughly equal to 8.0, 3.1, 1.0.
+mv1, k1 = min(zip([abs(c - 8.0) for c in cost1], range(nopts)))
+xr1 = +corr
+lapack.ptsv(1.0 + 10**deltas[k1] * Ad, 10**deltas[k1] *As, xr1)
+mv2, k2 = min(zip([abs(c - 3.1) for c in cost1], range(nopts)))
+xr2 = +corr
+lapack.ptsv(1.0 + 10**deltas[k2] * Ad, 10**deltas[k2] *As, xr2)
+mv3, k3 = min(zip([abs(c - 1.0) for c in cost1], range(nopts)))
+xr3 = +corr
+lapack.ptsv(1.0 + 10**deltas[k3] * Ad, 10**deltas[k3] *As, xr3)
+
+pylab.figure(2, facecolor='w')
+pylab.plot(cost1, cost2, [blas.nrm2(corr)], [0], 'o',
+ [0], [blas.nrm2(corr[1:] - corr[:-1])], 'o')
+pylab.plot([cost1[k1]], [cost2[k1]], 'o', [cost1[k2]], [cost2[k2]], 'o',
+ [cost1[k3]], [cost2[k3]], 'o')
+pylab.text(cost1[k1], cost2[k1],'1')
+pylab.text(cost1[k2], cost2[k2],'2')
+pylab.text(cost1[k3], cost2[k3],'3')
+pylab.title('Optimal trade-off curve (fig. 6.9)')
+pylab.xlabel('|| xhat - xcor ||_2')
+pylab.ylabel('|| D*xhat ||_2')
+pylab.axis([-0.4, 20, -0.1, 5])
+pylab.grid()
+
+pylab.figure(3, facecolor='w', figsize=(8,7.5))
+pylab.subplot(311)
+pylab.plot(t, xr1)
+pylab.axis([0, 4000, -0.6, 0.6])
+pylab.ylabel('xhat1[i]')
+pylab.title('Three smoothed sigals (fig. 6.10).')
+
+pylab.subplot(312)
+pylab.plot(t, xr2)
+pylab.ylabel('xhat2[i]')
+pylab.axis([0, 4000, -0.6, 0.6])
+
+pylab.subplot(313)
+pylab.plot(t, xr3)
+pylab.axis([0, 4000, -0.6, 0.6])
+pylab.ylabel('xhat3[i]')
+pylab.xlabel('i')
+pylab.show()
diff --git a/examples/book/chap6/tv b/examples/book/chap6/tv
new file mode 100755
index 0000000..0b4948f
--- /dev/null
+++ b/examples/book/chap6/tv
@@ -0,0 +1,286 @@
+#!/usr/bin/python
+
+# Figures 6.11-14, pages 315-317.
+# Total variation reconstruction.
+
+from math import pi
+from cvxopt import random, blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, sin, mul, div
+solvers.options['show_progress'] = 0
+import pylab
+
+n = 2000
+t = matrix( range(n), tc='d' )
+ex = matrix( n/4*[1.0] + n/4*[-1.0] + n/4*[1.0] + n/4*[-1.0] ) + \
+ 0.5 * sin( 2.0*pi/n * t )
+corr = ex + 0.1 * random.normal(n,1)
+
+pylab.figure(1, facecolor='w', figsize=(8,5))
+pylab.subplot(211)
+pylab.plot(t, ex)
+pylab.ylabel('x[i]')
+pylab.xlabel('i')
+pylab.axis([0, 2000, -2, 2])
+pylab.title('Original and corrupted signal (fig. 6.11)')
+pylab.subplot(212)
+pylab.plot(t, corr)
+pylab.ylabel('xcor[i]')
+pylab.xlabel('i')
+pylab.axis([0, 2000, -2, 2])
+
+
+# Quadratic smoothing.
+# A = D'*D is an n by n tridiagonal matrix with -1.0 on the
+# upper/lower diagonal and 1, 2, 2, ..., 2, 2, 1 on the diagonal.
+Ad = matrix([1.0] + (n-2)*[2.0] + [1.0])
+As = matrix(-1.0, (n-1,1))
+
+nopts = 100
+deltas = -10.0 + 20.0/(nopts-1) * matrix(range(nopts))
+
+cost1, cost2 = [], []
+for delta in deltas:
+ xr = +corr
+ lapack.ptsv(1.0 + 10**delta * Ad, 10**delta * As, xr)
+ cost1 += [blas.nrm2(xr - corr)]
+ cost2 += [blas.nrm2(xr[1:] - xr[:-1])]
+
+# Find solutions with ||xhat - xcorr || roughly equal to 4, 7, 10.
+mv1, k1 = min(zip([abs(c - 10.0) for c in cost1], range(nopts)))
+xr1 = +corr
+lapack.ptsv(1.0 + 10**deltas[k1] * Ad, 10**deltas[k1] * As, xr1)
+mv2, k2 = min(zip([abs(c - 7.0) for c in cost1], range(nopts)))
+xr2 = +corr
+lapack.ptsv(1.0 + 10**deltas[k2] * Ad, 10**deltas[k2] * As, xr2)
+mv3, k3 = min(zip([abs(c - 4.0) for c in cost1], range(nopts)))
+xr3 = +corr
+lapack.ptsv(1.0 + 10**deltas[k3] * Ad, 10**deltas[k3] * As, xr3)
+
+pylab.figure(2, facecolor='w')
+pylab.plot(cost1, cost2, [blas.nrm2(corr)], [0], 'o',
+ [0], [blas.nrm2(corr[1:] - corr[:-1])], 'o')
+pylab.plot([cost1[k1]], [cost2[k1]], 'o',
+ [cost1[k2]], [cost2[k2]], 'o', [cost1[k3]], [cost2[k3]], 'o')
+pylab.text(cost1[k1], cost2[k1], '1')
+pylab.text(cost1[k2], cost2[k2], '2')
+pylab.text(cost1[k3], cost2[k3], '3')
+pylab.title('Optimal trade-off curve (quadratic smoothing)')
+pylab.xlabel('|| xhat - xcor ||_2')
+pylab.ylabel('|| D*xhat ||_2')
+pylab.axis([-0.4, 50, -0.1, 8.0])
+pylab.grid()
+
+pylab.figure(3, facecolor='w', figsize=(8,7.5))
+pylab.subplot(311)
+pylab.plot(t, xr1)
+pylab.axis([0, 2000, -2.0, 2.0])
+pylab.ylabel('xhat1[i]')
+pylab.title('Three quadratically smoothed sigals (fig. 6.12).')
+pylab.subplot(312)
+pylab.plot(t, xr2)
+pylab.ylabel('xhat2[i]')
+pylab.axis([0, 2000, -2.0, 2.0])
+pylab.subplot(313)
+pylab.plot(t, xr3)
+pylab.axis([0, 2000, -2.0, 2.0])
+pylab.ylabel('xhat3[i]')
+pylab.xlabel('i')
+print "Close figures to start total variation reconstruction."
+pylab.show()
+
+
+# Total variation smoothing.
+#
+# minimize (1/2) * ||x-corr||_2^2 + delta * || D*x ||_1
+#
+# minimize (1/2) * ||x-corr||_2^2 + delta * 1'*y
+# subject to -y <= D*x <= y
+#
+# Variables x (n), y (n-1).
+
+def tv(delta):
+ """
+ minimize (1/2) * ||x-corr||_2^2 + delta * sum(y)
+ subject to -y <= D*x <= y
+
+ Variables x (n), y (n-1).
+ """
+
+ def F(x=None):
+ """
+ Function and gradient evaluation of
+
+ f = 1/2 * || x[:n]-corr ||_2^2 + delta * sum(x[n:]).
+ """
+
+ nvars = 2*n - 1
+ if x is None: return 0, matrix(0.0, (nvars,1))
+ f = 0.5 * blas.nrm2( x[:n]-corr )**2 + delta * sum(x[n:])
+ gradf = matrix(0.0, (1,nvars))
+ gradf[:n] = x[:n]-corr
+ gradf[n:] = delta
+ return f, gradf
+
+
+ def G(u, v, alpha=1.0, beta=0.0, trans='N'):
+ """
+ v := alpha*[D, -I; -D, -I] * u + beta * v (trans = 'N')
+ v := alpha*[D, -I; -D, -I]' * u + beta * v (trans = 'T')
+
+ For an n-vector z, D*z = z[1:] - z[:-1].
+ For an (n-1)-vector z, D'*z = [-z;0] + [0; z].
+ """
+
+ v *= beta
+ if trans == 'N':
+ y = u[1:n] - u[:n-1]
+ v[:n-1] += alpha*(y - u[n:])
+ v[n-1:] += alpha*(-y - u[n:])
+ else:
+ y = u[:n-1] - u[n-1:]
+ v[:n-1] -= alpha * y
+ v[1:n] += alpha * y
+ v[n:] -= alpha * (u[:n-1] + u[n-1:])
+
+ h = matrix(0.0, (2*(n-1),1))
+
+
+ # Customized solver for KKT system with coefficient
+ #
+ # [ z[0]*I 0 D' -D' ]
+ # [ 0 0 -I -I ]
+ # [ D -I -D1 0 ]
+ # [ -D -I 0 -D2 ].
+
+ # Diagonal and subdiagonal.
+ Sd = matrix(0.0, (n,1))
+ Se = matrix(0.0, (n-1,1))
+
+ def kktsolver(x, z, dnl, dl):
+ """
+ Factor the tridiagonal matrix
+
+ S = z[0]*I + 4.0 * D' * diag( d1.*d2./(d1+d2) ) * D
+
+ with d1 = dl[:n-1]**2 = diag(D1^-1),
+ d2 = dl[n-1:]**2 = diag(D2^-1).
+ """
+
+ d1 = dl[:n-1]**2
+ d2 = dl[n-1:]**2
+ d = 4.0*div( mul(d1,d2), d1+d2)
+ Sd[:] = z[0]
+ Sd[:n-1] += d
+ Sd[1:] += d
+ Se[:] = -d
+ lapack.pttrf(Sd, Se)
+ def g(x, y, znl, zl):
+
+ """
+ Solve
+
+ [ z[0]*I 0 D' -D' ] [x[:n] ] [bx[:n] ]
+ [ 0 0 -I -I ] [x[n:] ] = [bx[n:] ]
+ [ D -I -D1 0 ] [zl[:n-1]] [bzl[:n-1]]
+ [ -D -I 0 -D2 ] [zl[n-1:]] [bzl[n-1:]].
+
+ First solve
+
+ S*x[:n] = bx[:n] + D' * ( (d1-d2) ./ (d1+d2) .* bx[n:]
+ + 2*d1.*d2./(d1+d2) .* (bzl[:n-1] - bzl[n-1:]) ).
+
+ Then take
+
+ x[n:] = (d1+d2)^-1 .* ( bx[n:] - d1.*bzl[:n-1]
+ - d2.*bzl[n-1:] + (d1-d2) .* D*x[:n] )
+ zl[:n-1] = d1 .* (D*x[:n] - x[n:] - bzl[:n-1])
+ zl[n-1:] = d2 .* (-D*x[:n] - x[n:] - bzl[n-1:]).
+ """
+
+ # y = (d1-d2) ./ (d1+d2) .* bx[n:] +
+ # 2*d1.*d2./(d1+d2) .* (bzl[:n-1] - bzl[n-1:])
+ y = mul( div(d1-d2, d1+d2), x[n:]) + \
+ mul( 0.5*d, zl[:n-1]-zl[n-1:] )
+
+ # x[:n] += D*y
+ x[:n-1] -= y
+ x[1:n] += y
+
+ # x[:n] := S^-1 * x[:n]
+ lapack.pttrs(Sd, Se, x)
+
+ # u = D*x[:n]
+ u = x[1:n] - x[0:n-1]
+
+ # x[n:] = (d1+d2)^-1 .* ( bx[n:] - d1.*bzl[:n-1]
+ # - d2.*bzl[n-1:] + (d1-d2) .* u)
+ x[n:] = div( x[n:] - mul(d1, zl[:n-1]) -
+ mul(d2, zl[n-1:]) + mul(d1-d2, u), d1+d2 )
+
+ # zl[:n-1] = d1 .* (D*x[:n] - x[n:] - bzl[:n-1])
+ # zl[n-1:] = d2 .* (-D*x[:n] - x[n:] - bzl[n-1:])
+ zl[:n-1] = mul(d1, u - x[n:] - zl[:n-1])
+ zl[n-1:] = mul(d2, -u - x[n:] - zl[n-1:])
+
+ return g
+
+ return solvers.nlcp(kktsolver, F, G, h)['x'][:n]
+
+
+nopts = 15
+deltas = -3.0 + (3.0-(-3.0))/(nopts-1) * matrix(range(nopts))
+cost1, cost2 = [], []
+for delta, k in zip(deltas, xrange(nopts)):
+ xtv = tv(10**delta)
+ cost1 += [blas.nrm2(xtv - corr)]
+ cost2 += [blas.asum(xtv[1:] - xtv[:-1])]
+mv1, k1 = min(zip([abs(c - 20.0) for c in cost2], range(nopts)))
+xtv1 = tv(10**deltas[k1])
+mv2, k2 = min(zip([abs(c - 8.0) for c in cost2], range(nopts)))
+xtv2 = tv(10**deltas[k2])
+mv3, k3 = min(zip([abs(c - 5.0) for c in cost2], range(nopts)))
+xtv3 = tv(10**deltas[k3])
+
+pylab.figure(1, facecolor='w', figsize=(8,5))
+pylab.subplot(211)
+pylab.plot(t, ex)
+pylab.ylabel('x[i]')
+pylab.xlabel('i')
+pylab.axis([0, 2000, -2, 2])
+pylab.title('Original and corrupted signal (fig. 6.11)')
+pylab.subplot(212)
+pylab.plot(t, corr)
+pylab.ylabel('xcor[i]')
+pylab.xlabel('i')
+pylab.axis([0, 2000, -2, 2])
+
+pylab.figure(2, facecolor='w') #figsize=(8,7.5))
+pylab.plot(cost1, cost2, [blas.nrm2(corr)], [0], 'o',
+ [0], [blas.asum(corr[1:] - corr[:-1])], 'o')
+pylab.plot([cost1[k1]], [cost2[k1]], 'o', [cost1[k2]], [cost2[k2]], 'o',
+ [cost1[k3]], [cost2[k3]], 'o')
+pylab.text(cost1[k1], cost2[k1],'1')
+pylab.text(cost1[k2], cost2[k2],'2')
+pylab.text(cost1[k3], cost2[k3],'3')
+pylab.grid()
+pylab.axis([-1, 50, -5, 250])
+pylab.xlabel('||xhat-xcor||_2')
+pylab.ylabel('||D*xhat||_1')
+pylab.title('Optimal trade-off curve (fig. 6.13)')
+
+pylab.figure(3, facecolor='w', figsize=(8,7.5))
+pylab.subplot(311)
+pylab.plot(t, xtv1)
+pylab.axis([0, 2000, -2.0, 2.0])
+pylab.ylabel('xhat1[i]')
+pylab.title('Three reconstructed signals (fig. 6.14)')
+pylab.subplot(312)
+pylab.plot(t, xtv2)
+pylab.ylabel('xhat2[i]')
+pylab.axis([0, 2000, -2.0, 2.0])
+pylab.subplot(313)
+pylab.plot(t, xtv3)
+pylab.axis([0, 2000, -2.0, 2.0])
+pylab.ylabel('xhat3[i]')
+pylab.xlabel('i')
+pylab.show()
diff --git a/examples/book/chap7/chernoff b/examples/book/chap7/chernoff
new file mode 100755
index 0000000..53b8d72
--- /dev/null
+++ b/examples/book/chap7/chernoff
@@ -0,0 +1,104 @@
+#!/usr/bin/python
+
+# Figure 7.8, page 384.
+# Chernoff lower bound.
+
+import pylab
+from cvxopt.base import matrix, mul, exp
+from cvxopt import solvers, blas, random
+solvers.options['show_progress'] = False
+
+# Extreme points and inequality description of Voronoi region around
+# first symbol (at the origin).
+m = 6
+V = matrix([ 1.0, 1.0,
+ -1.0, 2.0,
+ -2.0, 1.0,
+ -2.0, -1.0,
+ 0.0, -2.0,
+ 1.5, -1.0,
+ 1.0, 1.0 ], (2,m+1))
+
+# A and b are lists with the inequality descriptions of the regions.
+A = [ matrix( [-(V[1,:m] - V[1,1:]), V[0,:m] - V[0,1:]] ).T ]
+b = [ mul(A[0], V[:,:m].T) * matrix(1.0, (2,1)) ]
+
+# List of symbols.
+C = [ matrix(0.0, (2,1)) ] + \
+ [ 2.0 * b[0][k] / blas.nrm2(A[0][k,:])**2 * A[0][k,:].T for k in
+ xrange(m) ]
+
+# Voronoi set around C[1]
+A += [ matrix(0.0, (3,2)) ]
+b += [ matrix(0.0, (3,1)) ]
+A[1][0,:] = -A[0][0,:]
+b[1][0] = -b[0][0]
+A[1][1,:] = (C[m] - C[1]).T
+b[1][1] = 0.5 * A[1][1,:] * ( C[m] + C[1] )
+A[1][2,:] = (C[2] - C[1]).T
+b[1][2] = 0.5 * A[1][2,:] * ( C[2] + C[1] )
+
+# Voronoi set around C[2], ..., C[5]
+for k in xrange(2, 6):
+ A += [ matrix(0.0, (3,2)) ]
+ b += [ matrix(0.0, (3,1)) ]
+ A[k][0,:] = -A[0][k-1,:]
+ b[k][0] = -b[0][k-1]
+ A[k][1,:] = (C[k-1] - C[k]).T
+ b[k][1] = 0.5 * A[k][1,:] * ( C[k-1] + C[k] )
+ A[k][2,:] = (C[k+1] - C[k]).T
+ b[k][2] = 0.5 * A[k][2,:] * ( C[k+1] + C[k] )
+
+# Voronoi set around C[6]
+A += [ matrix(0.0, (3,2)) ]
+b += [ matrix(0.0, (3,1)) ]
+A[6][0,:] = -A[0][5,:]
+b[6][0] = -b[0][5]
+A[6][1,:] = (C[1] - C[6]).T
+b[6][1] = 0.5 * A[6][1,:] * ( C[1] + C[6] )
+A[6][2,:] = (C[5] - C[6]).T
+b[6][2] = 0.5 * A[6][2,:] * ( C[5] + C[6] )
+
+
+# For regions k=1, ..., 6, let pk be the optimal value of
+#
+# minimize x'*x
+# subject to A*x <= b.
+#
+# The Chernoff upper bound is 1.0 - sum exp( - pk / (2 sigma^2)).
+
+P = matrix([1.0, 0.0, 0.0, 1.0], (2,2))
+q = matrix(0.0, (2,1))
+optvals = matrix([ blas.nrm2( solvers.qp(P, q, A[k], b[k] )['x'] )**2
+ for k in xrange(1,7) ])
+nopts = 200
+sigmas = 0.2 + (0.5 - 0.2)/nopts * matrix(range(nopts), tc='d')
+bnds = [ 1.0 - sum( exp( - optvals / (2*sigma**2) )) for sigma
+ in sigmas]
+
+pylab.figure(facecolor='w')
+pylab.plot(sigmas, bnds, '-')
+pylab.axis([0.2, 0.5, 0.9, 1.0])
+pylab.title('Chernoff lower bound (fig. 7.8)')
+pylab.xlabel('sigma')
+pylab.ylabel('Probability of correct detection')
+pylab.show()
+
+if 0: # uncomment out for the Monte Carlo estimation.
+ N = 100000
+ mcest = []
+ ones = matrix(1.0, (1,m))
+ for sigma in sigmas:
+ X = sigma * random.normal(2, N)
+ S = b[0][:,N*[0]] - A[0]*X
+ S = ones * (S - abs(S))
+ mcest += [ N - len(filter(lambda x: x < 0.0, S)) ]
+
+ pylab.figure(facecolor='w')
+ pylab.plot(sigmas, bnds, '-', sigmas, (1.0/N)*matrix(mcest), '--')
+ pylab.plot(sigmas, bnds, '-')
+ pylab.axis([0.2, 0.5, 0.9, 1.0])
+ pylab.title('Chernoff lower bound (fig. 7.8)')
+ pylab.xlabel('sigma')
+ pylab.ylabel('Probability of correct detection')
+ pylab.show()
diff --git a/examples/book/chap7/expdesign b/examples/book/chap7/expdesign
new file mode 100755
index 0000000..5887458
--- /dev/null
+++ b/examples/book/chap7/expdesign
@@ -0,0 +1,185 @@
+#!/usr/bin/python
+
+# Figures 7.9-12, pages 389-390.
+# Experiment design.
+
+from math import pi, log, sqrt
+import pylab
+from cvxopt import base, blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, mul, cos, sin
+solvers.options['show_progress'] = False
+
+V = matrix([-2.1213, 2.1213,
+ -2.2981, 1.9284,
+ -2.4575, 1.7207,
+ -2.5981, 1.5000,
+ -2.7189, 1.2679,
+ -2.8191, 1.0261,
+ -2.8978, 0.7765,
+ -2.9544, 0.5209,
+ -2.9886, 0.2615,
+ -3.0000, 0.0000,
+ 1.5000, 0.0000,
+ 1.4772, -0.2605,
+ 1.4095, -0.5130,
+ 1.2990, -0.7500,
+ 1.1491, -0.9642,
+ 0.9642, -1.1491,
+ 0.7500, -1.2990,
+ 0.5130, -1.4095,
+ 0.2605, -1.4772,
+ 0.0000, -1.5000 ], (2,20))
+
+n = V.size[1]
+G = spmatrix(-1.0, range(n), range(n))
+h = matrix(0.0, (n,1))
+A = matrix(1.0, (1,n))
+b = matrix(1.0)
+
+
+# D-design
+#
+# minimize f(x) = -log det V*diag(x)*V'
+# subject to x >= 0
+# sum(x) = 1
+#
+# The gradient and Hessian of f are
+#
+# gradf = -diag(V' * X^-1 * V)
+# H = (V' * X^-1 * V)**2.
+#
+# where X = V * diag(x) * V'.
+
+def F(x=None, z=None):
+ if x is None: return 0, matrix(1.0, (n,1))
+ X = V * spmatrix(x, range(n), range(n)) * V.T
+ L = +X
+ try: lapack.potrf(L)
+ except ArithmeticError: return None
+ f = - 2.0 * (log(L[0,0]) + log(L[1,1]))
+ W = +V
+ blas.trsm(L, W)
+ gradf = matrix(-1.0, (1,2)) * W**2
+ if z is None: return f, gradf
+ H = matrix(0.0, (n,n))
+ blas.syrk(W, H, trans='T')
+ return f, gradf, z[0] * H**2
+xd = solvers.cp(F, G, h, A, b)['x']
+
+pylab.figure(1, facecolor='w', figsize=(5,5))
+pylab.plot(V[0,:], V[1,:],'ow', [0], [0], 'k+')
+I = [ k for k in xrange(n) if xd[k] > 1e-5 ]
+pylab.plot(V[0,I], V[1,I],'or')
+
+# Enclosing ellipse is {x | x' * (V*diag(xe)*V')^-1 * x = sqrt(2)}
+nopts = 1000
+angles = matrix( [ a*2.0*pi/nopts for a in xrange(nopts) ], (1,nopts) )
+circle = matrix(0.0, (2,nopts))
+circle[0,:], circle[1,:] = cos(angles), sin(angles)
+
+W = V * spmatrix(xd, range(n), range(n)) * V.T
+lapack.potrf(W)
+ellipse = sqrt(2.0) * circle
+blas.trmm(W, ellipse)
+pylab.plot(ellipse[0,:], ellipse[1,:], 'k--')
+pylab.axis([-5, 5, -5, 5])
+pylab.title('D-optimal design (fig. 7.9)')
+pylab.axis('off')
+
+
+# E-design.
+#
+# maximize w
+# subject to w*I <= V*diag(x)*V'
+# x >= 0
+# sum(x) = 1
+
+novars = n+1
+c = matrix(0.0, (novars,1))
+c[-1] = -1.0
+Gs = [matrix(0.0, (4,novars))]
+for k in xrange(n): Gs[0][:,k] = -(V[:,k]*V[:,k].T)[:]
+Gs[0][[0,3],-1] = 1.0
+hs = [matrix(0.0, (2,2))]
+Ge = matrix(0.0, (n, novars))
+Ge[:,:n] = G
+Ae = matrix(n*[1.0] + [0.0], (1,novars))
+sol = solvers.sdp(c, Ge, h, Gs, hs, Ae, b)
+xe = sol['x'][:n]
+Z = sol['zs'][0]
+mu = sol['y'][0]
+
+pylab.figure(2, facecolor='w', figsize=(5,5))
+pylab.plot(V[0,:], V[1,:],'ow', [0], [0], 'k+')
+I = [ k for k in xrange(n) if xe[k] > 1e-5 ]
+pylab.plot(V[0,I], V[1,I],'or')
+
+# Enclosing ellipse follows from the solution of the dual problem:
+#
+# minimize mu
+# subject to diag(V'*Z*V) <= mu*1
+# Z >= 0
+
+lapack.potrf(Z)
+ellipse = sqrt(mu) * circle
+blas.trsm(Z, ellipse, transA='T')
+pylab.plot(ellipse[0,:], ellipse[1,:], 'k--')
+pylab.axis([-5, 5, -5, 5])
+pylab.title('E-optimal design (fig. 7.10)')
+pylab.axis('off')
+
+
+# A-design.
+#
+# minimize tr (V*diag(x)*V')^{-1}
+# subject to x >= 0
+# sum(x) = 1
+#
+# minimize tr Y
+# subject to [ V*diag(x)*V', I ]
+# [ I, Y ] >= 0
+# x >= 0
+# sum(x) = 1
+
+novars = 3 + n
+c = matrix(0.0, (novars,1))
+c[[-3, -1]] = 1.0
+Gs = [matrix(0.0, (16, novars))]
+for k in xrange(n):
+ Gk = matrix(0.0, (4,4))
+ Gk[:2,:2] = -V[:,k] * V[:,k].T
+ Gs[0][:,k] = Gk[:]
+Gs[0][10,-3] = -1.0
+Gs[0][11,-2] = -1.0
+Gs[0][15,-1] = -1.0
+hs = [matrix(0.0, (4,4))]
+hs[0][2,0] = 1.0
+hs[0][3,1] = 1.0
+Ga = matrix(0.0, (n, novars))
+Ga[:,:n] = G
+Aa = matrix(n*[1.0] + 3*[0.0], (1,novars))
+sol = solvers.sdp(c, Ga, h, Gs, hs, Aa, b)
+xa = sol['x'][:n]
+Z = sol['zs'][0][:2,:2]
+mu = sol['y'][0]
+
+pylab.figure(3, facecolor='w', figsize=(5,5))
+pylab.plot(V[0,:], V[1,:],'ow', [0], [0], 'k+')
+I = [ k for k in xrange(n) if xa[k] > 1e-5 ]
+pylab.plot(V[0,I], V[1,I],'or')
+
+# Enclosing ellipse follows from the solution of the dual problem:
+#
+# maximize -mu - 2 * tr Z12
+# subject to diag(V'*Z11*V) <= mu*1
+# [ Z11, Z12 ]
+# [ Z21, I ] >= 0
+
+lapack.potrf(Z)
+ellipse = sqrt(mu) * circle
+blas.trsm(Z, ellipse, transA='T')
+pylab.plot(ellipse[0,:], ellipse[1,:], 'k--')
+pylab.axis([-5, 5, -5, 5])
+pylab.title('A-optimal design (fig. 7.11)')
+pylab.axis('off')
+pylab.show()
diff --git a/examples/book/chap7/logreg b/examples/book/chap7/logreg
new file mode 100755
index 0000000..17c2d43
--- /dev/null
+++ b/examples/book/chap7/logreg
@@ -0,0 +1,47 @@
+#!/usr/bin/python
+
+# Figures 7.1, page 355.
+# Logistic regression.
+
+import pylab, pickle
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, log, exp, div
+solvers.options['show_progress'] = False
+
+data = pickle.load(open("logreg.pic"))
+u, y = data['u'], data['y']
+
+# minimize sum_{y_k = 1} (a*uk + b) + sum log (1 + exp(a*u + b))
+#
+# two variables a, b.
+
+m = u.size[0]
+A = matrix(1.0, (m,2))
+A[:,0] = u
+c = -matrix([sum( uk for uk, yk in zip(u,y) if yk ), sum(y) ])
+
+# minimize c'*x + sum log (1 + exp(A*x))
+#
+# variable x (2).
+
+def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (2,1))
+ w = exp(A*x)
+ f = c.T*x + sum(log(1+w))
+ grad = c + A.T * div(w, 1+w)
+ if z is None: return f, grad.T
+ H = A.T * spmatrix(div(w,(1+w)**2), range(m), range(m)) * A
+ return f, grad.T, z[0]*H
+sol = solvers.cp(F)
+a, b = sol['x'][0], sol['x'][1]
+
+pylab.figure(facecolor='w')
+nopts = 200
+pts = -1.0 + 12.0/nopts * matrix(range(nopts))
+w = exp(a*pts + b)
+pylab.plot(u, y, 'o', pts, div(w, 1+w), '-')
+pylab.title('Logistic regression (fig. 7.1)')
+pylab.axis([-1, 11, -0.1, 1.1])
+pylab.xlabel('u')
+pylab.ylabel('Prob(y=1)')
+pylab.show()
diff --git a/examples/book/chap7/logreg.pic b/examples/book/chap7/logreg.pic
new file mode 100644
index 0000000..cb1da1a
--- /dev/null
+++ b/examples/book/chap7/logreg.pic
@@ -0,0 +1,226 @@
+(dp0
+S'y'
+p1
+ccvxopt.base
+matrix
+p2
+((lp3
+I1
+aI0
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+a(I100
+I1
+tp10
+S'd'
+p11
+tp12
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+s.
\ No newline at end of file
diff --git a/examples/book/chap7/maxent b/examples/book/chap7/maxent
new file mode 100755
index 0000000..9b77c93
--- /dev/null
+++ b/examples/book/chap7/maxent
@@ -0,0 +1,95 @@
+#!/usr/bin/python
+
+# Figures 7.2 and 7.3, pages 363 and 364.
+# Maximum entropy distribution.
+
+import pylab
+from cvxopt import solvers, blas
+from cvxopt.base import matrix, spmatrix, log, div
+solvers.options['show_progress'] = False
+
+# minimize p'*log p
+# subject to -0.1 <= a'*p <= 0.1
+# 0.5 <= (a**2)'*p <= 0.6
+# -0.3 <= (3*a**3 - 2*a)'*p <= -0.2
+# 0.3 <= sum_{k:ak < 0} pk <= 0.4
+# sum(p) = 1
+#
+# a in R^100 is made of 100 equidistant points in [-1,1].
+# The variable is p (100).
+
+n = 100
+a = -1.0 + (2.0/(n-1)) * matrix(range(n), (1,n))
+I = [k for k in xrange(n) if a[k] < 0]
+G = matrix([-a, a, -a**2, a**2, -(3 * a**3 - 2*a), (3 * a**3 - 2*a),
+ matrix(0.0, (2,n))])
+G[6,I] = -1.0
+G[7,I] = 1.0
+h = matrix([0.1, 0.1, -0.5, 0.6, 0.3, -0.2, -0.3, 0.4 ])
+
+A, b = matrix(1.0, (1,n)), matrix(1.0)
+
+# minimize x'*log x
+# subject to G*x <= h
+# A*x = b
+#
+# variable x (n).
+
+def F(x=None, z=None):
+ if x is None: return 0, matrix(1.0, (n,1))
+ if min(x) <= 0: return None
+ f = x.T*log(x)
+ grad = 1.0 + log(x)
+ if z is None: return f, grad.T
+ H = spmatrix(x**-1, range(n), range(n))
+ return f, grad.T, z[0]*H
+sol = solvers.cp(F, G, h, A, b)
+p = sol['x']
+
+
+# Upper/lower bounds on cumulative distribution.
+#
+# minimize/maximize ck'*p = sum_{i<=alphak} pi
+# subject to G*x <= h
+# A*x = b
+# x >= 0
+#
+# Solve via dual:
+#
+# maximize -h'*z - b'*w
+# subject to +/- c + G'*z + A'*w >= 0
+# z >= 0
+#
+# with variables z (8), w (1).
+
+cc = matrix(0.0, (9,1))
+cc[:8], cc[8] = h, b
+GG = spmatrix([], [], [], (n+8, 9))
+GG[:n,:8] = -G.T
+GG[:n,8] = -A.T
+GG[n::n+9] = -1.0
+hh = matrix(0.0, (n+8,n))
+hh[:n,:] = matrix([i>=j for i in xrange(n) for j in xrange(n)],
+ (n,n), 'd') # upper triangular matrix of ones
+l = [-blas.dot(cc, solvers.lp(cc, GG, hh[:,k])['x']) for k in xrange(n)]
+u = [blas.dot(cc, solvers.lp(cc, GG, -hh[:,k])['x']) for k in xrange(n)]
+
+def f(x,y): return x+2*[y]
+def stepl(x): return reduce(f, x[1:], [x[0]])
+def stepr(x): return reduce(f, x[:-1], []) + [x[-1]]
+
+pylab.figure(1, facecolor='w')
+pylab.plot(stepl(a), stepr(p), '-')
+pylab.title('Maximum entropy distribution (fig. 7.2)')
+pylab.xlabel('a')
+pylab.ylabel('p = Prob(X = a)')
+
+pylab.figure(2, facecolor='w')
+pylab.plot([-1.0] + stepl(a), [0.0] + stepr(hh[:n,:].T*p), '-',
+ [-1.0] + stepl(a), [0.0] + stepr(l), 'r-',
+ [-1.0] + stepl(a), [0.0] + stepr(u), 'r-')
+pylab.title('Cumulative distribution (fig. 7.3)')
+pylab.xlabel('a')
+pylab.ylabel('Prob(X <= a)')
+pylab.axis([-1.1, 1.1, -0.1, 1.1])
+pylab.show()
diff --git a/examples/book/chap7/probbounds b/examples/book/chap7/probbounds
new file mode 100755
index 0000000..959ef62
--- /dev/null
+++ b/examples/book/chap7/probbounds
@@ -0,0 +1,204 @@
+#!/usr/bin/python
+
+# Figures 7.6 and 7.7, page 383.
+# Chebyshev bounds.
+
+import pylab
+from math import pi, sqrt
+from cvxopt.base import matrix, spmatrix, mul, cos, sin
+from cvxopt import solvers, blas, lapack
+solvers.options['show_progress'] = False
+
+# Extreme points and inequality description of Voronoi region around
+# first symbol (0,0).
+m = 6
+V = matrix([ 1.0, 1.0,
+ -1.0, 2.0,
+ -2.0, 1.0,
+ -2.0, -1.0,
+ 0.0, -2.0,
+ 1.5, -1.0,
+ 1.0, 1.0 ], (2,m+1))
+
+A0 = matrix([-(V[1,:m] - V[1,1:]), V[0,:m] - V[0,1:]]).T
+b0 = mul(A0, V[:,:m].T) * matrix(1.0, (2,1))
+
+# List of symbols.
+C = [ matrix(0.0, (2,1)) ] + \
+ [ 2.0 * b0[k] / blas.nrm2(A0[k,:])**2 * A0[k,:].T for k in
+ xrange(m) ]
+
+# Voronoi set around C[1]
+A1, b1 = matrix(0.0, (3,2)), matrix(0.0, (3,1))
+A1[0,:] = -A0[0,:]
+b1[0] = -b0[0]
+A1[1,:] = (C[m] - C[1]).T
+b1[1] = 0.5 * A1[1,:] * ( C[m] + C[1] )
+A1[2,:] = (C[2] - C[1]).T
+b1[2] = 0.5 * A1[2,:] * ( C[2] + C[1] )
+
+# Voronoi set around C[2]
+A2, b2 = matrix(0.0, (3,2)), matrix(0.0, (3,1))
+A2[0,:] = -A0[1,:]
+b2[0] = -b0[1]
+A2[1,:] = (C[1] - C[2]).T
+b2[1] = 0.5 * A2[1,:] * ( C[1] + C[2] )
+A2[2,:] = (C[3] - C[2]).T
+b2[2] = 0.5 * A2[2,:] * ( C[3] + C[2] )
+
+
+def cheb(A, b, Sigma):
+
+ # Calculates Chebyshev lower bound on Prob(A*x <= b) where
+ # x in R^2 has mean zero and covariance Sigma.
+ #
+ # maximize 1 - tr(Sigma*P) - r
+ # subject to [ P, q - (tauk/2)*ak ]
+ # [ (q - (tauk/2)*ak)', r - 1 + tauk*bk ] >= 0,
+ # k = 0,...,m-1
+ # [ P, q ]
+ # [ q', r ] >= 0
+ # tauk >= 0, k=0,...,m-1.
+ #
+ # variables P[0,0], P[1,0], P[1,1], q[0], q[1], r, tau[0], ...,
+ # tau[m-1].
+
+ m = A.size[0]
+ novars = 3 + 2 + 1 + m
+
+ # Cost function.
+ c = matrix(0.0, (novars,1))
+ c[0], c[1], c[2] = Sigma[0,0], 2*Sigma[1,0], Sigma[1,1]
+ c[5] = 1.0
+
+ Gs = [ spmatrix([],[],[], (9,novars)) for k in xrange(m+1) ]
+
+ # Coefficients of P, q, r in LMI constraints.
+ for k in xrange(m+1):
+ Gs[k][0,0] = -1.0 # P[0,0]
+ Gs[k][1,1] = -1.0 # P[1,0]
+ Gs[k][4,2] = -1.0 # P[1,1]
+ Gs[k][2,3] = -1.0 # q[0]
+ Gs[k][5,4] = -1.0 # q[1]
+ Gs[k][8,5] = -1.0 # r
+ # Coefficients of tau.
+ for k in xrange(m):
+ Gs[k][2, 6+k] = 0.5 * A[k,0]
+ Gs[k][5, 6+k] = 0.5 * A[k,1]
+ Gs[k][8, 6+k] = -b[k]
+
+ hs = [ matrix(8*[0.0] + [-1.0], (3,3)) for k in xrange(m) ] + \
+ [ matrix(0.0, (3,3)) ]
+
+ # Constraints tau >= 0.
+ Gl, hl = spmatrix(-1.0, range(m), range(6,6+m)), matrix(0.0, (m,1))
+
+ sol = solvers.sdp(c, Gl, hl, Gs, hs)
+ P = matrix(sol['x'][[0,1,1,2]], (2,2))
+ q = matrix(sol['x'][[3,4]], (2,1))
+ r = sol['x'][5]
+ bound = 1.0 - Sigma[0]*P[0] - 2*Sigma[1]*P[1] - Sigma[3]*P[3] - r
+
+ # Worst-case distribution from dual solution.
+ X = [ Z[2,:2].T / Z[2,2] for Z in sol['zs'] if Z[2,2] > 1e-5 ]
+
+ return bound, P, q, r, X
+
+
+# Compute bound for s0 with sigma = 1.0.
+# Write ellipse {x | x'*P*x + 2*q'*x + r = 1} in the form
+# {xc + L^{-T}*u | ||u||_2 = 1}
+
+Sigma = matrix([1.0, 0.0, 0.0, 1.0], (2,2))
+bnd, P, q, r, X = cheb(A0, b0, Sigma)
+xc = -q
+L = +P
+lapack.posv(L, xc)
+L /= sqrt(1 - r - blas.dot(q, xc))
+
+def makefig1():
+ pylab.figure(1, facecolor='w', figsize=(6,6))
+ pylab.plot(V[0,:], V[1,:], '-')
+ nopts = 1000
+ angles = matrix( [a*2.0*pi/nopts for a in xrange(nopts) ],
+ (1,nopts) )
+ circle = matrix(0.0, (2,nopts))
+ circle[0,:], circle[1,:] = cos(angles), sin(angles)
+ for k in xrange(len(C)):
+ c = C[k]
+ pylab.plot([c[0]], [c[1]], 'ow')
+ pylab.text(c[0], c[1], "s%d" %k)
+ pylab.plot(c[0] + circle[0,:], c[1]+circle[1,:], ':')
+ if k >= 1:
+ v = V[:,k-1]
+ if k==1:
+ dir = 0.5 * (C[k] + C[-1]) - v
+ else:
+ dir = 0.5 * (C[k] + C[k-1]) - v
+ pylab.plot([v[0], v[0] + 5*dir[0]],
+ [v[1], v[1] + 5*dir[1]], 'b-')
+ ellipse = +circle
+ blas.trsm(L, ellipse, transA='T')
+ pylab.plot(xc[0] + ellipse[0,:], xc[1]+ellipse[1,:], 'r-')
+ for Xk in X:
+ pylab.plot([Xk[0]], [Xk[1]], 'ro')
+
+ pylab.axis([-5, 5, -5, 5])
+ pylab.title('Geometrical interpretation of Chebyshev bound (fig. 7.7)')
+ pylab.axis('off')
+makefig1()
+print "Close figure to continue."
+pylab.show()
+
+
+# Compute bounds for s0 with sigma in [0,2.5]
+nosigmas = 150
+sigmas = 0.001 + (2.5 - 0.001) / nosigmas * matrix(range(nosigmas),
+ tc='d')
+I = matrix([1.0, 0.0, 0.0, 1.0], (2,2))
+print "Computing lower bounds for symbol 0 ..."
+bnds0 = [ cheb(A0, b0, sigma**2*I)[0] for sigma in sigmas ]
+
+pylab.figure(2,facecolor='w')
+pylab.plot(sigmas, bnds0)
+pylab.axis([0, 2.5, 0.0, 1.0])
+pylab.title('Chebyshev lower bounds (fig 7.6)')
+pylab.text(sigmas[nosigmas/2], bnds0[nosigmas/2], 's0')
+pylab.xlabel('sigma')
+pylab.ylabel('Probability of correct detection')
+print "Close figure to continue."
+pylab.show()
+
+# Bounds for s1.
+b1 -= A1*C[1] # put s1 at the origin
+print "Computing lower bounds for symbol 1 ..."
+bnds1 = [ cheb(A1, b1, sigma**2*I)[0] for sigma in sigmas ]
+
+pylab.figure(2,facecolor='w')
+pylab.plot(sigmas,bnds0, '-b', sigmas, bnds1, 'r')
+pylab.axis([0, 2.5, 0.0, 1.0])
+pylab.title('Chebyshev lower bounds (fig 7.6)')
+pylab.text(sigmas[nosigmas/2], bnds0[nosigmas/2], 's0')
+pylab.text(sigmas[nosigmas/2], bnds1[nosigmas/2], 's1')
+pylab.xlabel('sigma')
+pylab.ylabel('Probability of correct detection')
+print "Close figure to continue."
+pylab.show()
+
+# Bounds for s2.
+b2 -= A2*C[2] # put s2 at the origin
+print "Computing lower bounds for symbol 2 ..."
+bnds2 = [ cheb(A2, b2, sigma**2*I)[0] for sigma in sigmas ]
+
+makefig1()
+pylab.figure(2,facecolor='w')
+pylab.plot(sigmas,bnds0, '-b', sigmas, bnds1, 'r', sigmas, bnds2, 'g')
+pylab.axis([0, 2.5, 0.0, 1.0])
+pylab.title('Chebyshev lower bounds (fig 7.6)')
+pylab.text(sigmas[nosigmas/2], bnds0[nosigmas/2], 's0')
+pylab.text(sigmas[nosigmas/2], bnds1[nosigmas/2], 's1')
+pylab.text(sigmas[nosigmas/2], bnds2[nosigmas/2], 's2')
+pylab.xlabel('sigma')
+pylab.ylabel('Probability of correct detection')
+
+pylab.show()
diff --git a/examples/book/chap8/centers b/examples/book/chap8/centers
new file mode 100755
index 0000000..39bde8c
--- /dev/null
+++ b/examples/book/chap8/centers
@@ -0,0 +1,206 @@
+#!/usr/bin/python
+
+# Figures 8.5-7, pages 417-421.
+# Centers of polyhedra.
+
+import pylab
+from math import log, pi
+from cvxopt import blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, sqrt, mul, cos, sin, log
+from cvxopt.modeling import variable, op
+solvers.options['show_progress'] = False
+
+# Extreme points (with first one appended at the end)
+X = matrix([ 0.55, 0.25, -0.20, -0.25, 0.00, 0.40, 0.55,
+ 0.00, 0.35, 0.20, -0.10, -0.30, -0.20, 0.00 ], (7,2))
+m = X.size[0] - 1
+
+# Inequality description G*x <= h with h = 1
+G, h = matrix(0.0, (m,2)), matrix(0.0, (m,1))
+G = (X[:m,:] - X[1:,:]) * matrix([0., -1., 1., 0.], (2,2))
+h = (G * X.T)[::m+1]
+G = mul(h[:,[0,0]]**-1, G)
+h = matrix(1.0, (m,1))
+
+
+# Chebyshev center
+#
+# maximizse R
+# subject to gk'*xc + R*||gk||_2 <= hk, k=1,...,m
+# R >= 0
+
+R = variable()
+xc = variable(2)
+op(-R, [ G[k,:]*xc + R*blas.nrm2(G[k,:]) <= h[k] for k in xrange(m) ] +
+ [ R >= 0] ).solve()
+R = R.value
+xc = xc.value
+
+pylab.figure(1, facecolor='w')
+
+# polyhedron
+for k in xrange(m):
+ edge = X[[k,k+1],:] + 0.1 * matrix([1., 0., 0., -1.], (2,2)) * \
+ (X[2*[k],:] - X[2*[k+1],:])
+ pylab.plot(edge[:,0], edge[:,1], 'k')
+
+
+# 1000 points on the unit circle
+nopts = 1000
+angles = matrix( [ a*2.0*pi/nopts for a in xrange(nopts) ], (1,nopts) )
+circle = matrix(0.0, (2,nopts))
+circle[0,:], circle[1,:] = R*cos(angles), R*sin(angles)
+circle += xc[:,nopts*[0]]
+
+# plot maximum inscribed disk
+pylab.fill(circle[0,:], circle[1,:], '#F0F0F0')
+pylab.plot([xc[0]], [xc[1]], 'ko')
+pylab.title('Chebyshev center (fig 8.5)')
+pylab.axis('equal')
+pylab.axis('off')
+
+
+# Maximum volume enclosed ellipsoid center
+#
+# minimize -log det B
+# subject to ||B * gk||_2 + gk'*c <= hk, k=1,...,m
+#
+# with variables B and c.
+#
+# minimize -log det L
+# subject to ||L' * gk||_2^2 / (hk - gk'*c) <= hk - gk'*c, k=1,...,m
+#
+# L lower triangular with positive diagonal and B*B = L*L'.
+#
+# minimize -log x[0] - log x[2]
+# subject to g( Dk*x + dk ) <= 0, k=1,...,m
+#
+# g(u,t) = u'*u/t - t
+# Dk = [ G[k,0] G[k,1] 0 0 0
+# 0 0 G[k,1] 0 0
+# 0 0 0 -G[k,0] -G[k,1] ]
+# dk = [0; 0; h[k]]
+#
+# 5 variables x = (L[0,0], L[1,0], L[1,1], c[0], c[1])
+
+D = [ matrix(0.0, (3,5)) for k in xrange(m) ]
+for k in xrange(m):
+ D[k][ [0, 3, 7, 11, 14] ] = matrix( [G[k,0], G[k,1], G[k,1],
+ -G[k,0], -G[k,1]] )
+d = [matrix([0.0, 0.0, hk]) for hk in h]
+
+def F(x=None, z=None):
+ if x is None:
+ return m, matrix([ 1.0, 0.0, 1.0, 0.0, 0.0 ])
+ if min(x[0], x[2], min(h-G*x[3:])) <= 0.0:
+ return None
+
+ y = [ Dk*x + dk for Dk, dk in zip(D, d) ]
+
+ f = matrix(0.0, (m+1,1))
+ f[0] = -log(x[0]) - log(x[2])
+ for k in xrange(m):
+ f[k+1] = y[k][:2].T * y[k][:2] / y[k][2] - y[k][2]
+
+ Df = matrix(0.0, (m+1,5))
+ Df[0,0], Df[0,2] = -1.0/x[0], -1.0/x[2]
+
+ # gradient of g is ( 2.0*(u/t); -(u/t)'*(u/t) -1)
+ for k in xrange(m):
+ a = y[k][:2] / y[k][2]
+ gradg = matrix(0.0, (3,1))
+ gradg[:2], gradg[2] = 2.0 * a, -a.T*a - 1
+ Df[k+1,:] = gradg.T * D[k]
+ if z is None: return f, Df
+
+ H = matrix(0.0, (5,5))
+ H[0,0] = z[0] / x[0]**2
+ H[2,2] = z[0] / x[2]**2
+
+ # Hessian of g is (2.0/t) * [ I, -u/t; -(u/t)', (u/t)*(u/t)' ]
+ for k in xrange(m):
+ a = y[k][:2] / y[k][2]
+ hessg = matrix(0.0, (3,3))
+ hessg[0,0], hessg[1,1] = 1.0, 1.0
+ hessg[:2,2], hessg[2,:2] = -a, -a.T
+ hessg[2, 2] = a.T*a
+ H += (z[k] * 2.0 / y[k][2]) * D[k].T * hessg * D[k]
+
+ return f, Df, H
+
+sol = solvers.cp(F)
+L = matrix([sol['x'][0], sol['x'][1], 0.0, sol['x'][2]], (2,2))
+c = matrix([sol['x'][3], sol['x'][4]])
+
+
+pylab.figure(2, facecolor='w')
+
+# polyhedron
+for k in xrange(m):
+ edge = X[[k,k+1],:] + 0.1 * matrix([1., 0., 0., -1.], (2,2)) * \
+ (X[2*[k],:] - X[2*[k+1],:])
+ pylab.plot(edge[:,0], edge[:,1], 'k')
+
+
+# 1000 points on the unit circle
+nopts = 1000
+angles = matrix( [ a*2.0*pi/nopts for a in xrange(nopts) ], (1,nopts) )
+circle = matrix(0.0, (2,nopts))
+circle[0,:], circle[1,:] = cos(angles), sin(angles)
+
+# ellipse = L * circle + c
+ellipse = L * circle + c[:, nopts*[0]]
+
+pylab.fill(ellipse[0,:], ellipse[1,:], '#F0F0F0')
+pylab.plot([c[0]], [c[1]], 'ko')
+pylab.title('Maximum volume inscribed ellipsoid center (fig 8.6)')
+pylab.axis('equal')
+pylab.axis('off')
+
+
+# Analytic center.
+#
+# minimize -sum log (h-G*x)
+#
+
+def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (2,1))
+ y = h-G*x
+ if min(y) <= 0: return None
+ f = -sum(log(y))
+ Df = (y**-1).T * G
+ if z is None: return matrix(f), Df
+ H = G.T * spmatrix(y**-1, range(m), range(m)) * G
+ return matrix(f), Df, z[0]*H
+
+sol = solvers.cp(F)
+xac = sol['x']
+Hac = G.T * spmatrix( (h-G*xac)**-1, range(m), range(m)) * G
+
+pylab.figure(3, facecolor='w')
+
+# polyhedron
+for k in xrange(m):
+ edge = X[[k,k+1],:] + 0.1 * matrix([1., 0., 0., -1.], (2,2)) * \
+ (X[2*[k],:] - X[2*[k+1],:])
+ pylab.plot(edge[:,0], edge[:,1], 'k')
+
+
+# 1000 points on the unit circle
+nopts = 1000
+angles = matrix( [ a*2.0*pi/nopts for a in xrange(nopts) ], (1,nopts) )
+circle = matrix(0.0, (2,nopts))
+circle[0,:], circle[1,:] = cos(angles), sin(angles)
+
+# ellipse = L^-T * circle + xc where Hac = L*L'
+lapack.potrf(Hac)
+ellipse = +circle
+blas.trsm(Hac, ellipse, transA='T')
+ellipse += xac[:, nopts*[0]]
+pylab.fill(ellipse[0,:], ellipse[1,:], '#F0F0F0')
+pylab.plot([xac[0]], [xac[1]], 'ko')
+
+pylab.title('Analytic center (fig 8.7)')
+pylab.axis('equal')
+pylab.axis('off')
+pylab.show()
diff --git a/examples/book/chap8/ellipsoids b/examples/book/chap8/ellipsoids
new file mode 100755
index 0000000..062a781
--- /dev/null
+++ b/examples/book/chap8/ellipsoids
@@ -0,0 +1,228 @@
+#!/usr/bin/python
+
+# Figures 8.3 and 8.4, pages 412 and 416.
+# Ellipsoidal approximations.
+
+import pylab
+from math import log, pi
+from cvxopt import blas, lapack, solvers
+from cvxopt.base import matrix, sqrt, mul, cos, sin
+solvers.options['show_progress'] = False
+
+# Extreme points (with first one appended at the end)
+X = matrix([ 0.55, 0.25, -0.20, -0.25, 0.00, 0.40, 0.55,
+ 0.00, 0.35, 0.20, -0.10, -0.30, -0.20, 0.00 ], (7,2))
+m = X.size[0] - 1
+
+# Inequality description G*x <= h with h = 1
+G, h = matrix(0.0, (m,2)), matrix(0.0, (m,1))
+G = (X[:m,:] - X[1:,:]) * matrix([0., -1., 1., 0.], (2,2))
+h = (G * X.T)[::m+1]
+G = mul(h[:,[0,0]]**-1, G)
+h = matrix(1.0, (m,1))
+
+
+# Loewner-John ellipsoid
+#
+# minimize log det A^-1
+# subject to xk'*A*xk - 2*xk'*b + b'*A^1*b <= 1, k=1,...,m
+#
+# 5 variables x = (A[0,0], A[1,0], A[1,1], b[0], b[1])
+
+def F(x=None, z=None):
+ if x is None:
+ return m, matrix([ 1.0, 0.0, 1.0, 0.0, 0.0 ])
+
+ # Factor A as A = L*L'. Compute inverse B = A^-1.
+ A = matrix( [x[0], x[1], x[1], x[2]], (2,2))
+ L = +A
+ try: lapack.potrf(L)
+ except: return None
+ B = +L
+ lapack.potri(B)
+ B[0,1] = B[1,0]
+
+ # f0 = -log det A
+ f = matrix(0.0, (m+1,1))
+ f[0] = -2.0 * (log(L[0,0]) + log(L[1,1]))
+
+ # fk = xk'*A*xk - 2*xk'*b + b*A^-1*b - 1
+ # = (xk - c)' * A * (xk - c) - 1 where c = A^-1*b
+ c = x[3:]
+ lapack.potrs(L, c)
+ for k in xrange(m):
+ f[k+1] = (X[k,:].T - c).T * A * (X[k,:].T - c) - 1.0
+
+ # gradf0 = (-A^-1, 0) = (-B, 0)
+ Df = matrix(0.0, (m+1,5))
+ Df[0,0], Df[0,1], Df[0,2] = -B[0,0], -2.0*B[1,0], -B[1,1]
+
+ # gradfk = (xk*xk' - A^-1*b*b'*A^-1, 2*(-xk + A^-1*b))
+ # = (xk*xk' - c*c', 2*(-xk+c))
+ Df[1:,0] = X[:m,0]**2 - c[0]**2
+ Df[1:,1] = 2.0 * (mul(X[:m,0], X[:m,1]) - c[0]*c[1])
+ Df[1:,2] = X[:m,1]**2 - c[1]**2
+ Df[1:,3] = 2.0 * (-X[:m,0] + c[0])
+ Df[1:,4] = 2.0 * (-X[:m,1] + c[1])
+
+ if z is None: return f, Df
+
+ # hessf0(Y, y) = (A^-1*Y*A^-1, 0) = (B*YB, 0)
+ H0 = matrix(0.0, (5,5))
+ H0[0,0] = B[0,0]**2
+ H0[1,0] = 2.0 * B[0,0] * B[1,0]
+ H0[2,0] = B[1,0]**2
+ H0[1,1] = 2.0 * ( B[0,0] * B[1,1] + B[1,0]**2 )
+ H0[2,1] = 2.0 * B[1,0] * B[1,1]
+ H0[2,2] = B[1,1]**2
+
+ # hessfi(Y, y)
+ # = ( A^-1*Y*A^-1*b*b'*A^-1 + A^-1*b*b'*A^-1*Y*A^-1
+ # - A^-1*y*b'*A^-1 - A^-1*b*y'*A^-1,
+ # -2*A^-1*Y*A^-1*b + 2*A^-1*y )
+ # = ( B*Y*c*c' + c*c'*Y*B - B*y*c' - c*y'*B, -2*B*Y*c + 2*B*y )
+ # = ( B*(Y*c-y)*c' + c*(Y*c-y)'*B, -2*B*(Y*c - y) )
+ H1 = matrix(0.0, (5,5))
+ H1[0,0] = 2.0 * c[0]**2 * B[0,0]
+ H1[1,0] = 2.0 * ( c[0] * c[1] * B[0,0] + c[0]**2 * B[1,0] )
+ H1[2,0] = 2.0 * c[0] * c[1] * B[1,0]
+ H1[3:,0] = -2.0 * c[0] * B[:,0]
+ H1[1,1] = 2.0 * c[0]**2 * B[1,1] + 4.0 * c[0]*c[1]*B[1,0] + \
+ 2.0 * c[1]**2 + B[0,0]
+ H1[2,1] = 2.0 * (c[1]**2 * B[1,0] + c[0]*c[1]*B[1,1])
+ H1[3:,1] = -2.0 * B * c[[1,0]]
+ H1[2,2] = 2.0 * c[1]**2 * B[1,1]
+ H1[3:,2] = -2.0 * c[1] * B[:,1]
+ H1[3:,3:] = 2*B
+
+ return f, Df, z[0]*H0 + sum(z[1:])*H1
+
+sol = solvers.cp(F)
+A = matrix( sol['x'][[0, 1, 1, 2]], (2,2))
+b = sol['x'][3:]
+
+pylab.figure(1, facecolor='w')
+pylab.plot(X[:,0], X[:,1], 'ko', X[:,0], X[:,1], '-k')
+
+# Ellipsoid in the form { x | || L' * (x-c) ||_2 <= 1 }
+L = +A
+lapack.potrf(L)
+c = +b
+lapack.potrs(L, c)
+
+# 1000 points on the unit circle
+nopts = 1000
+angles = matrix( [ a*2.0*pi/nopts for a in xrange(nopts) ], (1,nopts) )
+circle = matrix(0.0, (2,nopts))
+circle[0,:], circle[1,:] = cos(angles), sin(angles)
+
+# ellipse = L^-T * circle + c
+blas.trsm(L, circle, transA='T')
+ellipse = circle + c[:, nopts*[0]]
+ellipse2 = 0.5 * circle + c[:, nopts*[0]]
+
+pylab.plot(ellipse[0,:], ellipse[1,:], 'k-')
+pylab.fill(ellipse2[0,:], ellipse2[1,:], '#F0F0F0')
+pylab.title('Loewner-John ellipsoid (fig 8.3)')
+pylab.axis('equal')
+pylab.axis('off')
+
+
+# Maximum volume enclosed ellipsoid
+#
+# minimize -log det B
+# subject to ||B * gk||_2 + gk'*c <= hk, k=1,...,m
+#
+# with variables B and c.
+#
+# minimize -log det L
+# subject to ||L' * gk||_2^2 / (hk - gk'*c) <= hk - gk'*c, k=1,...,m
+#
+# L lower triangular with positive diagonal and B*B = L*L'.
+#
+# minimize -log x[0] - log x[2]
+# subject to g( Dk*x + dk ) <= 0, k=1,...,m
+#
+# g(u,t) = u'*u/t - t
+# Dk = [ G[k,0] G[k,1] 0 0 0
+# 0 0 G[k,1] 0 0
+# 0 0 0 -G[k,0] -G[k,1] ]
+# dk = [0; 0; h[k]]
+#
+# 5 variables x = (L[0,0], L[1,0], L[1,1], c[0], c[1])
+
+D = [ matrix(0.0, (3,5)) for k in xrange(m) ]
+for k in xrange(m):
+ D[k][ [0, 3, 7, 11, 14] ] = matrix( [G[k,0], G[k,1], G[k,1],
+ -G[k,0], -G[k,1]] )
+d = [matrix([0.0, 0.0, hk]) for hk in h]
+
+def F(x=None, z=None):
+ if x is None:
+ return m, matrix([ 1.0, 0.0, 1.0, 0.0, 0.0 ])
+ if min(x[0], x[2], min(h-G*x[3:])) <= 0.0:
+ return None
+
+ y = [ Dk*x + dk for Dk, dk in zip(D, d) ]
+
+ f = matrix(0.0, (m+1,1))
+ f[0] = -log(x[0]) - log(x[2])
+ for k in xrange(m):
+ f[k+1] = y[k][:2].T * y[k][:2] / y[k][2] - y[k][2]
+
+ Df = matrix(0.0, (m+1,5))
+ Df[0,0], Df[0,2] = -1.0/x[0], -1.0/x[2]
+
+ # gradient of g is ( 2.0*(u/t); -(u/t)'*(u/t) -1)
+ for k in xrange(m):
+ a = y[k][:2] / y[k][2]
+ gradg = matrix(0.0, (3,1))
+ gradg[:2], gradg[2] = 2.0 * a, -a.T*a - 1
+ Df[k+1,:] = gradg.T * D[k]
+ if z is None: return f, Df
+
+ H = matrix(0.0, (5,5))
+ H[0,0] = z[0] / x[0]**2
+ H[2,2] = z[0] / x[2]**2
+
+ # Hessian of g is (2.0/t) * [ I, -u/t; -(u/t)', (u/t)*(u/t)' ]
+ for k in xrange(m):
+ a = y[k][:2] / y[k][2]
+ hessg = matrix(0.0, (3,3))
+ hessg[0,0], hessg[1,1] = 1.0, 1.0
+ hessg[:2,2], hessg[2,:2] = -a, -a.T
+ hessg[2, 2] = a.T*a
+ H += (z[k] * 2.0 / y[k][2]) * D[k].T * hessg * D[k]
+
+ return f, Df, H
+
+sol = solvers.cp(F)
+L = matrix([sol['x'][0], sol['x'][1], 0.0, sol['x'][2]], (2,2))
+c = matrix([sol['x'][3], sol['x'][4]])
+
+pylab.figure(2, facecolor='w')
+
+# polyhedron
+for k in xrange(m):
+ edge = X[[k,k+1],:] + 0.1 * matrix([1., 0., 0., -1.], (2,2)) * \
+ (X[2*[k],:] - X[2*[k+1],:])
+ pylab.plot(edge[:,0], edge[:,1], 'k')
+
+
+# 1000 points on the unit circle
+nopts = 1000
+angles = matrix( [ a*2.0*pi/nopts for a in xrange(nopts) ], (1,nopts) )
+circle = matrix(0.0, (2,nopts))
+circle[0,:], circle[1,:] = cos(angles), sin(angles)
+
+# ellipse = L * circle + c
+ellipse = L * circle + c[:, nopts*[0]]
+ellipse2 = 2.0 * L * circle + c[:, nopts*[0]]
+
+pylab.plot(ellipse2[0,:], ellipse2[1,:], 'k-')
+pylab.fill(ellipse[0,:], ellipse[1,:], '#F0F0F0')
+pylab.title('Maximum volume inscribed ellipsoid (fig 8.4)')
+pylab.axis('equal')
+pylab.axis('off')
+
+pylab.show()
diff --git a/examples/book/chap8/floorplan b/examples/book/chap8/floorplan
new file mode 100755
index 0000000..2cd5903
--- /dev/null
+++ b/examples/book/chap8/floorplan
@@ -0,0 +1,210 @@
+#!/usr/bin/python
+#
+# Figure 8.20, page 444.
+# Floor planning example.
+
+import pylab
+from cvxopt import solvers
+from cvxopt.base import matrix, spmatrix, mul, div
+
+def floorplan(Amin):
+
+ # minimize W+H
+ # subject to Amin1 / h1 <= w1
+ # Amin2 / h2 <= w2
+ # Amin3 / h3 <= w3
+ # Amin4 / h4 <= w4
+ # Amin5 / h5 <= w5
+ # x1 >= 0
+ # x2 >= 0
+ # x4 >= 0
+ # x1 + w1 + rho <= x3
+ # x2 + w2 + rho <= x3
+ # x3 + w3 + rho <= x5
+ # x4 + w4 + rho <= x5
+ # x5 + w5 <= W
+ # y2 >= 0
+ # y3 >= 0
+ # y5 >= 0
+ # y2 + h2 + rho <= y1
+ # y1 + h1 + rho <= y4
+ # y3 + h3 + rho <= y4
+ # y4 + h4 <= H
+ # y5 + h5 <= H
+ # h1/gamma <= w1 <= gamma*h1
+ # h2/gamma <= w2 <= gamma*h2
+ # h3/gamma <= w3 <= gamma*h3
+ # h4/gamma <= w4 <= gamma*h4
+ # h5/gamma <= w5 <= gamma*h5
+ #
+ # 22 Variables W, H, x (5), y (5), w (5), h (5).
+ #
+ # W, H: scalars; bounding box width and height
+ # x, y: 5-vectors; coordinates of bottom left corners of blocks
+ # w, h: 5-vectors; widths and heigths of the 5 blocks
+
+ rho, gamma = 1.0, 5.0 # min spacing, min aspect ratio
+
+ # The objective is to minimize W + H. There are five nonlinear
+ # constraints
+ #
+ # -w1 + Amin1 / h1 <= 0
+ # -w2 + Amin2 / h2 <= 0
+ # -w3 + Amin3 / h3 <= 0
+ # -w4 + Amin4 / h4 <= 0
+ # -w5 + Amin5 / h5 <= 0.
+
+ def F(x=None, z=None):
+ if x is None:
+ return 5, matrix(17*[0.0] + 5*[1.0])
+ if min(x[17:]) <= 0.0:
+ return None
+ f = matrix(0.0, (6,1))
+ f[0] = x[0] + x[1]
+ f[1:] = -x[12:17] + div(Amin, x[17:])
+ Df = matrix(0.0, (6,22))
+ Df[0, [0,1]] = 1.0
+ Df[1:,12:17] = spmatrix(-1.0, range(5), range(5))
+ Df[1:,17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
+ if z is None:
+ return f, Df
+ H = spmatrix( 2.0* mul(z[1:], div(Amin, x[17::]**3)),
+ range(17,22), range(17,22) )
+ return f, Df, H
+
+ # linear inequalities
+ G = matrix(0.0, (26,22))
+ h = matrix(0.0, (26,1))
+
+ # -x1 <= 0
+ G[0,2] = -1.0
+
+ # -x2 <= 0
+ G[1,3] = -1.0
+
+ # -x4 <= 0
+ G[2,5] = -1.0
+
+ # x1 - x3 + w1 <= -rho
+ G[3, [2, 4, 12]], h[3] = [1.0, -1.0, 1.0], -rho
+
+ # x2 - x3 + w2 <= -rho
+ G[4, [3, 4, 13]], h[4] = [1.0, -1.0, 1.0], -rho
+
+ # x3 - x5 + w3 <= -rho
+ G[5, [4, 6, 14]], h[5] = [1.0, -1.0, 1.0], -rho
+
+ # x4 - x5 + w4 <= -rho
+ G[6, [5, 6, 15]], h[6] = [1.0, -1.0, 1.0], -rho
+
+ # -W + x5 + w5 <= 0
+ G[7, [0, 6, 16]] = -1.0, 1.0, 1.0
+
+ # -y2 <= 0
+ G[8,8] = -1.0
+
+ # -y3 <= 0
+ G[9,9] = -1.0
+
+ # -y5 <= 0
+ G[10,11] = -1.0
+
+ # -y1 + y2 + h2 <= -rho
+ G[11, [7, 8, 18]], h[11] = [-1.0, 1.0, 1.0], -rho
+
+ # y1 - y4 + h1 <= -rho
+ G[12, [7, 10, 17]], h[12] = [1.0, -1.0, 1.0], -rho
+
+ # y3 - y4 + h3 <= -rho
+ G[13, [9, 10, 19]], h[13] = [1.0, -1.0, 1.0], -rho
+
+ # -H + y4 + h4 <= 0
+ G[14, [1, 10, 20]] = -1.0, 1.0, 1.0
+
+ # -H + y5 + h5 <= 0
+ G[15, [1, 11, 21]] = -1.0, 1.0, 1.0
+
+ # -w1 + h1/gamma <= 0
+ G[16, [12, 17]] = -1.0, 1.0/gamma
+
+ # w1 - gamma * h1 <= 0
+ G[17, [12, 17]] = 1.0, -gamma
+
+ # -w2 + h2/gamma <= 0
+ G[18, [13, 18]] = -1.0, 1.0/gamma
+
+ # w2 - gamma * h2 <= 0
+ G[19, [13, 18]] = 1.0, -gamma
+
+ # -w3 + h3/gamma <= 0
+ G[20, [14, 18]] = -1.0, 1.0/gamma
+
+ # w3 - gamma * h3 <= 0
+ G[21, [14, 19]] = 1.0, -gamma
+
+ # -w4 + h4/gamma <= 0
+ G[22, [15, 19]] = -1.0, 1.0/gamma
+
+ # w4 - gamma * h4 <= 0
+ G[23, [15, 20]] = 1.0, -gamma
+
+ # -w5 + h5/gamma <= 0
+ G[24, [16, 21]] = -1.0, 1.0/gamma
+
+ # w5 - gamma * h5 <= 0.0
+ G[25, [16, 21]] = 1.0, -gamma
+
+ # solve and return W, H, x, y, w, h
+ sol = solvers.cp(F, G, h)
+ return sol['x'][0], sol['x'][1], sol['x'][2:7], sol['x'][7:12], \
+ sol['x'][12:17], sol['x'][17:]
+
+solvers.options['show_progress'] = False
+
+pylab.figure(facecolor='w')
+
+pylab.subplot(221)
+Amin = matrix([100., 100., 100., 100., 100.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]], '#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(222)
+Amin = matrix([20., 50., 80., 150., 200.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]], '#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(223)
+Amin = matrix([180., 80., 80., 80., 80.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]],'#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.subplot(224)
+Amin = matrix([20., 150., 20., 200., 110.])
+W, H, x, y, w, h = floorplan(Amin)
+for k in xrange(5):
+ pylab.fill([x[k], x[k], x[k]+w[k], x[k]+w[k]],
+ [y[k], y[k]+h[k], y[k]+h[k], y[k]],'#D0D0D0')
+ pylab.text(x[k]+.5*w[k], y[k]+.5*h[k], "%d" %(k+1))
+pylab.axis([-1.0, 26, -1.0, 26])
+pylab.xticks([])
+pylab.yticks([])
+
+pylab.show()
diff --git a/examples/book/chap8/linsep b/examples/book/chap8/linsep
new file mode 100755
index 0000000..15f1c89
--- /dev/null
+++ b/examples/book/chap8/linsep
@@ -0,0 +1,134 @@
+#!/usr/bin/python
+
+# Figures 8.10-12, page 426-429.
+# Approximate linear discrimination.
+
+import pylab, pickle
+from cvxopt import solvers
+from cvxopt.blas import dot
+from cvxopt.base import matrix, spmatrix, log, exp, div
+from cvxopt.modeling import variable, op
+solvers.options['show_progress'] = False
+
+data = pickle.load(open("linsep.pic"))
+X, Y = data['X'], data['Y']
+n, N, M = X.size[0], X.size[1], Y.size[1]
+
+# Via linear programming.
+#
+# minimize sum(u) + sum(v)
+# subject to a'*X - b >= 1 - u
+# a'*Y - b <= -1 + v
+# u >= 0, v >= 0
+
+a, b = variable(2), variable()
+u, v = variable(N), variable(M)
+op( sum(u)+sum(v), [X.T*a-b >= 1-u, Y.T*a-b <= -1+v,
+ u>=0, v>=0] ).solve()
+a = a.value
+b = b.value
+
+pylab.figure(1, facecolor='w', figsize=(5,5))
+pts = matrix([-10.0, 10.0], (1,2))
+pylab.plot(X[0,:], X[1,:], 'ow', Y[0,:], Y[1,:], 'ok',
+ pts, (b - a[0]*pts)/a[1], '-r',
+ pts, (b+1.0 - a[0]*pts)/a[1], '--r',
+ pts, (b-1.0 - a[0]*pts)/a[1], '--r' )
+pylab.title('Separation via linear programming (fig. 8.10)')
+pylab.axis([-10, 10, -10, 10])
+pylab.axis('off')
+pylab.xticks([])
+pylab.yticks([])
+
+# Support vector classifier.
+#
+# minimize t + gamma*(1'*u + 1'*v)
+# subject to a'*X - b >= 1 - u
+# a'*Y - b <= -1 + v
+# u >= 0, v >= 0
+# [t*I a; a' t] >= 0
+
+gamma = 0.1
+nv = n + 2 + N + M # variables (a, b, t, u, v)
+ni = 2 * (N + M)
+
+c = matrix(0.0, (nv,1))
+c[3], c[4:] = 1.0, gamma
+
+IN = spmatrix(1.0, range(N), range(N))
+IM = spmatrix(1.0, range(M), range(M))
+Gl = matrix(0.0, (ni, nv))
+hl = matrix(0.0, (ni, 1))
+Gl[:N, :n] = -X.T
+Gl[:N, n] = 1.0
+Gl[:N, n+2:n+2+N] = -IN
+hl[:N] = -1.0
+Gl[N:N+M, :n] = Y.T
+Gl[N:N+M, n] = -1.0
+Gl[N:N+M, -M:] = -IM
+hl[N:N+M] = -1.0
+Gl[N+M:N+M+N, n+2:n+2+N] = -IN
+Gl[N+M+N:, -M:] = -IM
+
+Gs = [spmatrix(0.0, [], [], (9, nv))]
+Gs[0][2,0] = -1.0
+Gs[0][6,0] = -1.0
+Gs[0][5,1] = -1.0
+Gs[0][7,1] = -1.0
+Gs[0][0,3] = -1.0
+Gs[0][4,3] = -1.0
+Gs[0][8,3] = -1.0
+hs = [matrix(0.0, (3,3))]
+
+sol = solvers.sdp(c, Gl, hl, Gs, hs)
+a = sol['x'][:2]
+b = sol['x'][2]
+
+pylab.figure(2, facecolor='w', figsize=(5,5))
+pts = matrix([-10.0, 10.0], (1,2))
+pylab.plot(X[0,:], X[1,:], 'ow', Y[0,:], Y[1,:], 'ok',
+ pts, (b - a[0]*pts)/a[1], '-r',
+ pts, (b+1.0 - a[0]*pts)/a[1], '--r',
+ pts, (b-1.0 - a[0]*pts)/a[1], '--r' )
+pylab.title('Support vector classifier (fig. 8.11)')
+pylab.axis([-10, 10, -10, 10])
+pylab.xticks([])
+pylab.yticks([])
+pylab.axis('off')
+
+
+# Via logistic modeling.
+#
+# minimize -sum(X'*a - b) + sum log (1 + exp([X';Y']*a - b))
+
+A = matrix(0.0, (N+M,n+1))
+A[:N,:n], A[N:,:n], A[:,n] = X.T, Y.T, -1.0
+c = -(matrix(1.0, (1,N)) * A[:N,:]).T
+
+# minimize c'*x + sum log (1 + exp(A*x))
+
+def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (n+1,1))
+ w = exp(A*x)
+ f = dot(c,x) + sum(log(1+w))
+ grad = c + A.T * div(w, 1+w)
+ if z is None: return matrix(f), grad.T
+ H = A.T * spmatrix(div(w,(1+w)**2), range(len(w)), range(len(w))) * A
+ return matrix(f), grad.T, z[0]*H
+
+sol = solvers.cp(F)
+a, b = sol['x'][:2], sol['x'][2]
+
+pylab.figure(3, facecolor='w', figsize=(5,5))
+pts = matrix([-10.0, 10.0], (1,2))
+pylab.plot(X[0,:], X[1,:], 'ow', Y[0,:], Y[1,:], 'ok',
+ pts, (b - a[0]*pts)/a[1], '-r',
+ pts, (b+1.0 - a[0]*pts)/a[1], '--r',
+ pts, (b-1.0 - a[0]*pts)/a[1], '--r' )
+pylab.title('Separation via logistic modeling (fig. 8.12)')
+pylab.axis([-10, 10, -10, 10])
+pylab.xticks([])
+pylab.yticks([])
+pylab.axis('off')
+
+pylab.show()
diff --git a/examples/book/chap8/linsep.pic b/examples/book/chap8/linsep.pic
new file mode 100644
index 0000000..f8031f7
--- /dev/null
+++ b/examples/book/chap8/linsep.pic
@@ -0,0 +1,225 @@
+(dp0
+S'Y'
+p1
+ccvxopt.base
+matrix
+p2
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\ No newline at end of file
diff --git a/examples/book/chap8/placement b/examples/book/chap8/placement
new file mode 100755
index 0000000..7f95fc2
--- /dev/null
+++ b/examples/book/chap8/placement
@@ -0,0 +1,176 @@
+#!/usr/bin/python
+
+# Figures 8.15-17, pages 435 and 436.
+# Linear, quadratic and fourth-order placement.
+#
+# The problem data are different from the example in the book.
+
+import pylab, pickle
+from cvxopt import lapack, solvers
+from cvxopt.base import matrix, spmatrix, sqrt, mul
+from cvxopt.modeling import variable, op
+solvers.options['show_progress'] = False
+
+data = pickle.load(open("placement.pic", "r"))
+Xf = data['X'] # M by n matrix with coordinates of M fixed nodes
+M = Xf.size[0]
+E = data['E'] # list of edges
+L = len(E) # number of edges
+N = max(max(e) for e in E) + 1 - M # number of free nodes; fixed nodes
+ # have the highest M indices.
+# arc-node incidence matrix
+A = matrix(0.0, (L,M+N))
+for k in xrange(L): A[k, E[k]] = matrix([1.0, -1.0], (1,2))
+
+
+# minimize sum h( sqrt( (A1*X[:,0] + B[:,0])**2 +
+# (A1*X[:,1] + B[:,1])**2 ) for different h
+
+
+A1 = A[:,:N]
+B = A[:,N:]*Xf
+
+
+# Linear placement: h(u) = u.
+#
+# minimize 1'*t
+# subject to [ ti*I (A[i,:]*[x,y] + B)' ]
+# [ A[i,:]*[x,y] + B ti ] >= 0,
+# i = 1, ..., L
+#
+# variables t (L), x (N), y (N).
+
+novars = L + 2*N
+c = matrix(0.0, (novars,1))
+c[:L] = 1.0
+G = [ spmatrix([], [], [], (9, novars)) for k in xrange(L) ]
+h = [ matrix(0.0, (3,3)) for k in xrange(L) ]
+for k in xrange(L):
+
+ # coefficient of tk
+ C = spmatrix(-1.0, [0,1,2], [0,1,2])
+ G[k][C.I + 3*C.J, k] = C.V
+
+ for j in xrange(N):
+ # coefficient of x[j]
+ C = spmatrix(-A[k,j], [2, 0], [0, 2])
+ G[k][C.I + 3*C.J, L+j] = C.V
+
+ # coefficient of y[j]
+ C = spmatrix(-A[k,j], [2, 1], [1, 2])
+ G[k][C.I + 3*C.J, L+N+j] = C.V
+
+ # constant
+ h[k][2,:2] = B[k,:]
+ h[k][:2,2] = B[k,:].T
+
+sol = solvers.sdp(c, Gs=G, hs=h)
+X1 = matrix(sol['x'][L:], (N,2))
+
+
+# Quadratic placement: h(u) = u^2.
+#
+# minimize sum (A*X[:,0] + B[:,0])**2 + (A*X[:,1] + B[:,1])**2
+#
+# with variable X (Nx2).
+
+Bc = -B
+lapack.gels(+A1, Bc)
+X2 = Bc[:N,:]
+
+
+# Fourth order placement: h(u) = u^4
+#
+# minimize g(AA*x + BB)
+#
+# where AA = [A1, 0; 0, A1]
+# BB = [B[:,0]; B[:,1]]
+# x = [X[:,0]; X[:,1]]
+# g(u,v) = sum((uk.^2 + vk.^2).^2)
+#
+# with variables x (2*N).
+
+AA = matrix(0.0, (2*L, 2*N))
+AA[:L, :N], AA[L:,N:] = A1, A1
+BB = matrix(B, (2*L,1))
+def F(x=None, z=None):
+ if x is None:
+ return 0, matrix(0.0, (2*N,1))
+ y = AA*x + BB
+ d = y[:L]**2 + y[L:]**2
+ f = sum(d**2)
+ gradg = matrix(0.0, (2*L,1))
+ gradg[:L], gradg[L:] = 4*mul(d,y[:L]), 4*mul(d,y[L:])
+ g = gradg.T * AA
+ if z is None: return f, g
+ H = matrix(0.0, (2*L, 2*L))
+ for k in xrange(L):
+ H[k,k], H[k+L,k+L] = 4*d[k], 4*d[k]
+ H[[k,k+L], [k,k+L]] += 8 * y[[k,k+L]] * y[[k,k+L]].T
+ return f, g, AA.T*H*AA
+
+sol = solvers.cp(F)
+X4 = matrix(sol['x'], (N,2))
+
+
+# Figures for linear placement.
+
+pylab.figure(1, figsize=(10,4), facecolor='w')
+pylab.subplot(121)
+X = matrix(0.0, (N+M,2))
+X[:N,:], X[N:,:] = X1, Xf
+pylab.plot(Xf[:,0], Xf[:,1], 'sw', X1[:,0], X1[:,1], 'or', ms=10)
+for s, t in E: pylab.plot([X[s,0], X[t,0]], [X[s,1],X[t,1]], ':')
+pylab.axis([-1.1, 1.1, -1.1, 1.1])
+pylab.axis('equal')
+pylab.title('Linear placement')
+
+pylab.subplot(122)
+lngths = sqrt((A1*X1 + B)**2 * matrix(1.0, (2,1)))
+pylab.hist(lngths, [.1*k for k in xrange(15)])
+x = pylab.arange(0, 1.6, 1.6/500)
+pylab.plot( x, 5.0/1.6*x, '--k')
+pylab.axis([0, 1.6, 0, 5.5])
+pylab.title('Length distribution')
+
+
+# Figures for quadratic placement.
+
+pylab.figure(2, figsize=(10,4), facecolor='w')
+pylab.subplot(121)
+X[:N,:], X[N:,:] = X2, Xf
+pylab.plot(Xf[:,0], Xf[:,1], 'sw', X2[:,0], X2[:,1], 'or', ms=10)
+for s, t in E: pylab.plot([X[s,0], X[t,0]], [X[s,1],X[t,1]], ':')
+pylab.axis([-1.1, 1.1, -1.1, 1.1])
+pylab.axis('equal')
+pylab.title('Quadratic placement')
+
+pylab.subplot(122)
+lngths = sqrt((A1*X2 + B)**2 * matrix(1.0, (2,1)))
+pylab.hist(lngths, [.1*k for k in xrange(15)])
+x = pylab.arange(0, 1.5, 1.5/500)
+pylab.plot( x, 5.0/1.5**2 * x**2, '--k')
+pylab.axis([0, 1.5, 0, 5.5])
+pylab.title('Length distribution')
+
+
+# Figures for fourth order placement.
+
+pylab.figure(3, figsize=(10,4), facecolor='w')
+pylab.subplot(121)
+X[:N,:], X[N:,:] = X4, Xf
+pylab.plot(Xf[:,0], Xf[:,1], 'sw', X4[:,0], X4[:,1], 'or', ms=10)
+for s, t in E: pylab.plot([X[s,0], X[t,0]], [X[s,1],X[t,1]], ':')
+pylab.axis([-1.1, 1.1, -1.1, 1.1])
+pylab.axis('equal')
+pylab.title('Fourth order placement')
+
+pylab.subplot(122)
+lngths = sqrt((A1*X4 + B)**2 * matrix(1.0, (2,1)))
+pylab.hist(lngths, [.1*k for k in xrange(15)])
+x = pylab.arange(0, 1.5, 1.5/500)
+pylab.plot( x, 6.0/1.4**4 * x**4, '--k')
+pylab.axis([0, 1.4, 0, 6.5])
+pylab.title('Length distribution')
+
+pylab.show()
diff --git a/examples/book/chap8/placement.pic b/examples/book/chap8/placement.pic
new file mode 100644
index 0000000..e4ed24e
--- /dev/null
+++ b/examples/book/chap8/placement.pic
@@ -0,0 +1,118 @@
+(dp0
+S'X'
+p1
+ccvxopt.base
+matrix
+p2
+((lp3
+F1.0
+aF1.0
+aF-1.0
+aF-1.0
+aF1.0
+aF-1.0
+aF-0.20000000000000001
+aF0.10000000000000001
+aF1.0
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+aF1.0
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+aF-0.20000000000000001
+aF-1.0
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+tp4
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+sS'E'
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\ No newline at end of file
diff --git a/examples/doc/README b/examples/doc/README
new file mode 100644
index 0000000..2a24119
--- /dev/null
+++ b/examples/doc/README
@@ -0,0 +1 @@
+This directory contains some examples from the CVXOPT documentation.
diff --git a/examples/doc/acent b/examples/doc/acent
new file mode 100755
index 0000000..336ec1f
--- /dev/null
+++ b/examples/doc/acent
@@ -0,0 +1,77 @@
+#!/usr/bin/python
+
+# The analytic centering example of section 4.8.
+
+from cvxopt.base import matrix, log, mul, div
+from cvxopt import blas, lapack, random
+from math import sqrt
+
+def acent(A,b):
+ """
+ Computes analytic center of A*x <= b with A m by n of rank n.
+ We assume that b > 0 and the feasible set is bounded.
+ """
+
+ MAXITERS = 100
+ ALPHA = 0.01
+ BETA = 0.5
+ TOL = 1e-8
+
+ ntdecrs = []
+ m, n = A.size
+ x = matrix(0.0, (n,1))
+ H = matrix(0.0, (n,n))
+ g = matrix(0.0, (n,1))
+
+ for iter in xrange(MAXITERS):
+
+ # Gradient is g = A^T * (1./(b-A*x)).
+ d = (b-A*x)**-1
+ g = A.T * d
+
+ # Hessian is H = A^T * diag(1./(b-A*x))^2 * A.
+ Asc = mul( d[:,n*[0]], A)
+ blas.syrk(Asc, H, trans='T')
+
+ # Newton step is v = H^-1 * g.
+ v = -g
+ lapack.posv(H, v)
+
+ # Directional derivative and Newton decrement.
+ lam = blas.dot(g, v)
+ ntdecrs += [ sqrt(-lam) ]
+ print "%2d. Newton decr. = %3.3e" %(iter,ntdecrs[-1])
+ if ntdecrs[-1] < TOL: return x, ntdecrs
+
+ # Backtracking line search.
+ y = mul(A*v, d)
+ step = 1.0
+ while 1-step*max(y) < 0: step *= BETA
+ while True:
+ if -sum(log(1-step*y)) < ALPHA*step*lam: break
+ step *= BETA
+ x += step*v
+
+
+# Generate an analytic centering problem
+#
+# -b1 <= Ar*x <= b2
+#
+# with random mxn Ar and random b1, b2.
+
+m, n = 500, 500
+Ar = random.normal(m,n);
+A = matrix([Ar, -Ar])
+b = random.uniform(2*m,1)
+
+x, ntdecrs = acent(A, b)
+try:
+ import pylab
+except ImportError:
+ pass
+else:
+ pylab.semilogy(range(len(ntdecrs)), ntdecrs, 'o',
+ range(len(ntdecrs)), ntdecrs, '-')
+ pylab.xlabel('Iteration number')
+ pylab.ylabel('Newton decrement')
+ pylab.show()
diff --git a/examples/doc/covsel b/examples/doc/covsel
new file mode 100755
index 0000000..ff45f43
--- /dev/null
+++ b/examples/doc/covsel
@@ -0,0 +1,90 @@
+#! /usr/bin/python
+
+# The covariance selection example of section 7.4.
+
+from cvxopt.base import matrix, spmatrix, log, mul
+from cvxopt import blas, lapack, amd, cholmod
+from pickle import load
+
+def covsel(Y):
+ """
+ Returns the solution of
+
+ minimize -logdet K + tr(KY)
+ subject to K_ij = 0 if (i,j) not in zip(I, J).
+
+ Y is a symmetric sparse matrix with nonzero diagonal elements.
+ I = Y.I, J = Y.J.
+ """
+
+ cholmod.options['supernodal'] = 2
+
+ I, J = Y.I, Y.J
+ n, m = Y.size[0], len(I)
+ # non-zero positions for one-argument indexing
+ N = I + J*n
+ # position of diagonal elements
+ D = [ k for k in xrange(m) if I[k]==J[k] ]
+
+ # starting point: symmetric identity with nonzero pattern I,J
+ K = spmatrix(0.0, I, J)
+ K[::n+1] = 1.0
+
+ # Kn is used in the line search
+ Kn = spmatrix(0.0, I, J)
+
+ # symbolic factorization of K
+ F = cholmod.symbolic(K)
+
+ # Kinv will be the inverse of K
+ Kinv = matrix(0.0, (n,n))
+
+ for iters in xrange(100):
+
+ # numeric factorization of K
+ cholmod.numeric(K, F)
+ d = cholmod.diag(F)
+
+ # compute Kinv by solving K*X = I
+ Kinv[:] = 0.0
+ Kinv[::n+1] = 1.0
+ cholmod.solve(F, Kinv)
+
+ # solve Newton system
+ grad = 2 * (Y.V - Kinv[N])
+ hess = 2 * ( mul(Kinv[I,J], Kinv[J,I]) +
+ mul(Kinv[I,I], Kinv[J,J]) )
+ v = -grad
+ lapack.posv(hess,v)
+
+ # stopping criterion
+ sqntdecr = -blas.dot(grad,v)
+ print "Newton decrement squared:%- 7.5e" %sqntdecr
+ if (sqntdecr < 1e-12):
+ print "number of iterations: ", iters+1
+ break
+
+ # line search
+ dx = +v
+ dx[D] *= 2
+ f = -2.0*sum(log(d)) # f = -log det K
+ s = 1
+ for lsiter in xrange(50):
+ Kn.V = K.V + s*dx
+ try:
+ cholmod.numeric(Kn, F)
+ except ArithmeticError:
+ s *= 0.5
+ else:
+ d = cholmod.diag(F)
+ fn = -2.0 * sum(log(d)) + 2*s*blas.dot(v,Y.V)
+ if (fn < f - 0.01*s*sqntdecr): break
+ else: s *= 0.5
+
+ K.V = Kn.V
+
+ return K
+
+Y = load(open("covsel.pic","r"))
+print "%d rows/columns, %d nonzeros\n" %(Y.size[0], len(Y))
+covsel(Y)
diff --git a/examples/doc/covsel.pic b/examples/doc/covsel.pic
new file mode 100644
index 0000000..c1a9588
--- /dev/null
+++ b/examples/doc/covsel.pic
@@ -0,0 +1,5261 @@
+ccvxopt.base
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\ No newline at end of file
diff --git a/examples/doc/l1 b/examples/doc/l1
new file mode 100755
index 0000000..92ab0f3
--- /dev/null
+++ b/examples/doc/l1
@@ -0,0 +1,127 @@
+#!/usr/bin/python
+
+# The 1-norm approximation example of section 8.6.
+
+from cvxopt import base, random, blas, lapack, solvers
+from cvxopt.base import matrix, spmatrix, mul, div
+from math import sqrt
+solvers.options['refinement'] = False
+
+def l1(P, q):
+
+ """
+ Returns the solution u, w of the ell-1 approximation problem
+
+ (primal) minimize ||P*u - q||_1
+
+ (dual) maximize q'*w
+ subject to P'*w = 0
+ ||w||_infty <= 1.
+ """
+
+ m, n = P.size
+
+ # Solve equivalent LP
+ #
+ # minimize [0; 1]' * [u; v]
+ # subject to [P, -I; -P, -I] * [u; v] <= [q; -q]
+ #
+ # maximize -[q; -q]' * z
+ # subject to [P', -P']*z = 0
+ # [-I, -I]*z + 1 = 0
+ # z >= 0
+
+ c = matrix(n*[0.0] + m*[1.0])
+ h = matrix([q, -q])
+
+ def Fi(x, y, alpha=1.0, beta=0.0, trans='N'):
+ if trans=='N':
+ # y := alpha * [P, -I; -P, -I] * x + beta*y
+ u = P*x[:n]
+ y[:m] = alpha * ( u - x[n:]) + beta*y[:m]
+ y[m:] = alpha * (-u - x[n:]) + beta*y[m:]
+
+ else:
+ # y := alpha * [P', -P'; -I, -I] * x + beta*y
+ y[:n] = alpha * P.T * (x[:m] - x[m:]) + beta*y[:n]
+ y[n:] = -alpha * (x[:m] + x[m:]) + beta*y[n:]
+
+
+ def kktsolver(d, R):
+
+ # Returns a function f(x,y,zl,zs) that solves
+ #
+ # [ 0 0 P' -P' ] [ x[:n] ] [ bx[:n] ]
+ # [ 0 0 -I -I ] [ x[n:] ] [ bx[n:] ]
+ # [ P -I -D1^{-1} 0 ] [ zl[:m]] = [ bzl[:m] ]
+ # [-P -I 0 -D2^{-1} ] [ zl[m:]] [ bzl[m:] ]
+ #
+ # where D1 = diag(d[:m])^2, D2 = diag(d[m:])^2.
+ #
+ # On entry bx, bzl are stored in x, zl.
+ # On exit x, zl contain the solution, with zl scaled (d.*zl is
+ # returned instead of zl).
+
+ # Factor A = 4*P'*D*P where D = d1.*d2 ./(d1+d2) and
+ # d1 = d[:m].^2, d2 = d[m:].^2.
+
+ d1, d2 = d[:m]**2, d[m:]**2
+ D = div( mul(d1,d2), d1+d2 )
+ A = P.T * spmatrix(4*D, range(m), range(m)) * P
+ lapack.potrf(A)
+
+ def f(x, y, zl, zs):
+
+ # Solve for x[:n]:
+ #
+ # A*x[:n] = bx[:n] + P' * ( ((D1-D2)*(D1+D2)^{-1})*bx[n:]
+ # + (2*D1*D2*(D1+D2)^{-1}) * (bzl[:m] - bzl[m:]) ).
+
+ x[:n] += P.T * ( mul( div(d1-d2, d1+d2), x[n:]) +
+ mul( 2*D, zl[:m]-zl[m:] ) )
+ lapack.potrs(A, x)
+
+ # x[n:] := (D1+D2)^{-1} * (bx[n:] - D1*bzl[:m] - D2*bzl[m:]
+ # + (D1-D2)*P*x[:n])
+
+ u = P*x[:n]
+ x[n:] = div( x[n:] - mul(d1, zl[:m]) - mul(d2, zl[m:]) +
+ mul(d1-d2, u), d1+d2 )
+
+ # z[:m] := d1[:m] .* ( P*x[:n] - x[n:] - bzl[:m])
+ # z[m:] := d2[m:] .* (-P*x[:n] - x[n:] - bzl[m:])
+
+ zl[:m] = mul(d[:m], u-x[n:]-zl[:m])
+ zl[m:] = mul(d[m:], -u-x[n:]-zl[m:])
+
+ return f
+
+
+ # Initial primal and dual points from least-squares solution.
+
+ # uls minimizes ||P*u-q||_2; rls is the LS residual.
+ uls = +q
+ lapack.gels(+P, uls)
+ rls = P*uls[:n] - q
+
+ # x0 = [ uls; 1.1*abs(rls) ]; s0 = [q;-q] - [P,-I; -P,-I] * x0
+ x0 = matrix( [uls[:n], 1.1*abs(rls)] )
+ s0 = +h
+ Fi(x0, s0, alpha=-1, beta=1)
+
+ # z0 = [ (1+w)/2; (1-w)/2 ] where w = (.9/||rls||_inf) * rls
+ # if rls is nonzero and w = 0 otherwise.
+ if max(abs(rls)) > 1e-10:
+ w = .9/max(abs(rls)) * rls
+ else:
+ w = matrix(0.0, (m,1))
+ z0 = matrix([.5*(1+w), .5*(1-w)])
+
+ sol = solvers.conelp(c, kktsolver, Gl=Fi, hl=h,
+ primalstart={'x': x0, 'sl':s0}, dualstart={'zl': z0})
+ return sol['x'][:n], sol['zl'][m:] - sol['zl'][:m]
+
+random.setseed()
+m, n = 500, 100
+P, q = random.normal(m,n), random.normal(m,1)
+x, y = l1(P,q)
diff --git a/examples/doc/mcsdp b/examples/doc/mcsdp
new file mode 100755
index 0000000..43b4c06
--- /dev/null
+++ b/examples/doc/mcsdp
@@ -0,0 +1,121 @@
+#!/usr/bin/python
+
+# The SDP example of section 8.6.
+
+from cvxopt import base, blas, lapack, random, solvers
+from cvxopt.base import matrix
+
+def mcsdp(w):
+ """
+ Returns solution x, z to
+
+ (primal) minimize sum(x)
+ subject to w + diag(x) >= 0
+
+ (dual) maximize -tr(w*z)
+ subject to diag(z) = 1
+ z >= 0.
+ """
+
+ n = w.size[0]
+
+ def Fs(x, y, alpha=1.0, beta=0.0, trans='N'):
+ """
+ y := alpha*(-diag(x)) + beta*y.
+ """
+ if trans=='N':
+ # x is a vector; y[0] is a matrix.
+ blas.scal(beta, y[0])
+ blas.axpy(x, y[0], alpha=-alpha, incy=n+1)
+
+ else:
+ # x[0] is a matrix; y is a vector.
+ blas.scal(beta, y)
+ blas.axpy(x[0], y, alpha=-alpha, incx=n+1)
+
+
+ def cngrnc(r, x, alpha=1.0):
+ """
+ Congruence transformation
+
+ x := alpha * r'*x*r.
+
+ r and x are square matrices.
+ """
+
+ # Scale diagonal of x by 1/2.
+ x[::n+1] *= 0.5
+
+ # a := tril(x)*r
+ a = +r
+ blas.trmm(x, a, side='L')
+
+ # x := alpha*(a*r' + r*a')
+ blas.syr2k(r, a, x, trans='T', alpha=alpha)
+
+
+ def kktsolver(d, r):
+
+ # t = r*r' as a nonsymmetric matrix.
+ t = matrix(0.0, (n,n))
+ blas.gemm(r[0], r[0], t, transB='T')
+
+ # Cholesky factorization of tsq = t.*t.
+ tsq = t**2
+ lapack.potrf(tsq)
+
+ def f(x, y, zl, zs):
+ """
+ Solve
+ -diag(zs) = bx
+ -diag(x) - inv(r*r')*zs*inv(r*r') = bs
+
+ On entry, x and zs contain bx and bs.
+ On exit, they contain the solution, with zs scaled
+ (inv(r)'*zs*inv(r) is returned instead of zs).
+
+ We first solve
+
+ ((r*r') .* (r*r')) * x = bx - diag(t*bs*t)
+
+ and take zs = -r' * (diag(x) + bs) * r.
+ """
+
+ # tbst := t * zs * t = t * bs * t
+ tbst = +zs[0]
+ cngrnc(t, tbst)
+
+ # x := x - diag(tbst) = bx - diag(r*r' * bs * r*r')
+ x -= tbst[::n+1]
+
+ # x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
+ lapack.potrs(tsq, x)
+
+ # zs := zs + diag(x) = bs + diag(x)
+ zs[0][::n+1] += x
+
+ # zs := -r' * zs * r = -r' * (diag(x) + bs) * r
+ cngrnc(r[0], zs[0], alpha=-1.0)
+
+ return f
+
+ c = matrix(1.0, (n,1))
+
+ # Initial feasible x: x = 1.0 - min(lambda(w)).
+ lmbda = matrix(0.0, (n,1))
+ lapack.syevx(+w, lmbda, range='I', il=1, iu=1)
+ x0 = matrix(-lmbda[0]+1.0, (n,1))
+ s0 = +w
+ s0[::n+1] += x0
+
+ # Initial feasible z is identity.
+ z0 = matrix(0.0, (n,n))
+ z0[::n+1] = 1.0
+
+ sol = solvers.conelp(c, kktsolver, Gs=Fs, hs=[w],
+ primalstart={'x': x0, 'ss': [s0]}, dualstart={'zs': [z0]})
+ return sol['x'], sol['zs'][0]
+
+n = 100
+w = random.normal(n,n)
+x, z = mcsdp(w)
diff --git a/examples/doc/normappr b/examples/doc/normappr
new file mode 100755
index 0000000..254a8f4
--- /dev/null
+++ b/examples/doc/normappr
@@ -0,0 +1,34 @@
+#!/usr/bin/python
+
+# The norm and penalty approximation problems of section 9.5.
+
+from cvxopt.random import normal, setseed
+from cvxopt.modeling import variable, op, max, sum
+
+setseed(1)
+m, n = 500, 100
+A = normal(m,n)
+b = normal(m)
+
+x1 = variable(n)
+prob1=op(max(abs(A*x1+b)))
+prob1.solve()
+
+x2 = variable(n)
+prob2=op(sum(abs(A*x2+b)))
+prob2.solve()
+
+x3 = variable(n)
+prob3=op(sum(max(0, abs(A*x3+b)-0.75, 2*abs(A*x3+b)-2.25)))
+prob3.solve()
+
+try: import pylab
+except ImportError: pass
+else:
+ pylab.subplot(311)
+ pylab.hist(A*x1.value + b, m/5)
+ pylab.subplot(312)
+ pylab.hist(A*x2.value + b, m/5)
+ pylab.subplot(313)
+ pylab.hist(A*x3.value + b, m/5)
+ pylab.show()
diff --git a/examples/filterdemo/README b/examples/filterdemo/README
new file mode 100644
index 0000000..81eb297
--- /dev/null
+++ b/examples/filterdemo/README
@@ -0,0 +1,12 @@
+The filterdemo computes a FIR lowpass filter by solving a linear
+program. It solves a discretization of the problem
+
+minimize d2
+subject to -1/d1 <= H(wk) <= d1, 0 <= w <= wc
+ max(abs(H(wk))) <= d2, ws <= w <= pi
+
+where H(w) = h_0 + sum_{i=1}^{n-1} h_i*cos(2*pi/n*i*w).
+The variables are h and d2.
+
+'filterdemo_cli' uses a simple a simple command-line interface.
+'filterdemo_gui' uses a graphical user interface based on GTK.
diff --git a/examples/filterdemo/filterdemo_cli b/examples/filterdemo/filterdemo_cli
new file mode 100755
index 0000000..15ac64a
--- /dev/null
+++ b/examples/filterdemo/filterdemo_cli
@@ -0,0 +1,136 @@
+#!/usr/bin/python
+import getopt, sys
+
+from cvxopt.base import matrix
+from cvxopt.solvers import options
+from cvxopt.modeling import op, variable, max
+
+from math import cos, log10, pi
+
+import pygtk
+pygtk.require('2.0')
+import gtk
+
+import matplotlib
+matplotlib.use('GTKAgg') # or 'GTK'
+from matplotlib.backends.backend_gtk import FigureCanvasGTK as FigureCanvas
+import pylab
+
+def frange(a,b,N):
+ return [ a+k*float((b-a))/N for k in xrange(N) ]
+
+def design_lowpass(N, d1, wc, ws, solver=None, Q=50):
+
+ h = variable(N+1)
+ d1 = 10**(d1/20.0) # convert from dB
+
+ n1 = int(round(N*Q*wc/pi));
+ w1 = matrix(frange(0,wc,n1))
+ G1 = matrix([cos(wi*j) for j in xrange(N+1) for wi in w1], (n1,N+1))
+
+ n2 = int(round(N*Q*(pi-ws)/pi));
+ w2 = matrix(frange(ws,pi,n2))
+ G2 = matrix([cos(wi*j) for j in xrange(N+1) for wi in w2], (n2,N+1))
+
+ options['show_progress'] = 0
+ options['LPX_K_MSGLEV'] = 0
+ options['MSK_IPAR_LOG']= 0
+ op(max(abs(G2*h)), [G1*h <= d1, G1*h >= 1.0/d1]).solve(solver=solver)
+
+ return (h.value, max(abs(G2*h.value)))
+
+def make_plot(h, d2, co, sb, pr, N, output=None):
+ w = matrix(frange(0,pi,N*50));
+ C = w*matrix(range(N+1), (1,N+1), 'd');
+ for i in xrange(len(C)): C[i] = cos(C[i])
+
+ fig = pylab.figure()
+ ax = fig.add_subplot(111)
+ ylim = [round((20*log10(d2)-40)/10)*10,10]
+ ax.plot(list(w/pi),[20*log10(abs(x)) for x in C*h])
+ ax.plot(2*[co],[-pr,ylim[0]],'g--')
+ ax.plot(2*[co],[10,pr],'g--')
+ ax.plot(2*[sb],[10,20*log10(d2)],'g--')
+ ax.plot([sb, 1],2*[20*log10(d2)],'g--')
+ ax.plot([0, co],2*[-pr],'g--')
+ ax.plot([0, co],2*[pr],'g--')
+
+ pylab.setp(ax,ylim=ylim)
+ pylab.setp(ax,xlabel="Normalized frequency")
+ pylab.setp(ax,ylabel="Attenuation [dB]")
+ ax.grid()
+
+def usage():
+ print """
+Usage:
+filterdemo_cli --cutoff=CO --stopband=SB --ripple=RP --order=N [options]
+
+Arguments:
+ CO: normalized cutoff frequency
+ SB: normalized stopband frequency, 0.1 <= co < sb-0.1 <= 0.5,
+ RP: maximum passband ripple in dB, 0.01 <= rp <= 3,
+ N : filterorder, 5 <= or <= 50.
+
+Options:
+--solver = SOLVER One of default, mosek, glpk
+--output = FILENAME Output filename.
+"""
+ sys.exit(2)
+
+def main():
+ try:
+ opts, args = getopt.getopt(sys.argv[1:], "",
+ ['cutoff=', 'stopband=', 'ripple=', 'order=',
+ 'solver=', 'output='])
+ except getopt.GetoptError:
+ usage()
+
+ if opts==[]: usage()
+
+ co, sb, pr, N, output = [None]*5
+ solver = "default"
+
+ try:
+ for o, a in opts:
+ if o == "--cutoff": co = float(a);
+ if o == "--stopband": sb = float(a);
+ if o == "--ripple": pr = float(a);
+ if o == "--order": N = int(a);
+ if o == "--solver": solver = a;
+ if o == "--output": output = a;
+ except: usage()
+
+ if None in [co, sb, pr, N]: usage()
+
+ if not (0.1 <= co < sb-0.01+1E-8 <= 0.5):
+ print "invalid cutoff and stopband frequencies"
+ usage()
+
+ if not (0.01 <= pr <= 3):
+ print "invalid value of passband ripple"
+ usage()
+
+ if not (5 <= N <= 50):
+ print "invalid filterorder"
+ usage()
+
+ if not solver in ['default','mosek','glpk']:
+ print "invalid solver"
+ usage()
+
+
+ try:
+ [h, d2] = design_lowpass(N, pr, co*pi, sb*pi, solver)
+ except:
+ print "Please tighten filter specifications."
+ sys.exit(2)
+
+
+ make_plot(h, d2, co, sb, pr, N, output);
+
+ if (output != None): savefig(output)
+
+ pylab.show()
+
+if __name__ == "__main__":
+ main()
diff --git a/examples/filterdemo/filterdemo_gui b/examples/filterdemo/filterdemo_gui
new file mode 100755
index 0000000..196f612
--- /dev/null
+++ b/examples/filterdemo/filterdemo_gui
@@ -0,0 +1,213 @@
+#!/usr/bin/python
+from cvxopt.base import matrix, cos
+from cvxopt.solvers import options
+from cvxopt.modeling import op, variable, max
+
+from math import log10, pi, floor
+
+import gtk
+
+import matplotlib
+matplotlib.use('GTK') # or 'GTK'
+from matplotlib.backends.backend_gtk import FigureCanvasGTK as FigureCanvas
+import pylab
+
+
+def frange(a,b,N):
+ return [ a+k*float((b-a))/N for k in xrange(N) ]
+
+
+def design_lowpass(N, d1, wc, ws, solver=None, Q=50):
+
+ h = variable(N+1)
+ d1 = 10**(d1/20.0) # convert from dB
+
+ n = matrix(range(N+1), (1,N+1), 'd')
+ n1 = int(round(N*Q*wc/pi));
+ G1 = cos(matrix(frange(0,wc,n1))*n)
+
+ n2 = int(round(N*Q*(pi-ws)/pi));
+ G2 = cos(matrix(frange(ws,pi,n2))*n)
+
+ op(max(abs(G2*h)), [G1*h <= d1, G1*h >= 1.0/d1]).solve(solver=solver)
+
+ return (h.value, max(abs(G2*h.value)))
+
+
+
+class MainGUI:
+
+ def check_values(self, param=None):
+ page = self.nb.get_current_page()
+ if page>=0:
+ N = self.fo_spinner.get_value_as_int()
+ co = self.co_spinner.get_value()
+ sb = self.sb_spinner.get_value()
+ pr = self.pr_spinner.get_value()
+ if (co == self.tabs[page][1] and sb == self.tabs[page][2] and
+ pr == self.tabs[page][3] and N == self.tabs[page][4]):
+ self.compute_filter.set_sensitive(False)
+ else:
+ self.compute_filter.set_sensitive(True)
+
+ def change_co(self, param1):
+ self.sb_spinner.set_range(param1.get_value()+0.01,
+ self.sb_spinner.get_range()[1]);
+ self.check_values()
+
+ def change_sb(self, param1):
+ self.co_spinner.set_range(0.1, param1.get_value()-0.01);
+ self.check_values()
+
+ def switch_page(self, page, page_num, page_int, notebook):
+ if len(self.tabs)>page_int:
+ self.tabs[page_int][0].draw()
+ self.co_spinner.set_value(self.tabs[page_int][1])
+ self.sb_spinner.set_value(self.tabs[page_int][2])
+ self.pr_spinner.set_value(self.tabs[page_int][3])
+ self.fo_spinner.set_value(self.tabs[page_int][4])
+ self.compute_filter.set_sensitive(False)
+
+ def new_tab(self, button, notebook):
+
+ N = self.fo_spinner.get_value_as_int()
+ co = self.co_spinner.get_value()
+ sb = self.sb_spinner.get_value()
+ pr = self.pr_spinner.get_value()
+
+ try:
+ h, d2 = design_lowpass(N, pr, pi*co, pi*sb)
+ except:
+ x = gtk.MessageDialog(flags=gtk.DIALOG_MODAL, \
+ type=gtk.MESSAGE_WARNING, message_format= \
+ "KKT matrix is nearly singular.\n"\
+ "Please tighten the filter specifications.");
+ x.run()
+ return
+
+ w = matrix(frange(0,pi,N*50));
+ C = cos(w*matrix(range(N+1),(1,N+1)));
+
+ fig = pylab.figure()
+ canvas = FigureCanvas(fig) # a gtk.DrawingArea
+ ax = fig.add_subplot(111)
+
+ ylim = [floor((20*log10(d2)-30)/100)*100,10]
+
+ ax.plot(list(w/pi),[20*log10(abs(x)) for x in C*h])
+ ax.plot(2*[co],[-pr,ylim[0]],'g--')
+ ax.plot(2*[co],[10,pr],'g--')
+ ax.plot(2*[sb],[10,20*log10(d2)],'g--')
+ ax.plot([sb, 1],2*[20*log10(d2)],'g--')
+ ax.plot([0, co],2*[-pr],'g--')
+ ax.plot([0, co],2*[pr],'g--')
+
+ pylab.setp(ax,ylim=ylim)
+ pylab.setp(ax,xlabel="Normalized frequency")
+ pylab.setp(ax,ylabel="Attenuation [dB]")
+ ax.grid()
+ canvas.show()
+ notebook.append_page(canvas)
+ notebook.set_current_page(notebook.get_n_pages()-1)
+
+ self.tabs.append([canvas,co,sb,pr,N])
+ self.compute_filter.set_sensitive(False)
+
+ def close_tab(self, button, notebook):
+ page = notebook.get_current_page()
+ notebook.remove_page(page)
+ if page>=0: del(self.tabs[page])
+ # Need to refresh the widget --
+ # This forces the widget to redraw itself.
+ notebook.queue_draw_area(0,0,-1,-1)
+
+ if notebook.get_n_pages() == 0:
+ self.compute_filter.set_sensitive(True)
+
+ def delete(self, widget, event=None):
+ gtk.main_quit()
+ return gtk.FALSE
+
+ def __init__(self):
+ window = gtk.Window (gtk.WINDOW_TOPLEVEL)
+ window.connect("delete_event", self.delete)
+ window.set_default_size(600, 400)
+ window.set_border_width(10)
+ table = gtk.Table(4,6,False)
+ window.add(table)
+
+ # Create a new notebook, place the position of the tabs
+ notebook = gtk.Notebook()
+ notebook.connect("switch-page", self.switch_page, notebook)
+ notebook.set_tab_pos(gtk.POS_BOTTOM)
+ table.attach(notebook, 0,6,0,1)
+ notebook.show()
+ self.nb = notebook
+ self.tabs = []
+
+ # Stopband frequency
+ co_label = gtk.Label("Cutoff")
+ co_label.show()
+ table.attach(co_label, 0,1,1,2, gtk.SHRINK, gtk.SHRINK)
+
+ co_adj = gtk.Adjustment(0.25, 0.1, 0.34, 0.01, 0, 0)
+ self.co_spinner = gtk.SpinButton(co_adj, 0.0, 2)
+ self.co_spinner.set_numeric(True)
+ self.co_spinner.connect("value-changed", self.change_co);
+ self.co_spinner.show()
+ table.attach(self.co_spinner, 0,1,2,3, gtk.SHRINK, gtk.SHRINK)
+
+ # Stopband frequency
+ sb_label = gtk.Label("Stopband")
+ sb_label.show()
+ table.attach(sb_label, 1,2,1,2, gtk.SHRINK, gtk.SHRINK)
+
+ sb_adj = gtk.Adjustment(0.35, 0.26, 0.5, 0.01, 0, 0)
+ self.sb_spinner = gtk.SpinButton(sb_adj, 0.0, 2)
+ self.sb_spinner.set_numeric(True)
+ self.sb_spinner.connect("value-changed", self.change_sb);
+ self.sb_spinner.show()
+ table.attach(self.sb_spinner, 1,2,2,3, gtk.SHRINK, gtk.SHRINK)
+
+ # Passband ripple
+ pr_label = gtk.Label("Passband ripple")
+ pr_label.show()
+ table.attach(pr_label, 2,3,1,2, gtk.SHRINK, gtk.SHRINK)
+
+ pr_adj = gtk.Adjustment(1, 0.3, 3, 0.01, 0, 0)
+ self.pr_spinner = gtk.SpinButton(pr_adj, 0.0, 2)
+ self.pr_spinner.connect("value-changed", self.check_values);
+ self.pr_spinner.set_numeric(True)
+ self.pr_spinner.show()
+ table.attach(self.pr_spinner, 2,3,2,3, gtk.SHRINK, gtk.SHRINK)
+
+ # Filter order
+ fo_label = gtk.Label("Filter order")
+ fo_label.show()
+ table.attach(fo_label, 3,4,1,2, gtk.SHRINK, gtk.SHRINK)
+
+ fo_adj = gtk.Adjustment(10, 5, 50, 1, 0, 0)
+ self.fo_spinner = gtk.SpinButton(fo_adj, 0.0, 0)
+ self.fo_spinner.connect("value-changed", self.check_values);
+ self.fo_spinner.set_numeric(True)
+ self.fo_spinner.show()
+ table.attach(self.fo_spinner, 3,4,2,3, gtk.SHRINK, gtk.SHRINK)
+
+ # Buttons
+ button = gtk.Button("compute filter")
+ button.connect("clicked", self.new_tab, notebook)
+ table.attach(button, 4,5,2,3, gtk.FILL, gtk.SHRINK)
+ button.show()
+ self.compute_filter = button
+
+ button = gtk.Button("close tab")
+ button.connect("clicked", self.close_tab, notebook)
+ table.attach(button, 5,6,2,3, gtk.FILL, gtk.SHRINK)
+ button.show()
+
+ table.show()
+ window.show()
+
+options['show_progress']=False
+gui = MainGUI()
+gtk.main()
diff --git a/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.bib b/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.bib
new file mode 100644
index 0000000..03fbfa8
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.bib
@@ -0,0 +1,98 @@
+ at string{SIREV = "{SIAM} Review"}
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Applic."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+ at string{TOMS = "{ACM} Trans. Math. Softw."}
+
+ at article{schu:01,
+ author = {J. Schulze},
+ title = {Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods},
+ journal = {BIT},
+ volume = {41},
+ number = {4},
+ pages = "800--841",
+ year = {2001}
+ }
+
+ at article{GeorgeLiu89,
+ author={George, A. and Liu, J. W. H.},
+ year={1989},
+ title={The Evolution of the Minimum Degree Ordering Algorithm},
+ journal=SIREV,
+ volume={31},
+ number={1},
+ pages={1--19}}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886-905}
+ }
+
+ at article{AmestoyDavisDuff04,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: An approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}
+ }
+
+ at misc{hsl:2002,
+ author = {HSL},
+ title = "{HSL} 2002: {A} collection of {F}ortran codes for large
+ scale scientific computation",
+ note = {{\tt www.cse.clrc.ac.uk/nag/hsl}},
+ year = 2002}
+
+
+ at article{RothbergEisenstat98,
+ author={Rothberg, E. and Eisenstat, S. C.},
+ title={Node selection strategies for bottom-up sparse matrix orderings},
+ journal=SIMAX,
+ year={1998}
+ ,volume={19}
+ ,number={3}
+ ,pages={682-695}
+ }
+
+ at article{KarypisKumar98e,
+ author={Karypis, G. and Kumar, V.},
+ title={A fast and high quality multilevel scheme for partitioning irregular graphs},
+ journal=SIAMJSC,
+ year={1998}
+ ,volume={20}
+ ,pages={359-392}
+ }
+
+ at article{Chaco,
+ author={B. Hendrickson and E. Rothberg},
+ title={Improving the runtime and quality of nested dissection ordering},
+ journal=SIAMJSC,
+ year={1999}
+ ,volume={20}
+ ,pages={468--489}
+ }
+
+ at article{PellegriniRomanAmestoy00,
+ author={Pellegrini, F. and Roman, J. and Amestoy, P.},
+ title={Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering},
+ journal={Concurrency: Practice and Experience},
+ year={2000}
+ ,volume={12}
+ ,pages={68-84}
+ }
+
+ at article{DavisGilbertLarimoreNg04,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,pages={353-376}
+ }
+
diff --git a/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.pdf b/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.pdf
new file mode 100644
index 0000000..0fcffe6
Binary files /dev/null and b/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.pdf differ
diff --git a/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.tex b/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.tex
new file mode 100644
index 0000000..2ea79e0
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Doc/AMD_UserGuide.tex
@@ -0,0 +1,1203 @@
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+%------------------------------------------------------------------------------
+\begin{document}
+%------------------------------------------------------------------------------
+
+\title{AMD Version 2.0 User Guide}
+\author{Patrick R. Amestoy\thanks{ENSEEIHT-IRIT,
+2 rue Camichel 31017 Toulouse, France.
+email: amestoy at enseeiht.fr. http://www.enseeiht.fr/$\sim$amestoy.}
+\and Timothy A. Davis\thanks{
+Dept.~of Computer and Information Science and Engineering,
+Univ.~of Florida, Gainesville, FL, USA.
+email: davis at cise.ufl.edu.
+http://www.cise.ufl.edu/$\sim$davis.
+This work was supported by the National
+Science Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270.
+Portions of the work were done while on sabbatical at Stanford University
+and Lawrence Berkeley National Laboratory (with funding from Stanford
+University and the SciDAC program).
+}
+\and Iain S. Duff\thanks{Rutherford Appleton Laboratory, Chilton, Didcot,
+Oxon OX11 0QX, England. email: i.s.duff at rl.ac.uk.
+http://www.numerical.rl.ac.uk/people/isd/isd.html.
+This work was supported by the EPSRC under grant GR/R46441.
+}}
+
+\date{Dec 12, 2006}
+\maketitle
+
+%------------------------------------------------------------------------------
+\begin{abstract}
+AMD is a set of routines that implements the approximate minimum degree ordering
+algorithm to permute sparse matrices prior to
+numerical factorization.
+There are versions written in both C and Fortran 77.
+A MATLAB interface is included.
+\end{abstract}
+%------------------------------------------------------------------------------
+
+Technical report TR-04-002 (revised), CISE Department, University of Florida,
+Gainesville, FL, 2006.
+
+AMD Version 2.0, Copyright\copyright 2006 by Timothy A.
+Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+AMD is available under alternate licences; contact T. Davis for details.
+
+{\bf AMD License:}
+ Your use or distribution of AMD or any modified version of
+ AMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+{\bf Availability:}
+ http://www.cise.ufl.edu/research/sparse/amd
+
+{\bf Acknowledgments:}
+
+ This work was supported by the National Science Foundation, under
+ grants ASC-9111263 and DMS-9223088 and CCR-0203270.
+ The conversion to C, the addition of the elimination tree
+ post-ordering, and the handling of dense rows and columns
+ were done while Davis was on sabbatical at
+ Stanford University and Lawrence Berkeley National Laboratory.
+
+%------------------------------------------------------------------------------
+\newpage
+\section{Overview}
+%------------------------------------------------------------------------------
+
+AMD is a set of routines for preordering a sparse matrix prior to
+numerical factorization. It uses an approximate minimum degree ordering
+algorithm \cite{AmestoyDavisDuff96,AmestoyDavisDuff04}
+to find a permutation matrix $\m{P}$
+so that the Cholesky factorization $\m{PAP}\tr=\m{LL}\tr$ has fewer
+(often much fewer) nonzero entries than the Cholesky factorization of $\m{A}$.
+The algorithm is typically much faster than other ordering methods
+and minimum degree ordering
+algorithms that compute an exact degree \cite{GeorgeLiu89}.
+Some methods, such as approximate deficiency
+\cite{RothbergEisenstat98} and graph-partitioning based methods
+\cite{Chaco,KarypisKumar98e,PellegriniRomanAmestoy00,schu:01}
+can produce better orderings, depending on the matrix.
+
+The algorithm starts with an undirected graph representation of a
+symmetric sparse matrix $\m{A}$. Node $i$ in the graph corresponds to row
+and column $i$ of the matrix, and there is an edge $(i,j)$ in the graph if
+$a_{ij}$ is nonzero.
+The degree of a node is initialized to the number of off-diagonal nonzeros
+in row $i$, which is the size of the set of nodes
+adjacent to $i$ in the graph.
+
+The selection of a pivot $a_{ii}$ from the diagonal of $\m{A}$ and the first
+step of Gaussian elimination corresponds to one step of graph elimination.
+Numerical fill-in causes new nonzero entries in the matrix
+(fill-in refers to
+nonzeros in $\m{L}$ that are not in $\m{A}$).
+Node $i$ is eliminated and edges are added to its neighbors
+so that they form a clique (or {\em element}). To reduce fill-in,
+node $i$ is selected as the node of least degree in the graph.
+This process repeats until the graph is eliminated.
+
+The clique is represented implicitly. Rather than listing all the
+new edges in the graph, a single list of nodes is kept which represents
+the clique. This list corresponds to the nonzero pattern of the first
+column of $\m{L}$. As the elimination proceeds, some of these cliques
+become subsets of subsequent cliques, and are removed. This graph
+can be stored in place, that is
+using the same amount of memory as the original graph.
+
+The most costly part of the minimum degree algorithm is the recomputation
+of the degrees of nodes adjacent to the current pivot element.
+Rather than keep track of the exact degree, the approximate minimum degree
+algorithm finds an upper bound on the degree that is easier to compute.
+For nodes of least degree, this bound tends to be tight. Using the
+approximate degree instead of the exact degree leads to a substantial savings
+in run time, particularly for very irregularly structured matrices.
+It has no effect on the quality of the ordering.
+
+In the C version of AMD, the elimination phase is followed by an
+elimination tree post-ordering. This has no effect on fill-in, but
+reorganizes the ordering so that the subsequent numerical factorization is
+more efficient. It also includes a pre-processing phase in which nodes of
+very high degree are removed (without causing fill-in), and placed last in the
+permutation $\m{P}$. This reduces the run time substantially if the matrix
+has a few rows with many nonzero entries, and has little effect on the quality
+of the ordering.
+The C version operates on the
+symmetric nonzero pattern of $\m{A}+\m{A}\tr$, so it can be given
+an unsymmetric matrix, or either the lower or upper triangular part of
+a symmetric matrix.
+
+The two Fortran versions of AMD are essentially identical to two versions of
+the AMD algorithm discussed in an earlier paper \cite{AmestoyDavisDuff96}
+(approximate minimum external degree, both with and without aggressive
+absorption).
+For a discussion of the long history of the minimum degree algorithm,
+see \cite{GeorgeLiu89}.
+
+%------------------------------------------------------------------------------
+\section{Availability}
+%------------------------------------------------------------------------------
+
+In addition to appearing as a Collected Algorithm of the ACM,
+AMD Version 2.0 is available at http://www.cise.ufl.edu/research/sparse.
+The Fortran version is available as the routine {\tt MC47} in HSL
+(formerly the Harwell Subroutine Library) \cite{hsl:2002}.
+
+%------------------------------------------------------------------------------
+\section{Using AMD in MATLAB}
+%------------------------------------------------------------------------------
+
+The MATLAB function {\tt amd} is now a built-in function in MATLAB 7.3
+(R2006b). Compiling the AMD mexFunction, here, causes a name conflict
+(it is MATLAB that is conflict with AMD, not the other way around ...).
+
+To avoid this issue, either use the built-in {\tt amd}, or use the
+{\tt amd2} function provided here. {\tt amd}
+and {\tt amd2} differ in how the optional parameters are passed
+(the 2nd input parameter).
+
+To use AMD2 in MATLAB, you must first compile the AMD2 mexFunction.
+Just type {\tt make} in the Unix system shell, while in the {\tt AMD/MATLAB}
+directory. You can also type {\tt amd\_make} in MATLAB, while in the
+{\tt AMD/MATLAB} directory. Place the {\tt AMD/MATLAB} directory in your
+MATLAB path. This can be done on any system with MATLAB, including Windows.
+See Section~\ref{Install} for more details on how to install AMD.
+
+The MATLAB statement {\tt p=amd(A)} finds a permutation vector {\tt p} such
+that the Cholesky factorization {\tt chol(A(p,p))} is typically sparser than
+{\tt chol(A)}.
+If {\tt A} is unsymmetric, {\tt amd(A)} is identical to {\tt amd(A+A')}
+(ignoring numerical cancellation).
+If {\tt A} is not symmetric positive definite,
+but has substantial diagonal entries and a mostly symmetric nonzero pattern,
+then this ordering is also suitable for LU factorization. A partial pivoting
+threshold may be required to prevent pivots from being selected off the
+diagonal, such as the statement {\tt [L,U,P] = lu (A (p,p), 0.1)}.
+Type {\tt help lu} for more details.
+The statement {\tt [L,U,P,Q] = lu (A (p,p))} in MATLAB 6.5 is
+not suitable, however, because it uses UMFPACK Version 4.0 and thus
+does not attempt to select pivots from the diagonal.
+UMFPACK Version 4.1 in MATLAB 7.0 and later
+uses several strategies, including a symmetric pivoting strategy, and
+will give you better results if you want to factorize an unsymmetric matrix
+of this type. Refer to the UMFPACK User Guide for more details, at
+http://www.cise.ufl.edu/research/sparse/umfpack.
+
+The AMD mexFunction is much faster than the built-in MATLAB symmetric minimum
+degree ordering methods, SYMAMD and SYMMMD. Its ordering quality is
+comparable to SYMAMD, and better than SYMMMD
+\cite{DavisGilbertLarimoreNg04}.
+
+An optional input argument can be used to modify the control parameters for
+AMD (aggressive absorption, dense row/column handling, and printing of
+statistics). An optional output
+argument provides statistics on the ordering, including an analysis of the
+fill-in and the floating-point operation count for a subsequent factorization.
+For more details (once AMD is installed),
+type {\tt help amd} in the MATLAB command window.
+
+%------------------------------------------------------------------------------
+\section{Using AMD in a C program}
+\label{Cversion}
+%------------------------------------------------------------------------------
+
+The C-callable AMD library consists of seven user-callable routines and one
+include file. There are two versions of each of the routines, with
+{\tt int} and {\tt long} integers.
+The routines with prefix
+{\tt amd\_l\_} use {\tt long} integer arguments; the others use
+{\tt int} integer arguments. If you compile AMD in the standard
+ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions
+are essentially identical. You will be able to solve problems using up to 2GB
+of memory. If you compile AMD in the standard LP64 mode, the size of an
+{\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get
+promoted to 64-bits.
+
+The following routines are fully described in Section~\ref{Primary}:
+
+\begin{itemize}
+\item {\tt amd\_order}
+({\tt long} version: {\tt amd\_l\_order})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ int n, Ap [n+1], Ai [nz], P [n] ;
+ double Control [AMD_CONTROL], Info [AMD_INFO] ;
+ int result = amd_order (n, Ap, Ai, P, Control, Info) ;
+ \end{verbatim}
+ }
+ Computes the approximate minimum degree ordering of an $n$-by-$n$ matrix
+ $\m{A}$. Returns a permutation vector {\tt P} of size {\tt n}, where
+ {\tt P[k] = i} if row and column {\tt i} are the {\tt k}th row and
+ column in the permuted matrix.
+ This routine allocates its own memory of size $1.2e+9n$ integers,
+ where $e$ is the number of nonzeros in $\m{A}+\m{A}\tr$.
+ It computes statistics about the matrix $\m{A}$, such as the symmetry of
+ its nonzero pattern, the number of nonzeros in $\m{L}$,
+ and the number of floating-point operations required for Cholesky and LU
+ factorizations (which are returned in the {\tt Info} array).
+ The user's input matrix is not modified.
+ It returns {\tt AMD\_OK} if successful,
+ {\tt AMD\_OK\_BUT\_JUMBLED} if successful (but the matrix had unsorted
+ and/or duplicate row indices),
+ {\tt AMD\_INVALID} if the matrix is invalid,
+ {\tt AMD\_OUT\_OF\_MEMORY} if out of memory.
+
+\item {\tt amd\_defaults}
+({\tt long} version: {\tt amd\_l\_defaults})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ double Control [AMD_CONTROL] ;
+ amd_defaults (Control) ;
+ \end{verbatim}
+ }
+ Sets the default control parameters in the {\tt Control} array. These can
+ then be modified as desired before passing the array to the other AMD
+ routines.
+
+\item {\tt amd\_control}
+({\tt long} version: {\tt amd\_l\_control})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ double Control [AMD_CONTROL] ;
+ amd_control (Control) ;
+ \end{verbatim}
+ }
+ Prints a description of the control parameters, and their values.
+
+\item {\tt amd\_info}
+({\tt long} version: {\tt amd\_l\_info})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ double Info [AMD_INFO] ;
+ amd_info (Info) ;
+ \end{verbatim}
+ }
+ Prints a description of the statistics computed by AMD, and their values.
+
+\item {\tt amd\_valid}
+({\tt long} version: {\tt amd\_valid})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ int n, Ap [n+1], Ai [nz] ;
+ int result = amd_valid (n, n, Ap, Ai) ;
+ \end{verbatim}
+ }
+ Returns {\tt AMD\_OK} or {\tt AMD\_OK\_BUT\_JUMBLED}
+ if the matrix is valid as input to {\tt amd\_order};
+ the latter is returned if the matrix has unsorted and/or duplicate
+ row indices in one or more columns.
+ Returns {\tt AMD\_INVALID} if the matrix cannot be passed to
+ {\tt amd\_order}.
+ For {\tt amd\_order}, the matrix must
+ also be square. The first two arguments are the number of rows and the
+ number of columns of the matrix. For its use in AMD, these must both
+ equal {\tt n}.
+
+\item {\tt amd\_2}
+({\tt long} version: {\tt amd\_l2})
+ AMD ordering kernel. It is faster than {\tt amd\_order}, and
+ can be called by the user, but it is difficult to use.
+ It does not check its inputs for errors.
+ It does not require the columns of its input matrix to be sorted,
+ but it destroys the matrix on output. Additional workspace must be passed.
+ Refer to the source file {\tt AMD/Source/amd\_2.c} for a description.
+
+\end{itemize}
+
+The nonzero pattern of the matrix $\m{A}$ is represented in compressed column
+form.
+For an $n$-by-$n$ matrix $\m{A}$ with {\tt nz} nonzero entries, the
+representation consists of two arrays: {\tt Ap} of size {\tt n+1} and {\tt Ai}
+of size {\tt nz}. The row indices of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}.
+For {\tt amd\_order},
+if duplicate row indices are present, or if the row indices in any given
+column are not sorted in ascending order, then {\tt amd\_order} creates
+an internal copy of the matrix with sorted rows and no duplicate entries,
+and orders the copy. This adds slightly to the time and memory usage of
+{\tt amd\_order}, but is not an error condition.
+
+The matrix is 0-based, and thus
+row indices must be in the range {\tt 0} to {\tt n-1}.
+The first entry {\tt Ap[0]} must be zero.
+The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+
+The matrix must be square, but it does not need to be symmetric.
+The {\tt amd\_order} routine constructs the nonzero pattern of
+$\m{B} = \m{A}+\m{A}\tr$ (without forming $\m{A}\tr$ explicitly if
+$\m{A}$ has sorted columns and no duplicate entries),
+and then orders the matrix $\m{B}$. Thus, either the
+lower triangular part of $\m{A}$, the upper triangular part,
+or any combination may be passed. The transpose $\m{A}\tr$ may also be
+passed to {\tt amd\_order}.
+The diagonal entries may be present, but are ignored.
+
+%------------------------------------------------------------------------------
+\subsection{Control parameters}
+\label{control_param}
+%------------------------------------------------------------------------------
+
+Control parameters are set in an optional {\tt Control} array.
+It is optional in the sense that if
+a {\tt NULL} pointer is passed for the {\tt Control} input argument,
+then default control parameters are used.
+%
+\begin{itemize}
+\item {\tt Control[AMD\_DENSE]} (or {\tt Control(1)} in MATLAB):
+controls the threshold for ``dense''
+rows/columns. A dense row/column in $\m{A}+\m{A}\tr$
+can cause AMD to spend significant time
+in ordering the matrix. If {\tt Control[AMD\_DENSE]} $\ge 0$,
+rows/columns with
+more than {\tt Control[AMD\_DENSE]} $\sqrt{n}$ entries are ignored during
+the ordering, and placed last in the output order. The default
+value of {\tt Control[AMD\_DENSE]} is 10. If negative, no rows/columns
+are treated as ``dense.'' Rows/columns with 16 or fewer off-diagonal
+entries are never considered ``dense.''
+%
+\item {\tt Control[AMD\_AGGRESSIVE]} (or {\tt Control(2)} in MATLAB):
+controls whether or not to use
+aggressive absorption, in which a prior element is absorbed into the current
+element if it is a subset of the current element, even if it is not
+adjacent to the current pivot element (refer
+to \cite{AmestoyDavisDuff96,AmestoyDavisDuff04}
+for more details). The default value is nonzero,
+which means that aggressive absorption will be performed. This nearly always
+leads to a better ordering (because the approximate degrees are more
+accurate) and a lower execution time. There are cases where it can
+lead to a slightly worse ordering, however. To turn it off, set
+{\tt Control[AMD\_AGGRESSIVE]} to 0.
+%
+\end{itemize}
+
+Statistics are returned in the {\tt Info} array
+(if {\tt Info} is {\tt NULL}, then no statistics are returned).
+Refer to {\tt amd.h} file, for more details
+(14 different statistics are returned, so the list is not included here).
+
+%------------------------------------------------------------------------------
+\subsection{Sample C program}
+%------------------------------------------------------------------------------
+
+The following program, {\tt amd\_demo.c}, illustrates the basic use of AMD.
+See Section~\ref{Synopsis} for a short description
+of each calling sequence.
+
+{\footnotesize
+\begin{verbatim}
+#include <stdio.h>
+#include "amd.h"
+
+int n = 5 ;
+int Ap [ ] = { 0, 2, 6, 10, 12, 14} ;
+int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ;
+int P [5] ;
+
+int main (void)
+{
+ int k ;
+ (void) amd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL) ;
+ for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ;
+ return (0) ;
+}
+\end{verbatim}
+}
+
+The {\tt Ap} and {\tt Ai} arrays represent the binary matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 1 & 1 & 0 & 0 & 0 \\
+ 1 & 1 & 1 & 0 & 1 \\
+ 0 & 1 & 1 & 1 & 0 \\
+ 0 & 0 & 1 & 1 & 0 \\
+ 0 & 1 & 1 & 0 & 1 \\
+\end{array}
+\right].
+\]
+The diagonal entries are ignored.
+%
+AMD constructs the pattern of $\m{A}+\m{A}\tr$,
+and returns a permutation vector of $(0, 3, 1, 4, 2)$.
+%
+Since the matrix is unsymmetric but with a mostly symmetric nonzero
+pattern, this would be a suitable permutation for an LU factorization of a
+matrix with this nonzero pattern and whose diagonal entries are not too small.
+The program uses default control settings and does not return any statistics
+about the ordering, factorization, or solution ({\tt Control} and {\tt Info}
+are both {\tt (double *) NULL}). It also ignores the status value returned by
+{\tt amd\_order}.
+
+More example programs are included with the AMD package.
+The {\tt amd\_demo.c} program provides a more detailed demo of AMD.
+Another example is the AMD mexFunction, {\tt amd\_mex.c}.
+
+%------------------------------------------------------------------------------
+\subsection{A note about zero-sized arrays}
+%------------------------------------------------------------------------------
+
+AMD uses several user-provided arrays of size {\tt n} or {\tt nz}.
+Either {\tt n} or {\tt nz} can be zero.
+If you attempt to {\tt malloc} an array of size zero,
+however, {\tt malloc} will return a null pointer which AMD will report
+as invalid. If you {\tt malloc} an array of
+size {\tt n} or {\tt nz} to pass to AMD, make sure that you handle the
+{\tt n} = 0 and {\tt nz = 0} cases correctly.
+
+%------------------------------------------------------------------------------
+\section{Synopsis of C-callable routines}
+\label{Synopsis}
+%------------------------------------------------------------------------------
+
+The matrix $\m{A}$ is {\tt n}-by-{\tt n} with {\tt nz} entries.
+
+{\footnotesize
+\begin{verbatim}
+#include "amd.h"
+int n, status, Ap [n+1], Ai [nz], P [n] ;
+double Control [AMD_CONTROL], Info [AMD_INFO] ;
+amd_defaults (Control) ;
+status = amd_order (n, Ap, Ai, P, Control, Info) ;
+amd_control (Control) ;
+amd_info (Info) ;
+status = amd_valid (n, n, Ap, Ai) ;
+\end{verbatim}
+}
+
+The {\tt amd\_l\_*} routines are identical, except that all {\tt int}
+arguments become {\tt long}:
+
+{\footnotesize
+\begin{verbatim}
+#include "amd.h"
+long n, status, Ap [n+1], Ai [nz], P [n] ;
+double Control [AMD_CONTROL], Info [AMD_INFO] ;
+amd_l_defaults (Control) ;
+status = amd_l_order (n, Ap, Ai, P, Control, Info) ;
+amd_l_control (Control) ;
+amd_l_info (Info) ;
+status = amd_l_valid (n, n, Ap, Ai) ;
+\end{verbatim}
+}
+
+%------------------------------------------------------------------------------
+\section{Using AMD in a Fortran program}
+%------------------------------------------------------------------------------
+
+Two Fortran versions of AMD are provided. The {\tt AMD} routine computes the
+approximate minimum degree ordering, using aggressive absorption. The
+{\tt AMDBAR} routine is identical, except that it does not perform aggressive
+absorption. The {\tt AMD} routine is essentially identical to the HSL
+routine {\tt MC47B/BD}.
+Note that earlier versions of the Fortran
+{\tt AMD} and {\tt AMDBAR} routines included an {\tt IOVFLO} argument,
+which is no longer present.
+
+In contrast to the C version, the Fortran routines require a symmetric
+nonzero pattern, with no diagonal entries present although the {\tt MC47A/AD}
+wrapper in HSL allows duplicates, ignores out-of-range entries, and only
+uses entries from the upper triangular part of the matrix. Although we
+have an experimental Fortran code for treating ``dense'' rows, the Fortran
+codes in this release do not treat
+``dense'' rows and columns of $\m{A}$ differently, and thus their run time
+can be high if there are a few dense rows and columns in the matrix.
+They do not perform a post-ordering of the elimination tree,
+compute statistics on the ordering, or check the validity of their input
+arguments. These facilities are provided by {\tt MC47A/AD} and other
+subroutines from HSL.
+Only one {\tt integer}
+version of each Fortran routine is provided.
+Both Fortran routines overwrite the user's input
+matrix, in contrast to the C version.
+%
+The C version does not return the elimination or assembly tree.
+The Fortran version returns an assembly tree;
+refer to the User Guide for details.
+The following is the syntax of the {\tt AMD} Fortran routine.
+The {\tt AMDBAR} routine is identical except for the routine name.
+
+{\footnotesize
+\begin{verbatim}
+ INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N), DEGREE (N), NV (N),
+ $ NEXT (N), LAST (N), HEAD (N), ELEN (N), W (N), LEN (N)
+ CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+ CALL AMDBAR (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+\end{verbatim}
+}
+
+The input matrix is provided to {\tt AMD} and {\tt AMDBAR}
+in three arrays, {\tt PE}, of size {\tt N},
+{\tt LEN}, of size {\tt N}, and {\tt IW}, of size {\tt IWLEN}. The size of
+{\tt IW} must be at least {\tt NZ+N}. The recommended size is
+{\tt 1.2*NZ + N}.
+On input, the indices of nonzero entries in row {\tt I} are stored in {\tt IW}.
+{\tt PE(I)} is the index in {\tt IW} of the start of row {\tt I}.
+{\tt LEN(I)} is the number of entries in row {\tt I}.
+The matrix is 1-based, with row and column indices in the range 1 to {\tt N}.
+Row {\tt I} is contained in
+{\tt IW (PE(I)} $\ldots \:$ {\tt PE(I) + LEN(I) - 1)}.
+The diagonal entries must not be present. The indices within each row must
+not contain any duplicates, but they need not be sorted. The rows
+themselves need not be in any particular order, and there may be empty space
+between the rows. If {\tt LEN(I)} is zero, then there are no off-diagonal
+entries in row {\tt I}, and {\tt PE(I)} is ignored. The integer
+{\tt PFREE} defines what part of {\tt IW} contains the user's input matrix,
+which is held in {\tt IW(1}~$\ldots~\:${\tt PFREE-1)}.
+The contents of {\tt IW} and {\tt LEN} are undefined on output,
+and {\tt PE} is modified to contain information about the ordering.
+
+As the algorithm proceeds, it modifies the {\tt IW} array, placing the
+pattern of the partially eliminated matrix in
+{\tt IW(PFREE} $\ldots \:${\tt IWLEN)}.
+If this space is exhausted, the space is compressed.
+The number of compressions performed on the {\tt IW} array is
+returned in the scalar {\tt NCMPA}. The value of {\tt PFREE} on output is the
+length of {\tt IW} required for no compressions to be needed.
+
+The output permutation is returned in the array {\tt LAST}, of size {\tt N}.
+If {\tt I=LAST(K)}, then {\tt I} is the {\tt K}th row in the permuted
+matrix. The inverse permutation is returned in the array {\tt ELEN}, where
+{\tt K=ELEN(I)} if {\tt I} is the {\tt K}th row in the permuted matrix.
+On output, the {\tt PE} and {\tt NV} arrays hold the assembly tree,
+a supernodal elimination tree that represents the relationship between
+columns of the Cholesky factor $\m{L}$.
+If {\tt NV(I)} $> 0$, then {\tt I} is a node in the assembly
+tree, and the parent of {\tt I} is {\tt -PE(I)}. If {\tt I} is a root of
+the tree, then {\tt PE(I)} is zero. The value of {\tt NV(I)} is the
+number of entries in the corresponding column of $\m{L}$, including the
+diagonal.
+If {\tt NV(I)} is zero, then {\tt I} is a non-principal node that is
+not in the assembly tree. Node {\tt -PE(I)} is the parent of node {\tt I}
+in a subtree, the root of which is a node in the assembly tree. All nodes
+in one subtree belong to the same supernode in the assembly tree.
+The other size {\tt N} arrays
+({\tt DEGREE}, {\tt HEAD}, {\tt NEXT}, and {\tt W}) are used as workspace,
+and are not defined on input or output.
+
+If you want to use a simpler user-interface and compute the elimination
+tree post-ordering, you should be able to call the C routines {\tt amd\_order}
+or {\tt amd\_l\_order} from a Fortran program. Just be sure to take into
+account the 0-based indexing in the {\tt P}, {\tt Ap}, and {\tt Ai} arguments
+to {\tt amd\_order} and {\tt amd\_l\_order}. A sample interface is provided
+in the files {\tt AMD/Demo/amd\_f77cross.f} and
+{\tt AMD/Demo/amd\_f77wrapper.c}. To compile the {\tt amd\_f77cross} program,
+type {\tt make cross} in the {\tt AMD/Demo} directory. The
+Fortran-to-C calling conventions are highly non-portable, so this example
+is not guaranteed to work with your compiler C and Fortran compilers.
+The output of {\tt amd\_f77cross} is in {\tt amd\_f77cross.out}.
+
+%------------------------------------------------------------------------------
+\section{Sample Fortran main program}
+%------------------------------------------------------------------------------
+
+The following program illustrates the basic usage of the Fortran version of AMD.
+The {\tt AP} and {\tt AI} arrays represent the binary matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 1 & 1 & 0 & 0 & 0 \\
+ 1 & 1 & 1 & 0 & 1 \\
+ 0 & 1 & 1 & 1 & 1 \\
+ 0 & 0 & 1 & 1 & 0 \\
+ 0 & 1 & 1 & 0 & 1 \\
+\end{array}
+\right]
+\]
+in a conventional 1-based column-oriented form,
+except that the diagonal entries are not present.
+The matrix has the same as nonzero pattern of $\m{A}+\m{A}\tr$ in the C
+program, in Section~\ref{Cversion}.
+The output permutation is $(4, 1, 3, 5, 2)$.
+It differs from the permutation returned by the C routine {\tt amd\_order}
+because a post-order of the elimination tree has not yet been performed.
+
+{\footnotesize
+\begin{verbatim}
+ INTEGER N, NZ, J, K, P, IWLEN, PFREE, NCMPA
+ PARAMETER (N = 5, NZ = 10, IWLEN = 17)
+ INTEGER AP (N+1), AI (NZ), LAST (N), PE (N), LEN (N), ELEN (N),
+ $ IW (IWLEN), DEGREE (N), NV (N), NEXT (N), HEAD (N), W (N)
+ DATA AP / 1, 2, 5, 8, 9, 11/
+ DATA AI / 2, 1,3,5, 2,4,5, 3, 2,3 /
+C load the matrix into the AMD workspace
+ DO 10 J = 1,N
+ PE (J) = AP (J)
+ LEN (J) = AP (J+1) - AP (J)
+10 CONTINUE
+ DO 20 P = 1,NZ
+ IW (P) = AI (P)
+20 CONTINUE
+ PFREE = NZ + 1
+C order the matrix (destroys the copy of A in IW, PE, and LEN)
+ CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, LAST, HEAD,
+ $ ELEN, DEGREE, NCMPA, W)
+ DO 60 K = 1, N
+ PRINT 50, K, LAST (K)
+50 FORMAT ('P (',I2,') = ', I2)
+60 CONTINUE
+ END
+\end{verbatim}
+}
+
+The {\tt Demo} directory contains an example of how the C version
+may be called from a Fortran program, but this is highly non-portable.
+For this reason, it is placed in the {\tt Demo} directory, not in the
+primary {\tt Source} directory.
+
+%------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%------------------------------------------------------------------------------
+
+The following discussion assumes you have the {\tt make} program, either in
+Unix, or in Windows with Cygwin.
+
+System-dependent configurations are in the {\tt ../UFconfig/UFconfig.mk}
+file. You can edit that file to customize the compilation. The default
+settings will work on most systems.
+Sample configuration files are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install the C-callable AMD library,
+go to the {\tt AMD} directory and type {\tt make}.
+The library will be placed in {\tt AMD/Lib/libamd.a}.
+Three demo programs of the AMD ordering routine will be compiled and tested in
+the {\tt AMD/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution.
+
+To compile and install the Fortran-callable AMD library,
+go to the {\tt AMD} directory and type {\tt make fortran}.
+The library will be placed in {\tt AMD/Lib/libamdf77.a}.
+A demo program will be compiled and tested in the {\tt AMD/Demo} directory.
+The output will be compared with an output file in the distribution.
+
+Typing {\tt make clean} will remove all but the final compiled libraries
+and demo programs. Typing {\tt make purge} or {\tt make distclean}
+removes all files not in the original distribution.
+If you compile AMD and then later change the {\tt ../UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+When you compile your program that uses the C-callable AMD library,
+you need to add the {\tt AMD/Lib/libamd.a} library
+and you need to tell your compiler to look in the
+{\tt AMD/Include} directory for include
+files. To compile a Fortran program that calls the Fortran AMD library,
+you need to add the {\tt AMD/Lib/libamdf77.a} library.
+See {\tt AMD/Demo/Makefile} for an example.
+
+If all you want to use is the AMD2 mexFunction in MATLAB, you can skip
+the use of the {\tt make} command entirely. Simply type
+{\tt amd\_make} in MATLAB while in the {\tt AMD/MATLAB} directory.
+This works on any system with MATLAB, including Windows.
+Alternately, type {\tt make} in the {\tt AMD/MATLAB} directory,
+or just use the built-in {\tt amd} in MATLAB 7.3 or later.
+
+If you are including AMD as a subset of a larger library and do not want
+to link the C standard I/O library, or if you simply do not need to use
+them, you can safely remove the {\tt amd\_control.c} and {\tt amd\_info.c}
+files. Similarly, if you use default parameters (or define your
+own {\tt Control} array), then you can exclude the {\tt amd\_defaults.c}
+file.
+Each of these files contains the user-callable routines of the same
+name. None of these auxiliary routines are directly called by
+{\tt amd\_order}.
+The {\tt amd\_dump.c} file contains debugging routines
+that are neither used nor compiled unless debugging is enabled.
+The {\tt amd\_internal.h} file must be edited to enable debugging;
+refer to the instructions in that file.
+The bare minimum files required to use just {\tt amd\_order} are
+{\tt amd.h} and {\tt amd\_internal.h}
+in the {\tt Include} directory,
+and
+{\tt amd\_1.c},
+{\tt amd\_2.c},
+{\tt amd\_aat.c},
+{\tt amd\_global.c},
+{\tt and\_order.c},
+{\tt amd\_postorder.c},
+{\tt amd\_post\_tree.c},
+{\tt amd\_preprocess.c},
+and
+{\tt amd\_valid.c}
+in the {\tt Source} directory.
+
+%------------------------------------------------------------------------------
+\newpage
+\section{The AMD routines}
+\label{Primary}
+%------------------------------------------------------------------------------
+
+The file {\tt AMD/Include/amd.h} listed below
+describes each user-callable routine in the C version of AMD,
+and gives details on their use.
+
+{\footnotesize
+\begin{verbatim}
+/* ========================================================================= */
+/* === AMD: approximate minimum degree ordering =========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for UF_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996. This package can perform both the AMD ordering (with
+ * aggressive absorption), and the AMDBAR ordering (without aggressive
+ * absorption) discussed in the above paper. This package differs from the
+ * Fortran codes discussed in the paper:
+ *
+ * (1) it can ignore "dense" rows and columns, leading to faster run times
+ * (2) it computes the ordering of A+A' if A is not symmetric
+ * (3) it is followed by a depth-first post-ordering of the assembly tree
+ * (or supernodal elimination tree)
+ *
+ * For historical reasons, the Fortran versions, amd.f and amdbar.f, have
+ * been left (nearly) unchanged. They compute the identical ordering as
+ * described in the above paper.
+ */
+
+#ifndef AMD_H
+#define AMD_H
+
+/* make it easy for C++ programs to include AMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED,
+ * AMD_INVALID, or AMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size AMD_CONTROL */
+ double Info [ ] /* output Info statistics, of size AMD_INFO */
+) ;
+
+UF_long amd_l_order /* see above for description of arguments */
+(
+ UF_long n,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ UF_long P [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/UF_long array of size n+1, containing column pointers of A.
+ * Ai: an int/UF_long array of size nz, containing the row indices of A,
+ * where nz = Ap [n].
+ * Control: a double array of size AMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/UF_long array of size n, containing the output permutation. If
+ * row i is the kth pivot row, then P [k] = i. In MATLAB notation,
+ * the reordered matrix is A (P,P).
+ * Info: a double array of size AMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then amd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered. This feature is new to v2.0 (v1.2 and earlier required this
+ * condition to hold for the input matrix).
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.cise.ufl.edu/research/sparse/umfpack.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, AMD returns AMD_INVALID.
+ *
+ * AMD returns:
+ *
+ * AMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * AMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The AMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for AMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause AMD to spend a lot of time in
+ * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns
+ * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [AMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [AMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [AMD_STATUS]: the return value of AMD, either AMD_OK,
+ * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID.
+ *
+ * Info [AMD_N]: n, the size of the input matrix
+ *
+ * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [AMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the
+ * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [AMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to AMD */
+/* ------------------------------------------------------------------------- */
+
+/* amd_2 is the primary AMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * amd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a
+ * description of each parameter. */
+
+void amd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+void amd_l2
+(
+ UF_long n,
+ UF_long Pe [ ],
+ UF_long Iw [ ],
+ UF_long Len [ ],
+ UF_long iwlen,
+ UF_long pfree,
+ UF_long Nv [ ],
+ UF_long Next [ ],
+ UF_long Last [ ],
+ UF_long Head [ ],
+ UF_long Elen [ ],
+ UF_long Degree [ ],
+ UF_long W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* amd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * amd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns AMD_INVALID if the
+ * matrix cannot be passed to amd_order. For amd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in AMD, these must both equal n.
+ *
+ * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier.
+ */
+
+int amd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+UF_long amd_l_valid
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* AMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that AMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*amd_free) (void *) ; /* pointer to free */
+EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* amd_defaults: sets the default control settings */
+void amd_defaults (double Control [ ]) ;
+void amd_l_defaults (double Control [ ]) ;
+
+/* amd_control: prints the control settings */
+void amd_control (double Control [ ]) ;
+void amd_l_control (double Control [ ]) ;
+
+/* amd_info: prints the statistics */
+void amd_info (double Info [ ]) ;
+void amd_l_info (double Info [ ]) ;
+
+#define AMD_CONTROL 5 /* size of Control array */
+#define AMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define AMD_STATUS 0 /* return value of amd_order and amd_l_order */
+#define AMD_N 1 /* A is n-by-n */
+#define AMD_NZ 2 /* number of nonzeros in A */
+#define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define AMD_NZDIAG 4 /* # of entries on diagonal */
+#define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define AMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define AMD_MEMORY 7 /* amount of memory used by AMD */
+#define AMD_NCMPA 8 /* number of garbage collections in AMD */
+#define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of AMD */
+/* ------------------------------------------------------------------------- */
+
+#define AMD_OK 0 /* success */
+#define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define AMD_INVALID -2 /* input arguments are not valid */
+#define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but
+ * columns were not sorted, and/or duplicate entries were present. AMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === AMD version ========================================================== */
+/* ========================================================================== */
+
+/* AMD Version 1.2 and later include the following definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * #ifdef AMD_VERSION
+ * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 1.1 and earlier of AMD do not include a #define'd version number.
+ */
+
+#define AMD_DATE "Dec 12, 2006"
+#define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define AMD_MAIN_VERSION 2
+#define AMD_SUB_VERSION 0
+#define AMD_SUBSUB_VERSION 4
+#define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+\end{verbatim}
+}
+
+
+%------------------------------------------------------------------------------
+\newpage
+% References
+%------------------------------------------------------------------------------
+
+\bibliographystyle{plain}
+\bibliography{AMD_UserGuide}
+
+\end{document}
diff --git a/src/C/SuiteSparse/AMD/Doc/ChangeLog b/src/C/SuiteSparse/AMD/Doc/ChangeLog
new file mode 100644
index 0000000..da57054
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Doc/ChangeLog
@@ -0,0 +1,121 @@
+Dec 12, 2006, version 2.0.4
+
+ * minor MATLAB code cleanup
+
+Nov 29, 2006, version 2.0.3
+
+ * changed MATLAB function name to amd2, so as not to conflict with
+ the now built-in version of AMD in MATLAB (which is the same thing
+ as the AMD here...).
+
+Sept 28, 2006, version 2.0.2
+
+ * #define SIZE_T_MAX not done if already defined (Mac OSX).
+
+Aug 31, 2006:
+
+ * trivial change to comments in amd.m
+
+Apr 30, 2006: AMD Version 2.0:
+
+ * long integer redefined as UF_long, controlled by UFconfig.h.
+
+ * amd_order no longer requires its input to have sorted columns. It can
+ also tolerate duplicate entries in each column. If these conditions
+ hold, but the matrix is otherwise valid, amd_order returns
+ AMD_OK_BUT_JUMBLED (a warning, not an error).
+
+ * amd_preprocess no longer deemed user-callable, since it is no longer
+ needed (it was used to ensure the input matrix had sorted columns with
+ no duplicate entries). It still exists, with additional parameters,
+ and is called by amd_order if necessary. amd_wpreprocess and
+ amd_preprocess_valid removed. Fortran interface routine amdpreproc
+ removed.
+
+ * Integer overflow computations modified, to extend the size of problem
+ that the "int" version can solve when used in an LP64 compilation.
+
+ * amd_demo2.c simplified (it tests AMD with a jumbled matrix).
+
+ * amd_valid returned TRUE/FALSE in v1.2. It now returns AMD_OK,
+ AMD_OK_BUT_JUMBLED, or AMD_INVALID. Only in the latter case is the
+ matrix unsuitable as input to amd_order.
+
+ * amd_internal.h include file moved from AMD/Source to AMD/Include.
+
+Nov 15, 2005:
+
+ * minor editting of comments; version number (1.2) unchanged.
+
+Aug. 30, 2005: AMD Version 1.2
+
+ * AMD v1.2 is upward compatible with v1.1 and v1.0, except that v1.2 no
+ longer includes the compile-time redefinition of malloc and free.
+
+ * Makefile modified to use UFconfig.mk. "Make" directory removed.
+
+ * License changed to GNU LGPL.
+
+ * Easier inclusion in C++ programs.
+
+ * option to allow compile-time redefinition of malloc and free
+ (added to v1.1) removed for v1.2. Replaced with a run-time
+ redefinition. AMD includes function pointers for malloc, free,
+ calloc, realloc, and printf, so that all those routines can be
+ redefined at compile time. These function pointers are global
+ variables, and so are not technically thread-safe, unless you
+ use defaults and don't need to change them (the common case)
+ or if you change them in one thread before using them in other
+ threads.
+
+ * added #define'd version number
+
+ * minor modification to AMD_2 to ensure all lines can be tested, without
+ conditional compilation.
+
+ * moved the prototype for AMD_2 from amd_internal.h to amd.h
+
+ * moved the prototype for AMD_valid from amd_internal.h to amd.h
+
+ * MATLAB mexFunction uses libamd.a (compiled with cc) instead of compiling
+ each AMD source file with the mex command
+
+ * long demo (amd_l_demo.c) added.
+
+Jan. 21, 2004: AMD Version 1.1
+
+ * No bugs found or fixed - new features added, only
+ * amd_preprocess added, to allow for more general input of the matrix A.
+ * ME=0 added to amd*.f, unused DEXT variable removed from amdbar.f,
+ to avoid spurious compiler warnings (this was not a bug).
+ * amd_demo2.c and amd_demo2.out added, to test/demo amd_preprocess.
+ * option to allow compile-time redefinition of malloc, free, printf added
+ * amd_demo.c shortened slightly (removed printing of PAP')
+ * User Guide modified (more details added)
+ * linewidth reduced from 80 to 79 columns
+
+Oct. 7, 2003: AMD version 1.0.1.
+
+ * MATLAB mexFunction modified, to remove call to mexCallMATLAB function.
+ This function can take a long time to call, particularly if you are
+ ordering many small matrices.
+
+May 6, 2003: AMD Version 1.0 released.
+
+ * converted to C (compare amd.f and amdbar.f with amd_2.c)
+ * dense rows/column removed prior to ordering
+ * elimination tree post-ordering added
+ * demos, user guide written
+ * statistics added (nz in L, flop count, symmetry of A)
+ * computes the pattern of A+A' if A is unsymmetric
+ * user's input matrix no longer overwritten
+ * degree lists initialized differently
+ * IOVFLO argument removed from Fortran versions (amd.f and amdbar.f)
+ * parameters added (dense row/column detection, aggressive absorption)
+ * MATLAB mexFunction added
+
+Jan, 1996:
+
+ * amdbar.f posted at http://www.netlib.org (with a restricted License)
+ * amd.f appears as MC47B/BD in the Harwell Subroutine Library
+ (without the IOVFLO argument)
diff --git a/src/C/SuiteSparse/AMD/Doc/License b/src/C/SuiteSparse/AMD/Doc/License
new file mode 100644
index 0000000..52e5087
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Doc/License
@@ -0,0 +1,39 @@
+AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis,
+Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+AMD is available under alternate licenses, contact T. Davis for details.
+
+AMD License:
+
+ Your use or distribution of AMD or any modified version of
+ AMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/amd
+
+-------------------------------------------------------------------------------
diff --git a/src/C/SuiteSparse/AMD/Doc/Makefile b/src/C/SuiteSparse/AMD/Doc/Makefile
new file mode 100644
index 0000000..8b593fa
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Doc/Makefile
@@ -0,0 +1,33 @@
+#------------------------------------------------------------------------------
+# AMD Makefile for compiling on Unix systems (for GNU or original make)
+#------------------------------------------------------------------------------
+
+default: dist
+
+include ../../UFconfig/UFconfig.mk
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+
+#------------------------------------------------------------------------------
+# Create the User Guide and Quick Start Guide
+#------------------------------------------------------------------------------
+
+AMD_UserGuide.pdf: AMD_UserGuide.tex AMD_UserGuide.bib
+ pdflatex AMD_UserGuide
+ bibtex AMD_UserGuide
+ pdflatex AMD_UserGuide
+ pdflatex AMD_UserGuide
+
+dist: AMD_UserGuide.pdf
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+
diff --git a/src/C/SuiteSparse/AMD/Doc/lesser.txt b/src/C/SuiteSparse/AMD/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Doc/lesser.txt
@@ -0,0 +1,504 @@
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+ Version 2.1, February 1999
+
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+
+ 16. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN
+WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY
+AND/OR REDISTRIBUTE THE LIBRARY AS PERMITTED ABOVE, BE LIABLE TO YOU
+FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR
+CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE
+LIBRARY (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING
+RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A
+FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF
+SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
+everyone can redistribute and change. You can do so by permitting
+redistribution under these terms (or, alternatively, under the terms of the
+ordinary General Public License).
+
+ To apply these terms, attach the following notices to the library. It is
+safest to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the library's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the library, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the
+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/src/C/SuiteSparse/AMD/Include/amd.h b/src/C/SuiteSparse/AMD/Include/amd.h
new file mode 100644
index 0000000..4c73b42
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Include/amd.h
@@ -0,0 +1,412 @@
+/* ========================================================================= */
+/* === AMD: approximate minimum degree ordering =========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for UF_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996. This package can perform both the AMD ordering (with
+ * aggressive absorption), and the AMDBAR ordering (without aggressive
+ * absorption) discussed in the above paper. This package differs from the
+ * Fortran codes discussed in the paper:
+ *
+ * (1) it can ignore "dense" rows and columns, leading to faster run times
+ * (2) it computes the ordering of A+A' if A is not symmetric
+ * (3) it is followed by a depth-first post-ordering of the assembly tree
+ * (or supernodal elimination tree)
+ *
+ * For historical reasons, the Fortran versions, amd.f and amdbar.f, have
+ * been left (nearly) unchanged. They compute the identical ordering as
+ * described in the above paper.
+ */
+
+#ifndef AMD_H
+#define AMD_H
+
+/* make it easy for C++ programs to include AMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED,
+ * AMD_INVALID, or AMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size AMD_CONTROL */
+ double Info [ ] /* output Info statistics, of size AMD_INFO */
+) ;
+
+UF_long amd_l_order /* see above for description of arguments */
+(
+ UF_long n,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ UF_long P [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/UF_long array of size n+1, containing column pointers of A.
+ * Ai: an int/UF_long array of size nz, containing the row indices of A,
+ * where nz = Ap [n].
+ * Control: a double array of size AMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/UF_long array of size n, containing the output permutation. If
+ * row i is the kth pivot row, then P [k] = i. In MATLAB notation,
+ * the reordered matrix is A (P,P).
+ * Info: a double array of size AMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then amd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered. This feature is new to v2.0 (v1.2 and earlier required this
+ * condition to hold for the input matrix).
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.cise.ufl.edu/research/sparse/umfpack.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, AMD returns AMD_INVALID.
+ *
+ * AMD returns:
+ *
+ * AMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * AMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The AMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for AMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause AMD to spend a lot of time in
+ * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns
+ * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [AMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [AMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [AMD_STATUS]: the return value of AMD, either AMD_OK,
+ * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID.
+ *
+ * Info [AMD_N]: n, the size of the input matrix
+ *
+ * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [AMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the
+ * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [AMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to AMD */
+/* ------------------------------------------------------------------------- */
+
+/* amd_2 is the primary AMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * amd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a
+ * description of each parameter. */
+
+void amd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+void amd_l2
+(
+ UF_long n,
+ UF_long Pe [ ],
+ UF_long Iw [ ],
+ UF_long Len [ ],
+ UF_long iwlen,
+ UF_long pfree,
+ UF_long Nv [ ],
+ UF_long Next [ ],
+ UF_long Last [ ],
+ UF_long Head [ ],
+ UF_long Elen [ ],
+ UF_long Degree [ ],
+ UF_long W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* amd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * amd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns AMD_INVALID if the
+ * matrix cannot be passed to amd_order. For amd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in AMD, these must both equal n.
+ *
+ * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier.
+ */
+
+int amd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+UF_long amd_l_valid
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* AMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that AMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*amd_free) (void *) ; /* pointer to free */
+EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* amd_defaults: sets the default control settings */
+void amd_defaults (double Control [ ]) ;
+void amd_l_defaults (double Control [ ]) ;
+
+/* amd_control: prints the control settings */
+void amd_control (double Control [ ]) ;
+void amd_l_control (double Control [ ]) ;
+
+/* amd_info: prints the statistics */
+void amd_info (double Info [ ]) ;
+void amd_l_info (double Info [ ]) ;
+
+#define AMD_CONTROL 5 /* size of Control array */
+#define AMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define AMD_STATUS 0 /* return value of amd_order and amd_l_order */
+#define AMD_N 1 /* A is n-by-n */
+#define AMD_NZ 2 /* number of nonzeros in A */
+#define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define AMD_NZDIAG 4 /* # of entries on diagonal */
+#define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define AMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define AMD_MEMORY 7 /* amount of memory used by AMD */
+#define AMD_NCMPA 8 /* number of garbage collections in AMD */
+#define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of AMD */
+/* ------------------------------------------------------------------------- */
+
+#define AMD_OK 0 /* success */
+#define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define AMD_INVALID -2 /* input arguments are not valid */
+#define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but
+ * columns were not sorted, and/or duplicate entries were present. AMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === AMD version ========================================================== */
+/* ========================================================================== */
+
+/* AMD Version 1.2 and later include the following definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * #ifdef AMD_VERSION
+ * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 1.1 and earlier of AMD do not include a #define'd version number.
+ */
+
+#define AMD_DATE "Dec 12, 2006"
+#define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define AMD_MAIN_VERSION 2
+#define AMD_SUB_VERSION 0
+#define AMD_SUBSUB_VERSION 4
+#define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/src/C/SuiteSparse/AMD/Include/amd_internal.h b/src/C/SuiteSparse/AMD/Include/amd_internal.h
new file mode 100644
index 0000000..68b6e4f
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Include/amd_internal.h
@@ -0,0 +1,350 @@
+/* ========================================================================= */
+/* === amd_internal.h ====================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* This file is for internal use in AMD itself, and does not normally need to
+ * be included in user code (it is included in UMFPACK, however). All others
+ * should use amd.h instead.
+ *
+ * The following compile-time definitions affect how AMD is compiled.
+ *
+ * -DNPRINT
+ *
+ * Disable all printing. stdio.h will not be included. Printing can
+ * be re-enabled at run-time by setting the global pointer amd_printf
+ * to printf (or mexPrintf for a MATLAB mexFunction).
+ *
+ * -DNMALLOC
+ *
+ * No memory manager is defined at compile-time. You MUST define the
+ * function pointers amd_malloc, amd_free, amd_realloc, and
+ * amd_calloc at run-time for AMD to work properly.
+ */
+
+/* ========================================================================= */
+/* === NDEBUG ============================================================== */
+/* ========================================================================= */
+
+/*
+ * Turning on debugging takes some work (see below). If you do not edit this
+ * file, then debugging is always turned off, regardless of whether or not
+ * -DNDEBUG is specified in your compiler options.
+ *
+ * If AMD is being compiled as a mexFunction, then MATLAB_MEX_FILE is defined,
+ * and mxAssert is used instead of assert. If debugging is not enabled, no
+ * MATLAB include files or functions are used. Thus, the AMD library libamd.a
+ * can be safely used in either a stand-alone C program or in another
+ * mexFunction, without any change.
+ */
+
+/*
+ AMD will be exceedingly slow when running in debug mode. The next three
+ lines ensure that debugging is turned off.
+*/
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/*
+ To enable debugging, uncomment the following line:
+#undef NDEBUG
+*/
+
+/* ------------------------------------------------------------------------- */
+/* ANSI include files */
+/* ------------------------------------------------------------------------- */
+
+/* from stdlib.h: size_t, malloc, free, realloc, and calloc */
+#include <stdlib.h>
+
+#if !defined(NPRINT) || !defined(NDEBUG)
+/* from stdio.h: printf. Not included if NPRINT is defined at compile time.
+ * fopen and fscanf are used when debugging. */
+#include <stdio.h>
+#endif
+
+/* from limits.h: INT_MAX and LONG_MAX */
+#include <limits.h>
+
+/* from math.h: sqrt */
+#include <math.h>
+
+/* ------------------------------------------------------------------------- */
+/* MATLAB include files (only if being used in or via MATLAB) */
+/* ------------------------------------------------------------------------- */
+
+#ifdef MATLAB_MEX_FILE
+#include "matrix.h"
+#include "mex.h"
+#endif
+
+/* ------------------------------------------------------------------------- */
+/* basic definitions */
+/* ------------------------------------------------------------------------- */
+
+#ifdef FLIP
+#undef FLIP
+#endif
+
+#ifdef MAX
+#undef MAX
+#endif
+
+#ifdef MIN
+#undef MIN
+#endif
+
+#ifdef EMPTY
+#undef EMPTY
+#endif
+
+#ifdef GLOBAL
+#undef GLOBAL
+#endif
+
+#ifdef PRIVATE
+#undef PRIVATE
+#endif
+
+/* FLIP is a "negation about -1", and is used to mark an integer i that is
+ * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY
+ * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i
+ * for all integers i. UNFLIP (i) is >= EMPTY. */
+#define EMPTY (-1)
+#define FLIP(i) (-(i)-2)
+#define UNFLIP(i) ((i < EMPTY) ? FLIP (i) : (i))
+
+/* for integer MAX/MIN, or for doubles when we don't care how NaN's behave: */
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+/* logical expression of p implies q: */
+#define IMPLIES(p,q) (!(p) || (q))
+
+/* Note that the IBM RS 6000 xlc predefines TRUE and FALSE in <types.h>. */
+/* The Compaq Alpha also predefines TRUE and FALSE. */
+#ifdef TRUE
+#undef TRUE
+#endif
+#ifdef FALSE
+#undef FALSE
+#endif
+
+#define TRUE (1)
+#define FALSE (0)
+#define PRIVATE static
+#define GLOBAL
+#define EMPTY (-1)
+
+/* Note that Linux's gcc 2.96 defines NULL as ((void *) 0), but other */
+/* compilers (even gcc 2.95.2 on Solaris) define NULL as 0 or (0). We */
+/* need to use the ANSI standard value of 0. */
+#ifdef NULL
+#undef NULL
+#endif
+
+#define NULL 0
+
+/* largest value of size_t */
+#ifndef SIZE_T_MAX
+#define SIZE_T_MAX ((size_t) (-1))
+#endif
+
+/* ------------------------------------------------------------------------- */
+/* integer type for AMD: int or UF_long */
+/* ------------------------------------------------------------------------- */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#if defined (DLONG) || defined (ZLONG)
+
+#define Int UF_long
+#define ID UF_long_id
+#define Int_MAX UF_long_max
+
+#define AMD_order amd_l_order
+#define AMD_defaults amd_l_defaults
+#define AMD_control amd_l_control
+#define AMD_info amd_l_info
+#define AMD_1 amd_l1
+#define AMD_2 amd_l2
+#define AMD_valid amd_l_valid
+#define AMD_aat amd_l_aat
+#define AMD_postorder amd_l_postorder
+#define AMD_post_tree amd_l_post_tree
+#define AMD_dump amd_l_dump
+#define AMD_debug amd_l_debug
+#define AMD_debug_init amd_l_debug_init
+#define AMD_preprocess amd_l_preprocess
+
+#else
+
+#define Int int
+#define ID "%d"
+#define Int_MAX INT_MAX
+
+#define AMD_order amd_order
+#define AMD_defaults amd_defaults
+#define AMD_control amd_control
+#define AMD_info amd_info
+#define AMD_1 amd_1
+#define AMD_2 amd_2
+#define AMD_valid amd_valid
+#define AMD_aat amd_aat
+#define AMD_postorder amd_postorder
+#define AMD_post_tree amd_post_tree
+#define AMD_dump amd_dump
+#define AMD_debug amd_debug
+#define AMD_debug_init amd_debug_init
+#define AMD_preprocess amd_preprocess
+
+#endif
+
+/* ========================================================================= */
+/* === PRINTF macro ======================================================== */
+/* ========================================================================= */
+
+/* All output goes through the PRINTF macro. */
+#define PRINTF(params) { if (amd_printf != NULL) (void) amd_printf params ; }
+
+/* ------------------------------------------------------------------------- */
+/* AMD routine definitions (user-callable) */
+/* ------------------------------------------------------------------------- */
+
+#include "amd.h"
+
+/* ------------------------------------------------------------------------- */
+/* AMD routine definitions (not user-callable) */
+/* ------------------------------------------------------------------------- */
+
+GLOBAL size_t AMD_aat
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Len [ ],
+ Int Tp [ ],
+ double Info [ ]
+) ;
+
+GLOBAL void AMD_1
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int P [ ],
+ Int Pinv [ ],
+ Int Len [ ],
+ Int slen,
+ Int S [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+GLOBAL void AMD_postorder
+(
+ Int nn,
+ Int Parent [ ],
+ Int Npiv [ ],
+ Int Fsize [ ],
+ Int Order [ ],
+ Int Child [ ],
+ Int Sibling [ ],
+ Int Stack [ ]
+) ;
+
+GLOBAL Int AMD_post_tree
+(
+ Int root,
+ Int k,
+ Int Child [ ],
+ const Int Sibling [ ],
+ Int Order [ ],
+ Int Stack [ ]
+#ifndef NDEBUG
+ , Int nn
+#endif
+) ;
+
+GLOBAL void AMD_preprocess
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Rp [ ],
+ Int Ri [ ],
+ Int W [ ],
+ Int Flag [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* debugging definitions */
+/* ------------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+
+/* from assert.h: assert macro */
+#include <assert.h>
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN Int AMD_debug ;
+
+GLOBAL void AMD_debug_init ( char *s ) ;
+
+GLOBAL void AMD_dump
+(
+ Int n,
+ Int Pe [ ],
+ Int Iw [ ],
+ Int Len [ ],
+ Int iwlen,
+ Int pfree,
+ Int Nv [ ],
+ Int Next [ ],
+ Int Last [ ],
+ Int Head [ ],
+ Int Elen [ ],
+ Int Degree [ ],
+ Int W [ ],
+ Int nel
+) ;
+
+#ifdef ASSERT
+#undef ASSERT
+#endif
+
+/* Use mxAssert if AMD is compiled into a mexFunction */
+#ifdef MATLAB_MEX_FILE
+#define ASSERT(expression) (mxAssert ((expression), ""))
+#else
+#define ASSERT(expression) (assert (expression))
+#endif
+
+#define AMD_DEBUG0(params) { PRINTF (params) ; }
+#define AMD_DEBUG1(params) { if (AMD_debug >= 1) PRINTF (params) ; }
+#define AMD_DEBUG2(params) { if (AMD_debug >= 2) PRINTF (params) ; }
+#define AMD_DEBUG3(params) { if (AMD_debug >= 3) PRINTF (params) ; }
+#define AMD_DEBUG4(params) { if (AMD_debug >= 4) PRINTF (params) ; }
+
+#else
+
+/* no debugging */
+#define ASSERT(expression)
+#define AMD_DEBUG0(params)
+#define AMD_DEBUG1(params)
+#define AMD_DEBUG2(params)
+#define AMD_DEBUG3(params)
+#define AMD_DEBUG4(params)
+
+#endif
diff --git a/src/C/SuiteSparse/AMD/Lib/libamd.def b/src/C/SuiteSparse/AMD/Lib/libamd.def
new file mode 100644
index 0000000..8ed43fc
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Lib/libamd.def
@@ -0,0 +1,12 @@
+LIBRARY libamd.dll
+EXPORTS
+amd_order
+amd_defaults
+amd_control
+amd_info
+amd_2
+amd_l_order
+amd_l_defaults
+amd_l_control
+amd_l_info
+amd_l2
diff --git a/src/C/SuiteSparse/AMD/Makefile b/src/C/SuiteSparse/AMD/Makefile
new file mode 100644
index 0000000..07c7aef
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Makefile
@@ -0,0 +1,67 @@
+#------------------------------------------------------------------------------
+# AMD Makefile (for GNU Make or original make)
+#------------------------------------------------------------------------------
+
+default: demo
+
+include ../UFconfig/UFconfig.mk
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not compile the FORTRAN versions, or MATLAB interface.
+demo:
+ ( cd Source ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not compile the FORTRAN versions.
+all:
+ ( cd Source ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# compile just the C-callable libraries (not mexFunctions or Demos)
+library:
+ ( cd Source ; $(MAKE) )
+
+# compile the FORTRAN libraries and demo programs (not compiled by "make all")
+fortran:
+ ( cd Source ; $(MAKE) fortran )
+ ( cd Demo ; $(MAKE) fortran )
+
+# compile a FORTRAN demo program that calls the C version of AMD
+# (not compiled by "make all")
+cross:
+ ( cd Demo ; $(MAKE) cross )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd Source ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Doc ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd Source ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+distclean: purge
+
+# create PDF documents for the original distribution
+doc:
+ ( cd Doc ; $(MAKE) )
+
+# get ready for distribution
+dist: purge
+ ( cd Demo ; $(MAKE) dist )
+ ( cd Doc ; $(MAKE) )
+
+ccode: library
+
+lib: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd MATLAB ; $(MAKE) )
diff --git a/src/C/SuiteSparse/AMD/README.txt b/src/C/SuiteSparse/AMD/README.txt
new file mode 100644
index 0000000..ea6b415
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/README.txt
@@ -0,0 +1,214 @@
+AMD: a set of routines for permuting sparse matrices prior to
+ factorization. Includes a version in C, a version in Fortran, and a MATLAB
+ mexFunction.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+Quick start (Unix, or Windows with Cygwin):
+
+ To compile, test, and install AMD, you may wish to first configure the
+ installation by editting the ../UFconfig/UFconfig.mk file. Next, cd to this
+ directory (AMD) and type "make" (or "make lib" if you do not have MATLAB).
+ To compile and run a demo program for the Fortran version, type
+ "make fortran". When done, type "make clean" to remove unused *.o files
+ (keeps the compiled libraries and demo programs). See the User Guide
+ (Doc/AMD_UserGuide.pdf), or ../UFconfig/UFconfig.mk for more details.
+
+Quick start (for MATLAB users);
+
+ To compile, test, and install the AMD mexFunction, cd to the
+ AMD/MATLAB directory and type amd_make at the MATLAB prompt.
+
+ NOTE: DO NOT ATTEMPT TO USE THIS CODE IN 64-BIT MATLAB (v7.3).
+ It is not yet ported to that version of MATLAB.
+
+-------------------------------------------------------------------------------
+
+AMD Version 2.0, Copyright (c) 2006 by Timothy A.
+Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+AMD is available under alternate licences; contact T. Davis for details.
+
+AMD License:
+
+ Your use or distribution of AMD or any modified version of
+ AMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/amd
+
+-------------------------------------------------------------------------------
+
+This is the AMD README file. It is a terse overview of AMD.
+Refer to the User Guide (Doc/AMD_UserGuide.pdf) for how to install
+and use AMD.
+
+Description:
+
+ AMD is a set of routines for pre-ordering sparse matrices prior to Cholesky
+ or LU factorization, using the approximate minimum degree ordering
+ algorithm. Written in ANSI/ISO C with a MATLAB interface, and in
+ Fortran 77.
+
+Authors:
+
+ Timothy A. Davis (davis at cise.ufl.edu), University of Florida.
+ Patrick R. Amestory, ENSEEIHT, Toulouse, France.
+ Iain S. Duff, Rutherford Appleton Laboratory, UK.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+ Portions of this work were done while on sabbatical at Stanford University
+ and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+ program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+ for making this sabbatical possible.
+
+-------------------------------------------------------------------------------
+Files and directories in the AMD distribution:
+-------------------------------------------------------------------------------
+
+ ---------------------------------------------------------------------------
+ Subdirectories of the AMD directory:
+ ---------------------------------------------------------------------------
+
+ Doc documentation
+ Source primary source code
+ Include include file for use in your code that calls AMD
+ Demo demo programs. also serves as test of the AMD installation.
+ MATLAB AMD mexFunction for MATLAB, and supporting m-files
+ Lib where the compiled C-callable and Fortran-callable
+ AMD libraries placed.
+
+ ---------------------------------------------------------------------------
+ Files in the AMD directory:
+ ---------------------------------------------------------------------------
+
+ Makefile top-level Makefile for GNU make or original make.
+ Windows users would require Cygwin to use "make"
+
+ README.txt this file
+
+ ---------------------------------------------------------------------------
+ Doc directory: documentation
+ ---------------------------------------------------------------------------
+
+ ChangeLog change log
+ License the AMD License
+ Makefile for creating the documentation
+ AMD_UserGuide.bib AMD User Guide (references)
+ AMD_UserGuide.tex AMD User Guide (LaTeX)
+ AMD_UserGuide.pdf AMD User Guide (PDF)
+ lesser.txt the GNU LGPL license
+
+ ---------------------------------------------------------------------------
+ Source directory:
+ ---------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ amd_order.c user-callable, primary AMD ordering routine
+ amd_control.c user-callable, prints the control parameters
+ amd_defaults.c user-callable, sets default control parameters
+ amd_info.c user-callable, prints the statistics from AMD
+
+ amd_1.c non-user-callable, construct A+A'
+ amd_2.c user-callable, primary ordering kernel
+ (a C version of amd.f and amdbar.f, with
+ post-ordering added)
+ amd_aat.c non-user-callable, computes nnz (A+A')
+ amd_dump.c non-user-callable, debugging routines
+ amd_postorder.c non-user-callable, postorder
+ amd_post_tree.c non-user-callable, postorder just one tree
+ amd_valid.c non-user-callable, verifies a matrix
+ amd_preprocess.c non-user-callable, computes A', removes duplic
+
+ amd.f user-callable Fortran 77 version
+ amdbar.f user-callable Fortran 77 version
+
+ ---------------------------------------------------------------------------
+ Include directory:
+ ---------------------------------------------------------------------------
+
+ amd.h include file for C programs that use AMD
+ amd_internal.h non-user-callable, include file for AMD
+
+ ---------------------------------------------------------------------------
+ Demo directory:
+ ---------------------------------------------------------------------------
+
+ Makefile for GNU make or original make
+
+ amd_demo.c C demo program for AMD
+ amd_demo.out output of amd_demo.c
+
+ amd_demo2.c C demo program for AMD, jumbled matrix
+ amd_demo2.out output of amd_demo2.c
+
+ amd_l_demo.c C demo program for AMD (UF_long version)
+ amd_l_demo.out output of amd_l_demo.c
+
+ amd_simple.c simple C demo program for AMD
+ amd_simple.out output of amd_simple.c
+
+ amd_f77demo.f Fortran 77 demo program for AMD
+ amd_f77demo.out output of amd_f77demo.f
+
+ amd_f77simple.c simple Fortran 77 demo program for AMD
+ amd_f77simple.out output of amd_f77simple.f
+
+ amd_f77cross.f Fortran 77 demo, calls the C version of AMD
+ amd_f77cross.out output of amd_f77cross.f
+ amd_f77wrapper.c Fortran-callable wrapper for C version of AMD
+
+ ---------------------------------------------------------------------------
+ MATLAB directory:
+ ---------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ Contents.m for "help amd2" listing of toolbox contents
+
+ amd2.m MATLAB help file for AMD
+ amd_make.m MATLAB m-file for compiling AMD mexFunction
+
+ amd_mex.c AMD mexFunction for MATLAB
+
+ amd_demo.m MATLAB demo for AMD
+ amd_demo.m.out diary output of amd_demo.m
+ can_24.mat input file for AMD demo
+
+ ---------------------------------------------------------------------------
+ Lib directory: libamd.a and libamdf77.a libraries placed here
+ ---------------------------------------------------------------------------
+
+ libamd.def AMD definitions for Windows
diff --git a/src/C/SuiteSparse/AMD/Source/GNUmakefile b/src/C/SuiteSparse/AMD/Source/GNUmakefile
new file mode 100644
index 0000000..571ad1c
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/GNUmakefile
@@ -0,0 +1,79 @@
+#-------------------------------------------------------------------------------
+# AMD Makefile for compiling on Unix systems (for GNU make only)
+#-------------------------------------------------------------------------------
+
+default: ../Lib/libamd.a
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+#-------------------------------------------------------------------------------
+# source files
+#-------------------------------------------------------------------------------
+
+AMD = amd_aat amd_1 amd_2 amd_dump amd_postorder amd_post_tree amd_defaults \
+ amd_order amd_control amd_info amd_valid amd_preprocess
+
+UFCONFIG = ../../UFconfig/UFconfig.h
+
+INC = ../Include/amd.h ../Include/amd_internal.h $(UFCONFIG)
+
+#-------------------------------------------------------------------------------
+# object files for each version
+#-------------------------------------------------------------------------------
+
+AMDI = $(addsuffix .o, $(subst amd_,amd_i_,$(AMD)))
+AMDL = $(addsuffix .o, $(subst amd_,amd_l_,$(AMD)))
+
+#-------------------------------------------------------------------------------
+# compile each int and long routine (with no real/complex version)
+#-------------------------------------------------------------------------------
+
+amd_global.o: amd_global.c $(INC)
+ $(C) -c $< -o $@
+
+amd_i_%.o: amd_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+amd_l_%.o: amd_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the libamd.a library (C versions only)
+#-------------------------------------------------------------------------------
+
+../Lib/libamd.a: amd_global.o $(AMDI) $(AMDL)
+ $(AR) ../Lib/libamd.a $^
+ - $(RANLIB) ../Lib/libamd.a
+
+#-------------------------------------------------------------------------------
+# compile the Fortran versions and the libamdf77.a library
+#-------------------------------------------------------------------------------
+
+fortran: ../Lib/libamdf77.a
+
+AMDF77 = amd.o amdbar.o
+
+amd.o: amd.f
+ $(F77) $(F77FLAGS) -c amd.f -o amd.o
+
+amdbar.o: amdbar.f
+ $(F77) $(F77FLAGS) -c amdbar.f -o amdbar.o
+
+../Lib/libamdf77.a: $(AMDF77)
+ $(AR) ../Lib/libamdf77.a $^
+ - $(RANLIB) ../Lib/libamdf77.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) ../Lib/libamd.a
+ - $(RM) ../Lib/libamdf77.a
diff --git a/src/C/SuiteSparse/AMD/Source/Makefile b/src/C/SuiteSparse/AMD/Source/Makefile
new file mode 100644
index 0000000..409046a
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/Makefile
@@ -0,0 +1,70 @@
+#-------------------------------------------------------------------------------
+# AMD Makefile for compiling on Unix systems (for original Make ONLY)
+#-------------------------------------------------------------------------------
+
+# This is a very ugly Makefile, and is only provided for those who do not
+# have GNU make. Note that it is not used if you have GNU make. It ignores
+# dependency checking and just compiles everything.
+
+default: everything
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+everything:
+ $(C) -DDINT -c amd_aat.c -o amd_i_aat.o
+ $(C) -DDINT -c amd_1.c -o amd_i_1.o
+ $(C) -DDINT -c amd_2.c -o amd_i_2.o
+ $(C) -DDINT -c amd_dump.c -o amd_i_dump.o
+ $(C) -DDINT -c amd_postorder.c -o amd_i_postorder.o
+ $(C) -DDINT -c amd_post_tree.c -o amd_i_post_tree.o
+ $(C) -DDINT -c amd_defaults.c -o amd_i_defaults.o
+ $(C) -DDINT -c amd_order.c -o amd_i_order.o
+ $(C) -DDINT -c amd_control.c -o amd_i_control.o
+ $(C) -DDINT -c amd_info.c -o amd_i_info.o
+ $(C) -DDINT -c amd_valid.c -o amd_i_valid.o
+ $(C) -DDINT -c amd_preprocess.c -o amd_i_preprocess.o
+ $(C) -DDLONG -c amd_aat.c -o amd_l_aat.o
+ $(C) -DDLONG -c amd_1.c -o amd_l_1.o
+ $(C) -DDLONG -c amd_2.c -o amd_l_2.o
+ $(C) -DDLONG -c amd_dump.c -o amd_l_dump.o
+ $(C) -DDLONG -c amd_postorder.c -o amd_l_postorder.o
+ $(C) -DDLONG -c amd_post_tree.c -o amd_l_post_tree.o
+ $(C) -DDLONG -c amd_defaults.c -o amd_l_defaults.o
+ $(C) -DDLONG -c amd_order.c -o amd_l_order.o
+ $(C) -DDLONG -c amd_control.c -o amd_l_control.o
+ $(C) -DDLONG -c amd_info.c -o amd_l_info.o
+ $(C) -DDLONG -c amd_valid.c -o amd_l_valid.o
+ $(C) -DDLONG -c amd_preprocess.c -o amd_l_preprocess.o
+ $(C) -c amd_global.c
+ $(AR) ../Lib/libamd.a amd_i_aat.o amd_i_1.o amd_i_2.o amd_i_dump.o \
+ amd_i_postorder.o amd_i_post_tree.o amd_i_defaults.o amd_i_order.o \
+ amd_i_control.o amd_i_info.o amd_i_valid.o amd_l_aat.o amd_l_1.o \
+ amd_l_2.o amd_l_dump.o amd_l_postorder.o amd_l_post_tree.o \
+ amd_l_defaults.o amd_l_order.o amd_l_control.o amd_l_info.o \
+ amd_l_valid.o amd_i_preprocess.o amd_l_preprocess.o amd_global.o
+ - $(RANLIB) ../Lib/libamd.a
+
+#-------------------------------------------------------------------------------
+# compile the Fortran versions and the libamdf77.a library
+#-------------------------------------------------------------------------------
+
+fortran:
+ $(F77) $(F77FLAGS) -c amd.f -o amd.o
+ $(F77) $(F77FLAGS) -c amdbar.f -o amdbar.o
+ $(AR) ../Lib/libamdf77.a amd.o amdbar.o
+ - $(RANLIB) ../Lib/libamdf77.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) ../Lib/libamd.a
+ - $(RM) ../Lib/libamdf77.a
diff --git a/src/C/SuiteSparse/AMD/Source/amd.f b/src/C/SuiteSparse/AMD/Source/amd.f
new file mode 100644
index 0000000..ccfe3e8
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd.f
@@ -0,0 +1,1214 @@
+C-----------------------------------------------------------------------
+C AMD: approximate minimum degree, with aggressive absorption
+C-----------------------------------------------------------------------
+
+ SUBROUTINE AMD
+ $ (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+
+ INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N),
+ $ DEGREE (N), NV (N), NEXT (N), LAST (N), HEAD (N),
+ $ ELEN (N), W (N), LEN (N)
+
+C Given a representation of the nonzero pattern of a symmetric matrix,
+C A, (excluding the diagonal) perform an approximate minimum
+C (UMFPACK/MA38-style) degree ordering to compute a pivot order
+C such that the introduction of nonzeros (fill-in) in the Cholesky
+C factors A = LL^T are kept low. At each step, the pivot
+C selected is the one with the minimum UMFPACK/MA38-style
+C upper-bound on the external degree.
+C
+C Aggresive absorption is used to tighten the bound on the degree.
+
+C **********************************************************************
+C ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+C **********************************************************************
+
+C References:
+C
+C [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern
+C multifrontal method for sparse LU factorization", SIAM J.
+C Matrix Analysis and Applications, vol. 18, no. 1, pp.
+C 140-158. Discusses UMFPACK / MA38, which first introduced
+C the approximate minimum degree used by this routine.
+C
+C [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An
+C approximate degree ordering algorithm," SIAM J. Matrix
+C Analysis and Applications, vol. 17, no. 4, pp. 886-905,
+C 1996. Discusses AMD, AMDBAR, and MC47B.
+C
+C [3] Alan George and Joseph Liu, "The evolution of the minimum
+C degree ordering algorithm," SIAM Review, vol. 31, no. 1,
+C pp. 1-19, 1989. We list below the features mentioned in
+C that paper that this code includes:
+C
+C mass elimination:
+C Yes. MA27 relied on supervariable detection for mass
+C elimination.
+C indistinguishable nodes:
+C Yes (we call these "supervariables"). This was also in
+C the MA27 code - although we modified the method of
+C detecting them (the previous hash was the true degree,
+C which we no longer keep track of). A supervariable is
+C a set of rows with identical nonzero pattern. All
+C variables in a supervariable are eliminated together.
+C Each supervariable has as its numerical name that of
+C one of its variables (its principal variable).
+C quotient graph representation:
+C Yes. We use the term "element" for the cliques formed
+C during elimination. This was also in the MA27 code.
+C The algorithm can operate in place, but it will work
+C more efficiently if given some "elbow room."
+C element absorption:
+C Yes. This was also in the MA27 code.
+C external degree:
+C Yes. The MA27 code was based on the true degree.
+C incomplete degree update and multiple elimination:
+C No. This was not in MA27, either. Our method of
+C degree update within MC47B/BD is element-based, not
+C variable-based. It is thus not well-suited for use
+C with incomplete degree update or multiple elimination.
+
+C-----------------------------------------------------------------------
+C Authors, and Copyright (C) 1995 by:
+C Timothy A. Davis, Patrick Amestoy, Iain S. Duff, & John K. Reid.
+C
+C Acknowledgements:
+C This work (and the UMFPACK package) was supported by the
+C National Science Foundation (ASC-9111263 and DMS-9223088).
+C The UMFPACK/MA38 approximate degree update algorithm, the
+C unsymmetric analog which forms the basis of MC47B/BD, was
+C developed while Tim Davis was supported by CERFACS (Toulouse,
+C France) in a post-doctoral position.
+C
+C Date: September, 1995
+C-----------------------------------------------------------------------
+
+C-----------------------------------------------------------------------
+C INPUT ARGUMENTS (unaltered):
+C-----------------------------------------------------------------------
+
+C n: The matrix order.
+C
+C Restriction: 1 .le. n .lt. (iovflo/2)-2, where iovflo is
+C the largest positive integer that your computer can represent.
+
+C iwlen: The length of iw (1..iwlen). On input, the matrix is
+C stored in iw (1..pfree-1). However, iw (1..iwlen) should be
+C slightly larger than what is required to hold the matrix, at
+C least iwlen .ge. pfree + n is recommended. Otherwise,
+C excessive compressions will take place.
+C *** We do not recommend running this algorithm with ***
+C *** iwlen .lt. pfree + n. ***
+C *** Better performance will be obtained if ***
+C *** iwlen .ge. pfree + n ***
+C *** or better yet ***
+C *** iwlen .gt. 1.2 * pfree ***
+C *** (where pfree is its value on input). ***
+C The algorithm will not run at all if iwlen .lt. pfree-1.
+C
+C Restriction: iwlen .ge. pfree-1
+
+C-----------------------------------------------------------------------
+C INPUT/OUPUT ARGUMENTS:
+C-----------------------------------------------------------------------
+
+C pe: On input, pe (i) is the index in iw of the start of row i, or
+C zero if row i has no off-diagonal non-zeros.
+C
+C During execution, it is used for both supervariables and
+C elements:
+C
+C * Principal supervariable i: index into iw of the
+C description of supervariable i. A supervariable
+C represents one or more rows of the matrix
+C with identical nonzero pattern.
+C * Non-principal supervariable i: if i has been absorbed
+C into another supervariable j, then pe (i) = -j.
+C That is, j has the same pattern as i.
+C Note that j might later be absorbed into another
+C supervariable j2, in which case pe (i) is still -j,
+C and pe (j) = -j2.
+C * Unabsorbed element e: the index into iw of the description
+C of element e, if e has not yet been absorbed by a
+C subsequent element. Element e is created when
+C the supervariable of the same name is selected as
+C the pivot.
+C * Absorbed element e: if element e is absorbed into element
+C e2, then pe (e) = -e2. This occurs when the pattern of
+C e (that is, Le) is found to be a subset of the pattern
+C of e2 (that is, Le2). If element e is "null" (it has
+C no nonzeros outside its pivot block), then pe (e) = 0.
+C
+C On output, pe holds the assembly tree/forest, which implicitly
+C represents a pivot order with identical fill-in as the actual
+C order (via a depth-first search of the tree).
+C
+C On output:
+C If nv (i) .gt. 0, then i represents a node in the assembly tree,
+C and the parent of i is -pe (i), or zero if i is a root.
+C If nv (i) = 0, then (i,-pe (i)) represents an edge in a
+C subtree, the root of which is a node in the assembly tree.
+
+C pfree: On input the tail end of the array, iw (pfree..iwlen),
+C is empty, and the matrix is stored in iw (1..pfree-1).
+C During execution, additional data is placed in iw, and pfree
+C is modified so that iw (pfree..iwlen) is always the unused part
+C of iw. On output, pfree is set equal to the size of iw that
+C would have been needed for no compressions to occur. If
+C ncmpa is zero, then pfree (on output) is less than or equal to
+C iwlen, and the space iw (pfree+1 ... iwlen) was not used.
+C Otherwise, pfree (on output) is greater than iwlen, and all the
+C memory in iw was used.
+
+C-----------------------------------------------------------------------
+C INPUT/MODIFIED (undefined on output):
+C-----------------------------------------------------------------------
+
+C len: On input, len (i) holds the number of entries in row i of the
+C matrix, excluding the diagonal. The contents of len (1..n)
+C are undefined on output.
+
+C iw: On input, iw (1..pfree-1) holds the description of each row i
+C in the matrix. The matrix must be symmetric, and both upper
+C and lower triangular parts must be present. The diagonal must
+C not be present. Row i is held as follows:
+C
+C len (i): the length of the row i data structure
+C iw (pe (i) ... pe (i) + len (i) - 1):
+C the list of column indices for nonzeros
+C in row i (simple supervariables), excluding
+C the diagonal. All supervariables start with
+C one row/column each (supervariable i is just
+C row i).
+C if len (i) is zero on input, then pe (i) is ignored
+C on input.
+C
+C Note that the rows need not be in any particular order,
+C and there may be empty space between the rows.
+C
+C During execution, the supervariable i experiences fill-in.
+C This is represented by placing in i a list of the elements
+C that cause fill-in in supervariable i:
+C
+C len (i): the length of supervariable i
+C iw (pe (i) ... pe (i) + elen (i) - 1):
+C the list of elements that contain i. This list
+C is kept short by removing absorbed elements.
+C iw (pe (i) + elen (i) ... pe (i) + len (i) - 1):
+C the list of supervariables in i. This list
+C is kept short by removing nonprincipal
+C variables, and any entry j that is also
+C contained in at least one of the elements
+C (j in Le) in the list for i (e in row i).
+C
+C When supervariable i is selected as pivot, we create an
+C element e of the same name (e=i):
+C
+C len (e): the length of element e
+C iw (pe (e) ... pe (e) + len (e) - 1):
+C the list of supervariables in element e.
+C
+C An element represents the fill-in that occurs when supervariable
+C i is selected as pivot (which represents the selection of row i
+C and all non-principal variables whose principal variable is i).
+C We use the term Le to denote the set of all supervariables
+C in element e. Absorbed supervariables and elements are pruned
+C from these lists when computationally convenient.
+C
+C CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+C The contents of iw are undefined on output.
+
+C-----------------------------------------------------------------------
+C OUTPUT (need not be set on input):
+C-----------------------------------------------------------------------
+
+C nv: During execution, abs (nv (i)) is equal to the number of rows
+C that are represented by the principal supervariable i. If i is
+C a nonprincipal variable, then nv (i) = 0. Initially,
+C nv (i) = 1 for all i. nv (i) .lt. 0 signifies that i is a
+C principal variable in the pattern Lme of the current pivot
+C element me. On output, nv (e) holds the true degree of element
+C e at the time it was created (including the diagonal part).
+
+C ncmpa: The number of times iw was compressed. If this is
+C excessive, then the execution took longer than what could have
+C been. To reduce ncmpa, try increasing iwlen to be 10% or 20%
+C larger than the value of pfree on input (or at least
+C iwlen .ge. pfree + n). The fastest performance will be
+C obtained when ncmpa is returned as zero. If iwlen is set to
+C the value returned by pfree on *output*, then no compressions
+C will occur.
+
+C elen: See the description of iw above. At the start of execution,
+C elen (i) is set to zero. During execution, elen (i) is the
+C number of elements in the list for supervariable i. When e
+C becomes an element, elen (e) = -nel is set, where nel is the
+C current step of factorization. elen (i) = 0 is done when i
+C becomes nonprincipal.
+C
+C For variables, elen (i) .ge. 0 holds until just before the
+C permutation vectors are computed. For elements,
+C elen (e) .lt. 0 holds.
+C
+C On output elen (1..n) holds the inverse permutation (the same
+C as the 'INVP' argument in Sparspak). That is, if k = elen (i),
+C then row i is the kth pivot row. Row i of A appears as the
+C (elen(i))-th row in the permuted matrix, PAP^T.
+
+C last: In a degree list, last (i) is the supervariable preceding i,
+C or zero if i is the head of the list. In a hash bucket,
+C last (i) is the hash key for i. last (head (hash)) is also
+C used as the head of a hash bucket if head (hash) contains a
+C degree list (see head, below).
+C
+C On output, last (1..n) holds the permutation (the same as the
+C 'PERM' argument in Sparspak). That is, if i = last (k), then
+C row i is the kth pivot row. Row last (k) of A is the k-th row
+C in the permuted matrix, PAP^T.
+
+C-----------------------------------------------------------------------
+C LOCAL (not input or output - used only during execution):
+C-----------------------------------------------------------------------
+
+C degree: If i is a supervariable, then degree (i) holds the
+C current approximation of the external degree of row i (an upper
+C bound). The external degree is the number of nonzeros in row i,
+C minus abs (nv (i)) (the diagonal part). The bound is equal to
+C the external degree if elen (i) is less than or equal to two.
+C
+C We also use the term "external degree" for elements e to refer
+C to |Le \ Lme|. If e is an element, then degree (e) holds |Le|,
+C which is the degree of the off-diagonal part of the element e
+C (not including the diagonal part).
+
+C head: head is used for degree lists. head (deg) is the first
+C supervariable in a degree list (all supervariables i in a
+C degree list deg have the same approximate degree, namely,
+C deg = degree (i)). If the list deg is empty then
+C head (deg) = 0.
+C
+C During supervariable detection head (hash) also serves as a
+C pointer to a hash bucket.
+C If head (hash) .gt. 0, there is a degree list of degree hash.
+C The hash bucket head pointer is last (head (hash)).
+C If head (hash) = 0, then the degree list and hash bucket are
+C both empty.
+C If head (hash) .lt. 0, then the degree list is empty, and
+C -head (hash) is the head of the hash bucket.
+C After supervariable detection is complete, all hash buckets
+C are empty, and the (last (head (hash)) = 0) condition is
+C restored for the non-empty degree lists.
+
+C next: next (i) is the supervariable following i in a link list, or
+C zero if i is the last in the list. Used for two kinds of
+C lists: degree lists and hash buckets (a supervariable can be
+C in only one kind of list at a time).
+
+C w: The flag array w determines the status of elements and
+C variables, and the external degree of elements.
+C
+C for elements:
+C if w (e) = 0, then the element e is absorbed
+C if w (e) .ge. wflg, then w (e) - wflg is the size of
+C the set |Le \ Lme|, in terms of nonzeros (the
+C sum of abs (nv (i)) for each principal variable i that
+C is both in the pattern of element e and NOT in the
+C pattern of the current pivot element, me).
+C if wflg .gt. w (e) .gt. 0, then e is not absorbed and has
+C not yet been seen in the scan of the element lists in
+C the computation of |Le\Lme| in loop 150 below.
+C
+C for variables:
+C during supervariable detection, if w (j) .ne. wflg then j is
+C not in the pattern of variable i
+C
+C The w array is initialized by setting w (i) = 1 for all i,
+C and by setting wflg = 2. It is reinitialized if wflg becomes
+C too large (to ensure that wflg+n does not cause integer
+C overflow).
+
+C-----------------------------------------------------------------------
+C LOCAL INTEGERS:
+C-----------------------------------------------------------------------
+
+ INTEGER DEG, DEGME, DEXT, DMAX, E, ELENME, ELN, HASH, HMOD, I,
+ $ ILAST, INEXT, J, JLAST, JNEXT, K, KNT1, KNT2, KNT3,
+ $ LENJ, LN, MAXMEM, ME, MEM, MINDEG, NEL, NEWMEM,
+ $ NLEFT, NVI, NVJ, NVPIV, SLENME, WE, WFLG, WNVI, X
+
+C deg: the degree of a variable or element
+C degme: size, |Lme|, of the current element, me (= degree (me))
+C dext: external degree, |Le \ Lme|, of some element e
+C dmax: largest |Le| seen so far
+C e: an element
+C elenme: the length, elen (me), of element list of pivotal var.
+C eln: the length, elen (...), of an element list
+C hash: the computed value of the hash function
+C hmod: the hash function is computed modulo hmod = max (1,n-1)
+C i: a supervariable
+C ilast: the entry in a link list preceding i
+C inext: the entry in a link list following i
+C j: a supervariable
+C jlast: the entry in a link list preceding j
+C jnext: the entry in a link list, or path, following j
+C k: the pivot order of an element or variable
+C knt1: loop counter used during element construction
+C knt2: loop counter used during element construction
+C knt3: loop counter used during compression
+C lenj: len (j)
+C ln: length of a supervariable list
+C maxmem: amount of memory needed for no compressions
+C me: current supervariable being eliminated, and the
+C current element created by eliminating that
+C supervariable
+C mem: memory in use assuming no compressions have occurred
+C mindeg: current minimum degree
+C nel: number of pivots selected so far
+C newmem: amount of new memory needed for current pivot element
+C nleft: n - nel, the number of nonpivotal rows/columns remaining
+C nvi: the number of variables in a supervariable i (= nv (i))
+C nvj: the number of variables in a supervariable j (= nv (j))
+C nvpiv: number of pivots in current element
+C slenme: number of variables in variable list of pivotal variable
+C we: w (e)
+C wflg: used for flagging the w array. See description of iw.
+C wnvi: wflg - nv (i)
+C x: either a supervariable or an element
+
+C-----------------------------------------------------------------------
+C LOCAL POINTERS:
+C-----------------------------------------------------------------------
+
+ INTEGER P, P1, P2, P3, PDST, PEND, PJ, PME, PME1, PME2, PN, PSRC
+
+C Any parameter (pe (...) or pfree) or local variable
+C starting with "p" (for Pointer) is an index into iw,
+C and all indices into iw use variables starting with
+C "p." The only exception to this rule is the iwlen
+C input argument.
+
+C p: pointer into lots of things
+C p1: pe (i) for some variable i (start of element list)
+C p2: pe (i) + elen (i) - 1 for some var. i (end of el. list)
+C p3: index of first supervariable in clean list
+C pdst: destination pointer, for compression
+C pend: end of memory to compress
+C pj: pointer into an element or variable
+C pme: pointer into the current element (pme1...pme2)
+C pme1: the current element, me, is stored in iw (pme1...pme2)
+C pme2: the end of the current element
+C pn: pointer into a "clean" variable, also used to compress
+C psrc: source pointer, for compression
+
+C-----------------------------------------------------------------------
+C FUNCTIONS CALLED:
+C-----------------------------------------------------------------------
+
+ INTRINSIC MAX, MIN, MOD
+
+C=======================================================================
+C INITIALIZATIONS
+C=======================================================================
+
+ WFLG = 2
+ MINDEG = 1
+ NCMPA = 0
+ NEL = 0
+ HMOD = MAX (1, N-1)
+ DMAX = 0
+ MEM = PFREE - 1
+ MAXMEM = MEM
+ ME = 0
+
+ DO 10 I = 1, N
+ LAST (I) = 0
+ HEAD (I) = 0
+ NV (I) = 1
+ W (I) = 1
+ ELEN (I) = 0
+ DEGREE (I) = LEN (I)
+10 CONTINUE
+
+C ----------------------------------------------------------------
+C initialize degree lists and eliminate rows with no off-diag. nz.
+C ----------------------------------------------------------------
+
+ DO 20 I = 1, N
+
+ DEG = DEGREE (I)
+
+ IF (DEG .GT. 0) THEN
+
+C ----------------------------------------------------------
+C place i in the degree list corresponding to its degree
+C ----------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ HEAD (DEG) = I
+
+ ELSE
+
+C ----------------------------------------------------------
+C we have a variable that can be eliminated at once because
+C there is no off-diagonal non-zero in its row.
+C ----------------------------------------------------------
+
+ NEL = NEL + 1
+ ELEN (I) = -NEL
+ PE (I) = 0
+ W (I) = 0
+
+ ENDIF
+
+20 CONTINUE
+
+C=======================================================================
+C WHILE (selecting pivots) DO
+C=======================================================================
+
+30 CONTINUE
+ IF (NEL .LT. N) THEN
+
+C=======================================================================
+C GET PIVOT OF MINIMUM DEGREE
+C=======================================================================
+
+C -------------------------------------------------------------
+C find next supervariable for elimination
+C -------------------------------------------------------------
+
+ DO 40 DEG = MINDEG, N
+ ME = HEAD (DEG)
+ IF (ME .GT. 0) GOTO 50
+40 CONTINUE
+50 CONTINUE
+ MINDEG = DEG
+
+C -------------------------------------------------------------
+C remove chosen variable from link list
+C -------------------------------------------------------------
+
+ INEXT = NEXT (ME)
+ IF (INEXT .NE. 0) LAST (INEXT) = 0
+ HEAD (DEG) = INEXT
+
+C -------------------------------------------------------------
+C me represents the elimination of pivots nel+1 to nel+nv(me).
+C place me itself as the first in this set. It will be moved
+C to the nel+nv(me) position when the permutation vectors are
+C computed.
+C -------------------------------------------------------------
+
+ ELENME = ELEN (ME)
+ ELEN (ME) = - (NEL + 1)
+ NVPIV = NV (ME)
+ NEL = NEL + NVPIV
+
+C=======================================================================
+C CONSTRUCT NEW ELEMENT
+C=======================================================================
+
+C -------------------------------------------------------------
+C At this point, me is the pivotal supervariable. It will be
+C converted into the current element. Scan list of the
+C pivotal supervariable, me, setting tree pointers and
+C constructing new list of supervariables for the new element,
+C me. p is a pointer to the current position in the old list.
+C -------------------------------------------------------------
+
+C flag the variable "me" as being in Lme by negating nv (me)
+ NV (ME) = -NVPIV
+ DEGME = 0
+
+ IF (ELENME .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C construct the new element in place
+C ----------------------------------------------------------
+
+ PME1 = PE (ME)
+ PME2 = PME1 - 1
+
+ DO 60 P = PME1, PME1 + LEN (ME) - 1
+ I = IW (P)
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C ----------------------------------------------------
+C i is a principal variable not yet placed in Lme.
+C store i in new list
+C ----------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ PME2 = PME2 + 1
+ IW (PME2) = I
+
+C ----------------------------------------------------
+C remove variable i from degree list.
+C ----------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+60 CONTINUE
+C this element takes no new memory in iw:
+ NEWMEM = 0
+
+ ELSE
+
+C ----------------------------------------------------------
+C construct the new element in empty space, iw (pfree ...)
+C ----------------------------------------------------------
+
+ P = PE (ME)
+ PME1 = PFREE
+ SLENME = LEN (ME) - ELENME
+
+ DO 120 KNT1 = 1, ELENME + 1
+
+ IF (KNT1 .GT. ELENME) THEN
+C search the supervariables in me.
+ E = ME
+ PJ = P
+ LN = SLENME
+ ELSE
+C search the elements in me.
+ E = IW (P)
+ P = P + 1
+ PJ = PE (E)
+ LN = LEN (E)
+ ENDIF
+
+C -------------------------------------------------------
+C search for different supervariables and add them to the
+C new list, compressing when necessary. this loop is
+C executed once for each element in the list and once for
+C all the supervariables in the list.
+C -------------------------------------------------------
+
+ DO 110 KNT2 = 1, LN
+ I = IW (PJ)
+ PJ = PJ + 1
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C -------------------------------------------------
+C compress iw, if necessary
+C -------------------------------------------------
+
+ IF (PFREE .GT. IWLEN) THEN
+C prepare for compressing iw by adjusting
+C pointers and lengths so that the lists being
+C searched in the inner and outer loops contain
+C only the remaining entries.
+
+ PE (ME) = P
+ LEN (ME) = LEN (ME) - KNT1
+ IF (LEN (ME) .EQ. 0) THEN
+C nothing left of supervariable me
+ PE (ME) = 0
+ ENDIF
+ PE (E) = PJ
+ LEN (E) = LN - KNT2
+ IF (LEN (E) .EQ. 0) THEN
+C nothing left of element e
+ PE (E) = 0
+ ENDIF
+
+ NCMPA = NCMPA + 1
+C store first item in pe
+C set first entry to -item
+ DO 70 J = 1, N
+ PN = PE (J)
+ IF (PN .GT. 0) THEN
+ PE (J) = IW (PN)
+ IW (PN) = -J
+ ENDIF
+70 CONTINUE
+
+C psrc/pdst point to source/destination
+ PDST = 1
+ PSRC = 1
+ PEND = PME1 - 1
+
+C while loop:
+80 CONTINUE
+ IF (PSRC .LE. PEND) THEN
+C search for next negative entry
+ J = -IW (PSRC)
+ PSRC = PSRC + 1
+ IF (J .GT. 0) THEN
+ IW (PDST) = PE (J)
+ PE (J) = PDST
+ PDST = PDST + 1
+C copy from source to destination
+ LENJ = LEN (J)
+ DO 90 KNT3 = 0, LENJ - 2
+ IW (PDST + KNT3) = IW (PSRC + KNT3)
+90 CONTINUE
+ PDST = PDST + LENJ - 1
+ PSRC = PSRC + LENJ - 1
+ ENDIF
+ GOTO 80
+ ENDIF
+
+C move the new partially-constructed element
+ P1 = PDST
+ DO 100 PSRC = PME1, PFREE - 1
+ IW (PDST) = IW (PSRC)
+ PDST = PDST + 1
+100 CONTINUE
+ PME1 = P1
+ PFREE = PDST
+ PJ = PE (E)
+ P = PE (ME)
+ ENDIF
+
+C -------------------------------------------------
+C i is a principal variable not yet placed in Lme
+C store i in new list
+C -------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ IW (PFREE) = I
+ PFREE = PFREE + 1
+
+C -------------------------------------------------
+C remove variable i from degree link list
+C -------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+110 CONTINUE
+
+ IF (E .NE. ME) THEN
+C set tree pointer and flag to indicate element e is
+C absorbed into new element me (the parent of e is me)
+ PE (E) = -ME
+ W (E) = 0
+ ENDIF
+120 CONTINUE
+
+ PME2 = PFREE - 1
+C this element takes newmem new memory in iw (possibly zero)
+ NEWMEM = PFREE - PME1
+ MEM = MEM + NEWMEM
+ MAXMEM = MAX (MAXMEM, MEM)
+ ENDIF
+
+C -------------------------------------------------------------
+C me has now been converted into an element in iw (pme1..pme2)
+C -------------------------------------------------------------
+
+C degme holds the external degree of new element
+ DEGREE (ME) = DEGME
+ PE (ME) = PME1
+ LEN (ME) = PME2 - PME1 + 1
+
+C -------------------------------------------------------------
+C make sure that wflg is not too large. With the current
+C value of wflg, wflg+n must not cause integer overflow
+C -------------------------------------------------------------
+
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 130 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+130 CONTINUE
+ WFLG = 2
+ ENDIF
+
+C=======================================================================
+C COMPUTE (w (e) - wflg) = |Le\Lme| FOR ALL ELEMENTS
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 1: compute the external degrees of previous elements
+C with respect to the current element. That is:
+C (w (e) - wflg) = |Le \ Lme|
+C for each element e that appears in any supervariable in Lme.
+C The notation Le refers to the pattern (list of
+C supervariables) of a previous element e, where e is not yet
+C absorbed, stored in iw (pe (e) + 1 ... pe (e) + iw (pe (e))).
+C The notation Lme refers to the pattern of the current element
+C (stored in iw (pme1..pme2)). If (w (e) - wflg) becomes
+C zero, then the element e will be absorbed in scan 2.
+C -------------------------------------------------------------
+
+ DO 150 PME = PME1, PME2
+ I = IW (PME)
+ ELN = ELEN (I)
+ IF (ELN .GT. 0) THEN
+C note that nv (i) has been negated to denote i in Lme:
+ NVI = -NV (I)
+ WNVI = WFLG - NVI
+ DO 140 P = PE (I), PE (I) + ELN - 1
+ E = IW (P)
+ WE = W (E)
+ IF (WE .GE. WFLG) THEN
+C unabsorbed element e has been seen in this loop
+ WE = WE - NVI
+ ELSE IF (WE .NE. 0) THEN
+C e is an unabsorbed element
+C this is the first we have seen e in all of Scan 1
+ WE = DEGREE (E) + WNVI
+ ENDIF
+ W (E) = WE
+140 CONTINUE
+ ENDIF
+150 CONTINUE
+
+C=======================================================================
+C DEGREE UPDATE AND ELEMENT ABSORPTION
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 2: for each i in Lme, sum up the degree of Lme (which
+C is degme), plus the sum of the external degrees of each Le
+C for the elements e appearing within i, plus the
+C supervariables in i. Place i in hash list.
+C -------------------------------------------------------------
+
+ DO 180 PME = PME1, PME2
+ I = IW (PME)
+ P1 = PE (I)
+ P2 = P1 + ELEN (I) - 1
+ PN = P1
+ HASH = 0
+ DEG = 0
+
+C ----------------------------------------------------------
+C scan the element list associated with supervariable i
+C ----------------------------------------------------------
+
+ DO 160 P = P1, P2
+ E = IW (P)
+C dext = | Le \ Lme |
+ DEXT = W (E) - WFLG
+ IF (DEXT .GT. 0) THEN
+ DEG = DEG + DEXT
+ IW (PN) = E
+ PN = PN + 1
+ HASH = HASH + E
+ ELSE IF (DEXT .EQ. 0) THEN
+C aggressive absorption: e is not adjacent to me, but
+C the |Le \ Lme| is 0, so absorb it into me
+ PE (E) = -ME
+ W (E) = 0
+ ELSE
+C element e has already been absorbed, due to
+C regular absorption, in do loop 120 above. Ignore it.
+ CONTINUE
+ ENDIF
+160 CONTINUE
+
+C count the number of elements in i (including me):
+ ELEN (I) = PN - P1 + 1
+
+C ----------------------------------------------------------
+C scan the supervariables in the list associated with i
+C ----------------------------------------------------------
+
+ P3 = PN
+ DO 170 P = P2 + 1, P1 + LEN (I) - 1
+ J = IW (P)
+ NVJ = NV (J)
+ IF (NVJ .GT. 0) THEN
+C j is unabsorbed, and not in Lme.
+C add to degree and add to new list
+ DEG = DEG + NVJ
+ IW (PN) = J
+ PN = PN + 1
+ HASH = HASH + J
+ ENDIF
+170 CONTINUE
+
+C ----------------------------------------------------------
+C update the degree and check for mass elimination
+C ----------------------------------------------------------
+
+ IF (DEG .EQ. 0) THEN
+
+C -------------------------------------------------------
+C mass elimination
+C -------------------------------------------------------
+
+C There is nothing left of this node except for an
+C edge to the current pivot element. elen (i) is 1,
+C and there are no variables adjacent to node i.
+C Absorb i into the current pivot element, me.
+
+ PE (I) = -ME
+ NVI = -NV (I)
+ DEGME = DEGME - NVI
+ NVPIV = NVPIV + NVI
+ NEL = NEL + NVI
+ NV (I) = 0
+ ELEN (I) = 0
+
+ ELSE
+
+C -------------------------------------------------------
+C update the upper-bound degree of i
+C -------------------------------------------------------
+
+C the following degree does not yet include the size
+C of the current element, which is added later:
+ DEGREE (I) = MIN (DEGREE (I), DEG)
+
+C -------------------------------------------------------
+C add me to the list for i
+C -------------------------------------------------------
+
+C move first supervariable to end of list
+ IW (PN) = IW (P3)
+C move first element to end of element part of list
+ IW (P3) = IW (P1)
+C add new element to front of list.
+ IW (P1) = ME
+C store the new length of the list in len (i)
+ LEN (I) = PN - P1 + 1
+
+C -------------------------------------------------------
+C place in hash bucket. Save hash key of i in last (i).
+C -------------------------------------------------------
+
+ HASH = MOD (HASH, HMOD) + 1
+ J = HEAD (HASH)
+ IF (J .LE. 0) THEN
+C the degree list is empty, hash head is -j
+ NEXT (I) = -J
+ HEAD (HASH) = -I
+ ELSE
+C degree list is not empty
+C use last (head (hash)) as hash head
+ NEXT (I) = LAST (J)
+ LAST (J) = I
+ ENDIF
+ LAST (I) = HASH
+ ENDIF
+180 CONTINUE
+
+ DEGREE (ME) = DEGME
+
+C -------------------------------------------------------------
+C Clear the counter array, w (...), by incrementing wflg.
+C -------------------------------------------------------------
+
+ DMAX = MAX (DMAX, DEGME)
+ WFLG = WFLG + DMAX
+
+C make sure that wflg+n does not cause integer overflow
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 190 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+190 CONTINUE
+ WFLG = 2
+ ENDIF
+C at this point, w (1..n) .lt. wflg holds
+
+C=======================================================================
+C SUPERVARIABLE DETECTION
+C=======================================================================
+
+ DO 250 PME = PME1, PME2
+ I = IW (PME)
+ IF (NV (I) .LT. 0) THEN
+C i is a principal variable in Lme
+
+C -------------------------------------------------------
+C examine all hash buckets with 2 or more variables. We
+C do this by examing all unique hash keys for super-
+C variables in the pattern Lme of the current element, me
+C -------------------------------------------------------
+
+ HASH = LAST (I)
+C let i = head of hash bucket, and empty the hash bucket
+ J = HEAD (HASH)
+ IF (J .EQ. 0) GOTO 250
+ IF (J .LT. 0) THEN
+C degree list is empty
+ I = -J
+ HEAD (HASH) = 0
+ ELSE
+C degree list is not empty, restore last () of head
+ I = LAST (J)
+ LAST (J) = 0
+ ENDIF
+ IF (I .EQ. 0) GOTO 250
+
+C while loop:
+200 CONTINUE
+ IF (NEXT (I) .NE. 0) THEN
+
+C ----------------------------------------------------
+C this bucket has one or more variables following i.
+C scan all of them to see if i can absorb any entries
+C that follow i in hash bucket. Scatter i into w.
+C ----------------------------------------------------
+
+ LN = LEN (I)
+ ELN = ELEN (I)
+C do not flag the first element in the list (me)
+ DO 210 P = PE (I) + 1, PE (I) + LN - 1
+ W (IW (P)) = WFLG
+210 CONTINUE
+
+C ----------------------------------------------------
+C scan every other entry j following i in bucket
+C ----------------------------------------------------
+
+ JLAST = I
+ J = NEXT (I)
+
+C while loop:
+220 CONTINUE
+ IF (J .NE. 0) THEN
+
+C -------------------------------------------------
+C check if j and i have identical nonzero pattern
+C -------------------------------------------------
+
+ IF (LEN (J) .NE. LN) THEN
+C i and j do not have same size data structure
+ GOTO 240
+ ENDIF
+ IF (ELEN (J) .NE. ELN) THEN
+C i and j do not have same number of adjacent el
+ GOTO 240
+ ENDIF
+C do not flag the first element in the list (me)
+ DO 230 P = PE (J) + 1, PE (J) + LN - 1
+ IF (W (IW (P)) .NE. WFLG) THEN
+C an entry (iw(p)) is in j but not in i
+ GOTO 240
+ ENDIF
+230 CONTINUE
+
+C -------------------------------------------------
+C found it! j can be absorbed into i
+C -------------------------------------------------
+
+ PE (J) = -I
+C both nv (i) and nv (j) are negated since they
+C are in Lme, and the absolute values of each
+C are the number of variables in i and j:
+ NV (I) = NV (I) + NV (J)
+ NV (J) = 0
+ ELEN (J) = 0
+C delete j from hash bucket
+ J = NEXT (J)
+ NEXT (JLAST) = J
+ GOTO 220
+
+C -------------------------------------------------
+240 CONTINUE
+C j cannot be absorbed into i
+C -------------------------------------------------
+
+ JLAST = J
+ J = NEXT (J)
+ GOTO 220
+ ENDIF
+
+C ----------------------------------------------------
+C no more variables can be absorbed into i
+C go to next i in bucket and clear flag array
+C ----------------------------------------------------
+
+ WFLG = WFLG + 1
+ I = NEXT (I)
+ IF (I .NE. 0) GOTO 200
+ ENDIF
+ ENDIF
+250 CONTINUE
+
+C=======================================================================
+C RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVAR. FROM ELEMENT
+C=======================================================================
+
+ P = PME1
+ NLEFT = N - NEL
+ DO 260 PME = PME1, PME2
+ I = IW (PME)
+ NVI = -NV (I)
+ IF (NVI .GT. 0) THEN
+C i is a principal variable in Lme
+C restore nv (i) to signify that i is principal
+ NV (I) = NVI
+
+C -------------------------------------------------------
+C compute the external degree (add size of current elem)
+C -------------------------------------------------------
+
+ DEG = MIN (DEGREE (I) + DEGME - NVI, NLEFT - NVI)
+
+C -------------------------------------------------------
+C place the supervariable at the head of the degree list
+C -------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ LAST (I) = 0
+ HEAD (DEG) = I
+
+C -------------------------------------------------------
+C save the new degree, and find the minimum degree
+C -------------------------------------------------------
+
+ MINDEG = MIN (MINDEG, DEG)
+ DEGREE (I) = DEG
+
+C -------------------------------------------------------
+C place the supervariable in the element pattern
+C -------------------------------------------------------
+
+ IW (P) = I
+ P = P + 1
+ ENDIF
+260 CONTINUE
+
+C=======================================================================
+C FINALIZE THE NEW ELEMENT
+C=======================================================================
+
+ NV (ME) = NVPIV + DEGME
+C nv (me) is now the degree of pivot (including diagonal part)
+C save the length of the list for the new element me
+ LEN (ME) = P - PME1
+ IF (LEN (ME) .EQ. 0) THEN
+C there is nothing left of the current pivot element
+ PE (ME) = 0
+ W (ME) = 0
+ ENDIF
+ IF (NEWMEM .NE. 0) THEN
+C element was not constructed in place: deallocate part
+C of it (final size is less than or equal to newmem,
+C since newly nonprincipal variables have been removed).
+ PFREE = P
+ MEM = MEM - NEWMEM + LEN (ME)
+ ENDIF
+
+C=======================================================================
+C END WHILE (selecting pivots)
+ GOTO 30
+ ENDIF
+C=======================================================================
+
+C=======================================================================
+C COMPUTE THE PERMUTATION VECTORS
+C=======================================================================
+
+C ----------------------------------------------------------------
+C The time taken by the following code is O(n). At this
+C point, elen (e) = -k has been done for all elements e,
+C and elen (i) = 0 has been done for all nonprincipal
+C variables i. At this point, there are no principal
+C supervariables left, and all elements are absorbed.
+C ----------------------------------------------------------------
+
+C ----------------------------------------------------------------
+C compute the ordering of unordered nonprincipal variables
+C ----------------------------------------------------------------
+
+ DO 290 I = 1, N
+ IF (ELEN (I) .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C i is an un-ordered row. Traverse the tree from i until
+C reaching an element, e. The element, e, was the
+C principal supervariable of i and all nodes in the path
+C from i to when e was selected as pivot.
+C ----------------------------------------------------------
+
+ J = -PE (I)
+C while (j is a variable) do:
+270 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ J = -PE (J)
+ GOTO 270
+ ENDIF
+ E = J
+
+C ----------------------------------------------------------
+C get the current pivot ordering of e
+C ----------------------------------------------------------
+
+ K = -ELEN (E)
+
+C ----------------------------------------------------------
+C traverse the path again from i to e, and compress the
+C path (all nodes point to e). Path compression allows
+C this code to compute in O(n) time. Order the unordered
+C nodes in the path, and place the element e at the end.
+C ----------------------------------------------------------
+
+ J = I
+C while (j is a variable) do:
+280 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ JNEXT = -PE (J)
+ PE (J) = -E
+ IF (ELEN (J) .EQ. 0) THEN
+C j is an unordered row
+ ELEN (J) = K
+ K = K + 1
+ ENDIF
+ J = JNEXT
+ GOTO 280
+ ENDIF
+C leave elen (e) negative, so we know it is an element
+ ELEN (E) = -K
+ ENDIF
+290 CONTINUE
+
+C ----------------------------------------------------------------
+C reset the inverse permutation (elen (1..n)) to be positive,
+C and compute the permutation (last (1..n)).
+C ----------------------------------------------------------------
+
+ DO 300 I = 1, N
+ K = ABS (ELEN (I))
+ LAST (K) = I
+ ELEN (I) = K
+300 CONTINUE
+
+C=======================================================================
+C RETURN THE MEMORY USAGE IN IW
+C=======================================================================
+
+C If maxmem is less than or equal to iwlen, then no compressions
+C occurred, and iw (maxmem+1 ... iwlen) was unused. Otherwise
+C compressions did occur, and iwlen would have had to have been
+C greater than or equal to maxmem for no compressions to occur.
+C Return the value of maxmem in the pfree argument.
+
+ PFREE = MAXMEM
+
+ RETURN
+ END
+
diff --git a/src/C/SuiteSparse/AMD/Source/amd_1.c b/src/C/SuiteSparse/AMD/Source/amd_1.c
new file mode 100644
index 0000000..a85c184
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_1.c
@@ -0,0 +1,181 @@
+/* ========================================================================= */
+/* === AMD_1 =============================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD_1: Construct A+A' for a sparse matrix A and perform the AMD ordering.
+ *
+ * The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style
+ * compressed-column form, with sorted row indices in each column, and no
+ * duplicate entries. Diagonal entries may be present, but they are ignored.
+ * Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ * Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The
+ * size of the matrix, n, must be greater than or equal to zero.
+ *
+ * This routine must be preceded by a call to AMD_aat, which computes the
+ * number of entries in each row/column in A+A', excluding the diagonal.
+ * Len [j], on input, is the number of entries in row/column j of A+A'. This
+ * routine constructs the matrix A+A' and then calls AMD_2. No error checking
+ * is performed (this was done in AMD_valid).
+ */
+
+#include "amd_internal.h"
+
+GLOBAL void AMD_1
+(
+ Int n, /* n > 0 */
+ const Int Ap [ ], /* input of size n+1, not modified */
+ const Int Ai [ ], /* input of size nz = Ap [n], not modified */
+ Int P [ ], /* size n output permutation */
+ Int Pinv [ ], /* size n output inverse permutation */
+ Int Len [ ], /* size n input, undefined on output */
+ Int slen, /* slen >= sum (Len [0..n-1]) + 7n,
+ * ideally slen = 1.2 * sum (Len) + 8n */
+ Int S [ ], /* size slen workspace */
+ double Control [ ], /* input array of size AMD_CONTROL */
+ double Info [ ] /* output array of size AMD_INFO */
+)
+{
+ Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head,
+ *Elen, *Degree, *s, *W, *Sp, *Tp ;
+
+ /* --------------------------------------------------------------------- */
+ /* construct the matrix for AMD_2 */
+ /* --------------------------------------------------------------------- */
+
+ ASSERT (n > 0) ;
+
+ iwlen = slen - 6*n ;
+ s = S ;
+ Pe = s ; s += n ;
+ Nv = s ; s += n ;
+ Head = s ; s += n ;
+ Elen = s ; s += n ;
+ Degree = s ; s += n ;
+ W = s ; s += n ;
+ Iw = s ; s += iwlen ;
+
+ ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
+
+ /* construct the pointers for A+A' */
+ Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */
+ Tp = W ;
+ pfree = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Pe [j] = pfree ;
+ Sp [j] = pfree ;
+ pfree += Len [j] ;
+ }
+
+ /* Note that this restriction on iwlen is slightly more restrictive than
+ * what is strictly required in AMD_2. AMD_2 can operate with no elbow
+ * room at all, but it will be very slow. For better performance, at
+ * least size-n elbow room is enforced. */
+ ASSERT (iwlen >= pfree + n) ;
+
+#ifndef NDEBUG
+ for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ;
+#endif
+
+ for (k = 0 ; k < n ; k++)
+ {
+ AMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ;
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+
+ /* construct A+A' */
+ for (p = p1 ; p < p2 ; )
+ {
+ /* scan the upper triangular part of A */
+ j = Ai [p] ;
+ ASSERT (j >= 0 && j < n) ;
+ if (j < k)
+ {
+ /* entry A (j,k) in the strictly upper triangular part */
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ;
+ Iw [Sp [j]++] = k ;
+ Iw [Sp [k]++] = j ;
+ p++ ;
+ }
+ else if (j == k)
+ {
+ /* skip the diagonal */
+ p++ ;
+ break ;
+ }
+ else /* j > k */
+ {
+ /* first entry below the diagonal */
+ break ;
+ }
+ /* scan lower triangular part of A, in column j until reaching
+ * row k. Start where last scan left off. */
+ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
+ pj2 = Ap [j+1] ;
+ for (pj = Tp [j] ; pj < pj2 ; )
+ {
+ i = Ai [pj] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i < k)
+ {
+ /* A (i,j) is only in the lower part, not in upper */
+ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ Iw [Sp [i]++] = j ;
+ Iw [Sp [j]++] = i ;
+ pj++ ;
+ }
+ else if (i == k)
+ {
+ /* entry A (k,j) in lower part and A (j,k) in upper */
+ pj++ ;
+ break ;
+ }
+ else /* i > k */
+ {
+ /* consider this entry later, when k advances to i */
+ break ;
+ }
+ }
+ Tp [j] = pj ;
+ }
+ Tp [k] = p ;
+ }
+
+ /* clean up, for remaining mismatched entries */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
+ {
+ i = Ai [pj] ;
+ ASSERT (i >= 0 && i < n) ;
+ /* A (i,j) is only in the lower part, not in upper */
+ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ Iw [Sp [i]++] = j ;
+ Iw [Sp [j]++] = i ;
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ;
+ ASSERT (Sp [n-1] == pfree) ;
+#endif
+
+ /* Tp and Sp no longer needed ] */
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ AMD_2 (n, Pe, Iw, Len, iwlen, pfree,
+ Nv, Pinv, P, Head, Elen, Degree, W, Control, Info) ;
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_2.c b/src/C/SuiteSparse/AMD/Source/amd_2.c
new file mode 100644
index 0000000..a760877
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_2.c
@@ -0,0 +1,1842 @@
+/* ========================================================================= */
+/* === AMD_2 =============================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD_2: performs the AMD ordering on a symmetric sparse matrix A, followed
+ * by a postordering (via depth-first search) of the assembly tree using the
+ * AMD_postorder routine.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === clear_flag ========================================================== */
+/* ========================================================================= */
+
+static Int clear_flag (Int wflg, Int wbig, Int W [ ], Int n)
+{
+ Int x ;
+ if (wflg < 2 || wflg >= wbig)
+ {
+ for (x = 0 ; x < n ; x++)
+ {
+ if (W [x] != 0) W [x] = 1 ;
+ }
+ wflg = 2 ;
+ }
+ /* at this point, W [0..n-1] < wflg holds */
+ return (wflg) ;
+}
+
+
+/* ========================================================================= */
+/* === AMD_2 =============================================================== */
+/* ========================================================================= */
+
+GLOBAL void AMD_2
+(
+ Int n, /* A is n-by-n, where n > 0 */
+ Int Pe [ ], /* Pe [0..n-1]: index in Iw of row i on input */
+ Int Iw [ ], /* workspace of size iwlen. Iw [0..pfree-1]
+ * holds the matrix on input */
+ Int Len [ ], /* Len [0..n-1]: length for row/column i on input */
+ Int iwlen, /* length of Iw. iwlen >= pfree + n */
+ Int pfree, /* Iw [pfree ... iwlen-1] is empty on input */
+
+ /* 7 size-n workspaces, not defined on input: */
+ Int Nv [ ], /* the size of each supernode on output */
+ Int Next [ ], /* the output inverse permutation */
+ Int Last [ ], /* the output permutation */
+ Int Head [ ],
+ Int Elen [ ], /* the size columns of L for each supernode */
+ Int Degree [ ],
+ Int W [ ],
+
+ /* control parameters and output statistics */
+ double Control [ ], /* array of size AMD_CONTROL */
+ double Info [ ] /* array of size AMD_INFO */
+)
+{
+
+/*
+ * Given a representation of the nonzero pattern of a symmetric matrix, A,
+ * (excluding the diagonal) perform an approximate minimum (UMFPACK/MA38-style)
+ * degree ordering to compute a pivot order such that the introduction of
+ * nonzeros (fill-in) in the Cholesky factors A = LL' is kept low. At each
+ * step, the pivot selected is the one with the minimum UMFAPACK/MA38-style
+ * upper-bound on the external degree. This routine can optionally perform
+ * aggresive absorption (as done by MC47B in the Harwell Subroutine
+ * Library).
+ *
+ * The approximate degree algorithm implemented here is the symmetric analog of
+ * the degree update algorithm in MA38 and UMFPACK (the Unsymmetric-pattern
+ * MultiFrontal PACKage, both by Davis and Duff). The routine is based on the
+ * MA27 minimum degree ordering algorithm by Iain Duff and John Reid.
+ *
+ * This routine is a translation of the original AMDBAR and MC47B routines,
+ * in Fortran, with the following modifications:
+ *
+ * (1) dense rows/columns are removed prior to ordering the matrix, and placed
+ * last in the output order. The presence of a dense row/column can
+ * increase the ordering time by up to O(n^2), unless they are removed
+ * prior to ordering.
+ *
+ * (2) the minimum degree ordering is followed by a postordering (depth-first
+ * search) of the assembly tree. Note that mass elimination (discussed
+ * below) combined with the approximate degree update can lead to the mass
+ * elimination of nodes with lower exact degree than the current pivot
+ * element. No additional fill-in is caused in the representation of the
+ * Schur complement. The mass-eliminated nodes merge with the current
+ * pivot element. They are ordered prior to the current pivot element.
+ * Because they can have lower exact degree than the current element, the
+ * merger of two or more of these nodes in the current pivot element can
+ * lead to a single element that is not a "fundamental supernode". The
+ * diagonal block can have zeros in it. Thus, the assembly tree used here
+ * is not guaranteed to be the precise supernodal elemination tree (with
+ * "funadmental" supernodes), and the postordering performed by this
+ * routine is not guaranteed to be a precise postordering of the
+ * elimination tree.
+ *
+ * (3) input parameters are added, to control aggressive absorption and the
+ * detection of "dense" rows/columns of A.
+ *
+ * (4) additional statistical information is returned, such as the number of
+ * nonzeros in L, and the flop counts for subsequent LDL' and LU
+ * factorizations. These are slight upper bounds, because of the mass
+ * elimination issue discussed above.
+ *
+ * (5) additional routines are added to interface this routine to MATLAB
+ * to provide a simple C-callable user-interface, to check inputs for
+ * errors, compute the symmetry of the pattern of A and the number of
+ * nonzeros in each row/column of A+A', to compute the pattern of A+A',
+ * to perform the assembly tree postordering, and to provide debugging
+ * ouput. Many of these functions are also provided by the Fortran
+ * Harwell Subroutine Library routine MC47A.
+ *
+ * (6) both int and UF_long versions are provided. In the descriptions below
+ * and integer is and int or UF_long depending on which version is
+ * being used.
+
+ **********************************************************************
+ ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+ **********************************************************************
+ ** If you want error checking, a more versatile input format, and a **
+ ** simpler user interface, use amd_order or amd_l_order instead. **
+ ** This routine is not meant to be user-callable. **
+ **********************************************************************
+
+ * ----------------------------------------------------------------------------
+ * References:
+ * ----------------------------------------------------------------------------
+ *
+ * [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern multifrontal
+ * method for sparse LU factorization", SIAM J. Matrix Analysis and
+ * Applications, vol. 18, no. 1, pp. 140-158. Discusses UMFPACK / MA38,
+ * which first introduced the approximate minimum degree used by this
+ * routine.
+ *
+ * [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An approximate
+ * minimum degree ordering algorithm," SIAM J. Matrix Analysis and
+ * Applications, vol. 17, no. 4, pp. 886-905, 1996. Discusses AMDBAR and
+ * MC47B, which are the Fortran versions of this routine.
+ *
+ * [3] Alan George and Joseph Liu, "The evolution of the minimum degree
+ * ordering algorithm," SIAM Review, vol. 31, no. 1, pp. 1-19, 1989.
+ * We list below the features mentioned in that paper that this code
+ * includes:
+ *
+ * mass elimination:
+ * Yes. MA27 relied on supervariable detection for mass elimination.
+ *
+ * indistinguishable nodes:
+ * Yes (we call these "supervariables"). This was also in the MA27
+ * code - although we modified the method of detecting them (the
+ * previous hash was the true degree, which we no longer keep track
+ * of). A supervariable is a set of rows with identical nonzero
+ * pattern. All variables in a supervariable are eliminated together.
+ * Each supervariable has as its numerical name that of one of its
+ * variables (its principal variable).
+ *
+ * quotient graph representation:
+ * Yes. We use the term "element" for the cliques formed during
+ * elimination. This was also in the MA27 code. The algorithm can
+ * operate in place, but it will work more efficiently if given some
+ * "elbow room."
+ *
+ * element absorption:
+ * Yes. This was also in the MA27 code.
+ *
+ * external degree:
+ * Yes. The MA27 code was based on the true degree.
+ *
+ * incomplete degree update and multiple elimination:
+ * No. This was not in MA27, either. Our method of degree update
+ * within MC47B is element-based, not variable-based. It is thus
+ * not well-suited for use with incomplete degree update or multiple
+ * elimination.
+ *
+ * Authors, and Copyright (C) 2004 by:
+ * Timothy A. Davis, Patrick Amestoy, Iain S. Duff, John K. Reid.
+ *
+ * Acknowledgements: This work (and the UMFPACK package) was supported by the
+ * National Science Foundation (ASC-9111263, DMS-9223088, and CCR-0203270).
+ * The UMFPACK/MA38 approximate degree update algorithm, the unsymmetric analog
+ * which forms the basis of AMD, was developed while Tim Davis was supported by
+ * CERFACS (Toulouse, France) in a post-doctoral position. This C version, and
+ * the etree postorder, were written while Tim Davis was on sabbatical at
+ * Stanford University and Lawrence Berkeley National Laboratory.
+
+ * ----------------------------------------------------------------------------
+ * INPUT ARGUMENTS (unaltered):
+ * ----------------------------------------------------------------------------
+
+ * n: The matrix order. Restriction: n >= 1.
+ *
+ * iwlen: The size of the Iw array. On input, the matrix is stored in
+ * Iw [0..pfree-1]. However, Iw [0..iwlen-1] should be slightly larger
+ * than what is required to hold the matrix, at least iwlen >= pfree + n.
+ * Otherwise, excessive compressions will take place. The recommended
+ * value of iwlen is 1.2 * pfree + n, which is the value used in the
+ * user-callable interface to this routine (amd_order.c). The algorithm
+ * will not run at all if iwlen < pfree. Restriction: iwlen >= pfree + n.
+ * Note that this is slightly more restrictive than the actual minimum
+ * (iwlen >= pfree), but AMD_2 will be very slow with no elbow room.
+ * Thus, this routine enforces a bare minimum elbow room of size n.
+ *
+ * pfree: On input the tail end of the array, Iw [pfree..iwlen-1], is empty,
+ * and the matrix is stored in Iw [0..pfree-1]. During execution,
+ * additional data is placed in Iw, and pfree is modified so that
+ * Iw [pfree..iwlen-1] is always the unused part of Iw.
+ *
+ * Control: A double array of size AMD_CONTROL containing input parameters
+ * that affect how the ordering is computed. If NULL, then default
+ * settings are used.
+ *
+ * Control [AMD_DENSE] is used to determine whether or not a given input
+ * row is "dense". A row is "dense" if the number of entries in the row
+ * exceeds Control [AMD_DENSE] times sqrt (n), except that rows with 16 or
+ * fewer entries are never considered "dense". To turn off the detection
+ * of dense rows, set Control [AMD_DENSE] to a negative number, or to a
+ * number larger than sqrt (n). The default value of Control [AMD_DENSE]
+ * is AMD_DEFAULT_DENSE, which is defined in amd.h as 10.
+ *
+ * Control [AMD_AGGRESSIVE] is used to determine whether or not aggressive
+ * absorption is to be performed. If nonzero, then aggressive absorption
+ * is performed (this is the default).
+
+ * ----------------------------------------------------------------------------
+ * INPUT/OUPUT ARGUMENTS:
+ * ----------------------------------------------------------------------------
+ *
+ * Pe: An integer array of size n. On input, Pe [i] is the index in Iw of
+ * the start of row i. Pe [i] is ignored if row i has no off-diagonal
+ * entries. Thus Pe [i] must be in the range 0 to pfree-1 for non-empty
+ * rows.
+ *
+ * During execution, it is used for both supervariables and elements:
+ *
+ * Principal supervariable i: index into Iw of the description of
+ * supervariable i. A supervariable represents one or more rows of
+ * the matrix with identical nonzero pattern. In this case,
+ * Pe [i] >= 0.
+ *
+ * Non-principal supervariable i: if i has been absorbed into another
+ * supervariable j, then Pe [i] = FLIP (j), where FLIP (j) is defined
+ * as (-(j)-2). Row j has the same pattern as row i. Note that j
+ * might later be absorbed into another supervariable j2, in which
+ * case Pe [i] is still FLIP (j), and Pe [j] = FLIP (j2) which is
+ * < EMPTY, where EMPTY is defined as (-1) in amd_internal.h.
+ *
+ * Unabsorbed element e: the index into Iw of the description of element
+ * e, if e has not yet been absorbed by a subsequent element. Element
+ * e is created when the supervariable of the same name is selected as
+ * the pivot. In this case, Pe [i] >= 0.
+ *
+ * Absorbed element e: if element e is absorbed into element e2, then
+ * Pe [e] = FLIP (e2). This occurs when the pattern of e (which we
+ * refer to as Le) is found to be a subset of the pattern of e2 (that
+ * is, Le2). In this case, Pe [i] < EMPTY. If element e is "null"
+ * (it has no nonzeros outside its pivot block), then Pe [e] = EMPTY,
+ * and e is the root of an assembly subtree (or the whole tree if
+ * there is just one such root).
+ *
+ * Dense variable i: if i is "dense", then Pe [i] = EMPTY.
+ *
+ * On output, Pe holds the assembly tree/forest, which implicitly
+ * represents a pivot order with identical fill-in as the actual order
+ * (via a depth-first search of the tree), as follows. If Nv [i] > 0,
+ * then i represents a node in the assembly tree, and the parent of i is
+ * Pe [i], or EMPTY if i is a root. If Nv [i] = 0, then (i, Pe [i])
+ * represents an edge in a subtree, the root of which is a node in the
+ * assembly tree. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Info: A double array of size AMD_INFO. If present, (that is, not NULL),
+ * then statistics about the ordering are returned in the Info array.
+ * See amd.h for a description.
+
+ * ----------------------------------------------------------------------------
+ * INPUT/MODIFIED (undefined on output):
+ * ----------------------------------------------------------------------------
+ *
+ * Len: An integer array of size n. On input, Len [i] holds the number of
+ * entries in row i of the matrix, excluding the diagonal. The contents
+ * of Len are undefined on output.
+ *
+ * Iw: An integer array of size iwlen. On input, Iw [0..pfree-1] holds the
+ * description of each row i in the matrix. The matrix must be symmetric,
+ * and both upper and lower triangular parts must be present. The
+ * diagonal must not be present. Row i is held as follows:
+ *
+ * Len [i]: the length of the row i data structure in the Iw array.
+ * Iw [Pe [i] ... Pe [i] + Len [i] - 1]:
+ * the list of column indices for nonzeros in row i (simple
+ * supervariables), excluding the diagonal. All supervariables
+ * start with one row/column each (supervariable i is just row i).
+ * If Len [i] is zero on input, then Pe [i] is ignored on input.
+ *
+ * Note that the rows need not be in any particular order, and there
+ * may be empty space between the rows.
+ *
+ * During execution, the supervariable i experiences fill-in. This is
+ * represented by placing in i a list of the elements that cause fill-in
+ * in supervariable i:
+ *
+ * Len [i]: the length of supervariable i in the Iw array.
+ * Iw [Pe [i] ... Pe [i] + Elen [i] - 1]:
+ * the list of elements that contain i. This list is kept short
+ * by removing absorbed elements.
+ * Iw [Pe [i] + Elen [i] ... Pe [i] + Len [i] - 1]:
+ * the list of supervariables in i. This list is kept short by
+ * removing nonprincipal variables, and any entry j that is also
+ * contained in at least one of the elements (j in Le) in the list
+ * for i (e in row i).
+ *
+ * When supervariable i is selected as pivot, we create an element e of
+ * the same name (e=i):
+ *
+ * Len [e]: the length of element e in the Iw array.
+ * Iw [Pe [e] ... Pe [e] + Len [e] - 1]:
+ * the list of supervariables in element e.
+ *
+ * An element represents the fill-in that occurs when supervariable i is
+ * selected as pivot (which represents the selection of row i and all
+ * non-principal variables whose principal variable is i). We use the
+ * term Le to denote the set of all supervariables in element e. Absorbed
+ * supervariables and elements are pruned from these lists when
+ * computationally convenient.
+ *
+ * CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+ * The contents of Iw are undefined on output.
+
+ * ----------------------------------------------------------------------------
+ * OUTPUT (need not be set on input):
+ * ----------------------------------------------------------------------------
+ *
+ * Nv: An integer array of size n. During execution, ABS (Nv [i]) is equal to
+ * the number of rows that are represented by the principal supervariable
+ * i. If i is a nonprincipal or dense variable, then Nv [i] = 0.
+ * Initially, Nv [i] = 1 for all i. Nv [i] < 0 signifies that i is a
+ * principal variable in the pattern Lme of the current pivot element me.
+ * After element me is constructed, Nv [i] is set back to a positive
+ * value.
+ *
+ * On output, Nv [i] holds the number of pivots represented by super
+ * row/column i of the original matrix, or Nv [i] = 0 for non-principal
+ * rows/columns. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Elen: An integer array of size n. See the description of Iw above. At the
+ * start of execution, Elen [i] is set to zero for all rows i. During
+ * execution, Elen [i] is the number of elements in the list for
+ * supervariable i. When e becomes an element, Elen [e] = FLIP (esize) is
+ * set, where esize is the size of the element (the number of pivots, plus
+ * the number of nonpivotal entries). Thus Elen [e] < EMPTY.
+ * Elen (i) = EMPTY set when variable i becomes nonprincipal.
+ *
+ * For variables, Elen (i) >= EMPTY holds until just before the
+ * postordering and permutation vectors are computed. For elements,
+ * Elen [e] < EMPTY holds.
+ *
+ * On output, Elen [i] is the degree of the row/column in the Cholesky
+ * factorization of the permuted matrix, corresponding to the original row
+ * i, if i is a super row/column. It is equal to EMPTY if i is
+ * non-principal. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Note that the contents of Elen on output differ from the Fortran
+ * version (Elen holds the inverse permutation in the Fortran version,
+ * which is instead returned in the Next array in this C version,
+ * described below).
+ *
+ * Last: In a degree list, Last [i] is the supervariable preceding i, or EMPTY
+ * if i is the head of the list. In a hash bucket, Last [i] is the hash
+ * key for i.
+ *
+ * Last [Head [hash]] is also used as the head of a hash bucket if
+ * Head [hash] contains a degree list (see the description of Head,
+ * below).
+ *
+ * On output, Last [0..n-1] holds the permutation. That is, if
+ * i = Last [k], then row i is the kth pivot row (where k ranges from 0 to
+ * n-1). Row Last [k] of A is the kth row in the permuted matrix, PAP'.
+ *
+ * Next: Next [i] is the supervariable following i in a link list, or EMPTY if
+ * i is the last in the list. Used for two kinds of lists: degree lists
+ * and hash buckets (a supervariable can be in only one kind of list at a
+ * time).
+ *
+ * On output Next [0..n-1] holds the inverse permutation. That is, if
+ * k = Next [i], then row i is the kth pivot row. Row i of A appears as
+ * the (Next[i])-th row in the permuted matrix, PAP'.
+ *
+ * Note that the contents of Next on output differ from the Fortran
+ * version (Next is undefined on output in the Fortran version).
+
+ * ----------------------------------------------------------------------------
+ * LOCAL WORKSPACE (not input or output - used only during execution):
+ * ----------------------------------------------------------------------------
+ *
+ * Degree: An integer array of size n. If i is a supervariable, then
+ * Degree [i] holds the current approximation of the external degree of
+ * row i (an upper bound). The external degree is the number of nonzeros
+ * in row i, minus ABS (Nv [i]), the diagonal part. The bound is equal to
+ * the exact external degree if Elen [i] is less than or equal to two.
+ *
+ * We also use the term "external degree" for elements e to refer to
+ * |Le \ Lme|. If e is an element, then Degree [e] is |Le|, which is the
+ * degree of the off-diagonal part of the element e (not including the
+ * diagonal part).
+ *
+ * Head: An integer array of size n. Head is used for degree lists.
+ * Head [deg] is the first supervariable in a degree list. All
+ * supervariables i in a degree list Head [deg] have the same approximate
+ * degree, namely, deg = Degree [i]. If the list Head [deg] is empty then
+ * Head [deg] = EMPTY.
+ *
+ * During supervariable detection Head [hash] also serves as a pointer to
+ * a hash bucket. If Head [hash] >= 0, there is a degree list of degree
+ * hash. The hash bucket head pointer is Last [Head [hash]]. If
+ * Head [hash] = EMPTY, then the degree list and hash bucket are both
+ * empty. If Head [hash] < EMPTY, then the degree list is empty, and
+ * FLIP (Head [hash]) is the head of the hash bucket. After supervariable
+ * detection is complete, all hash buckets are empty, and the
+ * (Last [Head [hash]] = EMPTY) condition is restored for the non-empty
+ * degree lists.
+ *
+ * W: An integer array of size n. The flag array W determines the status of
+ * elements and variables, and the external degree of elements.
+ *
+ * for elements:
+ * if W [e] = 0, then the element e is absorbed.
+ * if W [e] >= wflg, then W [e] - wflg is the size of the set
+ * |Le \ Lme|, in terms of nonzeros (the sum of ABS (Nv [i]) for
+ * each principal variable i that is both in the pattern of
+ * element e and NOT in the pattern of the current pivot element,
+ * me).
+ * if wflg > W [e] > 0, then e is not absorbed and has not yet been
+ * seen in the scan of the element lists in the computation of
+ * |Le\Lme| in Scan 1 below.
+ *
+ * for variables:
+ * during supervariable detection, if W [j] != wflg then j is
+ * not in the pattern of variable i.
+ *
+ * The W array is initialized by setting W [i] = 1 for all i, and by
+ * setting wflg = 2. It is reinitialized if wflg becomes too large (to
+ * ensure that wflg+n does not cause integer overflow).
+
+ * ----------------------------------------------------------------------------
+ * LOCAL INTEGERS:
+ * ----------------------------------------------------------------------------
+ */
+
+ Int deg, degme, dext, lemax, e, elenme, eln, i, ilast, inext, j,
+ jlast, jnext, k, knt1, knt2, knt3, lenj, ln, me, mindeg, nel, nleft,
+ nvi, nvj, nvpiv, slenme, wbig, we, wflg, wnvi, ok, ndense, ncmpa,
+ dense, aggressive ;
+
+ unsigned Int hash ; /* unsigned, so that hash % n is well defined.*/
+
+/*
+ * deg: the degree of a variable or element
+ * degme: size, |Lme|, of the current element, me (= Degree [me])
+ * dext: external degree, |Le \ Lme|, of some element e
+ * lemax: largest |Le| seen so far (called dmax in Fortran version)
+ * e: an element
+ * elenme: the length, Elen [me], of element list of pivotal variable
+ * eln: the length, Elen [...], of an element list
+ * hash: the computed value of the hash function
+ * i: a supervariable
+ * ilast: the entry in a link list preceding i
+ * inext: the entry in a link list following i
+ * j: a supervariable
+ * jlast: the entry in a link list preceding j
+ * jnext: the entry in a link list, or path, following j
+ * k: the pivot order of an element or variable
+ * knt1: loop counter used during element construction
+ * knt2: loop counter used during element construction
+ * knt3: loop counter used during compression
+ * lenj: Len [j]
+ * ln: length of a supervariable list
+ * me: current supervariable being eliminated, and the current
+ * element created by eliminating that supervariable
+ * mindeg: current minimum degree
+ * nel: number of pivots selected so far
+ * nleft: n - nel, the number of nonpivotal rows/columns remaining
+ * nvi: the number of variables in a supervariable i (= Nv [i])
+ * nvj: the number of variables in a supervariable j (= Nv [j])
+ * nvpiv: number of pivots in current element
+ * slenme: number of variables in variable list of pivotal variable
+ * wbig: = INT_MAX - n for the int version, UF_long_max - n for the
+ * UF_long version. wflg is not allowed to be >= wbig.
+ * we: W [e]
+ * wflg: used for flagging the W array. See description of Iw.
+ * wnvi: wflg - Nv [i]
+ * x: either a supervariable or an element
+ *
+ * ok: true if supervariable j can be absorbed into i
+ * ndense: number of "dense" rows/columns
+ * dense: rows/columns with initial degree > dense are considered "dense"
+ * aggressive: true if aggressive absorption is being performed
+ * ncmpa: number of garbage collections
+
+ * ----------------------------------------------------------------------------
+ * LOCAL DOUBLES, used for statistical output only (except for alpha):
+ * ----------------------------------------------------------------------------
+ */
+
+ double f, r, ndiv, s, nms_lu, nms_ldl, dmax, alpha, lnz, lnzme ;
+
+/*
+ * f: nvpiv
+ * r: degme + nvpiv
+ * ndiv: number of divisions for LU or LDL' factorizations
+ * s: number of multiply-subtract pairs for LU factorization, for the
+ * current element me
+ * nms_lu number of multiply-subtract pairs for LU factorization
+ * nms_ldl number of multiply-subtract pairs for LDL' factorization
+ * dmax: the largest number of entries in any column of L, including the
+ * diagonal
+ * alpha: "dense" degree ratio
+ * lnz: the number of nonzeros in L (excluding the diagonal)
+ * lnzme: the number of nonzeros in L (excl. the diagonal) for the
+ * current element me
+
+ * ----------------------------------------------------------------------------
+ * LOCAL "POINTERS" (indices into the Iw array)
+ * ----------------------------------------------------------------------------
+*/
+
+ Int p, p1, p2, p3, p4, pdst, pend, pj, pme, pme1, pme2, pn, psrc ;
+
+/*
+ * Any parameter (Pe [...] or pfree) or local variable starting with "p" (for
+ * Pointer) is an index into Iw, and all indices into Iw use variables starting
+ * with "p." The only exception to this rule is the iwlen input argument.
+ *
+ * p: pointer into lots of things
+ * p1: Pe [i] for some variable i (start of element list)
+ * p2: Pe [i] + Elen [i] - 1 for some variable i
+ * p3: index of first supervariable in clean list
+ * p4:
+ * pdst: destination pointer, for compression
+ * pend: end of memory to compress
+ * pj: pointer into an element or variable
+ * pme: pointer into the current element (pme1...pme2)
+ * pme1: the current element, me, is stored in Iw [pme1...pme2]
+ * pme2: the end of the current element
+ * pn: pointer into a "clean" variable, also used to compress
+ * psrc: source pointer, for compression
+*/
+
+/* ========================================================================= */
+/* INITIALIZATIONS */
+/* ========================================================================= */
+
+ /* Note that this restriction on iwlen is slightly more restrictive than
+ * what is actually required in AMD_2. AMD_2 can operate with no elbow
+ * room at all, but it will be slow. For better performance, at least
+ * size-n elbow room is enforced. */
+ ASSERT (iwlen >= pfree + n) ;
+ ASSERT (n > 0) ;
+
+ /* initialize output statistics */
+ lnz = 0 ;
+ ndiv = 0 ;
+ nms_lu = 0 ;
+ nms_ldl = 0 ;
+ dmax = 1 ;
+ me = EMPTY ;
+
+ mindeg = 0 ;
+ ncmpa = 0 ;
+ nel = 0 ;
+ lemax = 0 ;
+
+ /* get control parameters */
+ if (Control != (double *) NULL)
+ {
+ alpha = Control [AMD_DENSE] ;
+ aggressive = (Control [AMD_AGGRESSIVE] != 0) ;
+ }
+ else
+ {
+ alpha = AMD_DEFAULT_DENSE ;
+ aggressive = AMD_DEFAULT_AGGRESSIVE ;
+ }
+ /* Note: if alpha is NaN, this is undefined: */
+ if (alpha < 0)
+ {
+ /* only remove completely dense rows/columns */
+ dense = n-2 ;
+ }
+ else
+ {
+ dense = alpha * sqrt ((double) n) ;
+ }
+ dense = MAX (16, dense) ;
+ dense = MIN (n, dense) ;
+ AMD_DEBUG1 (("\n\nAMD (debug), alpha %g, aggr. "ID"\n",
+ alpha, aggressive)) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Last [i] = EMPTY ;
+ Head [i] = EMPTY ;
+ Next [i] = EMPTY ;
+ /* if separate Hhead array is used for hash buckets: *
+ Hhead [i] = EMPTY ;
+ */
+ Nv [i] = 1 ;
+ W [i] = 1 ;
+ Elen [i] = 0 ;
+ Degree [i] = Len [i] ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("\n======Nel "ID" initial\n", nel)) ;
+ AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last,
+ Head, Elen, Degree, W, -1) ;
+#endif
+
+ /* initialize wflg */
+ wbig = Int_MAX - n ;
+ wflg = clear_flag (0, wbig, W, n) ;
+
+ /* --------------------------------------------------------------------- */
+ /* initialize degree lists and eliminate dense and empty rows */
+ /* --------------------------------------------------------------------- */
+
+ ndense = 0 ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ deg = Degree [i] ;
+ ASSERT (deg >= 0 && deg < n) ;
+ if (deg == 0)
+ {
+
+ /* -------------------------------------------------------------
+ * we have a variable that can be eliminated at once because
+ * there is no off-diagonal non-zero in its row. Note that
+ * Nv [i] = 1 for an empty variable i. It is treated just
+ * the same as an eliminated element i.
+ * ------------------------------------------------------------- */
+
+ Elen [i] = FLIP (1) ;
+ nel++ ;
+ Pe [i] = EMPTY ;
+ W [i] = 0 ;
+
+ }
+ else if (deg > dense)
+ {
+
+ /* -------------------------------------------------------------
+ * Dense variables are not treated as elements, but as unordered,
+ * non-principal variables that have no parent. They do not take
+ * part in the postorder, since Nv [i] = 0. Note that the Fortran
+ * version does not have this option.
+ * ------------------------------------------------------------- */
+
+ AMD_DEBUG1 (("Dense node "ID" degree "ID"\n", i, deg)) ;
+ ndense++ ;
+ Nv [i] = 0 ; /* do not postorder this node */
+ Elen [i] = EMPTY ;
+ nel++ ;
+ Pe [i] = EMPTY ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------
+ * place i in the degree list corresponding to its degree
+ * ------------------------------------------------------------- */
+
+ inext = Head [deg] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = i ;
+ Next [i] = inext ;
+ Head [deg] = i ;
+
+ }
+ }
+
+/* ========================================================================= */
+/* WHILE (selecting pivots) DO */
+/* ========================================================================= */
+
+ while (nel < n)
+ {
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("\n======Nel "ID"\n", nel)) ;
+ if (AMD_debug >= 2)
+ {
+ AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next,
+ Last, Head, Elen, Degree, W, nel) ;
+ }
+#endif
+
+/* ========================================================================= */
+/* GET PIVOT OF MINIMUM DEGREE */
+/* ========================================================================= */
+
+ /* ----------------------------------------------------------------- */
+ /* find next supervariable for elimination */
+ /* ----------------------------------------------------------------- */
+
+ ASSERT (mindeg >= 0 && mindeg < n) ;
+ for (deg = mindeg ; deg < n ; deg++)
+ {
+ me = Head [deg] ;
+ if (me != EMPTY) break ;
+ }
+ mindeg = deg ;
+ ASSERT (me >= 0 && me < n) ;
+ AMD_DEBUG1 (("=================me: "ID"\n", me)) ;
+
+ /* ----------------------------------------------------------------- */
+ /* remove chosen variable from link list */
+ /* ----------------------------------------------------------------- */
+
+ inext = Next [me] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = EMPTY ;
+ Head [deg] = inext ;
+
+ /* ----------------------------------------------------------------- */
+ /* me represents the elimination of pivots nel to nel+Nv[me]-1. */
+ /* place me itself as the first in this set. */
+ /* ----------------------------------------------------------------- */
+
+ elenme = Elen [me] ;
+ nvpiv = Nv [me] ;
+ ASSERT (nvpiv > 0) ;
+ nel += nvpiv ;
+
+/* ========================================================================= */
+/* CONSTRUCT NEW ELEMENT */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * At this point, me is the pivotal supervariable. It will be
+ * converted into the current element. Scan list of the pivotal
+ * supervariable, me, setting tree pointers and constructing new list
+ * of supervariables for the new element, me. p is a pointer to the
+ * current position in the old list.
+ * ----------------------------------------------------------------- */
+
+ /* flag the variable "me" as being in Lme by negating Nv [me] */
+ Nv [me] = -nvpiv ;
+ degme = 0 ;
+ ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ;
+
+ if (elenme == 0)
+ {
+
+ /* ------------------------------------------------------------- */
+ /* construct the new element in place */
+ /* ------------------------------------------------------------- */
+
+ pme1 = Pe [me] ;
+ pme2 = pme1 - 1 ;
+
+ for (p = pme1 ; p <= pme1 + Len [me] - 1 ; p++)
+ {
+ i = Iw [p] ;
+ ASSERT (i >= 0 && i < n && Nv [i] >= 0) ;
+ nvi = Nv [i] ;
+ if (nvi > 0)
+ {
+
+ /* ----------------------------------------------------- */
+ /* i is a principal variable not yet placed in Lme. */
+ /* store i in new list */
+ /* ----------------------------------------------------- */
+
+ /* flag i as being in Lme by negating Nv [i] */
+ degme += nvi ;
+ Nv [i] = -nvi ;
+ Iw [++pme2] = i ;
+
+ /* ----------------------------------------------------- */
+ /* remove variable i from degree list. */
+ /* ----------------------------------------------------- */
+
+ ilast = Last [i] ;
+ inext = Next [i] ;
+ ASSERT (ilast >= EMPTY && ilast < n) ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = ilast ;
+ if (ilast != EMPTY)
+ {
+ Next [ilast] = inext ;
+ }
+ else
+ {
+ /* i is at the head of the degree list */
+ ASSERT (Degree [i] >= 0 && Degree [i] < n) ;
+ Head [Degree [i]] = inext ;
+ }
+ }
+ }
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------- */
+ /* construct the new element in empty space, Iw [pfree ...] */
+ /* ------------------------------------------------------------- */
+
+ p = Pe [me] ;
+ pme1 = pfree ;
+ slenme = Len [me] - elenme ;
+
+ for (knt1 = 1 ; knt1 <= elenme + 1 ; knt1++)
+ {
+
+ if (knt1 > elenme)
+ {
+ /* search the supervariables in me. */
+ e = me ;
+ pj = p ;
+ ln = slenme ;
+ AMD_DEBUG2 (("Search sv: "ID" "ID" "ID"\n", me,pj,ln)) ;
+ }
+ else
+ {
+ /* search the elements in me. */
+ e = Iw [p++] ;
+ ASSERT (e >= 0 && e < n) ;
+ pj = Pe [e] ;
+ ln = Len [e] ;
+ AMD_DEBUG2 (("Search element e "ID" in me "ID"\n", e,me)) ;
+ ASSERT (Elen [e] < EMPTY && W [e] > 0 && pj >= 0) ;
+ }
+ ASSERT (ln >= 0 && (ln == 0 || (pj >= 0 && pj < iwlen))) ;
+
+ /* ---------------------------------------------------------
+ * search for different supervariables and add them to the
+ * new list, compressing when necessary. this loop is
+ * executed once for each element in the list and once for
+ * all the supervariables in the list.
+ * --------------------------------------------------------- */
+
+ for (knt2 = 1 ; knt2 <= ln ; knt2++)
+ {
+ i = Iw [pj++] ;
+ ASSERT (i >= 0 && i < n && (i == me || Elen [i] >= EMPTY));
+ nvi = Nv [i] ;
+ AMD_DEBUG2 ((": "ID" "ID" "ID" "ID"\n",
+ i, Elen [i], Nv [i], wflg)) ;
+
+ if (nvi > 0)
+ {
+
+ /* ------------------------------------------------- */
+ /* compress Iw, if necessary */
+ /* ------------------------------------------------- */
+
+ if (pfree >= iwlen)
+ {
+
+ AMD_DEBUG1 (("GARBAGE COLLECTION\n")) ;
+
+ /* prepare for compressing Iw by adjusting pointers
+ * and lengths so that the lists being searched in
+ * the inner and outer loops contain only the
+ * remaining entries. */
+
+ Pe [me] = p ;
+ Len [me] -= knt1 ;
+ /* check if nothing left of supervariable me */
+ if (Len [me] == 0) Pe [me] = EMPTY ;
+ Pe [e] = pj ;
+ Len [e] = ln - knt2 ;
+ /* nothing left of element e */
+ if (Len [e] == 0) Pe [e] = EMPTY ;
+
+ ncmpa++ ; /* one more garbage collection */
+
+ /* store first entry of each object in Pe */
+ /* FLIP the first entry in each object */
+ for (j = 0 ; j < n ; j++)
+ {
+ pn = Pe [j] ;
+ if (pn >= 0)
+ {
+ ASSERT (pn >= 0 && pn < iwlen) ;
+ Pe [j] = Iw [pn] ;
+ Iw [pn] = FLIP (j) ;
+ }
+ }
+
+ /* psrc/pdst point to source/destination */
+ psrc = 0 ;
+ pdst = 0 ;
+ pend = pme1 - 1 ;
+
+ while (psrc <= pend)
+ {
+ /* search for next FLIP'd entry */
+ j = FLIP (Iw [psrc++]) ;
+ if (j >= 0)
+ {
+ AMD_DEBUG2 (("Got object j: "ID"\n", j)) ;
+ Iw [pdst] = Pe [j] ;
+ Pe [j] = pdst++ ;
+ lenj = Len [j] ;
+ /* copy from source to destination */
+ for (knt3 = 0 ; knt3 <= lenj - 2 ; knt3++)
+ {
+ Iw [pdst++] = Iw [psrc++] ;
+ }
+ }
+ }
+
+ /* move the new partially-constructed element */
+ p1 = pdst ;
+ for (psrc = pme1 ; psrc <= pfree-1 ; psrc++)
+ {
+ Iw [pdst++] = Iw [psrc] ;
+ }
+ pme1 = p1 ;
+ pfree = pdst ;
+ pj = Pe [e] ;
+ p = Pe [me] ;
+
+ }
+
+ /* ------------------------------------------------- */
+ /* i is a principal variable not yet placed in Lme */
+ /* store i in new list */
+ /* ------------------------------------------------- */
+
+ /* flag i as being in Lme by negating Nv [i] */
+ degme += nvi ;
+ Nv [i] = -nvi ;
+ Iw [pfree++] = i ;
+ AMD_DEBUG2 ((" s: "ID" nv "ID"\n", i, Nv [i]));
+
+ /* ------------------------------------------------- */
+ /* remove variable i from degree link list */
+ /* ------------------------------------------------- */
+
+ ilast = Last [i] ;
+ inext = Next [i] ;
+ ASSERT (ilast >= EMPTY && ilast < n) ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = ilast ;
+ if (ilast != EMPTY)
+ {
+ Next [ilast] = inext ;
+ }
+ else
+ {
+ /* i is at the head of the degree list */
+ ASSERT (Degree [i] >= 0 && Degree [i] < n) ;
+ Head [Degree [i]] = inext ;
+ }
+ }
+ }
+
+ if (e != me)
+ {
+ /* set tree pointer and flag to indicate element e is
+ * absorbed into new element me (the parent of e is me) */
+ AMD_DEBUG1 ((" Element "ID" => "ID"\n", e, me)) ;
+ Pe [e] = FLIP (me) ;
+ W [e] = 0 ;
+ }
+ }
+
+ pme2 = pfree - 1 ;
+ }
+
+ /* ----------------------------------------------------------------- */
+ /* me has now been converted into an element in Iw [pme1..pme2] */
+ /* ----------------------------------------------------------------- */
+
+ /* degme holds the external degree of new element */
+ Degree [me] = degme ;
+ Pe [me] = pme1 ;
+ Len [me] = pme2 - pme1 + 1 ;
+ ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ;
+
+ Elen [me] = FLIP (nvpiv + degme) ;
+ /* FLIP (Elen (me)) is now the degree of pivot (including
+ * diagonal part). */
+
+#ifndef NDEBUG
+ AMD_DEBUG2 (("New element structure: length= "ID"\n", pme2-pme1+1)) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++) AMD_DEBUG3 ((" "ID"", Iw[pme]));
+ AMD_DEBUG3 (("\n")) ;
+#endif
+
+ /* ----------------------------------------------------------------- */
+ /* make sure that wflg is not too large. */
+ /* ----------------------------------------------------------------- */
+
+ /* With the current value of wflg, wflg+n must not cause integer
+ * overflow */
+
+ wflg = clear_flag (wflg, wbig, W, n) ;
+
+/* ========================================================================= */
+/* COMPUTE (W [e] - wflg) = |Le\Lme| FOR ALL ELEMENTS */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * Scan 1: compute the external degrees of previous elements with
+ * respect to the current element. That is:
+ * (W [e] - wflg) = |Le \ Lme|
+ * for each element e that appears in any supervariable in Lme. The
+ * notation Le refers to the pattern (list of supervariables) of a
+ * previous element e, where e is not yet absorbed, stored in
+ * Iw [Pe [e] + 1 ... Pe [e] + Len [e]]. The notation Lme
+ * refers to the pattern of the current element (stored in
+ * Iw [pme1..pme2]). If aggressive absorption is enabled, and
+ * (W [e] - wflg) becomes zero, then the element e will be absorbed
+ * in Scan 2.
+ * ----------------------------------------------------------------- */
+
+ AMD_DEBUG2 (("me: ")) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ eln = Elen [i] ;
+ AMD_DEBUG3 ((""ID" Elen "ID": \n", i, eln)) ;
+ if (eln > 0)
+ {
+ /* note that Nv [i] has been negated to denote i in Lme: */
+ nvi = -Nv [i] ;
+ ASSERT (nvi > 0 && Pe [i] >= 0 && Pe [i] < iwlen) ;
+ wnvi = wflg - nvi ;
+ for (p = Pe [i] ; p <= Pe [i] + eln - 1 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ AMD_DEBUG4 ((" e "ID" we "ID" ", e, we)) ;
+ if (we >= wflg)
+ {
+ /* unabsorbed element e has been seen in this loop */
+ AMD_DEBUG4 ((" unabsorbed, first time seen")) ;
+ we -= nvi ;
+ }
+ else if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ /* this is the first we have seen e in all of Scan 1 */
+ AMD_DEBUG4 ((" unabsorbed")) ;
+ we = Degree [e] + wnvi ;
+ }
+ AMD_DEBUG4 (("\n")) ;
+ W [e] = we ;
+ }
+ }
+ }
+ AMD_DEBUG2 (("\n")) ;
+
+/* ========================================================================= */
+/* DEGREE UPDATE AND ELEMENT ABSORPTION */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * Scan 2: for each i in Lme, sum up the degree of Lme (which is
+ * degme), plus the sum of the external degrees of each Le for the
+ * elements e appearing within i, plus the supervariables in i.
+ * Place i in hash list.
+ * ----------------------------------------------------------------- */
+
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n && Nv [i] < 0 && Elen [i] >= 0) ;
+ AMD_DEBUG2 (("Updating: i "ID" "ID" "ID"\n", i, Elen[i], Len [i]));
+ p1 = Pe [i] ;
+ p2 = p1 + Elen [i] - 1 ;
+ pn = p1 ;
+ hash = 0 ;
+ deg = 0 ;
+ ASSERT (p1 >= 0 && p1 < iwlen && p2 >= -1 && p2 < iwlen) ;
+
+ /* ------------------------------------------------------------- */
+ /* scan the element list associated with supervariable i */
+ /* ------------------------------------------------------------- */
+
+ /* UMFPACK/MA38-style approximate degree: */
+ if (aggressive)
+ {
+ for (p = p1 ; p <= p2 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ /* dext = | Le \ Lme | */
+ dext = we - wflg ;
+ if (dext > 0)
+ {
+ deg += dext ;
+ Iw [pn++] = e ;
+ hash += e ;
+ AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ;
+ }
+ else
+ {
+ /* external degree of e is zero, absorb e into me*/
+ AMD_DEBUG1 ((" Element "ID" =>"ID" (aggressive)\n",
+ e, me)) ;
+ ASSERT (dext == 0) ;
+ Pe [e] = FLIP (me) ;
+ W [e] = 0 ;
+ }
+ }
+ }
+ }
+ else
+ {
+ for (p = p1 ; p <= p2 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ dext = we - wflg ;
+ ASSERT (dext >= 0) ;
+ deg += dext ;
+ Iw [pn++] = e ;
+ hash += e ;
+ AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ;
+ }
+ }
+ }
+
+ /* count the number of elements in i (including me): */
+ Elen [i] = pn - p1 + 1 ;
+
+ /* ------------------------------------------------------------- */
+ /* scan the supervariables in the list associated with i */
+ /* ------------------------------------------------------------- */
+
+ /* The bulk of the AMD run time is typically spent in this loop,
+ * particularly if the matrix has many dense rows that are not
+ * removed prior to ordering. */
+ p3 = pn ;
+ p4 = p1 + Len [i] ;
+ for (p = p2 + 1 ; p < p4 ; p++)
+ {
+ j = Iw [p] ;
+ ASSERT (j >= 0 && j < n) ;
+ nvj = Nv [j] ;
+ if (nvj > 0)
+ {
+ /* j is unabsorbed, and not in Lme. */
+ /* add to degree and add to new list */
+ deg += nvj ;
+ Iw [pn++] = j ;
+ hash += j ;
+ AMD_DEBUG4 ((" s: "ID" hash "ID" Nv[j]= "ID"\n",
+ j, hash, nvj)) ;
+ }
+ }
+
+ /* ------------------------------------------------------------- */
+ /* update the degree and check for mass elimination */
+ /* ------------------------------------------------------------- */
+
+ /* with aggressive absorption, deg==0 is identical to the
+ * Elen [i] == 1 && p3 == pn test, below. */
+ ASSERT (IMPLIES (aggressive, (deg==0) == (Elen[i]==1 && p3==pn))) ;
+
+ if (Elen [i] == 1 && p3 == pn)
+ {
+
+ /* --------------------------------------------------------- */
+ /* mass elimination */
+ /* --------------------------------------------------------- */
+
+ /* There is nothing left of this node except for an edge to
+ * the current pivot element. Elen [i] is 1, and there are
+ * no variables adjacent to node i. Absorb i into the
+ * current pivot element, me. Note that if there are two or
+ * more mass eliminations, fillin due to mass elimination is
+ * possible within the nvpiv-by-nvpiv pivot block. It is this
+ * step that causes AMD's analysis to be an upper bound.
+ *
+ * The reason is that the selected pivot has a lower
+ * approximate degree than the true degree of the two mass
+ * eliminated nodes. There is no edge between the two mass
+ * eliminated nodes. They are merged with the current pivot
+ * anyway.
+ *
+ * No fillin occurs in the Schur complement, in any case,
+ * and this effect does not decrease the quality of the
+ * ordering itself, just the quality of the nonzero and
+ * flop count analysis. It also means that the post-ordering
+ * is not an exact elimination tree post-ordering. */
+
+ AMD_DEBUG1 ((" MASS i "ID" => parent e "ID"\n", i, me)) ;
+ Pe [i] = FLIP (me) ;
+ nvi = -Nv [i] ;
+ degme -= nvi ;
+ nvpiv += nvi ;
+ nel += nvi ;
+ Nv [i] = 0 ;
+ Elen [i] = EMPTY ;
+
+ }
+ else
+ {
+
+ /* --------------------------------------------------------- */
+ /* update the upper-bound degree of i */
+ /* --------------------------------------------------------- */
+
+ /* the following degree does not yet include the size
+ * of the current element, which is added later: */
+
+ Degree [i] = MIN (Degree [i], deg) ;
+
+ /* --------------------------------------------------------- */
+ /* add me to the list for i */
+ /* --------------------------------------------------------- */
+
+ /* move first supervariable to end of list */
+ Iw [pn] = Iw [p3] ;
+ /* move first element to end of element part of list */
+ Iw [p3] = Iw [p1] ;
+ /* add new element, me, to front of list. */
+ Iw [p1] = me ;
+ /* store the new length of the list in Len [i] */
+ Len [i] = pn - p1 + 1 ;
+
+ /* --------------------------------------------------------- */
+ /* place in hash bucket. Save hash key of i in Last [i]. */
+ /* --------------------------------------------------------- */
+
+ /* NOTE: this can fail if hash is negative, because the ANSI C
+ * standard does not define a % b when a and/or b are negative.
+ * That's why hash is defined as an unsigned Int, to avoid this
+ * problem. */
+ hash = hash % n ;
+ ASSERT (((Int) hash) >= 0 && ((Int) hash) < n) ;
+
+ /* if the Hhead array is not used: */
+ j = Head [hash] ;
+ if (j <= EMPTY)
+ {
+ /* degree list is empty, hash head is FLIP (j) */
+ Next [i] = FLIP (j) ;
+ Head [hash] = FLIP (i) ;
+ }
+ else
+ {
+ /* degree list is not empty, use Last [Head [hash]] as
+ * hash head. */
+ Next [i] = Last [j] ;
+ Last [j] = i ;
+ }
+
+ /* if a separate Hhead array is used: *
+ Next [i] = Hhead [hash] ;
+ Hhead [hash] = i ;
+ */
+
+ Last [i] = hash ;
+ }
+ }
+
+ Degree [me] = degme ;
+
+ /* ----------------------------------------------------------------- */
+ /* Clear the counter array, W [...], by incrementing wflg. */
+ /* ----------------------------------------------------------------- */
+
+ /* make sure that wflg+n does not cause integer overflow */
+ lemax = MAX (lemax, degme) ;
+ wflg += lemax ;
+ wflg = clear_flag (wflg, wbig, W, n) ;
+ /* at this point, W [0..n-1] < wflg holds */
+
+/* ========================================================================= */
+/* SUPERVARIABLE DETECTION */
+/* ========================================================================= */
+
+ AMD_DEBUG1 (("Detecting supervariables:\n")) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ AMD_DEBUG2 (("Consider i "ID" nv "ID"\n", i, Nv [i])) ;
+ if (Nv [i] < 0)
+ {
+ /* i is a principal variable in Lme */
+
+ /* ---------------------------------------------------------
+ * examine all hash buckets with 2 or more variables. We do
+ * this by examing all unique hash keys for supervariables in
+ * the pattern Lme of the current element, me
+ * --------------------------------------------------------- */
+
+ /* let i = head of hash bucket, and empty the hash bucket */
+ ASSERT (Last [i] >= 0 && Last [i] < n) ;
+ hash = Last [i] ;
+
+ /* if Hhead array is not used: */
+ j = Head [hash] ;
+ if (j == EMPTY)
+ {
+ /* hash bucket and degree list are both empty */
+ i = EMPTY ;
+ }
+ else if (j < EMPTY)
+ {
+ /* degree list is empty */
+ i = FLIP (j) ;
+ Head [hash] = EMPTY ;
+ }
+ else
+ {
+ /* degree list is not empty, restore Last [j] of head j */
+ i = Last [j] ;
+ Last [j] = EMPTY ;
+ }
+
+ /* if separate Hhead array is used: *
+ i = Hhead [hash] ;
+ Hhead [hash] = EMPTY ;
+ */
+
+ ASSERT (i >= EMPTY && i < n) ;
+ AMD_DEBUG2 (("----i "ID" hash "ID"\n", i, hash)) ;
+
+ while (i != EMPTY && Next [i] != EMPTY)
+ {
+
+ /* -----------------------------------------------------
+ * this bucket has one or more variables following i.
+ * scan all of them to see if i can absorb any entries
+ * that follow i in hash bucket. Scatter i into w.
+ * ----------------------------------------------------- */
+
+ ln = Len [i] ;
+ eln = Elen [i] ;
+ ASSERT (ln >= 0 && eln >= 0) ;
+ ASSERT (Pe [i] >= 0 && Pe [i] < iwlen) ;
+ /* do not flag the first element in the list (me) */
+ for (p = Pe [i] + 1 ; p <= Pe [i] + ln - 1 ; p++)
+ {
+ ASSERT (Iw [p] >= 0 && Iw [p] < n) ;
+ W [Iw [p]] = wflg ;
+ }
+
+ /* ----------------------------------------------------- */
+ /* scan every other entry j following i in bucket */
+ /* ----------------------------------------------------- */
+
+ jlast = i ;
+ j = Next [i] ;
+ ASSERT (j >= EMPTY && j < n) ;
+
+ while (j != EMPTY)
+ {
+ /* ------------------------------------------------- */
+ /* check if j and i have identical nonzero pattern */
+ /* ------------------------------------------------- */
+
+ AMD_DEBUG3 (("compare i "ID" and j "ID"\n", i,j)) ;
+
+ /* check if i and j have the same Len and Elen */
+ ASSERT (Len [j] >= 0 && Elen [j] >= 0) ;
+ ASSERT (Pe [j] >= 0 && Pe [j] < iwlen) ;
+ ok = (Len [j] == ln) && (Elen [j] == eln) ;
+ /* skip the first element in the list (me) */
+ for (p = Pe [j] + 1 ; ok && p <= Pe [j] + ln - 1 ; p++)
+ {
+ ASSERT (Iw [p] >= 0 && Iw [p] < n) ;
+ if (W [Iw [p]] != wflg) ok = 0 ;
+ }
+ if (ok)
+ {
+ /* --------------------------------------------- */
+ /* found it! j can be absorbed into i */
+ /* --------------------------------------------- */
+
+ AMD_DEBUG1 (("found it! j "ID" => i "ID"\n", j,i));
+ Pe [j] = FLIP (i) ;
+ /* both Nv [i] and Nv [j] are negated since they */
+ /* are in Lme, and the absolute values of each */
+ /* are the number of variables in i and j: */
+ Nv [i] += Nv [j] ;
+ Nv [j] = 0 ;
+ Elen [j] = EMPTY ;
+ /* delete j from hash bucket */
+ ASSERT (j != Next [j]) ;
+ j = Next [j] ;
+ Next [jlast] = j ;
+
+ }
+ else
+ {
+ /* j cannot be absorbed into i */
+ jlast = j ;
+ ASSERT (j != Next [j]) ;
+ j = Next [j] ;
+ }
+ ASSERT (j >= EMPTY && j < n) ;
+ }
+
+ /* -----------------------------------------------------
+ * no more variables can be absorbed into i
+ * go to next i in bucket and clear flag array
+ * ----------------------------------------------------- */
+
+ wflg++ ;
+ i = Next [i] ;
+ ASSERT (i >= EMPTY && i < n) ;
+
+ }
+ }
+ }
+ AMD_DEBUG2 (("detect done\n")) ;
+
+/* ========================================================================= */
+/* RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVARIABLES FROM ELEMENT */
+/* ========================================================================= */
+
+ p = pme1 ;
+ nleft = n - nel ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ nvi = -Nv [i] ;
+ AMD_DEBUG3 (("Restore i "ID" "ID"\n", i, nvi)) ;
+ if (nvi > 0)
+ {
+ /* i is a principal variable in Lme */
+ /* restore Nv [i] to signify that i is principal */
+ Nv [i] = nvi ;
+
+ /* --------------------------------------------------------- */
+ /* compute the external degree (add size of current element) */
+ /* --------------------------------------------------------- */
+
+ deg = Degree [i] + degme - nvi ;
+ deg = MIN (deg, nleft - nvi) ;
+ ASSERT (IMPLIES (aggressive, deg > 0) && deg >= 0 && deg < n) ;
+
+ /* --------------------------------------------------------- */
+ /* place the supervariable at the head of the degree list */
+ /* --------------------------------------------------------- */
+
+ inext = Head [deg] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = i ;
+ Next [i] = inext ;
+ Last [i] = EMPTY ;
+ Head [deg] = i ;
+
+ /* --------------------------------------------------------- */
+ /* save the new degree, and find the minimum degree */
+ /* --------------------------------------------------------- */
+
+ mindeg = MIN (mindeg, deg) ;
+ Degree [i] = deg ;
+
+ /* --------------------------------------------------------- */
+ /* place the supervariable in the element pattern */
+ /* --------------------------------------------------------- */
+
+ Iw [p++] = i ;
+
+ }
+ }
+ AMD_DEBUG2 (("restore done\n")) ;
+
+/* ========================================================================= */
+/* FINALIZE THE NEW ELEMENT */
+/* ========================================================================= */
+
+ AMD_DEBUG2 (("ME = "ID" DONE\n", me)) ;
+ Nv [me] = nvpiv ;
+ /* save the length of the list for the new element me */
+ Len [me] = p - pme1 ;
+ if (Len [me] == 0)
+ {
+ /* there is nothing left of the current pivot element */
+ /* it is a root of the assembly tree */
+ Pe [me] = EMPTY ;
+ W [me] = 0 ;
+ }
+ if (elenme != 0)
+ {
+ /* element was not constructed in place: deallocate part of */
+ /* it since newly nonprincipal variables may have been removed */
+ pfree = p ;
+ }
+
+ /* The new element has nvpiv pivots and the size of the contribution
+ * block for a multifrontal method is degme-by-degme, not including
+ * the "dense" rows/columns. If the "dense" rows/columns are included,
+ * the frontal matrix is no larger than
+ * (degme+ndense)-by-(degme+ndense).
+ */
+
+ if (Info != (double *) NULL)
+ {
+ f = nvpiv ;
+ r = degme + ndense ;
+ dmax = MAX (dmax, f + r) ;
+
+ /* number of nonzeros in L (excluding the diagonal) */
+ lnzme = f*r + (f-1)*f/2 ;
+ lnz += lnzme ;
+
+ /* number of divide operations for LDL' and for LU */
+ ndiv += lnzme ;
+
+ /* number of multiply-subtract pairs for LU */
+ s = f*r*r + r*(f-1)*f + (f-1)*f*(2*f-1)/6 ;
+ nms_lu += s ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ nms_ldl += (s + lnzme)/2 ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG2 (("finalize done nel "ID" n "ID"\n ::::\n", nel, n)) ;
+ for (pme = Pe [me] ; pme <= Pe [me] + Len [me] - 1 ; pme++)
+ {
+ AMD_DEBUG3 ((" "ID"", Iw [pme])) ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+#endif
+
+ }
+
+/* ========================================================================= */
+/* DONE SELECTING PIVOTS */
+/* ========================================================================= */
+
+ if (Info != (double *) NULL)
+ {
+
+ /* count the work to factorize the ndense-by-ndense submatrix */
+ f = ndense ;
+ dmax = MAX (dmax, (double) ndense) ;
+
+ /* number of nonzeros in L (excluding the diagonal) */
+ lnzme = (f-1)*f/2 ;
+ lnz += lnzme ;
+
+ /* number of divide operations for LDL' and for LU */
+ ndiv += lnzme ;
+
+ /* number of multiply-subtract pairs for LU */
+ s = (f-1)*f*(2*f-1)/6 ;
+ nms_lu += s ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ nms_ldl += (s + lnzme)/2 ;
+
+ /* number of nz's in L (excl. diagonal) */
+ Info [AMD_LNZ] = lnz ;
+
+ /* number of divide ops for LU and LDL' */
+ Info [AMD_NDIV] = ndiv ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ Info [AMD_NMULTSUBS_LDL] = nms_ldl ;
+
+ /* number of multiply-subtract pairs for LU */
+ Info [AMD_NMULTSUBS_LU] = nms_lu ;
+
+ /* number of "dense" rows/columns */
+ Info [AMD_NDENSE] = ndense ;
+
+ /* largest front is dmax-by-dmax */
+ Info [AMD_DMAX] = dmax ;
+
+ /* number of garbage collections in AMD */
+ Info [AMD_NCMPA] = ncmpa ;
+
+ /* successful ordering */
+ Info [AMD_STATUS] = AMD_OK ;
+ }
+
+/* ========================================================================= */
+/* POST-ORDERING */
+/* ========================================================================= */
+
+/* -------------------------------------------------------------------------
+ * Variables at this point:
+ *
+ * Pe: holds the elimination tree. The parent of j is FLIP (Pe [j]),
+ * or EMPTY if j is a root. The tree holds both elements and
+ * non-principal (unordered) variables absorbed into them.
+ * Dense variables are non-principal and unordered.
+ *
+ * Elen: holds the size of each element, including the diagonal part.
+ * FLIP (Elen [e]) > 0 if e is an element. For unordered
+ * variables i, Elen [i] is EMPTY.
+ *
+ * Nv: Nv [e] > 0 is the number of pivots represented by the element e.
+ * For unordered variables i, Nv [i] is zero.
+ *
+ * Contents no longer needed:
+ * W, Iw, Len, Degree, Head, Next, Last.
+ *
+ * The matrix itself has been destroyed.
+ *
+ * n: the size of the matrix.
+ * No other scalars needed (pfree, iwlen, etc.)
+ * ------------------------------------------------------------------------- */
+
+ /* restore Pe */
+ for (i = 0 ; i < n ; i++)
+ {
+ Pe [i] = FLIP (Pe [i]) ;
+ }
+
+ /* restore Elen, for output information, and for postordering */
+ for (i = 0 ; i < n ; i++)
+ {
+ Elen [i] = FLIP (Elen [i]) ;
+ }
+
+/* Now the parent of j is Pe [j], or EMPTY if j is a root. Elen [e] > 0
+ * is the size of element e. Elen [i] is EMPTY for unordered variable i. */
+
+#ifndef NDEBUG
+ AMD_DEBUG2 (("\nTree:\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ AMD_DEBUG2 ((" "ID" parent: "ID" ", i, Pe [i])) ;
+ ASSERT (Pe [i] >= EMPTY && Pe [i] < n) ;
+ if (Nv [i] > 0)
+ {
+ /* this is an element */
+ e = i ;
+ AMD_DEBUG2 ((" element, size is "ID"\n", Elen [i])) ;
+ ASSERT (Elen [e] > 0) ;
+ }
+ AMD_DEBUG2 (("\n")) ;
+ }
+ AMD_DEBUG2 (("\nelements:\n")) ;
+ for (e = 0 ; e < n ; e++)
+ {
+ if (Nv [e] > 0)
+ {
+ AMD_DEBUG3 (("Element e= "ID" size "ID" nv "ID" \n", e,
+ Elen [e], Nv [e])) ;
+ }
+ }
+ AMD_DEBUG2 (("\nvariables:\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Int cnt ;
+ if (Nv [i] == 0)
+ {
+ AMD_DEBUG3 (("i unordered: "ID"\n", i)) ;
+ j = Pe [i] ;
+ cnt = 0 ;
+ AMD_DEBUG3 ((" j: "ID"\n", j)) ;
+ if (j == EMPTY)
+ {
+ AMD_DEBUG3 ((" i is a dense variable\n")) ;
+ }
+ else
+ {
+ ASSERT (j >= 0 && j < n) ;
+ while (Nv [j] == 0)
+ {
+ AMD_DEBUG3 ((" j : "ID"\n", j)) ;
+ j = Pe [j] ;
+ AMD_DEBUG3 ((" j:: "ID"\n", j)) ;
+ cnt++ ;
+ if (cnt > n) break ;
+ }
+ e = j ;
+ AMD_DEBUG3 ((" got to e: "ID"\n", e)) ;
+ }
+ }
+ }
+#endif
+
+/* ========================================================================= */
+/* compress the paths of the variables */
+/* ========================================================================= */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ if (Nv [i] == 0)
+ {
+
+ /* -------------------------------------------------------------
+ * i is an un-ordered row. Traverse the tree from i until
+ * reaching an element, e. The element, e, was the principal
+ * supervariable of i and all nodes in the path from i to when e
+ * was selected as pivot.
+ * ------------------------------------------------------------- */
+
+ AMD_DEBUG1 (("Path compression, i unordered: "ID"\n", i)) ;
+ j = Pe [i] ;
+ ASSERT (j >= EMPTY && j < n) ;
+ AMD_DEBUG3 ((" j: "ID"\n", j)) ;
+ if (j == EMPTY)
+ {
+ /* Skip a dense variable. It has no parent. */
+ AMD_DEBUG3 ((" i is a dense variable\n")) ;
+ continue ;
+ }
+
+ /* while (j is a variable) */
+ while (Nv [j] == 0)
+ {
+ AMD_DEBUG3 ((" j : "ID"\n", j)) ;
+ j = Pe [j] ;
+ AMD_DEBUG3 ((" j:: "ID"\n", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ }
+ /* got to an element e */
+ e = j ;
+ AMD_DEBUG3 (("got to e: "ID"\n", e)) ;
+
+ /* -------------------------------------------------------------
+ * traverse the path again from i to e, and compress the path
+ * (all nodes point to e). Path compression allows this code to
+ * compute in O(n) time.
+ * ------------------------------------------------------------- */
+
+ j = i ;
+ /* while (j is a variable) */
+ while (Nv [j] == 0)
+ {
+ jnext = Pe [j] ;
+ AMD_DEBUG3 (("j "ID" jnext "ID"\n", j, jnext)) ;
+ Pe [j] = e ;
+ j = jnext ;
+ ASSERT (j >= 0 && j < n) ;
+ }
+ }
+ }
+
+/* ========================================================================= */
+/* postorder the assembly tree */
+/* ========================================================================= */
+
+ AMD_postorder (n, Pe, Nv, Elen,
+ W, /* output order */
+ Head, Next, Last) ; /* workspace */
+
+/* ========================================================================= */
+/* compute output permutation and inverse permutation */
+/* ========================================================================= */
+
+ /* W [e] = k means that element e is the kth element in the new
+ * order. e is in the range 0 to n-1, and k is in the range 0 to
+ * the number of elements. Use Head for inverse order. */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Head [k] = EMPTY ;
+ Next [k] = EMPTY ;
+ }
+ for (e = 0 ; e < n ; e++)
+ {
+ k = W [e] ;
+ ASSERT ((k == EMPTY) == (Nv [e] == 0)) ;
+ if (k != EMPTY)
+ {
+ ASSERT (k >= 0 && k < n) ;
+ Head [k] = e ;
+ }
+ }
+
+ /* construct output inverse permutation in Next,
+ * and permutation in Last */
+ nel = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ e = Head [k] ;
+ if (e == EMPTY) break ;
+ ASSERT (e >= 0 && e < n && Nv [e] > 0) ;
+ Next [e] = nel ;
+ nel += Nv [e] ;
+ }
+ ASSERT (nel == n - ndense) ;
+
+ /* order non-principal variables (dense, & those merged into supervar's) */
+ for (i = 0 ; i < n ; i++)
+ {
+ if (Nv [i] == 0)
+ {
+ e = Pe [i] ;
+ ASSERT (e >= EMPTY && e < n) ;
+ if (e != EMPTY)
+ {
+ /* This is an unordered variable that was merged
+ * into element e via supernode detection or mass
+ * elimination of i when e became the pivot element.
+ * Place i in order just before e. */
+ ASSERT (Next [i] == EMPTY && Nv [e] > 0) ;
+ Next [i] = Next [e] ;
+ Next [e]++ ;
+ }
+ else
+ {
+ /* This is a dense unordered variable, with no parent.
+ * Place it last in the output order. */
+ Next [i] = nel++ ;
+ }
+ }
+ }
+ ASSERT (nel == n) ;
+
+ AMD_DEBUG2 (("\n\nPerm:\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ k = Next [i] ;
+ ASSERT (k >= 0 && k < n) ;
+ Last [k] = i ;
+ AMD_DEBUG2 ((" perm ["ID"] = "ID"\n", k, i)) ;
+ }
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_aat.c b/src/C/SuiteSparse/AMD/Source/amd_aat.c
new file mode 100644
index 0000000..5c92931
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_aat.c
@@ -0,0 +1,185 @@
+/* ========================================================================= */
+/* === AMD_aat ============================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD_aat: compute the symmetry of the pattern of A, and count the number of
+ * nonzeros each column of A+A' (excluding the diagonal). Assumes the input
+ * matrix has no errors, with sorted columns and no duplicates
+ * (AMD_valid (n, n, Ap, Ai) must be AMD_OK, but this condition is not
+ * checked).
+ */
+
+#include "amd_internal.h"
+
+GLOBAL size_t AMD_aat /* returns nz in A+A' */
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/
+ Int Tp [ ], /* workspace of size n */
+ double Info [ ]
+)
+{
+ Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ;
+ double sym ;
+ size_t nzaat ;
+
+#ifndef NDEBUG
+ AMD_debug_init ("AMD AAT") ;
+ for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ;
+ ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
+#endif
+
+ if (Info != (double *) NULL)
+ {
+ /* clear the Info array, if it exists */
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ Info [AMD_STATUS] = AMD_OK ;
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Len [k] = 0 ;
+ }
+
+ nzdiag = 0 ;
+ nzboth = 0 ;
+ nz = Ap [n] ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+ AMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ;
+
+ /* construct A+A' */
+ for (p = p1 ; p < p2 ; )
+ {
+ /* scan the upper triangular part of A */
+ j = Ai [p] ;
+ if (j < k)
+ {
+ /* entry A (j,k) is in the strictly upper triangular part,
+ * add both A (j,k) and A (k,j) to the matrix A+A' */
+ Len [j]++ ;
+ Len [k]++ ;
+ AMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j));
+ p++ ;
+ }
+ else if (j == k)
+ {
+ /* skip the diagonal */
+ p++ ;
+ nzdiag++ ;
+ break ;
+ }
+ else /* j > k */
+ {
+ /* first entry below the diagonal */
+ break ;
+ }
+ /* scan lower triangular part of A, in column j until reaching
+ * row k. Start where last scan left off. */
+ ASSERT (Tp [j] != EMPTY) ;
+ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
+ pj2 = Ap [j+1] ;
+ for (pj = Tp [j] ; pj < pj2 ; )
+ {
+ i = Ai [pj] ;
+ if (i < k)
+ {
+ /* A (i,j) is only in the lower part, not in upper.
+ * add both A (i,j) and A (j,i) to the matrix A+A' */
+ Len [i]++ ;
+ Len [j]++ ;
+ AMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n",
+ i,j, j,i)) ;
+ pj++ ;
+ }
+ else if (i == k)
+ {
+ /* entry A (k,j) in lower part and A (j,k) in upper */
+ pj++ ;
+ nzboth++ ;
+ break ;
+ }
+ else /* i > k */
+ {
+ /* consider this entry later, when k advances to i */
+ break ;
+ }
+ }
+ Tp [j] = pj ;
+ }
+ /* Tp [k] points to the entry just below the diagonal in column k */
+ Tp [k] = p ;
+ }
+
+ /* clean up, for remaining mismatched entries */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
+ {
+ i = Ai [pj] ;
+ /* A (i,j) is only in the lower part, not in upper.
+ * add both A (i,j) and A (j,i) to the matrix A+A' */
+ Len [i]++ ;
+ Len [j]++ ;
+ AMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n",
+ i,j, j,i)) ;
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* compute the symmetry of the nonzero pattern of A */
+ /* --------------------------------------------------------------------- */
+
+ /* Given a matrix A, the symmetry of A is:
+ * B = tril (spones (A), -1) + triu (spones (A), 1) ;
+ * sym = nnz (B & B') / nnz (B) ;
+ * or 1 if nnz (B) is zero.
+ */
+
+ if (nz == nzdiag)
+ {
+ sym = 1 ;
+ }
+ else
+ {
+ sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ;
+ }
+
+ nzaat = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ nzaat += Len [k] ;
+ }
+
+ AMD_DEBUG1 (("AMD nz in A+A', excluding diagonal (nzaat) = %g\n",
+ (double) nzaat)) ;
+ AMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n",
+ nzboth, nz, nzdiag, sym)) ;
+
+ if (Info != (double *) NULL)
+ {
+ Info [AMD_STATUS] = AMD_OK ;
+ Info [AMD_N] = n ;
+ Info [AMD_NZ] = nz ;
+ Info [AMD_SYMMETRY] = sym ; /* symmetry of pattern of A */
+ Info [AMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */
+ Info [AMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */
+ }
+
+ return (nzaat) ;
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_control.c b/src/C/SuiteSparse/AMD/Source/amd_control.c
new file mode 100644
index 0000000..a38eb4d
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_control.c
@@ -0,0 +1,62 @@
+/* ========================================================================= */
+/* === AMD_control ========================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Prints the control parameters for AMD. See amd.h
+ * for details. If the Control array is not present, the defaults are
+ * printed instead.
+ */
+
+#include "amd_internal.h"
+
+GLOBAL void AMD_control
+(
+ double Control [ ]
+)
+{
+ double alpha ;
+ Int aggressive ;
+
+ if (Control != (double *) NULL)
+ {
+ alpha = Control [AMD_DENSE] ;
+ aggressive = Control [AMD_AGGRESSIVE] != 0 ;
+ }
+ else
+ {
+ alpha = AMD_DEFAULT_DENSE ;
+ aggressive = AMD_DEFAULT_AGGRESSIVE ;
+ }
+
+ PRINTF (("\namd version %d.%d, %s: approximate minimum degree ordering:\n"
+ " dense row parameter: %g\n", AMD_MAIN_VERSION, AMD_SUB_VERSION,
+ AMD_DATE, alpha)) ;
+
+ if (alpha < 0)
+ {
+ PRINTF ((" no rows treated as dense\n")) ;
+ }
+ else
+ {
+ PRINTF ((
+ " (rows with more than max (%g * sqrt (n), 16) entries are\n"
+ " considered \"dense\", and placed last in output permutation)\n",
+ alpha)) ;
+ }
+
+ if (aggressive)
+ {
+ PRINTF ((" aggressive absorption: yes\n\n")) ;
+ }
+ else
+ {
+ PRINTF ((" aggressive absorption: no\n\n")) ;
+ }
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_defaults.c b/src/C/SuiteSparse/AMD/Source/amd_defaults.c
new file mode 100644
index 0000000..59c10e4
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_defaults.c
@@ -0,0 +1,37 @@
+/* ========================================================================= */
+/* === AMD_defaults ======================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Sets default control parameters for AMD. See amd.h
+ * for details.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === AMD defaults ======================================================== */
+/* ========================================================================= */
+
+GLOBAL void AMD_defaults
+(
+ double Control [ ]
+)
+{
+ Int i ;
+ if (Control != (double *) NULL)
+ {
+ for (i = 0 ; i < AMD_CONTROL ; i++)
+ {
+ Control [i] = 0 ;
+ }
+ Control [AMD_DENSE] = AMD_DEFAULT_DENSE ;
+ Control [AMD_AGGRESSIVE] = AMD_DEFAULT_AGGRESSIVE ;
+ }
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_dump.c b/src/C/SuiteSparse/AMD/Source/amd_dump.c
new file mode 100644
index 0000000..cac782e
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_dump.c
@@ -0,0 +1,177 @@
+/* ========================================================================= */
+/* === AMD_dump ============================================================ */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Debugging routines for AMD. Not used if NDEBUG is not defined at compile-
+ * time (the default). See comments in amd_internal.h on how to enable
+ * debugging. Not user-callable.
+ */
+
+#include "amd_internal.h"
+
+#ifndef NDEBUG
+
+/* This global variable is present only when debugging */
+GLOBAL Int AMD_debug = -999 ; /* default is no debug printing */
+
+/* ========================================================================= */
+/* === AMD_debug_init ====================================================== */
+/* ========================================================================= */
+
+/* Sets the debug print level, by reading the file debug.amd (if it exists) */
+
+GLOBAL void AMD_debug_init ( char *s )
+{
+ FILE *f ;
+ f = fopen ("debug.amd", "r") ;
+ if (f == (FILE *) NULL)
+ {
+ AMD_debug = -999 ;
+ }
+ else
+ {
+ fscanf (f, ID, &AMD_debug) ;
+ fclose (f) ;
+ }
+ if (AMD_debug >= 0) printf ("%s: AMD_debug_init, D= "ID"\n", s, AMD_debug);
+}
+
+/* ========================================================================= */
+/* === AMD_dump ============================================================ */
+/* ========================================================================= */
+
+/* Dump AMD's data structure, except for the hash buckets. This routine
+ * cannot be called when the hash buckets are non-empty.
+ */
+
+GLOBAL void AMD_dump (
+ Int n, /* A is n-by-n */
+ Int Pe [ ], /* pe [0..n-1]: index in iw of start of row i */
+ Int Iw [ ], /* workspace of size iwlen, iwlen [0..pfree-1]
+ * holds the matrix on input */
+ Int Len [ ], /* len [0..n-1]: length for row i */
+ Int iwlen, /* length of iw */
+ Int pfree, /* iw [pfree ... iwlen-1] is empty on input */
+ Int Nv [ ], /* nv [0..n-1] */
+ Int Next [ ], /* next [0..n-1] */
+ Int Last [ ], /* last [0..n-1] */
+ Int Head [ ], /* head [0..n-1] */
+ Int Elen [ ], /* size n */
+ Int Degree [ ], /* size n */
+ Int W [ ], /* size n */
+ Int nel
+)
+{
+ Int i, pe, elen, nv, len, e, p, k, j, deg, w, cnt, ilast ;
+
+ if (AMD_debug < 0) return ;
+ ASSERT (pfree <= iwlen) ;
+ AMD_DEBUG3 (("\nAMD dump, pfree: "ID"\n", pfree)) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ pe = Pe [i] ;
+ elen = Elen [i] ;
+ nv = Nv [i] ;
+ len = Len [i] ;
+ w = W [i] ;
+
+ if (elen >= EMPTY)
+ {
+ if (nv == 0)
+ {
+ AMD_DEBUG3 (("\nI "ID": nonprincipal: ", i)) ;
+ ASSERT (elen == EMPTY) ;
+ if (pe == EMPTY)
+ {
+ AMD_DEBUG3 ((" dense node\n")) ;
+ ASSERT (w == 1) ;
+ }
+ else
+ {
+ ASSERT (pe < EMPTY) ;
+ AMD_DEBUG3 ((" i "ID" -> parent "ID"\n", i, FLIP (Pe[i])));
+ }
+ }
+ else
+ {
+ AMD_DEBUG3 (("\nI "ID": active principal supervariable:\n",i));
+ AMD_DEBUG3 ((" nv(i): "ID" Flag: %d\n", nv, (nv < 0))) ;
+ ASSERT (elen >= 0) ;
+ ASSERT (nv > 0 && pe >= 0) ;
+ p = pe ;
+ AMD_DEBUG3 ((" e/s: ")) ;
+ if (elen == 0) AMD_DEBUG3 ((" : ")) ;
+ ASSERT (pe + len <= pfree) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ j = Iw [p] ;
+ AMD_DEBUG3 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ if (k == elen-1) AMD_DEBUG3 ((" : ")) ;
+ p++ ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+ }
+ }
+ else
+ {
+ e = i ;
+ if (w == 0)
+ {
+ AMD_DEBUG3 (("\nE "ID": absorbed element: w "ID"\n", e, w)) ;
+ ASSERT (nv > 0 && pe < 0) ;
+ AMD_DEBUG3 ((" e "ID" -> parent "ID"\n", e, FLIP (Pe [e]))) ;
+ }
+ else
+ {
+ AMD_DEBUG3 (("\nE "ID": unabsorbed element: w "ID"\n", e, w)) ;
+ ASSERT (nv > 0 && pe >= 0) ;
+ p = pe ;
+ AMD_DEBUG3 ((" : ")) ;
+ ASSERT (pe + len <= pfree) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ j = Iw [p] ;
+ AMD_DEBUG3 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ p++ ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+ }
+ }
+ }
+
+ /* this routine cannot be called when the hash buckets are non-empty */
+ AMD_DEBUG3 (("\nDegree lists:\n")) ;
+ if (nel >= 0)
+ {
+ cnt = 0 ;
+ for (deg = 0 ; deg < n ; deg++)
+ {
+ if (Head [deg] == EMPTY) continue ;
+ ilast = EMPTY ;
+ AMD_DEBUG3 ((ID": \n", deg)) ;
+ for (i = Head [deg] ; i != EMPTY ; i = Next [i])
+ {
+ AMD_DEBUG3 ((" "ID" : next "ID" last "ID" deg "ID"\n",
+ i, Next [i], Last [i], Degree [i])) ;
+ ASSERT (i >= 0 && i < n && ilast == Last [i] &&
+ deg == Degree [i]) ;
+ cnt += Nv [i] ;
+ ilast = i ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+ }
+ ASSERT (cnt == n - nel) ;
+ }
+
+}
+
+#endif
diff --git a/src/C/SuiteSparse/AMD/Source/amd_global.c b/src/C/SuiteSparse/AMD/Source/amd_global.c
new file mode 100644
index 0000000..f306593
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_global.c
@@ -0,0 +1,84 @@
+/* ========================================================================= */
+/* === amd_global ========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+#include <stdlib.h>
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#include "matrix.h"
+#endif
+
+#ifndef NULL
+#define NULL 0
+#endif
+
+/* ========================================================================= */
+/* === Default AMD memory manager ========================================== */
+/* ========================================================================= */
+
+/* The user can redefine these global pointers at run-time to change the memory
+ * manager used by AMD. AMD only uses malloc and free; realloc and calloc are
+ * include for completeness, in case another package wants to use the same
+ * memory manager as AMD.
+ *
+ * If compiling as a MATLAB mexFunction, the default memory manager is mxMalloc.
+ * You can also compile AMD as a standard ANSI-C library and link a mexFunction
+ * against it, and then redefine these pointers at run-time, in your
+ * mexFunction.
+ *
+ * If -DNMALLOC is defined at compile-time, no memory manager is specified at
+ * compile-time. You must then define these functions at run-time, before
+ * calling AMD, for AMD to work properly.
+ */
+
+#ifndef NMALLOC
+#ifdef MATLAB_MEX_FILE
+/* MATLAB mexFunction: */
+void *(*amd_malloc) (size_t) = mxMalloc ;
+void (*amd_free) (void *) = mxFree ;
+void *(*amd_realloc) (void *, size_t) = mxRealloc ;
+void *(*amd_calloc) (size_t, size_t) = mxCalloc ;
+#else
+/* standard ANSI-C: */
+void *(*amd_malloc) (size_t) = malloc ;
+void (*amd_free) (void *) = free ;
+void *(*amd_realloc) (void *, size_t) = realloc ;
+void *(*amd_calloc) (size_t, size_t) = calloc ;
+#endif
+#else
+/* no memory manager defined at compile-time; you MUST define one at run-time */
+void *(*amd_malloc) (size_t) = NULL ;
+void (*amd_free) (void *) = NULL ;
+void *(*amd_realloc) (void *, size_t) = NULL ;
+void *(*amd_calloc) (size_t, size_t) = NULL ;
+#endif
+
+/* ========================================================================= */
+/* === Default AMD printf routine ========================================== */
+/* ========================================================================= */
+
+/* The user can redefine this global pointer at run-time to change the printf
+ * routine used by AMD. If NULL, no printing occurs.
+ *
+ * If -DNPRINT is defined at compile-time, stdio.h is not included. Printing
+ * can then be enabled at run-time by setting amd_printf to a non-NULL function.
+ */
+
+#ifndef NPRINT
+#ifdef MATLAB_MEX_FILE
+int (*amd_printf) (const char *, ...) = mexPrintf ;
+#else
+#include <stdio.h>
+int (*amd_printf) (const char *, ...) = printf ;
+#endif
+#else
+int (*amd_printf) (const char *, ...) = NULL ;
+#endif
diff --git a/src/C/SuiteSparse/AMD/Source/amd_info.c b/src/C/SuiteSparse/AMD/Source/amd_info.c
new file mode 100644
index 0000000..9cce8a9
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_info.c
@@ -0,0 +1,119 @@
+/* ========================================================================= */
+/* === AMD_info ============================================================ */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Prints the output statistics for AMD. See amd.h
+ * for details. If the Info array is not present, nothing is printed.
+ */
+
+#include "amd_internal.h"
+
+#define PRI(format,x) { if (x >= 0) { PRINTF ((format, x)) ; }}
+
+GLOBAL void AMD_info
+(
+ double Info [ ]
+)
+{
+ double n, ndiv, nmultsubs_ldl, nmultsubs_lu, lnz, lnzd ;
+
+ if (!Info)
+ {
+ return ;
+ }
+
+ n = Info [AMD_N] ;
+ ndiv = Info [AMD_NDIV] ;
+ nmultsubs_ldl = Info [AMD_NMULTSUBS_LDL] ;
+ nmultsubs_lu = Info [AMD_NMULTSUBS_LU] ;
+ lnz = Info [AMD_LNZ] ;
+ lnzd = (n >= 0 && lnz >= 0) ? (n + lnz) : (-1) ;
+
+ /* AMD return status */
+ PRINTF ((
+ "\namd: approximate minimum degree ordering, results:\n"
+ " status: ")) ;
+ if (Info [AMD_STATUS] == AMD_OK)
+ {
+ PRINTF (("OK\n")) ;
+ }
+ else if (Info [AMD_STATUS] == AMD_OUT_OF_MEMORY)
+ {
+ PRINTF (("out of memory\n")) ;
+ }
+ else if (Info [AMD_STATUS] == AMD_INVALID)
+ {
+ PRINTF (("invalid matrix\n")) ;
+ }
+ else if (Info [AMD_STATUS] == AMD_OK_BUT_JUMBLED)
+ {
+ PRINTF (("OK, but jumbled\n")) ;
+ }
+ else
+ {
+ PRINTF (("unknown\n")) ;
+ }
+
+ /* statistics about the input matrix */
+ PRI (" n, dimension of A: %.20g\n", n);
+ PRI (" nz, number of nonzeros in A: %.20g\n",
+ Info [AMD_NZ]) ;
+ PRI (" symmetry of A: %.4f\n",
+ Info [AMD_SYMMETRY]) ;
+ PRI (" number of nonzeros on diagonal: %.20g\n",
+ Info [AMD_NZDIAG]) ;
+ PRI (" nonzeros in pattern of A+A' (excl. diagonal): %.20g\n",
+ Info [AMD_NZ_A_PLUS_AT]) ;
+ PRI (" # dense rows/columns of A+A': %.20g\n",
+ Info [AMD_NDENSE]) ;
+
+ /* statistics about AMD's behavior */
+ PRI (" memory used, in bytes: %.20g\n",
+ Info [AMD_MEMORY]) ;
+ PRI (" # of memory compactions: %.20g\n",
+ Info [AMD_NCMPA]) ;
+
+ /* statistics about the ordering quality */
+ PRINTF (("\n"
+ " The following approximate statistics are for a subsequent\n"
+ " factorization of A(P,P) + A(P,P)'. They are slight upper\n"
+ " bounds if there are no dense rows/columns in A+A', and become\n"
+ " looser if dense rows/columns exist.\n\n")) ;
+
+ PRI (" nonzeros in L (excluding diagonal): %.20g\n",
+ lnz) ;
+ PRI (" nonzeros in L (including diagonal): %.20g\n",
+ lnzd) ;
+ PRI (" # divide operations for LDL' or LU: %.20g\n",
+ ndiv) ;
+ PRI (" # multiply-subtract operations for LDL': %.20g\n",
+ nmultsubs_ldl) ;
+ PRI (" # multiply-subtract operations for LU: %.20g\n",
+ nmultsubs_lu) ;
+ PRI (" max nz. in any column of L (incl. diagonal): %.20g\n",
+ Info [AMD_DMAX]) ;
+
+ /* total flop counts for various factorizations */
+
+ if (n >= 0 && ndiv >= 0 && nmultsubs_ldl >= 0 && nmultsubs_lu >= 0)
+ {
+ PRINTF (("\n"
+ " chol flop count for real A, sqrt counted as 1 flop: %.20g\n"
+ " LDL' flop count for real A: %.20g\n"
+ " LDL' flop count for complex A: %.20g\n"
+ " LU flop count for real A (with no pivoting): %.20g\n"
+ " LU flop count for complex A (with no pivoting): %.20g\n\n",
+ n + ndiv + 2*nmultsubs_ldl,
+ ndiv + 2*nmultsubs_ldl,
+ 9*ndiv + 8*nmultsubs_ldl,
+ ndiv + 2*nmultsubs_lu,
+ 9*ndiv + 8*nmultsubs_lu)) ;
+ }
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_order.c b/src/C/SuiteSparse/AMD/Source/amd_order.c
new file mode 100644
index 0000000..438d3b7
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_order.c
@@ -0,0 +1,200 @@
+/* ========================================================================= */
+/* === AMD_order =========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable AMD minimum degree ordering routine. See amd.h for
+ * documentation.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === AMD_order =========================================================== */
+/* ========================================================================= */
+
+GLOBAL Int AMD_order
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int P [ ],
+ double Control [ ],
+ double Info [ ]
+)
+{
+ Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ;
+ size_t nzaat, slen ;
+ double mem = 0 ;
+
+#ifndef NDEBUG
+ AMD_debug_init ("amd") ;
+#endif
+
+ /* clear the Info array, if it exists */
+ info = Info != (double *) NULL ;
+ if (info)
+ {
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ Info [AMD_N] = n ;
+ Info [AMD_STATUS] = AMD_OK ;
+ }
+
+ /* make sure inputs exist and n is >= 0 */
+ if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0)
+ {
+ if (info) Info [AMD_STATUS] = AMD_INVALID ;
+ return (AMD_INVALID) ; /* arguments are invalid */
+ }
+
+ if (n == 0)
+ {
+ return (AMD_OK) ; /* n is 0 so there's nothing to do */
+ }
+
+ nz = Ap [n] ;
+ if (info)
+ {
+ Info [AMD_NZ] = nz ;
+ }
+ if (nz < 0)
+ {
+ if (info) Info [AMD_STATUS] = AMD_INVALID ;
+ return (AMD_INVALID) ;
+ }
+
+ /* check if n or nz will cause size_t overflow */
+ if (((size_t) n) >= SIZE_T_MAX / sizeof (Int)
+ || ((size_t) nz) >= SIZE_T_MAX / sizeof (Int))
+ {
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ; /* problem too large */
+ }
+
+ /* check the input matrix: AMD_OK, AMD_INVALID, or AMD_OK_BUT_JUMBLED */
+ status = AMD_valid (n, n, Ap, Ai) ;
+
+ if (status == AMD_INVALID)
+ {
+ if (info) Info [AMD_STATUS] = AMD_INVALID ;
+ return (AMD_INVALID) ; /* matrix is invalid */
+ }
+
+ /* allocate two size-n integer workspaces */
+ Len = amd_malloc (n * sizeof (Int)) ;
+ Pinv = amd_malloc (n * sizeof (Int)) ;
+ mem += n ;
+ mem += n ;
+ if (!Len || !Pinv)
+ {
+ /* :: out of memory :: */
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+
+ if (status == AMD_OK_BUT_JUMBLED)
+ {
+ /* sort the input matrix and remove duplicate entries */
+ AMD_DEBUG1 (("Matrix is jumbled\n")) ;
+ Rp = amd_malloc ((n+1) * sizeof (Int)) ;
+ Ri = amd_malloc (MAX (nz,1) * sizeof (Int)) ;
+ mem += (n+1) ;
+ mem += MAX (nz,1) ;
+ if (!Rp || !Ri)
+ {
+ /* :: out of memory :: */
+ amd_free (Rp) ;
+ amd_free (Ri) ;
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+ /* use Len and Pinv as workspace to create R = A' */
+ AMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ;
+ Cp = Rp ;
+ Ci = Ri ;
+ }
+ else
+ {
+ /* order the input matrix as-is. No need to compute R = A' first */
+ Rp = NULL ;
+ Ri = NULL ;
+ Cp = (Int *) Ap ;
+ Ci = (Int *) Ai ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* determine the symmetry and count off-diagonal nonzeros in A+A' */
+ /* --------------------------------------------------------------------- */
+
+ nzaat = AMD_aat (n, Cp, Ci, Len, P, Info) ;
+ AMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ;
+ ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ;
+
+ /* --------------------------------------------------------------------- */
+ /* allocate workspace for matrix, elbow room, and 6 size-n vectors */
+ /* --------------------------------------------------------------------- */
+
+ S = NULL ;
+ slen = nzaat ; /* space for matrix */
+ ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */
+ slen += nzaat/5 ; /* add elbow room */
+ for (i = 0 ; ok && i < 7 ; i++)
+ {
+ ok = ((slen + n) > slen) ; /* check for size_t overflow */
+ slen += n ; /* size-n elbow room, 6 size-n work */
+ }
+ mem += slen ;
+ ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */
+ ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */
+ if (ok)
+ {
+ S = amd_malloc (slen * sizeof (Int)) ;
+ }
+ AMD_DEBUG1 (("slen %g\n", (double) slen)) ;
+ if (!S)
+ {
+ /* :: out of memory :: (or problem too large) */
+ amd_free (Rp) ;
+ amd_free (Ri) ;
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+ if (info)
+ {
+ /* memory usage, in bytes. */
+ Info [AMD_MEMORY] = mem * sizeof (Int) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ AMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info) ;
+
+ /* --------------------------------------------------------------------- */
+ /* free the workspace */
+ /* --------------------------------------------------------------------- */
+
+ amd_free (Rp) ;
+ amd_free (Ri) ;
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ amd_free (S) ;
+ if (info) Info [AMD_STATUS] = status ;
+ return (status) ; /* successful ordering */
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_post_tree.c b/src/C/SuiteSparse/AMD/Source/amd_post_tree.c
new file mode 100644
index 0000000..9695b18
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_post_tree.c
@@ -0,0 +1,121 @@
+/* ========================================================================= */
+/* === AMD_post_tree ======================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Post-ordering of a supernodal elimination tree. */
+
+#include "amd_internal.h"
+
+GLOBAL Int AMD_post_tree
+(
+ Int root, /* root of the tree */
+ Int k, /* start numbering at k */
+ Int Child [ ], /* input argument of size nn, undefined on
+ * output. Child [i] is the head of a link
+ * list of all nodes that are children of node
+ * i in the tree. */
+ const Int Sibling [ ], /* input argument of size nn, not modified.
+ * If f is a node in the link list of the
+ * children of node i, then Sibling [f] is the
+ * next child of node i.
+ */
+ Int Order [ ], /* output order, of size nn. Order [i] = k
+ * if node i is the kth node of the reordered
+ * tree. */
+ Int Stack [ ] /* workspace of size nn */
+#ifndef NDEBUG
+ , Int nn /* nodes are in the range 0..nn-1. */
+#endif
+)
+{
+ Int f, head, h, i ;
+
+#if 0
+ /* --------------------------------------------------------------------- */
+ /* recursive version (Stack [ ] is not used): */
+ /* --------------------------------------------------------------------- */
+
+ /* this is simple, but can caouse stack overflow if nn is large */
+ i = root ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ k = AMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ;
+ }
+ Order [i] = k++ ;
+ return (k) ;
+#endif
+
+ /* --------------------------------------------------------------------- */
+ /* non-recursive version, using an explicit stack */
+ /* --------------------------------------------------------------------- */
+
+ /* push root on the stack */
+ head = 0 ;
+ Stack [0] = root ;
+
+ while (head >= 0)
+ {
+ /* get head of stack */
+ ASSERT (head < nn) ;
+ i = Stack [head] ;
+ AMD_DEBUG1 (("head of stack "ID" \n", i)) ;
+ ASSERT (i >= 0 && i < nn) ;
+
+ if (Child [i] != EMPTY)
+ {
+ /* the children of i are not yet ordered */
+ /* push each child onto the stack in reverse order */
+ /* so that small ones at the head of the list get popped first */
+ /* and the biggest one at the end of the list gets popped last */
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ head++ ;
+ ASSERT (head < nn) ;
+ ASSERT (f >= 0 && f < nn) ;
+ }
+ h = head ;
+ ASSERT (head < nn) ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (h > 0) ;
+ Stack [h--] = f ;
+ AMD_DEBUG1 (("push "ID" on stack\n", f)) ;
+ ASSERT (f >= 0 && f < nn) ;
+ }
+ ASSERT (Stack [h] == i) ;
+
+ /* delete child list so that i gets ordered next time we see it */
+ Child [i] = EMPTY ;
+ }
+ else
+ {
+ /* the children of i (if there were any) are already ordered */
+ /* remove i from the stack and order it. Front i is kth front */
+ head-- ;
+ AMD_DEBUG1 (("pop "ID" order "ID"\n", i, k)) ;
+ Order [i] = k++ ;
+ ASSERT (k <= nn) ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("\nStack:")) ;
+ for (h = head ; h >= 0 ; h--)
+ {
+ Int j = Stack [h] ;
+ AMD_DEBUG1 ((" "ID, j)) ;
+ ASSERT (j >= 0 && j < nn) ;
+ }
+ AMD_DEBUG1 (("\n\n")) ;
+ ASSERT (head < nn) ;
+#endif
+
+ }
+ return (k) ;
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_postorder.c b/src/C/SuiteSparse/AMD/Source/amd_postorder.c
new file mode 100644
index 0000000..57c6ef2
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_postorder.c
@@ -0,0 +1,207 @@
+/* ========================================================================= */
+/* === AMD_postorder ======================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Perform a postordering (via depth-first search) of an assembly tree. */
+
+#include "amd_internal.h"
+
+GLOBAL void AMD_postorder
+(
+ /* inputs, not modified on output: */
+ Int nn, /* nodes are in the range 0..nn-1 */
+ Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */
+ Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j,
+ * or zero if j is not a node. */
+ Int Fsize [ ], /* Fsize [j]: size of node j */
+
+ /* output, not defined on input: */
+ Int Order [ ], /* output post-order */
+
+ /* workspaces of size nn: */
+ Int Child [ ],
+ Int Sibling [ ],
+ Int Stack [ ]
+)
+{
+ Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ;
+
+ for (j = 0 ; j < nn ; j++)
+ {
+ Child [j] = EMPTY ;
+ Sibling [j] = EMPTY ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* place the children in link lists - bigger elements tend to be last */
+ /* --------------------------------------------------------------------- */
+
+ for (j = nn-1 ; j >= 0 ; j--)
+ {
+ if (Nv [j] > 0)
+ {
+ /* this is an element */
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ /* place the element in link list of the children its parent */
+ /* bigger elements will tend to be at the end of the list */
+ Sibling [j] = Child [parent] ;
+ Child [parent] = j ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ {
+ Int nels, ff, nchild ;
+ AMD_DEBUG1 (("\n\n================================ AMD_postorder:\n"));
+ nels = 0 ;
+ for (j = 0 ; j < nn ; j++)
+ {
+ if (Nv [j] > 0)
+ {
+ AMD_DEBUG1 (( ""ID" : nels "ID" npiv "ID" size "ID
+ " parent "ID" maxfr "ID"\n", j, nels,
+ Nv [j], Fsize [j], Parent [j], Fsize [j])) ;
+ /* this is an element */
+ /* dump the link list of children */
+ nchild = 0 ;
+ AMD_DEBUG1 ((" Children: ")) ;
+ for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff])
+ {
+ AMD_DEBUG1 ((ID" ", ff)) ;
+ ASSERT (Parent [ff] == j) ;
+ nchild++ ;
+ ASSERT (nchild < nn) ;
+ }
+ AMD_DEBUG1 (("\n")) ;
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ ASSERT (Nv [parent] > 0) ;
+ }
+ nels++ ;
+ }
+ }
+ }
+ AMD_DEBUG1 (("\n\nGo through the children of each node, and put\n"
+ "the biggest child last in each list:\n")) ;
+#endif
+
+ /* --------------------------------------------------------------------- */
+ /* place the largest child last in the list of children for each node */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ if (Nv [i] > 0 && Child [i] != EMPTY)
+ {
+
+#ifndef NDEBUG
+ Int nchild ;
+ AMD_DEBUG1 (("Before partial sort, element "ID"\n", i)) ;
+ nchild = 0 ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (f >= 0 && f < nn) ;
+ AMD_DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ;
+ nchild++ ;
+ ASSERT (nchild <= nn) ;
+ }
+#endif
+
+ /* find the biggest element in the child list */
+ fprev = EMPTY ;
+ maxfrsize = EMPTY ;
+ bigfprev = EMPTY ;
+ bigf = EMPTY ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (f >= 0 && f < nn) ;
+ frsize = Fsize [f] ;
+ if (frsize >= maxfrsize)
+ {
+ /* this is the biggest seen so far */
+ maxfrsize = frsize ;
+ bigfprev = fprev ;
+ bigf = f ;
+ }
+ fprev = f ;
+ }
+ ASSERT (bigf != EMPTY) ;
+
+ fnext = Sibling [bigf] ;
+
+ AMD_DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID
+ " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ;
+
+ if (fnext != EMPTY)
+ {
+ /* if fnext is EMPTY then bigf is already at the end of list */
+
+ if (bigfprev == EMPTY)
+ {
+ /* delete bigf from the element of the list */
+ Child [i] = fnext ;
+ }
+ else
+ {
+ /* delete bigf from the middle of the list */
+ Sibling [bigfprev] = fnext ;
+ }
+
+ /* put bigf at the end of the list */
+ Sibling [bigf] = EMPTY ;
+ ASSERT (Child [i] != EMPTY) ;
+ ASSERT (fprev != bigf) ;
+ ASSERT (fprev != EMPTY) ;
+ Sibling [fprev] = bigf ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("After partial sort, element "ID"\n", i)) ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (f >= 0 && f < nn) ;
+ AMD_DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ;
+ ASSERT (Nv [f] > 0) ;
+ nchild-- ;
+ }
+ ASSERT (nchild == 0) ;
+#endif
+
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* postorder the assembly tree */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ Order [i] = EMPTY ;
+ }
+
+ k = 0 ;
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ if (Parent [i] == EMPTY && Nv [i] > 0)
+ {
+ AMD_DEBUG1 (("Root of assembly tree "ID"\n", i)) ;
+ k = AMD_post_tree (i, k, Child, Sibling, Order, Stack
+#ifndef NDEBUG
+ , nn
+#endif
+ ) ;
+ }
+ }
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_preprocess.c b/src/C/SuiteSparse/AMD/Source/amd_preprocess.c
new file mode 100644
index 0000000..6b8bd66
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_preprocess.c
@@ -0,0 +1,119 @@
+/* ========================================================================= */
+/* === AMD_preprocess ====================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Sorts, removes duplicate entries, and transposes from the nonzero pattern of
+ * a column-form matrix A, to obtain the matrix R. The input matrix can have
+ * duplicate entries and/or unsorted columns (AMD_valid (n,Ap,Ai) must not be
+ * AMD_INVALID).
+ *
+ * This input condition is NOT checked. This routine is not user-callable.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === AMD_preprocess ====================================================== */
+/* ========================================================================= */
+
+/* AMD_preprocess does not check its input for errors or allocate workspace.
+ * On input, the condition (AMD_valid (n,n,Ap,Ai) != AMD_INVALID) must hold.
+ */
+
+GLOBAL void AMD_preprocess
+(
+ Int n, /* input matrix: A is n-by-n */
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+
+ /* output matrix R: */
+ Int Rp [ ], /* size n+1 */
+ Int Ri [ ], /* size nz (or less, if duplicates present) */
+
+ Int W [ ], /* workspace of size n */
+ Int Flag [ ] /* workspace of size n */
+)
+{
+
+ /* --------------------------------------------------------------------- */
+ /* local variables */
+ /* --------------------------------------------------------------------- */
+
+ Int i, j, p, p2 ;
+
+ ASSERT (AMD_valid (n, n, Ap, Ai) != AMD_INVALID) ;
+
+ /* --------------------------------------------------------------------- */
+ /* count the entries in each row of A (excluding duplicates) */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */
+ Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ if (Flag [i] != j)
+ {
+ /* row index i has not yet appeared in column j */
+ W [i]++ ; /* one more entry in row i */
+ Flag [i] = j ; /* flag row index i as appearing in col j*/
+ }
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* compute the row pointers for R */
+ /* --------------------------------------------------------------------- */
+
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Rp [i] ;
+ Flag [i] = EMPTY ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* construct the row form matrix R */
+ /* --------------------------------------------------------------------- */
+
+ /* R = row form of pattern of A */
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ if (Flag [i] != j)
+ {
+ /* row index i has not yet appeared in column j */
+ Ri [W [i]++] = j ; /* put col j in row i */
+ Flag [i] = j ; /* flag row index i as appearing in col j*/
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ ASSERT (AMD_valid (n, n, Rp, Ri) == AMD_OK) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (W [j] == Rp [j+1]) ;
+ }
+#endif
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amd_valid.c b/src/C/SuiteSparse/AMD/Source/amd_valid.c
new file mode 100644
index 0000000..cd91e21
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amd_valid.c
@@ -0,0 +1,92 @@
+/* ========================================================================= */
+/* === AMD_valid =========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.0, Copyright (c) 2006 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Check if a column-form matrix is valid or not. The matrix A is
+ * n_row-by-n_col. The row indices of entries in column j are in
+ * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are:
+ *
+ * n_row >= 0
+ * n_col >= 0
+ * nz = Ap [n_col] >= 0 number of entries in the matrix
+ * Ap [0] == 0
+ * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col.
+ * Ai [0 ... nz-1] must be in the range 0 to n_row-1.
+ *
+ * If any of the above conditions hold, AMD_INVALID is returned. If the
+ * following condition holds, AMD_OK_BUT_JUMBLED is returned (a warning,
+ * not an error):
+ *
+ * row indices in Ai [Ap [j] ... Ap [j+1]-1] are not sorted in ascending
+ * order, and/or duplicate entries exist.
+ *
+ * Otherwise, AMD_OK is returned.
+ *
+ * In v1.2 and earlier, this function returned TRUE if the matrix was valid
+ * (now returns AMD_OK), or FALSE otherwise (now returns AMD_INVALID or
+ * AMD_OK_BUT_JUMBLED).
+ */
+
+#include "amd_internal.h"
+
+GLOBAL Int AMD_valid
+(
+ /* inputs, not modified on output: */
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ const Int Ap [ ], /* column pointers of A, of size n_col+1 */
+ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */
+)
+{
+ Int nz, j, p1, p2, ilast, i, p, result = AMD_OK ;
+ if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL)
+ {
+ return (AMD_INVALID) ;
+ }
+ nz = Ap [n_col] ;
+ if (Ap [0] != 0 || nz < 0)
+ {
+ /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */
+ AMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ;
+ return (AMD_INVALID) ;
+ }
+ for (j = 0 ; j < n_col ; j++)
+ {
+ p1 = Ap [j] ;
+ p2 = Ap [j+1] ;
+ AMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ;
+ if (p1 > p2)
+ {
+ /* column pointers must be ascending */
+ AMD_DEBUG0 (("column "ID" pointer bad\n", j)) ;
+ return (AMD_INVALID) ;
+ }
+ ilast = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ AMD_DEBUG3 (("row: "ID"\n", i)) ;
+ if (i < 0 || i >= n_row)
+ {
+ /* row index out of range */
+ AMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i));
+ return (AMD_INVALID) ;
+ }
+ if (i <= ilast)
+ {
+ /* row index unsorted, or duplicate entry present */
+ AMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i));
+ result = AMD_OK_BUT_JUMBLED ;
+ }
+ ilast = i ;
+ }
+ }
+ return (result) ;
+}
diff --git a/src/C/SuiteSparse/AMD/Source/amdbar.f b/src/C/SuiteSparse/AMD/Source/amdbar.f
new file mode 100644
index 0000000..1384392
--- /dev/null
+++ b/src/C/SuiteSparse/AMD/Source/amdbar.f
@@ -0,0 +1,1206 @@
+C-----------------------------------------------------------------------
+C AMDBAR: approximate minimum degree, without aggressive absorption
+C-----------------------------------------------------------------------
+
+ SUBROUTINE AMDBAR
+ $ (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+
+ INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N),
+ $ DEGREE (N), NV (N), NEXT (N), LAST (N), HEAD (N),
+ $ ELEN (N), W (N), LEN (N)
+
+C Given a representation of the nonzero pattern of a symmetric matrix,
+C A, (excluding the diagonal) perform an approximate minimum
+C (UMFPACK/MA38-style) degree ordering to compute a pivot order
+C such that the introduction of nonzeros (fill-in) in the Cholesky
+C factors A = LL^T are kept low. At each step, the pivot
+C selected is the one with the minimum UMFPACK/MA38-style
+C upper-bound on the external degree.
+C
+C This routine does not do aggresive absorption (as done by AMD).
+
+C **********************************************************************
+C ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+C **********************************************************************
+
+C References:
+C
+C [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern
+C multifrontal method for sparse LU factorization", SIAM J.
+C Matrix Analysis and Applications, vol. 18, no. 1, pp.
+C 140-158. Discusses UMFPACK / MA38, which first introduced
+C the approximate minimum degree used by this routine.
+C
+C [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An
+C approximate degree ordering algorithm," SIAM J. Matrix
+C Analysis and Applications, vol. 17, no. 4, pp. 886-905,
+C 1996. Discusses AMD, AMDBAR, and MC47B.
+C
+C [3] Alan George and Joseph Liu, "The evolution of the minimum
+C degree ordering algorithm," SIAM Review, vol. 31, no. 1,
+C pp. 1-19, 1989. We list below the features mentioned in
+C that paper that this code includes:
+C
+C mass elimination:
+C Yes. MA27 relied on supervariable detection for mass
+C elimination.
+C indistinguishable nodes:
+C Yes (we call these "supervariables"). This was also in
+C the MA27 code - although we modified the method of
+C detecting them (the previous hash was the true degree,
+C which we no longer keep track of). A supervariable is
+C a set of rows with identical nonzero pattern. All
+C variables in a supervariable are eliminated together.
+C Each supervariable has as its numerical name that of
+C one of its variables (its principal variable).
+C quotient graph representation:
+C Yes. We use the term "element" for the cliques formed
+C during elimination. This was also in the MA27 code.
+C The algorithm can operate in place, but it will work
+C more efficiently if given some "elbow room."
+C element absorption:
+C Yes. This was also in the MA27 code.
+C external degree:
+C Yes. The MA27 code was based on the true degree.
+C incomplete degree update and multiple elimination:
+C No. This was not in MA27, either. Our method of
+C degree update within MC47B/BD is element-based, not
+C variable-based. It is thus not well-suited for use
+C with incomplete degree update or multiple elimination.
+
+C-----------------------------------------------------------------------
+C Authors, and Copyright (C) 1995 by:
+C Timothy A. Davis, Patrick Amestoy, Iain S. Duff, & John K. Reid.
+C
+C Acknowledgements:
+C This work (and the UMFPACK package) was supported by the
+C National Science Foundation (ASC-9111263 and DMS-9223088).
+C The UMFPACK/MA38 approximate degree update algorithm, the
+C unsymmetric analog which forms the basis of MC47B/BD, was
+C developed while Tim Davis was supported by CERFACS (Toulouse,
+C France) in a post-doctoral position.
+C
+C Date: September, 1995
+C-----------------------------------------------------------------------
+
+C-----------------------------------------------------------------------
+C INPUT ARGUMENTS (unaltered):
+C-----------------------------------------------------------------------
+
+C n: The matrix order.
+C
+C Restriction: 1 .le. n .lt. (iovflo/2)-2, where iovflo is
+C the largest positive integer that your computer can represent.
+
+C iwlen: The length of iw (1..iwlen). On input, the matrix is
+C stored in iw (1..pfree-1). However, iw (1..iwlen) should be
+C slightly larger than what is required to hold the matrix, at
+C least iwlen .ge. pfree + n is recommended. Otherwise,
+C excessive compressions will take place.
+C *** We do not recommend running this algorithm with ***
+C *** iwlen .lt. pfree + n. ***
+C *** Better performance will be obtained if ***
+C *** iwlen .ge. pfree + n ***
+C *** or better yet ***
+C *** iwlen .gt. 1.2 * pfree ***
+C *** (where pfree is its value on input). ***
+C The algorithm will not run at all if iwlen .lt. pfree-1.
+C
+C Restriction: iwlen .ge. pfree-1
+
+C-----------------------------------------------------------------------
+C INPUT/OUPUT ARGUMENTS:
+C-----------------------------------------------------------------------
+
+C pe: On input, pe (i) is the index in iw of the start of row i, or
+C zero if row i has no off-diagonal non-zeros.
+C
+C During execution, it is used for both supervariables and
+C elements:
+C
+C * Principal supervariable i: index into iw of the
+C description of supervariable i. A supervariable
+C represents one or more rows of the matrix
+C with identical nonzero pattern.
+C * Non-principal supervariable i: if i has been absorbed
+C into another supervariable j, then pe (i) = -j.
+C That is, j has the same pattern as i.
+C Note that j might later be absorbed into another
+C supervariable j2, in which case pe (i) is still -j,
+C and pe (j) = -j2.
+C * Unabsorbed element e: the index into iw of the description
+C of element e, if e has not yet been absorbed by a
+C subsequent element. Element e is created when
+C the supervariable of the same name is selected as
+C the pivot.
+C * Absorbed element e: if element e is absorbed into element
+C e2, then pe (e) = -e2. This occurs when the pattern of
+C e (that is, Le) is found to be a subset of the pattern
+C of e2 (that is, Le2). If element e is "null" (it has
+C no nonzeros outside its pivot block), then pe (e) = 0.
+C
+C On output, pe holds the assembly tree/forest, which implicitly
+C represents a pivot order with identical fill-in as the actual
+C order (via a depth-first search of the tree).
+C
+C On output:
+C If nv (i) .gt. 0, then i represents a node in the assembly tree,
+C and the parent of i is -pe (i), or zero if i is a root.
+C If nv (i) = 0, then (i,-pe (i)) represents an edge in a
+C subtree, the root of which is a node in the assembly tree.
+
+C pfree: On input the tail end of the array, iw (pfree..iwlen),
+C is empty, and the matrix is stored in iw (1..pfree-1).
+C During execution, additional data is placed in iw, and pfree
+C is modified so that iw (pfree..iwlen) is always the unused part
+C of iw. On output, pfree is set equal to the size of iw that
+C would have been needed for no compressions to occur. If
+C ncmpa is zero, then pfree (on output) is less than or equal to
+C iwlen, and the space iw (pfree+1 ... iwlen) was not used.
+C Otherwise, pfree (on output) is greater than iwlen, and all the
+C memory in iw was used.
+
+C-----------------------------------------------------------------------
+C INPUT/MODIFIED (undefined on output):
+C-----------------------------------------------------------------------
+
+C len: On input, len (i) holds the number of entries in row i of the
+C matrix, excluding the diagonal. The contents of len (1..n)
+C are undefined on output.
+
+C iw: On input, iw (1..pfree-1) holds the description of each row i
+C in the matrix. The matrix must be symmetric, and both upper
+C and lower triangular parts must be present. The diagonal must
+C not be present. Row i is held as follows:
+C
+C len (i): the length of the row i data structure
+C iw (pe (i) ... pe (i) + len (i) - 1):
+C the list of column indices for nonzeros
+C in row i (simple supervariables), excluding
+C the diagonal. All supervariables start with
+C one row/column each (supervariable i is just
+C row i).
+C if len (i) is zero on input, then pe (i) is ignored
+C on input.
+C
+C Note that the rows need not be in any particular order,
+C and there may be empty space between the rows.
+C
+C During execution, the supervariable i experiences fill-in.
+C This is represented by placing in i a list of the elements
+C that cause fill-in in supervariable i:
+C
+C len (i): the length of supervariable i
+C iw (pe (i) ... pe (i) + elen (i) - 1):
+C the list of elements that contain i. This list
+C is kept short by removing absorbed elements.
+C iw (pe (i) + elen (i) ... pe (i) + len (i) - 1):
+C the list of supervariables in i. This list
+C is kept short by removing nonprincipal
+C variables, and any entry j that is also
+C contained in at least one of the elements
+C (j in Le) in the list for i (e in row i).
+C
+C When supervariable i is selected as pivot, we create an
+C element e of the same name (e=i):
+C
+C len (e): the length of element e
+C iw (pe (e) ... pe (e) + len (e) - 1):
+C the list of supervariables in element e.
+C
+C An element represents the fill-in that occurs when supervariable
+C i is selected as pivot (which represents the selection of row i
+C and all non-principal variables whose principal variable is i).
+C We use the term Le to denote the set of all supervariables
+C in element e. Absorbed supervariables and elements are pruned
+C from these lists when computationally convenient.
+C
+C CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+C The contents of iw are undefined on output.
+
+C-----------------------------------------------------------------------
+C OUTPUT (need not be set on input):
+C-----------------------------------------------------------------------
+
+C nv: During execution, abs (nv (i)) is equal to the number of rows
+C that are represented by the principal supervariable i. If i is
+C a nonprincipal variable, then nv (i) = 0. Initially,
+C nv (i) = 1 for all i. nv (i) .lt. 0 signifies that i is a
+C principal variable in the pattern Lme of the current pivot
+C element me. On output, nv (e) holds the true degree of element
+C e at the time it was created (including the diagonal part).
+
+C ncmpa: The number of times iw was compressed. If this is
+C excessive, then the execution took longer than what could have
+C been. To reduce ncmpa, try increasing iwlen to be 10% or 20%
+C larger than the value of pfree on input (or at least
+C iwlen .ge. pfree + n). The fastest performance will be
+C obtained when ncmpa is returned as zero. If iwlen is set to
+C the value returned by pfree on *output*, then no compressions
+C will occur.
+
+C elen: See the description of iw above. At the start of execution,
+C elen (i) is set to zero. During execution, elen (i) is the
+C number of elements in the list for supervariable i. When e
+C becomes an element, elen (e) = -nel is set, where nel is the
+C current step of factorization. elen (i) = 0 is done when i
+C becomes nonprincipal.
+C
+C For variables, elen (i) .ge. 0 holds until just before the
+C permutation vectors are computed. For elements,
+C elen (e) .lt. 0 holds.
+C
+C On output elen (1..n) holds the inverse permutation (the same
+C as the 'INVP' argument in Sparspak). That is, if k = elen (i),
+C then row i is the kth pivot row. Row i of A appears as the
+C (elen(i))-th row in the permuted matrix, PAP^T.
+
+C last: In a degree list, last (i) is the supervariable preceding i,
+C or zero if i is the head of the list. In a hash bucket,
+C last (i) is the hash key for i. last (head (hash)) is also
+C used as the head of a hash bucket if head (hash) contains a
+C degree list (see head, below).
+C
+C On output, last (1..n) holds the permutation (the same as the
+C 'PERM' argument in Sparspak). That is, if i = last (k), then
+C row i is the kth pivot row. Row last (k) of A is the k-th row
+C in the permuted matrix, PAP^T.
+
+C-----------------------------------------------------------------------
+C LOCAL (not input or output - used only during execution):
+C-----------------------------------------------------------------------
+
+C degree: If i is a supervariable, then degree (i) holds the
+C current approximation of the external degree of row i (an upper
+C bound). The external degree is the number of nonzeros in row i,
+C minus abs (nv (i)) (the diagonal part). The bound is equal to
+C the external degree if elen (i) is less than or equal to two.
+C
+C We also use the term "external degree" for elements e to refer
+C to |Le \ Lme|. If e is an element, then degree (e) holds |Le|,
+C which is the degree of the off-diagonal part of the element e
+C (not including the diagonal part).
+
+C head: head is used for degree lists. head (deg) is the first
+C supervariable in a degree list (all supervariables i in a
+C degree list deg have the same approximate degree, namely,
+C deg = degree (i)). If the list deg is empty then
+C head (deg) = 0.
+C
+C During supervariable detection head (hash) also serves as a
+C pointer to a hash bucket.
+C If head (hash) .gt. 0, there is a degree list of degree hash.
+C The hash bucket head pointer is last (head (hash)).
+C If head (hash) = 0, then the degree list and hash bucket are
+C both empty.
+C If head (hash) .lt. 0, then the degree list is empty, and
+C -head (hash) is the head of the hash bucket.
+C After supervariable detection is complete, all hash buckets
+C are empty, and the (last (head (hash)) = 0) condition is
+C restored for the non-empty degree lists.
+
+C next: next (i) is the supervariable following i in a link list, or
+C zero if i is the last in the list. Used for two kinds of
+C lists: degree lists and hash buckets (a supervariable can be
+C in only one kind of list at a time).
+
+C w: The flag array w determines the status of elements and
+C variables, and the external degree of elements.
+C
+C for elements:
+C if w (e) = 0, then the element e is absorbed
+C if w (e) .ge. wflg, then w (e) - wflg is the size of
+C the set |Le \ Lme|, in terms of nonzeros (the
+C sum of abs (nv (i)) for each principal variable i that
+C is both in the pattern of element e and NOT in the
+C pattern of the current pivot element, me).
+C if wflg .gt. w (e) .gt. 0, then e is not absorbed and has
+C not yet been seen in the scan of the element lists in
+C the computation of |Le\Lme| in loop 150 below.
+C
+C for variables:
+C during supervariable detection, if w (j) .ne. wflg then j is
+C not in the pattern of variable i
+C
+C The w array is initialized by setting w (i) = 1 for all i,
+C and by setting wflg = 2. It is reinitialized if wflg becomes
+C too large (to ensure that wflg+n does not cause integer
+C overflow).
+
+C-----------------------------------------------------------------------
+C LOCAL INTEGERS:
+C-----------------------------------------------------------------------
+
+ INTEGER DEG, DEGME, DMAX, E, ELENME, ELN, HASH, HMOD, I,
+ $ ILAST, INEXT, J, JLAST, JNEXT, K, KNT1, KNT2, KNT3,
+ $ LENJ, LN, MAXMEM, ME, MEM, MINDEG, NEL, NEWMEM,
+ $ NLEFT, NVI, NVJ, NVPIV, SLENME, WE, WFLG, WNVI, X
+
+C deg: the degree of a variable or element
+C degme: size, |Lme|, of the current element, me (= degree (me))
+C dext: external degree, |Le \ Lme|, of some element e
+C dmax: largest |Le| seen so far
+C e: an element
+C elenme: the length, elen (me), of element list of pivotal var.
+C eln: the length, elen (...), of an element list
+C hash: the computed value of the hash function
+C hmod: the hash function is computed modulo hmod = max (1,n-1)
+C i: a supervariable
+C ilast: the entry in a link list preceding i
+C inext: the entry in a link list following i
+C j: a supervariable
+C jlast: the entry in a link list preceding j
+C jnext: the entry in a link list, or path, following j
+C k: the pivot order of an element or variable
+C knt1: loop counter used during element construction
+C knt2: loop counter used during element construction
+C knt3: loop counter used during compression
+C lenj: len (j)
+C ln: length of a supervariable list
+C maxmem: amount of memory needed for no compressions
+C me: current supervariable being eliminated, and the
+C current element created by eliminating that
+C supervariable
+C mem: memory in use assuming no compressions have occurred
+C mindeg: current minimum degree
+C nel: number of pivots selected so far
+C newmem: amount of new memory needed for current pivot element
+C nleft: n - nel, the number of nonpivotal rows/columns remaining
+C nvi: the number of variables in a supervariable i (= nv (i))
+C nvj: the number of variables in a supervariable j (= nv (j))
+C nvpiv: number of pivots in current element
+C slenme: number of variables in variable list of pivotal variable
+C we: w (e)
+C wflg: used for flagging the w array. See description of iw.
+C wnvi: wflg - nv (i)
+C x: either a supervariable or an element
+
+C-----------------------------------------------------------------------
+C LOCAL POINTERS:
+C-----------------------------------------------------------------------
+
+ INTEGER P, P1, P2, P3, PDST, PEND, PJ, PME, PME1, PME2, PN, PSRC
+
+C Any parameter (pe (...) or pfree) or local variable
+C starting with "p" (for Pointer) is an index into iw,
+C and all indices into iw use variables starting with
+C "p." The only exception to this rule is the iwlen
+C input argument.
+
+C p: pointer into lots of things
+C p1: pe (i) for some variable i (start of element list)
+C p2: pe (i) + elen (i) - 1 for some var. i (end of el. list)
+C p3: index of first supervariable in clean list
+C pdst: destination pointer, for compression
+C pend: end of memory to compress
+C pj: pointer into an element or variable
+C pme: pointer into the current element (pme1...pme2)
+C pme1: the current element, me, is stored in iw (pme1...pme2)
+C pme2: the end of the current element
+C pn: pointer into a "clean" variable, also used to compress
+C psrc: source pointer, for compression
+
+C-----------------------------------------------------------------------
+C FUNCTIONS CALLED:
+C-----------------------------------------------------------------------
+
+ INTRINSIC MAX, MIN, MOD
+
+C=======================================================================
+C INITIALIZATIONS
+C=======================================================================
+
+ WFLG = 2
+ MINDEG = 1
+ NCMPA = 0
+ NEL = 0
+ HMOD = MAX (1, N-1)
+ DMAX = 0
+ MEM = PFREE - 1
+ MAXMEM = MEM
+ ME = 0
+
+ DO 10 I = 1, N
+ LAST (I) = 0
+ HEAD (I) = 0
+ NV (I) = 1
+ W (I) = 1
+ ELEN (I) = 0
+ DEGREE (I) = LEN (I)
+10 CONTINUE
+
+C ----------------------------------------------------------------
+C initialize degree lists and eliminate rows with no off-diag. nz.
+C ----------------------------------------------------------------
+
+ DO 20 I = 1, N
+
+ DEG = DEGREE (I)
+
+ IF (DEG .GT. 0) THEN
+
+C ----------------------------------------------------------
+C place i in the degree list corresponding to its degree
+C ----------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ HEAD (DEG) = I
+
+ ELSE
+
+C ----------------------------------------------------------
+C we have a variable that can be eliminated at once because
+C there is no off-diagonal non-zero in its row.
+C ----------------------------------------------------------
+
+ NEL = NEL + 1
+ ELEN (I) = -NEL
+ PE (I) = 0
+ W (I) = 0
+
+ ENDIF
+
+20 CONTINUE
+
+C=======================================================================
+C WHILE (selecting pivots) DO
+C=======================================================================
+
+30 CONTINUE
+ IF (NEL .LT. N) THEN
+
+C=======================================================================
+C GET PIVOT OF MINIMUM DEGREE
+C=======================================================================
+
+C -------------------------------------------------------------
+C find next supervariable for elimination
+C -------------------------------------------------------------
+
+ DO 40 DEG = MINDEG, N
+ ME = HEAD (DEG)
+ IF (ME .GT. 0) GOTO 50
+40 CONTINUE
+50 CONTINUE
+ MINDEG = DEG
+
+C -------------------------------------------------------------
+C remove chosen variable from link list
+C -------------------------------------------------------------
+
+ INEXT = NEXT (ME)
+ IF (INEXT .NE. 0) LAST (INEXT) = 0
+ HEAD (DEG) = INEXT
+
+C -------------------------------------------------------------
+C me represents the elimination of pivots nel+1 to nel+nv(me).
+C place me itself as the first in this set. It will be moved
+C to the nel+nv(me) position when the permutation vectors are
+C computed.
+C -------------------------------------------------------------
+
+ ELENME = ELEN (ME)
+ ELEN (ME) = - (NEL + 1)
+ NVPIV = NV (ME)
+ NEL = NEL + NVPIV
+
+C=======================================================================
+C CONSTRUCT NEW ELEMENT
+C=======================================================================
+
+C -------------------------------------------------------------
+C At this point, me is the pivotal supervariable. It will be
+C converted into the current element. Scan list of the
+C pivotal supervariable, me, setting tree pointers and
+C constructing new list of supervariables for the new element,
+C me. p is a pointer to the current position in the old list.
+C -------------------------------------------------------------
+
+C flag the variable "me" as being in Lme by negating nv (me)
+ NV (ME) = -NVPIV
+ DEGME = 0
+
+ IF (ELENME .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C construct the new element in place
+C ----------------------------------------------------------
+
+ PME1 = PE (ME)
+ PME2 = PME1 - 1
+
+ DO 60 P = PME1, PME1 + LEN (ME) - 1
+ I = IW (P)
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C ----------------------------------------------------
+C i is a principal variable not yet placed in Lme.
+C store i in new list
+C ----------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ PME2 = PME2 + 1
+ IW (PME2) = I
+
+C ----------------------------------------------------
+C remove variable i from degree list.
+C ----------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+60 CONTINUE
+C this element takes no new memory in iw:
+ NEWMEM = 0
+
+ ELSE
+
+C ----------------------------------------------------------
+C construct the new element in empty space, iw (pfree ...)
+C ----------------------------------------------------------
+
+ P = PE (ME)
+ PME1 = PFREE
+ SLENME = LEN (ME) - ELENME
+
+ DO 120 KNT1 = 1, ELENME + 1
+
+ IF (KNT1 .GT. ELENME) THEN
+C search the supervariables in me.
+ E = ME
+ PJ = P
+ LN = SLENME
+ ELSE
+C search the elements in me.
+ E = IW (P)
+ P = P + 1
+ PJ = PE (E)
+ LN = LEN (E)
+ ENDIF
+
+C -------------------------------------------------------
+C search for different supervariables and add them to the
+C new list, compressing when necessary. this loop is
+C executed once for each element in the list and once for
+C all the supervariables in the list.
+C -------------------------------------------------------
+
+ DO 110 KNT2 = 1, LN
+ I = IW (PJ)
+ PJ = PJ + 1
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C -------------------------------------------------
+C compress iw, if necessary
+C -------------------------------------------------
+
+ IF (PFREE .GT. IWLEN) THEN
+C prepare for compressing iw by adjusting
+C pointers and lengths so that the lists being
+C searched in the inner and outer loops contain
+C only the remaining entries.
+
+ PE (ME) = P
+ LEN (ME) = LEN (ME) - KNT1
+ IF (LEN (ME) .EQ. 0) THEN
+C nothing left of supervariable me
+ PE (ME) = 0
+ ENDIF
+ PE (E) = PJ
+ LEN (E) = LN - KNT2
+ IF (LEN (E) .EQ. 0) THEN
+C nothing left of element e
+ PE (E) = 0
+ ENDIF
+
+ NCMPA = NCMPA + 1
+C store first item in pe
+C set first entry to -item
+ DO 70 J = 1, N
+ PN = PE (J)
+ IF (PN .GT. 0) THEN
+ PE (J) = IW (PN)
+ IW (PN) = -J
+ ENDIF
+70 CONTINUE
+
+C psrc/pdst point to source/destination
+ PDST = 1
+ PSRC = 1
+ PEND = PME1 - 1
+
+C while loop:
+80 CONTINUE
+ IF (PSRC .LE. PEND) THEN
+C search for next negative entry
+ J = -IW (PSRC)
+ PSRC = PSRC + 1
+ IF (J .GT. 0) THEN
+ IW (PDST) = PE (J)
+ PE (J) = PDST
+ PDST = PDST + 1
+C copy from source to destination
+ LENJ = LEN (J)
+ DO 90 KNT3 = 0, LENJ - 2
+ IW (PDST + KNT3) = IW (PSRC + KNT3)
+90 CONTINUE
+ PDST = PDST + LENJ - 1
+ PSRC = PSRC + LENJ - 1
+ ENDIF
+ GOTO 80
+ ENDIF
+
+C move the new partially-constructed element
+ P1 = PDST
+ DO 100 PSRC = PME1, PFREE - 1
+ IW (PDST) = IW (PSRC)
+ PDST = PDST + 1
+100 CONTINUE
+ PME1 = P1
+ PFREE = PDST
+ PJ = PE (E)
+ P = PE (ME)
+ ENDIF
+
+C -------------------------------------------------
+C i is a principal variable not yet placed in Lme
+C store i in new list
+C -------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ IW (PFREE) = I
+ PFREE = PFREE + 1
+
+C -------------------------------------------------
+C remove variable i from degree link list
+C -------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+110 CONTINUE
+
+ IF (E .NE. ME) THEN
+C set tree pointer and flag to indicate element e is
+C absorbed into new element me (the parent of e is me)
+ PE (E) = -ME
+ W (E) = 0
+ ENDIF
+120 CONTINUE
+
+ PME2 = PFREE - 1
+C this element takes newmem new memory in iw (possibly zero)
+ NEWMEM = PFREE - PME1
+ MEM = MEM + NEWMEM
+ MAXMEM = MAX (MAXMEM, MEM)
+ ENDIF
+
+C -------------------------------------------------------------
+C me has now been converted into an element in iw (pme1..pme2)
+C -------------------------------------------------------------
+
+C degme holds the external degree of new element
+ DEGREE (ME) = DEGME
+ PE (ME) = PME1
+ LEN (ME) = PME2 - PME1 + 1
+
+C -------------------------------------------------------------
+C make sure that wflg is not too large. With the current
+C value of wflg, wflg+n must not cause integer overflow
+C -------------------------------------------------------------
+
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 130 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+130 CONTINUE
+ WFLG = 2
+ ENDIF
+
+C=======================================================================
+C COMPUTE (w (e) - wflg) = |Le\Lme| FOR ALL ELEMENTS
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 1: compute the external degrees of previous elements
+C with respect to the current element. That is:
+C (w (e) - wflg) = |Le \ Lme|
+C for each element e that appears in any supervariable in Lme.
+C The notation Le refers to the pattern (list of
+C supervariables) of a previous element e, where e is not yet
+C absorbed, stored in iw (pe (e) + 1 ... pe (e) + iw (pe (e))).
+C The notation Lme refers to the pattern of the current element
+C (stored in iw (pme1..pme2)). If (w (e) - wflg) becomes
+C zero, then the element e will be absorbed in scan 2.
+C -------------------------------------------------------------
+
+ DO 150 PME = PME1, PME2
+ I = IW (PME)
+ ELN = ELEN (I)
+ IF (ELN .GT. 0) THEN
+C note that nv (i) has been negated to denote i in Lme:
+ NVI = -NV (I)
+ WNVI = WFLG - NVI
+ DO 140 P = PE (I), PE (I) + ELN - 1
+ E = IW (P)
+ WE = W (E)
+ IF (WE .GE. WFLG) THEN
+C unabsorbed element e has been seen in this loop
+ WE = WE - NVI
+ ELSE IF (WE .NE. 0) THEN
+C e is an unabsorbed element
+C this is the first we have seen e in all of Scan 1
+ WE = DEGREE (E) + WNVI
+ ENDIF
+ W (E) = WE
+140 CONTINUE
+ ENDIF
+150 CONTINUE
+
+C=======================================================================
+C DEGREE UPDATE AND ELEMENT ABSORPTION
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 2: for each i in Lme, sum up the degree of Lme (which
+C is degme), plus the sum of the external degrees of each Le
+C for the elements e appearing within i, plus the
+C supervariables in i. Place i in hash list.
+C -------------------------------------------------------------
+
+ DO 180 PME = PME1, PME2
+ I = IW (PME)
+ P1 = PE (I)
+ P2 = P1 + ELEN (I) - 1
+ PN = P1
+ HASH = 0
+ DEG = 0
+
+C ----------------------------------------------------------
+C scan the element list associated with supervariable i
+C ----------------------------------------------------------
+
+C UMFPACK/MA38-style approximate degree:
+ DO 160 P = P1, P2
+ E = IW (P)
+ WE = W (E)
+ IF (WE .NE. 0) THEN
+C e is an unabsorbed element
+ DEG = DEG + WE - WFLG
+ IW (PN) = E
+ PN = PN + 1
+ HASH = HASH + E
+ ENDIF
+160 CONTINUE
+
+C count the number of elements in i (including me):
+ ELEN (I) = PN - P1 + 1
+
+C ----------------------------------------------------------
+C scan the supervariables in the list associated with i
+C ----------------------------------------------------------
+
+ P3 = PN
+ DO 170 P = P2 + 1, P1 + LEN (I) - 1
+ J = IW (P)
+ NVJ = NV (J)
+ IF (NVJ .GT. 0) THEN
+C j is unabsorbed, and not in Lme.
+C add to degree and add to new list
+ DEG = DEG + NVJ
+ IW (PN) = J
+ PN = PN + 1
+ HASH = HASH + J
+ ENDIF
+170 CONTINUE
+
+C ----------------------------------------------------------
+C update the degree and check for mass elimination
+C ----------------------------------------------------------
+
+ IF (ELEN (I) .EQ. 1 .AND. P3 .EQ. PN) THEN
+
+C -------------------------------------------------------
+C mass elimination
+C -------------------------------------------------------
+
+C There is nothing left of this node except for an
+C edge to the current pivot element. elen (i) is 1,
+C and there are no variables adjacent to node i.
+C Absorb i into the current pivot element, me.
+
+ PE (I) = -ME
+ NVI = -NV (I)
+ DEGME = DEGME - NVI
+ NVPIV = NVPIV + NVI
+ NEL = NEL + NVI
+ NV (I) = 0
+ ELEN (I) = 0
+
+ ELSE
+
+C -------------------------------------------------------
+C update the upper-bound degree of i
+C -------------------------------------------------------
+
+C the following degree does not yet include the size
+C of the current element, which is added later:
+ DEGREE (I) = MIN (DEGREE (I), DEG)
+
+C -------------------------------------------------------
+C add me to the list for i
+C -------------------------------------------------------
+
+C move first supervariable to end of list
+ IW (PN) = IW (P3)
+C move first element to end of element part of list
+ IW (P3) = IW (P1)
+C add new element to front of list.
+ IW (P1) = ME
+C store the new length of the list in len (i)
+ LEN (I) = PN - P1 + 1
+
+C -------------------------------------------------------
+C place in hash bucket. Save hash key of i in last (i).
+C -------------------------------------------------------
+
+ HASH = MOD (HASH, HMOD) + 1
+ J = HEAD (HASH)
+ IF (J .LE. 0) THEN
+C the degree list is empty, hash head is -j
+ NEXT (I) = -J
+ HEAD (HASH) = -I
+ ELSE
+C degree list is not empty
+C use last (head (hash)) as hash head
+ NEXT (I) = LAST (J)
+ LAST (J) = I
+ ENDIF
+ LAST (I) = HASH
+ ENDIF
+180 CONTINUE
+
+ DEGREE (ME) = DEGME
+
+C -------------------------------------------------------------
+C Clear the counter array, w (...), by incrementing wflg.
+C -------------------------------------------------------------
+
+ DMAX = MAX (DMAX, DEGME)
+ WFLG = WFLG + DMAX
+
+C make sure that wflg+n does not cause integer overflow
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 190 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+190 CONTINUE
+ WFLG = 2
+ ENDIF
+C at this point, w (1..n) .lt. wflg holds
+
+C=======================================================================
+C SUPERVARIABLE DETECTION
+C=======================================================================
+
+ DO 250 PME = PME1, PME2
+ I = IW (PME)
+ IF (NV (I) .LT. 0) THEN
+C i is a principal variable in Lme
+
+C -------------------------------------------------------
+C examine all hash buckets with 2 or more variables. We
+C do this by examing all unique hash keys for super-
+C variables in the pattern Lme of the current element, me
+C -------------------------------------------------------
+
+ HASH = LAST (I)
+C let i = head of hash bucket, and empty the hash bucket
+ J = HEAD (HASH)
+ IF (J .EQ. 0) GOTO 250
+ IF (J .LT. 0) THEN
+C degree list is empty
+ I = -J
+ HEAD (HASH) = 0
+ ELSE
+C degree list is not empty, restore last () of head
+ I = LAST (J)
+ LAST (J) = 0
+ ENDIF
+ IF (I .EQ. 0) GOTO 250
+
+C while loop:
+200 CONTINUE
+ IF (NEXT (I) .NE. 0) THEN
+
+C ----------------------------------------------------
+C this bucket has one or more variables following i.
+C scan all of them to see if i can absorb any entries
+C that follow i in hash bucket. Scatter i into w.
+C ----------------------------------------------------
+
+ LN = LEN (I)
+ ELN = ELEN (I)
+C do not flag the first element in the list (me)
+ DO 210 P = PE (I) + 1, PE (I) + LN - 1
+ W (IW (P)) = WFLG
+210 CONTINUE
+
+C ----------------------------------------------------
+C scan every other entry j following i in bucket
+C ----------------------------------------------------
+
+ JLAST = I
+ J = NEXT (I)
+
+C while loop:
+220 CONTINUE
+ IF (J .NE. 0) THEN
+
+C -------------------------------------------------
+C check if j and i have identical nonzero pattern
+C -------------------------------------------------
+
+ IF (LEN (J) .NE. LN) THEN
+C i and j do not have same size data structure
+ GOTO 240
+ ENDIF
+ IF (ELEN (J) .NE. ELN) THEN
+C i and j do not have same number of adjacent el
+ GOTO 240
+ ENDIF
+C do not flag the first element in the list (me)
+ DO 230 P = PE (J) + 1, PE (J) + LN - 1
+ IF (W (IW (P)) .NE. WFLG) THEN
+C an entry (iw(p)) is in j but not in i
+ GOTO 240
+ ENDIF
+230 CONTINUE
+
+C -------------------------------------------------
+C found it! j can be absorbed into i
+C -------------------------------------------------
+
+ PE (J) = -I
+C both nv (i) and nv (j) are negated since they
+C are in Lme, and the absolute values of each
+C are the number of variables in i and j:
+ NV (I) = NV (I) + NV (J)
+ NV (J) = 0
+ ELEN (J) = 0
+C delete j from hash bucket
+ J = NEXT (J)
+ NEXT (JLAST) = J
+ GOTO 220
+
+C -------------------------------------------------
+240 CONTINUE
+C j cannot be absorbed into i
+C -------------------------------------------------
+
+ JLAST = J
+ J = NEXT (J)
+ GOTO 220
+ ENDIF
+
+C ----------------------------------------------------
+C no more variables can be absorbed into i
+C go to next i in bucket and clear flag array
+C ----------------------------------------------------
+
+ WFLG = WFLG + 1
+ I = NEXT (I)
+ IF (I .NE. 0) GOTO 200
+ ENDIF
+ ENDIF
+250 CONTINUE
+
+C=======================================================================
+C RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVAR. FROM ELEMENT
+C=======================================================================
+
+ P = PME1
+ NLEFT = N - NEL
+ DO 260 PME = PME1, PME2
+ I = IW (PME)
+ NVI = -NV (I)
+ IF (NVI .GT. 0) THEN
+C i is a principal variable in Lme
+C restore nv (i) to signify that i is principal
+ NV (I) = NVI
+
+C -------------------------------------------------------
+C compute the external degree (add size of current elem)
+C -------------------------------------------------------
+
+ DEG = MAX (1, MIN (DEGREE (I) + DEGME-NVI, NLEFT-NVI))
+
+C -------------------------------------------------------
+C place the supervariable at the head of the degree list
+C -------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ LAST (I) = 0
+ HEAD (DEG) = I
+
+C -------------------------------------------------------
+C save the new degree, and find the minimum degree
+C -------------------------------------------------------
+
+ MINDEG = MIN (MINDEG, DEG)
+ DEGREE (I) = DEG
+
+C -------------------------------------------------------
+C place the supervariable in the element pattern
+C -------------------------------------------------------
+
+ IW (P) = I
+ P = P + 1
+ ENDIF
+260 CONTINUE
+
+C=======================================================================
+C FINALIZE THE NEW ELEMENT
+C=======================================================================
+
+ NV (ME) = NVPIV + DEGME
+C nv (me) is now the degree of pivot (including diagonal part)
+C save the length of the list for the new element me
+ LEN (ME) = P - PME1
+ IF (LEN (ME) .EQ. 0) THEN
+C there is nothing left of the current pivot element
+ PE (ME) = 0
+ W (ME) = 0
+ ENDIF
+ IF (NEWMEM .NE. 0) THEN
+C element was not constructed in place: deallocate part
+C of it (final size is less than or equal to newmem,
+C since newly nonprincipal variables have been removed).
+ PFREE = P
+ MEM = MEM - NEWMEM + LEN (ME)
+ ENDIF
+
+C=======================================================================
+C END WHILE (selecting pivots)
+ GOTO 30
+ ENDIF
+C=======================================================================
+
+C=======================================================================
+C COMPUTE THE PERMUTATION VECTORS
+C=======================================================================
+
+C ----------------------------------------------------------------
+C The time taken by the following code is O(n). At this
+C point, elen (e) = -k has been done for all elements e,
+C and elen (i) = 0 has been done for all nonprincipal
+C variables i. At this point, there are no principal
+C supervariables left, and all elements are absorbed.
+C ----------------------------------------------------------------
+
+C ----------------------------------------------------------------
+C compute the ordering of unordered nonprincipal variables
+C ----------------------------------------------------------------
+
+ DO 290 I = 1, N
+ IF (ELEN (I) .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C i is an un-ordered row. Traverse the tree from i until
+C reaching an element, e. The element, e, was the
+C principal supervariable of i and all nodes in the path
+C from i to when e was selected as pivot.
+C ----------------------------------------------------------
+
+ J = -PE (I)
+C while (j is a variable) do:
+270 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ J = -PE (J)
+ GOTO 270
+ ENDIF
+ E = J
+
+C ----------------------------------------------------------
+C get the current pivot ordering of e
+C ----------------------------------------------------------
+
+ K = -ELEN (E)
+
+C ----------------------------------------------------------
+C traverse the path again from i to e, and compress the
+C path (all nodes point to e). Path compression allows
+C this code to compute in O(n) time. Order the unordered
+C nodes in the path, and place the element e at the end.
+C ----------------------------------------------------------
+
+ J = I
+C while (j is a variable) do:
+280 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ JNEXT = -PE (J)
+ PE (J) = -E
+ IF (ELEN (J) .EQ. 0) THEN
+C j is an unordered row
+ ELEN (J) = K
+ K = K + 1
+ ENDIF
+ J = JNEXT
+ GOTO 280
+ ENDIF
+C leave elen (e) negative, so we know it is an element
+ ELEN (E) = -K
+ ENDIF
+290 CONTINUE
+
+C ----------------------------------------------------------------
+C reset the inverse permutation (elen (1..n)) to be positive,
+C and compute the permutation (last (1..n)).
+C ----------------------------------------------------------------
+
+ DO 300 I = 1, N
+ K = ABS (ELEN (I))
+ LAST (K) = I
+ ELEN (I) = K
+300 CONTINUE
+
+C=======================================================================
+C RETURN THE MEMORY USAGE IN IW
+C=======================================================================
+
+C If maxmem is less than or equal to iwlen, then no compressions
+C occurred, and iw (maxmem+1 ... iwlen) was unused. Otherwise
+C compressions did occur, and iwlen would have had to have been
+C greater than or equal to maxmem for no compressions to occur.
+C Return the value of maxmem in the pfree argument.
+
+ PFREE = MAXMEM
+
+ RETURN
+ END
+
diff --git a/src/C/SuiteSparse/CHOLMOD/Check/License.txt b/src/C/SuiteSparse/CHOLMOD/Check/License.txt
new file mode 100644
index 0000000..8a20b17
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Check/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Check module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/src/C/SuiteSparse/CHOLMOD/Check/cholmod_check.c b/src/C/SuiteSparse/CHOLMOD/Check/cholmod_check.c
new file mode 100644
index 0000000..49a638b
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Check/cholmod_check.c
@@ -0,0 +1,2618 @@
+/* ========================================================================== */
+/* === Check/cholmod_check ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Routines to check and print the contents of the 5 CHOLMOD objects:
+ *
+ * No CHOLMOD routine calls the check or print routines. If a user wants to
+ * check CHOLMOD's input parameters, a separate call to the appropriate check
+ * routine should be used before calling other CHOLMOD routines.
+ *
+ * cholmod_check_common check statistics and workspace in Common
+ * cholmod_check_sparse check sparse matrix in compressed column form
+ * cholmod_check_dense check dense matrix
+ * cholmod_check_factor check factorization
+ * cholmod_check_triplet check sparse matrix in triplet form
+ *
+ * cholmod_print_common print statistics in Common
+ * cholmod_print_sparse print sparse matrix in compressed column form
+ * cholmod_print_dense print dense matrix
+ * cholmod_print_factor print factorization
+ * cholmod_print_triplet print sparse matrix in triplet form
+ *
+ * In addition, this file contains routines to check and print three types of
+ * integer vectors:
+ *
+ * cholmod_check_perm check a permutation of 0:n-1 (no duplicates)
+ * cholmod_check_subset check a subset of 0:n-1 (duplicates OK)
+ * cholmod_check_parent check an elimination tree
+ *
+ * cholmod_print_perm print a permutation
+ * cholmod_print_subset print a subset
+ * cholmod_print_parent print an elimination tree
+ *
+ * Each Common->print level prints the items at or below the given level:
+ *
+ * 0: print nothing; just check the data structures and return TRUE/FALSE
+ * 1: error messages
+ * 2: warning messages
+ * 3: one-line summary of each object printed
+ * 4: short summary of each object (first and last few entries)
+ * 5: entire contents of the object
+ *
+ * No CHOLMOD routine calls these routines, so no printing occurs unless
+ * the user specifically calls a cholmod_print_* routine. Thus, the default
+ * print level is 3.
+ *
+ * Common->precise controls the # of digits printed for numerical entries
+ * (5 if FALSE, 15 if TRUE).
+ *
+ * If Common->print_function is NULL, then no printing occurs. The
+ * cholmod_check_* and cholmod_print_* routines still check their inputs and
+ * return TRUE/FALSE if the object is valid or not.
+ *
+ * This file also includes debugging routines that are enabled only when
+ * NDEBUG is defined in cholmod_internal.h (cholmod_dump_*).
+ */
+
+#ifndef NCHECK
+
+#include "cholmod_internal.h"
+#include "cholmod_check.h"
+
+/* ========================================================================== */
+/* === printing definitions ================================================= */
+/* ========================================================================== */
+
+#ifdef LONG
+#define I8 "%8ld"
+#define I_8 "%-8ld"
+#else
+#define I8 "%8d"
+#define I_8 "%-8d"
+#endif
+
+#define PR(i,format,arg) \
+{ \
+ if (print >= i && Common->print_function != NULL) \
+ { \
+ (Common->print_function) (format, arg) ; \
+ } \
+}
+
+#define P1(format,arg) PR(1,format,arg)
+#define P2(format,arg) PR(2,format,arg)
+#define P3(format,arg) PR(3,format,arg)
+#define P4(format,arg) PR(4,format,arg)
+
+#define ERR(msg) \
+{ \
+ P1 ("\nCHOLMOD ERROR: %s: ", type) ; \
+ if (name != NULL) \
+ { \
+ P1 ("%s", name) ; \
+ } \
+ P1 (": %s\n", msg) ; \
+ ERROR (CHOLMOD_INVALID, "invalid") ; \
+ return (FALSE) ; \
+}
+
+/* print a numerical value */
+#define PRINTVALUE(value) \
+{ \
+ if (Common->precise) \
+ { \
+ P4 (" %23.15e", value) ; \
+ } \
+ else \
+ { \
+ P4 (" %.5g", value) ; \
+ } \
+}
+
+/* start printing */
+#define ETC_START(count,limit) \
+{ \
+ count = (init_print == 4) ? (limit) : (-1) ; \
+}
+
+/* re-enable printing if condition is met */
+#define ETC_ENABLE(condition,count,limit) \
+{ \
+ if ((condition) && init_print == 4) \
+ { \
+ count = limit ; \
+ print = 4 ; \
+ } \
+}
+
+/* turn off printing if limit is reached */
+#define ETC_DISABLE(count) \
+{ \
+ if ((count >= 0) && (count-- == 0) && print == 4) \
+ { \
+ P4 ("%s", " ...\n") ; \
+ print = 3 ; \
+ } \
+}
+
+/* re-enable printing, or turn if off after limit is reached */
+#define ETC(condition,count,limit) \
+{ \
+ ETC_ENABLE (condition, count, limit) ; \
+ ETC_DISABLE (count) ; \
+}
+
+#define BOOLSTR(x) ((x) ? "true " : "false")
+
+/* ========================================================================== */
+/* === print_value ========================================================== */
+/* ========================================================================== */
+
+static void print_value
+(
+ Int print,
+ Int xtype,
+ double *Xx,
+ double *Xz,
+ Int p,
+ cholmod_common *Common)
+{
+ if (xtype == CHOLMOD_REAL)
+ {
+ PRINTVALUE (Xx [p]) ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ P4 ("%s", "(") ;
+ PRINTVALUE (Xx [2*p ]) ;
+ P4 ("%s", " , ") ;
+ PRINTVALUE (Xx [2*p+1]) ;
+ P4 ("%s", ")") ;
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ P4 ("%s", "(") ;
+ PRINTVALUE (Xx [p]) ;
+ P4 ("%s", " , ") ;
+ PRINTVALUE (Xz [p]) ;
+ P4 ("%s", ")") ;
+ }
+}
+
+/* ========================================================================== */
+/* === cholmod_check_common ================================================= */
+/* ========================================================================== */
+
+/* Print and verify the contents of Common */
+
+static int check_common
+(
+ Int print,
+ char *name,
+ cholmod_common *Common
+)
+{
+ double fl, lnz ;
+ double *Xwork ;
+ Int *Flag, *Head ;
+ UF_long mark ;
+ Int i, nrow, nmethods, ordering, xworksize, amd_printed, init_print ;
+ char *type = "common" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print control parameters and statistics */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ init_print = print ;
+
+ P2 ("%s", "\n") ;
+
+ P1 ("CHOLMOD version %d", CHOLMOD_MAIN_VERSION) ;
+ P1 (".%d", CHOLMOD_SUB_VERSION) ;
+ P1 (".%d", CHOLMOD_SUBSUB_VERSION) ;
+ P1 (", %s: ", CHOLMOD_DATE) ;
+
+ if (name != NULL)
+ {
+ P1 ("%s: ", name) ;
+ }
+ switch (Common->status)
+ {
+
+ case CHOLMOD_OK:
+ P1 ("%s", "status: OK\n") ;
+ break ;
+
+ case CHOLMOD_OUT_OF_MEMORY:
+ P1 ("%s", "status: ERROR, out of memory\n") ;
+ break ;
+
+ case CHOLMOD_INVALID:
+ P1 ("%s", "status: ERROR, invalid parameter\n") ;
+ break ;
+
+ case CHOLMOD_TOO_LARGE:
+ P1 ("%s", "status: ERROR, problem too large\n") ;
+ break ;
+
+ case CHOLMOD_NOT_INSTALLED:
+ P1 ("%s", "status: ERROR, method not installed\n") ;
+ break ;
+
+ case CHOLMOD_NOT_POSDEF:
+ P1 ("%s", "status: warning, matrix not positive definite\n") ;
+ break ;
+
+ case CHOLMOD_DSMALL:
+ P1 ("%s", "status: warning, diagonal entry has tiny abs. value\n") ;
+ break ;
+
+ default:
+ ERR ("unknown status") ;
+ }
+
+ P2 (" Architecture: %s\n", CHOLMOD_ARCHITECTURE) ;
+ P3 (" sizeof(int): %d\n", (int) sizeof (int)) ;
+ P3 (" sizeof(UF_long): %d\n", (int) sizeof (UF_long)) ;
+ P3 (" sizeof(void *): %d\n", (int) sizeof (void *)) ;
+ P3 (" sizeof(double): %d\n", (int) sizeof (double)) ;
+ P3 (" sizeof(Int): %d (CHOLMOD's basic integer)\n", (int) sizeof (Int)) ;
+ P3 (" sizeof(BLAS_INT): %d (integer used in the BLAS)\n",
+ (int) sizeof (BLAS_INT)) ;
+
+ if (Common->fl != EMPTY)
+ {
+ P2 ("%s", " Results from most recent analysis:\n") ;
+ P2 (" Cholesky flop count: %.5g\n", Common->fl) ;
+ P2 (" Nonzeros in L: %.5g\n", Common->lnz) ;
+ }
+ if (Common->modfl != EMPTY)
+ {
+ P2 (" Update/downdate flop count: %.5g\n", Common->modfl) ;
+ }
+
+ P2 (" memory blocks in use: %8.0f\n", (double) (Common->malloc_count)) ;
+ P2 (" memory in use (MB): %8.1f\n",
+ (double) (Common->memory_inuse) / 1048576.) ;
+ P2 (" peak memory usage (MB): %8.1f\n",
+ (double) (Common->memory_usage) / 1048576.) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* primary control parameters and related ordering statistics */
+ /* ---------------------------------------------------------------------- */
+
+ P3 (" maxrank: update/downdate rank: "ID"\n",
+ (Int) CHOLMOD(maxrank) (0, Common)) ;
+ P3 (" supernodal control: %d", Common->supernodal) ;
+ P3 (" %g ", Common->supernodal_switch) ;
+ if (Common->supernodal <= CHOLMOD_SIMPLICIAL)
+ {
+ P3 ("%s", "(always do simplicial)\n") ;
+ }
+ else if (Common->supernodal == CHOLMOD_AUTO)
+ {
+ P3 ("(supernodal if flops/lnz >= %g)\n", Common->supernodal_switch) ;
+ }
+ else
+ {
+ P3 ("%s", "(always do supernodal)\n") ;
+ }
+
+ nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ;
+ nmethods = MAX (0, nmethods) ;
+
+ if (nmethods > 0)
+ {
+ P3 ("%s", " nmethods: number of ordering methods to try: ") ;
+ P3 (""ID"\n", nmethods) ;
+ }
+ else
+ {
+ P3 ("%s", " nmethods=0: default strategy: Try user permutation if "
+ "given. Try AMD.\n") ;
+#ifndef NPARTITION
+ if (Common->default_nesdis)
+ {
+ P3 ("%s", " Try NESDIS if AMD reports flops/nnz(L) >= 500 and "
+ "nnz(L)/nnz(A) >= 5.\n") ;
+ }
+ else
+ {
+ P3 ("%s", " Try METIS if AMD reports flops/nnz(L) >= 500 and "
+ "nnz(L)/nnz(A) >= 5.\n") ;
+ }
+#endif
+ P3 ("%s", " Select best ordering tried.\n") ;
+ Common->method [0].ordering = CHOLMOD_GIVEN ;
+ Common->method [1].ordering = CHOLMOD_AMD ;
+ Common->method [2].ordering = CHOLMOD_METIS ;
+#ifndef NPARTITION
+ nmethods = 3 ;
+#else
+ nmethods = 2 ;
+#endif
+ }
+
+ amd_printed = FALSE ;
+ for (i = 0 ; i < nmethods ; i++)
+ {
+ P3 (" method "ID": ", i) ;
+ ordering = Common->method [i].ordering ;
+ fl = Common->method [i].fl ;
+ lnz = Common->method [i].lnz ;
+ switch (ordering)
+ {
+
+ case CHOLMOD_NATURAL:
+ P3 ("%s", "natural\n") ;
+ break ;
+
+ case CHOLMOD_GIVEN:
+ P3 ("%s", "user permutation (if given)\n") ;
+ break ;
+
+ case CHOLMOD_AMD:
+ P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ;
+ amd_printed = TRUE ;
+ break ;
+
+ case CHOLMOD_COLAMD:
+ P3 ("%s", "AMD if factorizing A, COLAMD if factorizing AA')\n");
+ amd_printed = TRUE ;
+ break ;
+
+ case CHOLMOD_METIS:
+ P3 ("%s", "METIS_NodeND nested dissection\n") ;
+ break ;
+
+ case CHOLMOD_NESDIS:
+ P3 ("%s", "CHOLMOD nested dissection\n") ;
+
+ P3 (" nd_small: # nodes in uncut subgraph: "ID"\n",
+ (Int) (Common->method [i].nd_small)) ;
+ P3 (" nd_compress: compress the graph: %s\n",
+ BOOLSTR (Common->method [i].nd_compress)) ;
+ P3 (" nd_camd: use constrained min degree: %s\n",
+ BOOLSTR (Common->method [i].nd_camd)) ;
+ break ;
+
+ default:
+ P3 (ID, ordering) ;
+ ERR ("unknown ordering method") ;
+ break ;
+
+ }
+
+ if (!(ordering == CHOLMOD_NATURAL || ordering == CHOLMOD_GIVEN))
+ {
+ if (Common->method [i].prune_dense < 0)
+ {
+ P3 (" prune_dense: for pruning dense nodes: %s\n",
+ " none pruned") ;
+ }
+ else
+ {
+ P3 (" prune_dense: for pruning dense nodes: "
+ "%.5g\n",
+ Common->method [i].prune_dense) ;
+ P3 (" a dense node has degree "
+ ">= max(16,(%.5g)*sqrt(n))\n",
+ Common->method [i].prune_dense) ;
+ }
+ }
+
+ if (ordering == CHOLMOD_COLAMD || ordering == CHOLMOD_NESDIS)
+ {
+ if (Common->method [i].prune_dense2 < 0)
+ {
+ P3 (" prune_dense2: for pruning dense rows for AA':"
+ " %s\n", " none pruned") ;
+ }
+ else
+ {
+ P3 (" prune_dense2: for pruning dense rows for AA':"
+ " %.5g\n", Common->method [i].prune_dense2) ;
+ P3 (" a dense row has degree "
+ ">= max(16,(%.5g)*sqrt(ncol))\n",
+ Common->method [i].prune_dense2) ;
+ }
+ }
+
+ if (fl != EMPTY) P3 (" flop count: %.5g\n", fl) ;
+ if (lnz != EMPTY) P3 (" nnz(L): %.5g\n", lnz) ;
+ }
+
+ /* backup AMD results, if any */
+ if (!amd_printed)
+ {
+ P3 ("%s", " backup method: ") ;
+ P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ;
+ fl = Common->method [nmethods].fl ;
+ lnz = Common->method [nmethods].lnz ;
+ if (fl != EMPTY) P3 (" AMD flop count: %.5g\n", fl) ;
+ if (lnz != EMPTY) P3 (" AMD nnz(L): %.5g\n", lnz) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* arcane control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->final_asis)
+ {
+ P4 ("%s", " final_asis: TRUE, leave as is\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_asis: FALSE, convert when done\n") ;
+ if (Common->final_super)
+ {
+ P4 ("%s", " final_super: TRUE, leave in supernodal form\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_super: FALSE, convert to simplicial form\n") ;
+ }
+ if (Common->final_ll)
+ {
+ P4 ("%s", " final_ll: TRUE, convert to LL' form\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_ll: FALSE, convert to LDL' form\n") ;
+ }
+ if (Common->final_pack)
+ {
+ P4 ("%s", " final_pack: TRUE, pack when done\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_pack: FALSE, do not pack when done\n") ;
+ }
+ if (Common->final_monotonic)
+ {
+ P4 ("%s", " final_monotonic: TRUE, ensure L is monotonic\n") ;
+ }
+ else
+ {
+ P4 ("%s",
+ " final_monotonic: FALSE, do not ensure L is monotonic\n") ;
+ }
+ P4 (" final_resymbol: remove zeros from amalgamation: %s\n",
+ BOOLSTR (Common->final_resymbol)) ;
+ }
+
+ P4 (" dbound: LDL' diagonal threshold: % .5g\n Entries with abs. value"
+ " less than dbound are replaced with +/- dbound.\n",
+ Common->dbound) ;
+
+ P4 (" grow0: memory reallocation: % .5g\n", Common->grow0) ;
+ P4 (" grow1: memory reallocation: % .5g\n", Common->grow1) ;
+ P4 (" grow2: memory reallocation: %g\n", (double) (Common->grow2)) ;
+
+ P4 ("%s", " nrelax, zrelax: supernodal amalgamation rule:\n") ;
+ P4 ("%s", " s = # columns in two adjacent supernodes\n") ;
+ P4 ("%s", " z = % of zeros in new supernode if they are merged.\n") ;
+ P4 ("%s", " Two supernodes are merged if") ;
+ P4 (" (s <= %g) or (no new zero entries) or\n",
+ (double) (Common->nrelax [0])) ;
+ P4 (" (s <= %g and ", (double) (Common->nrelax [1])) ;
+ P4 ("z < %.5g%%) or", Common->zrelax [0] * 100) ;
+ P4 (" (s <= %g and ", (double) (Common->nrelax [2])) ;
+ P4 ("z < %.5g%%) or", Common->zrelax [1] * 100) ;
+ P4 (" (z < %.5g%%)\n", Common->zrelax [2] * 100) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check workspace */
+ /* ---------------------------------------------------------------------- */
+
+ mark = Common->mark ;
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ Head = Common->Head ;
+ if (nrow > 0)
+ {
+ if (mark < 0 || Flag == NULL || Head == NULL)
+ {
+ ERR ("workspace corrupted (Flag and/or Head missing)") ;
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (Flag [i] >= mark)
+ {
+ PRINT0 (("Flag ["ID"]="ID", mark = %ld\n", i, Flag [i], mark)) ;
+ ERR ("workspace corrupted (Flag)") ;
+ }
+ }
+ for (i = 0 ; i <= nrow ; i++)
+ {
+ if (Head [i] != EMPTY)
+ {
+ PRINT0 (("Head ["ID"] = "ID",\n", i, Head [i])) ;
+ ERR ("workspace corrupted (Head)") ;
+ }
+ }
+ }
+ xworksize = Common->xworksize ;
+ Xwork = Common->Xwork ;
+ if (xworksize > 0)
+ {
+ if (Xwork == NULL)
+ {
+ ERR ("workspace corrupted (Xwork missing)") ;
+ }
+ for (i = 0 ; i < xworksize ; i++)
+ {
+ if (Xwork [i] != 0.)
+ {
+ PRINT0 (("Xwork ["ID"] = %g\n", i, Xwork [i])) ;
+ ERR ("workspace corrupted (Xwork)") ;
+ }
+ }
+ }
+
+ /* workspace and parameters are valid */
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_common)
+(
+ cholmod_common *Common
+)
+{
+ return (check_common (0, NULL, Common)) ;
+}
+
+
+int CHOLMOD(print_common)
+(
+ /* ---- input ---- */
+ char *name, /* printed name of Common object */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int print = (Common == NULL) ? 3 : (Common->print) ;
+ return (check_common (print, name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_sparse ================================================= */
+/* ========================================================================== */
+
+/* Ensure that a sparse matrix in column-oriented form is valid, and optionally
+ * print it. Returns the number of entries on the diagonal or -1 if error.
+ *
+ * workspace: Iwork (nrow)
+ */
+
+static UF_long check_sparse
+(
+ Int *Wi,
+ Int print,
+ char *name,
+ cholmod_sparse *A,
+ UF_long *nnzdiag,
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az ;
+ Int *Ap, *Ai, *Anz ;
+ Int nrow, ncol, nzmax, sorted, packed, j, p, pend, i, nz, ilast,
+ space, init_print, dnz, count, xtype ;
+ char *type = "sparse" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD sparse: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (A == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ nzmax = A->nzmax ;
+ sorted = A->sorted ;
+ packed = A->packed ;
+ xtype = A->xtype ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ nz = CHOLMOD(nnz) (A, Common) ;
+
+ P3 (" "ID"", nrow) ;
+ P3 ("-by-"ID", ", ncol) ;
+ P3 ("nz "ID",", nz) ;
+ if (A->stype > 0)
+ {
+ P3 ("%s", " upper.") ;
+ }
+ else if (A->stype < 0)
+ {
+ P3 ("%s", " lower.") ;
+ }
+ else
+ {
+ P3 ("%s", " up/lo.") ;
+ }
+
+ P4 ("\n nzmax "ID", ", nzmax) ;
+ if (nz > nzmax)
+ {
+ ERR ("nzmax too small") ;
+ }
+ if (!sorted)
+ {
+ P4 ("%s", "un") ;
+ }
+ P4 ("%s", "sorted, ") ;
+ if (!packed)
+ {
+ P4 ("%s", "un") ;
+ }
+ P4 ("%s", "packed, ") ;
+
+ switch (A->itype)
+ {
+ case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ;
+ case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ;
+ case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ;
+ default: ERR ("unknown itype") ;
+ }
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (A->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("float unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ if (A->itype != ITYPE || A->dtype != DTYPE)
+ {
+ ERR ("integer and real type must match routine") ;
+ }
+
+ if (A->stype && nrow != ncol)
+ {
+ ERR ("symmetric but not square") ;
+ }
+
+ /* check for existence of Ap, Ai, Anz, Ax, and Az arrays */
+ if (Ap == NULL)
+ {
+ ERR ("p array not present") ;
+ }
+ if (Ai == NULL)
+ {
+ ERR ("i array not present") ;
+ }
+ if (!packed && Anz == NULL)
+ {
+ ERR ("nz array not present") ;
+ }
+ if (xtype != CHOLMOD_PATTERN && Ax == NULL)
+ {
+ ERR ("x array not present") ;
+ }
+ if (xtype == CHOLMOD_ZOMPLEX && Az == NULL)
+ {
+ ERR ("z array not present") ;
+ }
+
+ /* packed matrices must start at Ap [0] = 0 */
+ if (packed && Ap [0] != 0)
+ {
+ ERR ("p [0] must be zero") ;
+ }
+ if (packed && (Ap [ncol] < Ap [0] || Ap [ncol] > nzmax))
+ {
+ ERR ("p [ncol] invalid") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace if needed */
+ /* ---------------------------------------------------------------------- */
+
+ if (!sorted)
+ {
+ if (Wi == NULL)
+ {
+ CHOLMOD(allocate_work) (0, nrow, 0, Common) ;
+ Wi = Common->Iwork ; /* size nrow, (i/i/l) */
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = EMPTY ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check and print each column */
+ /* ---------------------------------------------------------------------- */
+
+ init_print = print ;
+ dnz = 0 ;
+ ETC_START (count, 8) ;
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ ETC (j == ncol-1, count, 4) ;
+ p = Ap [j] ;
+ if (packed)
+ {
+ pend = Ap [j+1] ;
+ nz = pend - p ;
+ }
+ else
+ {
+ /* Note that Anz [j] < 0 is treated as zero */
+ nz = MAX (0, Anz [j]) ;
+ pend = p + nz ;
+ }
+ /* Note that space can be negative if the matrix is non-monotonic */
+ space = Ap [j+1] - p ;
+ P4 (" col "ID":", j) ;
+ P4 (" nz "ID"", nz) ;
+ P4 (" start "ID"", p) ;
+ P4 (" end "ID"", pend) ;
+ if (!packed)
+ {
+ P4 (" space "ID"", space) ;
+ }
+ P4 ("%s", ":\n") ;
+ if (p < 0 || pend > nzmax)
+ {
+ ERR ("pointer invalid") ;
+ }
+ if (nz < 0 || nz > nrow)
+ {
+ ERR ("nz invalid") ;
+ }
+ ilast = EMPTY ;
+
+ for ( ; p < pend ; p++)
+ {
+ ETC (j == ncol-1 && p >= pend-4, count, -1) ;
+ i = Ai [p] ;
+ P4 (" "I8":", i) ;
+
+ print_value (print, xtype, Ax, Az, p, Common) ;
+
+ if (i == j)
+ {
+ dnz++ ;
+ }
+ if (i < 0 || i >= nrow)
+ {
+ ERR ("row index out of range") ;
+ }
+ if (sorted && i <= ilast)
+ {
+ ERR ("row indices out of order") ;
+ }
+ if (!sorted && Wi [i] == j)
+ {
+ ERR ("duplicate row index") ;
+ }
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ if (!sorted)
+ {
+ Wi [i] = j ;
+ }
+ }
+ }
+
+ /* matrix is valid */
+ P4 (" nnz on diagonal: "ID"\n", dnz) ;
+ P3 ("%s", " OK\n") ;
+ *nnzdiag = dnz ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ UF_long nnzdiag ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_sparse (NULL, 0, NULL, A, &nnzdiag, Common)) ;
+}
+
+
+int CHOLMOD(print_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to print */
+ char *name, /* printed name of sparse matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ UF_long nnzdiag ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_sparse (NULL, Common->print, name, A, &nnzdiag, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_dense ================================================== */
+/* ========================================================================== */
+
+/* Ensure a dense matrix is valid, and optionally print it. */
+
+static int check_dense
+(
+ Int print,
+ char *name,
+ cholmod_dense *X,
+ cholmod_common *Common
+)
+{
+ double *Xx, *Xz ;
+ Int i, j, d, nrow, ncol, nzmax, nz, init_print, count, xtype ;
+ char *type = "dense" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD dense: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (X == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ nzmax = X->nzmax ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ xtype = X->xtype ;
+
+ P3 (" "ID"", nrow) ;
+ P3 ("-by-"ID", ", ncol) ;
+ P4 ("\n leading dimension "ID", ", d) ;
+ P4 ("nzmax "ID", ", nzmax) ;
+ if (d * ncol > nzmax)
+ {
+ ERR ("nzmax too small") ;
+ }
+ if (d < nrow)
+ {
+ ERR ("leading dimension must be >= # of rows") ;
+ }
+ if (Xx == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_PATTERN: ERR ("pattern unsupported") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (X->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("single unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check and print each entry */
+ /* ---------------------------------------------------------------------- */
+
+ if (print >= 4)
+ {
+ init_print = print ;
+ ETC_START (count, 9) ;
+ nz = nrow * ncol ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ ETC (j == ncol-1, count, 5) ;
+ P4 (" col "ID":\n", j) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ ETC (j == ncol-1 && i >= nrow-4, count, -1) ;
+ P4 (" "I8":", i) ;
+
+ print_value (print, xtype, Xx, Xz, i+j*d, Common) ;
+
+ P4 ("%s", "\n") ;
+ }
+ }
+ }
+
+ /* dense is valid */
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_dense (0, NULL, X, Common)) ;
+}
+
+
+int CHOLMOD(print_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to print */
+ char *name, /* printed name of dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_dense (Common->print, name, X, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_subset ================================================= */
+/* ========================================================================== */
+
+/* Ensure S (0:len-1) is a subset of 0:n-1. Duplicates are allowed. S may be
+ * NULL. A negative len denotes the set 0:n-1.
+ *
+ * To check the rset and cset for A(rset,cset), where nc and nr are the length
+ * of cset and rset respectively:
+ *
+ * cholmod_check_subset (cset, nc, A->ncol, Common) ;
+ * cholmod_check_subset (rset, nr, A->nrow, Common) ;
+ *
+ * workspace: none
+ */
+
+static int check_subset
+(
+ Int *S,
+ UF_long len,
+ size_t n,
+ Int print,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int i, k, init_print, count ;
+ char *type = "subset" ;
+
+ init_print = print ;
+
+ if (S == NULL)
+ {
+ /* zero len denotes S = [ ], negative len denotes S = 0:n-1 */
+ len = (len < 0) ? (-1) : 0 ;
+ }
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD subset: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ P3 (" len: %ld ", len) ;
+ if (len < 0)
+ {
+ P3 ("%s", "(denotes 0:n-1) ") ;
+ }
+ P3 ("n: "ID"", (Int) n) ;
+ P4 ("%s", "\n") ;
+
+ if (len <= 0 || S == NULL)
+ {
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+ }
+
+ if (print >= 4)
+ {
+ ETC_START (count, 8) ;
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ ETC (k == ((Int) len) - 4, count, -1) ;
+ i = S [k] ;
+ P4 (" "I8":", k) ;
+ P4 (" "ID"\n", i) ;
+ if (i < 0 || i >= ((Int) n))
+ {
+ ERR ("entry out range") ;
+ }
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ i = S [k] ;
+ if (i < 0 || i >= ((Int) n))
+ {
+ ERR ("entry out range") ;
+ }
+ }
+ }
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_subset)
+(
+ /* ---- input ---- */
+ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_subset (Set, len, n, 0, NULL, Common)) ;
+}
+
+
+int CHOLMOD(print_subset)
+(
+ /* ---- input ---- */
+ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Set */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_subset (Set, len, n, Common->print, name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_perm =================================================== */
+/* ========================================================================== */
+
+/* Ensure that Perm [0..len-1] is a permutation of a subset of 0:n-1. Perm
+ * may be NULL, which is interpreted as the identity permutation. There can
+ * be no duplicate entries (len must be <= n).
+ *
+ * If n <= Common->nrow, then this routine takes O(len) time and does not
+ * allocate any memory, by using Common->Flag. Otherwise, it takes O(n) time
+ * and ensures that Common->Iwork is at least n*sizeof(Int) in size.
+ *
+ * To check the fset: cholmod_check_perm (fset, fsize, ncol, Common) ;
+ * To check a permutation: cholmod_check_perm (Perm, n, n, Common) ;
+ *
+ * workspace: Flag (n) if n <= Common->nrow, Iwork (n) otherwise.
+ */
+
+static int check_perm
+(
+ Int *Wi,
+ Int print,
+ char *name,
+ Int *Perm,
+ size_t len,
+ size_t n,
+ cholmod_common *Common
+)
+{
+ Int *Flag ;
+ Int i, k, mark, init_print, count ;
+ char *type = "perm" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* checks that take O(1) time */
+ /* ---------------------------------------------------------------------- */
+
+ if (Perm == NULL || n == 0)
+ {
+ /* Perm is valid implicit identity, or empty */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* checks that take O(n) time or require memory allocation */
+ /* ---------------------------------------------------------------------- */
+
+ init_print = print ;
+ ETC_START (count, 8) ;
+
+ if (Wi == NULL && n <= Common->nrow)
+ {
+ /* use the Common->Flag array if it's big enough */
+ mark = CHOLMOD(clear_flag) (Common) ;
+ Flag = Common->Flag ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ;
+ if (print >= 4)
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ ETC (k >= ((Int) len) - 4, count, -1) ;
+ i = Perm [k] ;
+ P4 (" "I8":", k) ;
+ P4 (""ID"\n", i) ;
+ if (i < 0 || i >= ((Int) n) || Flag [i] == mark)
+ {
+ CHOLMOD(clear_flag) (Common) ;
+ ERR ("invalid permutation") ;
+ }
+ Flag [i] = mark ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i >= ((Int) n) || Flag [i] == mark)
+ {
+ CHOLMOD(clear_flag) (Common) ;
+ ERR ("invalid permutation") ;
+ }
+ Flag [i] = mark ;
+ }
+ }
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ;
+ }
+ else
+ {
+ if (Wi == NULL)
+ {
+ /* use Common->Iwork instead, but initialize it first */
+ CHOLMOD(allocate_work) (0, n, 0, Common) ;
+ Wi = Common->Iwork ; /* size n, (i/i/i) is OK */
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ for (i = 0 ; i < ((Int) n) ; i++)
+ {
+ Wi [i] = FALSE ;
+ }
+ if (print >= 4)
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ ETC (k >= ((Int) len) - 4, count, -1) ;
+ i = Perm [k] ;
+ P4 (" "I8":", k) ;
+ P4 (""ID"\n", i) ;
+ if (i < 0 || i >= ((Int) n) || Wi [i])
+ {
+ ERR ("invalid permutation") ;
+ }
+ Wi [i] = TRUE ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i >= ((Int) n) || Wi [i])
+ {
+ ERR ("invalid permutation") ;
+ }
+ Wi [i] = TRUE ;
+ }
+ }
+ }
+
+ /* perm is valid */
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_perm)
+(
+ /* ---- input ---- */
+ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_perm (NULL, 0, NULL, Perm, len, n, Common)) ;
+}
+
+
+int CHOLMOD(print_perm)
+(
+ /* ---- input ---- */
+ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Perm */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok, print ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ print = Common->print ;
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD perm: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+ P3 (" len: "ID"", (Int) len) ;
+ P3 (" n: "ID"", (Int) n) ;
+ P4 ("%s", "\n") ;
+ ok = check_perm (NULL, print, name, Perm, len, n, Common) ;
+ if (ok)
+ {
+ P3 ("%s", " OK\n") ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_parent ================================================= */
+/* ========================================================================== */
+
+/* Ensure that Parent is a valid elimination tree of nodes 0 to n-1.
+ * If j is a root of the tree then Parent [j] is EMPTY (-1).
+ *
+ * NOTE: this check will fail if applied to the component tree (CParent) in
+ * cholmod_nested_dissection, unless it has been postordered and renumbered.
+ *
+ * workspace: none
+ */
+
+static int check_parent
+(
+ Int *Parent,
+ size_t n,
+ Int print,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int j, p, init_print, count ;
+ char *type = "parent" ;
+
+ init_print = print ;
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD parent: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ P3 (" n: "ID"", (Int) n) ;
+ P4 ("%s", "\n") ;
+
+ if (Parent == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* checks that take O(n) time */
+ /* ---------------------------------------------------------------------- */
+
+ ETC_START (count, 8) ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ ETC (j == ((Int) n) - 4, count, -1) ;
+ p = Parent [j] ;
+ P4 (" "I8":", j) ;
+ P4 (" "ID"\n", p) ;
+ if (!(p == EMPTY || p > j))
+ {
+ ERR ("invalid") ;
+ }
+ }
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_parent)
+(
+ /* ---- input ---- */
+ Int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_parent (Parent, n, 0, NULL, Common)) ;
+}
+
+
+int CHOLMOD(print_parent)
+(
+ /* ---- input ---- */
+ Int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ char *name, /* printed name of Parent */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_parent (Parent, n, Common->print, name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_factor ================================================= */
+/* ========================================================================== */
+
+static int check_factor
+(
+ Int *Wi,
+ Int print,
+ char *name,
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz, *Lnext, *Lprev, *Perm, *ColCount, *Lpi, *Lpx, *Super,
+ *Ls ;
+ Int n, nzmax, j, p, pend, i, nz, ordering, space, is_monotonic, minor,
+ count, precise, init_print, ilast, lnz, head, tail, jprev, plast,
+ jnext, examine_super, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol,
+ ps2, psxend, ssize, xsize, maxcsize, maxesize, nsrow2, jj, ii, xtype ;
+ char *type = "factor" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD factor: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (L == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ n = L->n ;
+ minor = L->minor ;
+ ordering = L->ordering ;
+ xtype = L->xtype ;
+
+ Perm = L->Perm ;
+ ColCount = L->ColCount ;
+ lnz = 0 ;
+
+ precise = Common->precise ;
+
+ P3 (" "ID"", n) ;
+ P3 ("-by-"ID"", n) ;
+
+ if (minor < n)
+ {
+ P3 (" not positive definite (column "ID")", minor) ;
+ }
+
+ switch (L->itype)
+ {
+ case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ;
+ case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ;
+ case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ;
+ default: ERR ("unknown itype") ;
+ }
+
+ switch (L->xtype)
+ {
+ case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (L->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("single unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ if (L->itype != ITYPE || L->dtype != DTYPE)
+ {
+ ERR ("integer and real type must match routine") ;
+ }
+
+ if (L->is_super)
+ {
+ P3 ("%s", " supernodal") ;
+ }
+ else
+ {
+ P3 ("%s", " simplicial") ;
+ }
+
+ if (L->is_ll)
+ {
+ P3 ("%s", ", LL'.") ;
+ }
+ else
+ {
+ P3 ("%s", ", LDL'.") ;
+ }
+
+ P4 ("%s", "\n ordering method used: ") ;
+ switch (L->ordering)
+ {
+ case CHOLMOD_POSTORDERED:P4 ("%s", "natural (postordered)") ; break ;
+ case CHOLMOD_NATURAL: P4 ("%s", "natural") ; break ;
+ case CHOLMOD_GIVEN: P4 ("%s", "user-provided") ; break ;
+ case CHOLMOD_AMD: P4 ("%s", "AMD") ; break ;
+ case CHOLMOD_COLAMD: P4 ("%s", "AMD for A, COLAMD for A*A'") ;break ;
+#ifndef NPARTITION
+ case CHOLMOD_METIS: P4 ("%s", "METIS NodeND") ; break ;
+ case CHOLMOD_NESDIS: P4 ("%s", "CHOLMOD nested dissection") ; break ;
+#endif
+ default: ERR ("unknown ordering") ;
+ }
+
+ P4 ("%s", "\n") ;
+
+ init_print = print ;
+
+ if (L->is_super && L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ ERR ("Supernodal zomplex L not supported") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check L->Perm */
+ /* ---------------------------------------------------------------------- */
+
+ if (!check_perm (Wi, print, name, Perm, n, n, Common))
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check L->ColCount */
+ /* ---------------------------------------------------------------------- */
+
+ if (ColCount == NULL)
+ {
+ ERR ("ColCount vector invalid") ;
+ }
+
+ ETC_START (count, 8) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ETC (j >= n-4, count, -1) ;
+ P4 (" col: "ID" ", j) ;
+ nz = ColCount [j] ;
+ P4 ("colcount: "ID"\n", nz) ;
+ if (nz < 0 || nz > n-j)
+ {
+ ERR ("ColCount out of range") ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check factor */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* check simplicial symbolic factor */
+ /* ------------------------------------------------------------------ */
+
+ /* nothing else to do */ ;
+
+ }
+ else if (L->xtype != CHOLMOD_PATTERN && !(L->is_super))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* check simplicial numerical factor */
+ /* ------------------------------------------------------------------ */
+
+ P4 ("monotonic: %d\n", L->is_monotonic) ;
+ nzmax = L->nzmax ;
+ P3 (" nzmax "ID".", nzmax) ;
+ P4 ("%s", "\n") ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+ Lprev = L->prev ;
+
+ /* check for existence of Lp, Li, Lnz, Lnext, Lprev, and Lx arrays */
+ if (Lp == NULL)
+ {
+ ERR ("p array not present") ;
+ }
+ if (Li == NULL)
+ {
+ ERR ("i array not present") ;
+ }
+ if (Lnz == NULL)
+ {
+ ERR ("nz array not present") ;
+ }
+ if (Lx == NULL)
+ {
+ ERR ("x array not present") ;
+ }
+ if (xtype == CHOLMOD_ZOMPLEX && Lz == NULL)
+ {
+ ERR ("z array not present") ;
+ }
+ if (Lnext == NULL)
+ {
+ ERR ("next array not present") ;
+ }
+ if (Lprev == NULL)
+ {
+ ERR ("prev array not present") ;
+ }
+
+ ETC_START (count, 8) ;
+
+ /* check each column of L */
+ plast = 0 ;
+ is_monotonic = TRUE ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ETC (j >= n-3, count, -1) ;
+ p = Lp [j] ;
+ nz = Lnz [j] ;
+ pend = p + nz ;
+ lnz += nz ;
+
+ P4 (" col "ID":", j) ;
+ P4 (" nz "ID"", nz) ;
+ P4 (" start "ID"", p) ;
+ P4 (" end "ID"", pend) ;
+
+ if (Lnext [j] < 0 || Lnext [j] > n)
+ {
+ ERR ("invalid link list") ;
+ }
+ space = Lp [Lnext [j]] - p ;
+
+ P4 (" space "ID"", space) ;
+ P4 (" free "ID":\n", space - nz) ;
+
+ if (p < 0 || pend > nzmax || space < 1)
+ {
+ ERR ("pointer invalid") ;
+ }
+ if (nz < 1 || nz > (n-j) || nz > space)
+ {
+ ERR ("nz invalid") ;
+ }
+ ilast = j-1 ;
+
+ if (p < plast)
+ {
+ is_monotonic = FALSE ;
+ }
+ plast = p ;
+
+ i = Li [p] ;
+ P4 (" "I8":", i) ;
+ if (i != j)
+ {
+ ERR ("diagonal missing") ;
+ }
+
+ print_value (print, xtype, Lx, Lz, p, Common) ;
+
+ P4 ("%s", "\n") ;
+ ilast = j ;
+ for (p++ ; p < pend ; p++)
+ {
+ ETC_DISABLE (count) ;
+ i = Li [p] ;
+ P4 (" "I8":", i) ;
+ if (i < j || i >= n)
+ {
+ ERR ("row index out of range") ;
+ }
+ if (i <= ilast)
+ {
+ ERR ("row indices out of order") ;
+ }
+
+ print_value (print, xtype, Lx, Lz, p, Common) ;
+
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ }
+ }
+
+ if (L->is_monotonic && !is_monotonic)
+ {
+ ERR ("columns not monotonic") ;
+ }
+
+ /* check the link list */
+ head = n+1 ;
+ tail = n ;
+ j = head ;
+ jprev = EMPTY ;
+ count = 0 ;
+ for ( ; ; )
+ {
+ if (j < 0 || j > n+1 || count > n+2)
+ {
+ ERR ("invalid link list") ;
+ }
+ jnext = Lnext [j] ;
+ if (j >= 0 && j < n)
+ {
+ if (jprev != Lprev [j])
+ {
+ ERR ("invalid link list") ;
+ }
+ }
+ count++ ;
+ if (j == tail)
+ {
+ break ;
+ }
+ jprev = j ;
+ j = jnext ;
+ }
+ if (Lnext [tail] != EMPTY || count != n+2)
+ {
+ ERR ("invalid link list") ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* check supernodal numeric or symbolic factor */
+ /* ------------------------------------------------------------------ */
+
+ nsuper = L->nsuper ;
+ ssize = L->ssize ;
+ xsize = L->xsize ;
+ maxcsize = L->maxcsize ;
+ maxesize = L->maxesize ;
+ Ls = L->s ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Super = L->super ;
+ Lx = L->x ;
+ ETC_START (count, 8) ;
+
+ P4 (" ssize "ID" ", ssize) ;
+ P4 ("xsize "ID" ", xsize) ;
+ P4 ("maxcsize "ID" ", maxcsize) ;
+ P4 ("maxesize "ID"\n", maxesize) ;
+
+ if (Ls == NULL)
+ {
+ ERR ("invalid: L->s missing") ;
+ }
+ if (Lpi == NULL)
+ {
+ ERR ("invalid: L->pi missing") ;
+ }
+ if (Lpx == NULL)
+ {
+ ERR ("invalid: L->px missing") ;
+ }
+ if (Super == NULL)
+ {
+ ERR ("invalid: L->super missing") ;
+ }
+
+ if (L->xtype != CHOLMOD_PATTERN)
+ {
+ /* numerical supernodal factor */
+ if (Lx == NULL)
+ {
+ ERR ("invalid: L->x missing") ;
+ }
+ if (Ls [0] == EMPTY)
+ {
+ ERR ("invalid: L->s not defined") ;
+ }
+ examine_super = TRUE ;
+ }
+ else
+ {
+ /* symbolic supernodal factor, but only if it has been computed */
+ examine_super = (Ls [0] != EMPTY) ;
+ }
+
+ if (examine_super)
+ {
+ if (Lpi [0] != 0 || MAX (1, Lpi [nsuper]) != ssize)
+ {
+ PRINT0 (("Lpi [0] "ID", Lpi [nsuper = "ID"] = "ID"\n",
+ Lpi [0], nsuper, Lpi [nsuper])) ;
+ ERR ("invalid: L->pi invalid") ;
+ }
+ if (Lpx [0] != 0 || MAX (1, Lpx [nsuper]) != xsize)
+ {
+ ERR ("invalid: L->px invalid") ;
+ }
+
+ /* check and print each supernode */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ psxend = Lpx [s+1] ;
+
+ ETC (s == nsuper-1, count, 4) ;
+
+ P4 (" supernode "ID", ", s) ;
+ P4 ("col "ID" ", k1) ;
+ P4 ("to "ID". ", k2-1) ;
+ P4 ("nz in first col: "ID".\n", nsrow) ;
+ P4 (" values start "ID", ", psx) ;
+ P4 ("end "ID"\n", psxend) ;
+
+ if (k1 > k2 || k1 < 0 || k2 > n || nsrow < nscol || nsrow2 < 0
+ || psxend - psx != nsrow * nscol)
+ {
+ ERR ("invalid supernode") ;
+ }
+
+ lnz += nscol * nsrow - (nscol*nscol - nscol)/2 ;
+
+ if (L->xtype != CHOLMOD_PATTERN)
+ {
+ /* print each column of the supernode */
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ ETC_ENABLE (s == nsuper-1 && jj >= nscol-3, count, -1) ;
+ j = k1 + jj ;
+ P4 (" col "ID"\n", j) ;
+ ilast = j ;
+ i = Ls [psi + jj] ;
+ P4 (" "I8":", i) ;
+ if (i != j)
+ {
+ ERR ("row index invalid") ;
+ }
+
+ /* PRINTVALUE (Lx [psx + jj + jj*nsrow]) ; */
+ print_value (print, xtype, Lx, NULL,
+ psx + jj + jj*nsrow, Common) ;
+
+ P4 ("%s", "\n") ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ ETC_DISABLE (count) ;
+ i = Ls [psi + ii] ;
+ P4 (" "I8":", i) ;
+ if (i <= ilast || i > n)
+ {
+ ERR ("row index out of range") ;
+ }
+
+ /* PRINTVALUE (Lx [psx + ii + jj*nsrow]) ; */
+ print_value (print, xtype, Lx, NULL,
+ psx + ii + jj*nsrow, Common) ;
+
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ }
+ }
+ }
+ else
+ {
+ /* just print the leading column of the supernode */
+ P4 (" col "ID"\n", k1) ;
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ ETC (s == nsuper-1 && jj >= nscol-3, count, -1) ;
+ j = k1 + jj ;
+ i = Ls [psi + jj] ;
+ P4 (" "I8"", i) ;
+ if (i != j)
+ {
+ ERR ("row index invalid") ;
+ }
+ P4 ("%s", "\n") ;
+ }
+ ilast = j ;
+ for (ii = nscol ; ii < nsrow ; ii++)
+ {
+ ETC_DISABLE (count) ;
+ i = Ls [psi + ii] ;
+ P4 (" "I8"", i) ;
+ if (i <= ilast || i > n)
+ {
+ ERR ("row index out of range") ;
+ }
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ }
+ }
+ }
+ }
+ }
+
+ /* factor is valid */
+ P3 (" nz "ID"", lnz) ;
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_factor)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_factor (NULL, 0, NULL, L, Common)) ;
+}
+
+
+int CHOLMOD(print_factor)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to print */
+ char *name, /* printed name of factor */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_factor (NULL, Common->print, name, L, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_triplet ================================================ */
+/* ========================================================================== */
+
+/* Ensure a triplet matrix is valid, and optionally print it. */
+
+static int check_triplet
+(
+ Int print,
+ char *name,
+ cholmod_triplet *T,
+ cholmod_common *Common
+)
+{
+ double *Tx, *Tz ;
+ Int *Ti, *Tj ;
+ Int i, j, p, nrow, ncol, nzmax, nz, xtype, init_print, count ;
+ char *type = "triplet" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD triplet: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (T == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ nzmax = T->nzmax ;
+ nz = T->nnz ;
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ xtype = T->xtype ;
+
+
+ P3 (" "ID"", nrow) ;
+ P3 ("-by-"ID", ", ncol) ;
+ P3 ("nz "ID",", nz) ;
+ if (T->stype > 0)
+ {
+ P3 ("%s", " upper.") ;
+ }
+ else if (T->stype < 0)
+ {
+ P3 ("%s", " lower.") ;
+ }
+ else
+ {
+ P3 ("%s", " up/lo.") ;
+ }
+
+ P4 ("\n nzmax "ID", ", nzmax) ;
+ if (nz > nzmax)
+ {
+ ERR ("nzmax too small") ;
+ }
+
+ switch (T->itype)
+ {
+ case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ;
+ case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ;
+ case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ;
+ default: ERR ("unknown itype") ;
+ }
+
+ switch (T->xtype)
+ {
+ case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (T->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("single unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ if (T->itype != ITYPE || T->dtype != DTYPE)
+ {
+ ERR ("integer and real type must match routine") ;
+ }
+
+ if (T->stype && nrow != ncol)
+ {
+ ERR ("symmetric but not square") ;
+ }
+
+ /* check for existence of Ti, Tj, Tx arrays */
+ if (Tj == NULL)
+ {
+ ERR ("j array not present") ;
+ }
+ if (Ti == NULL)
+ {
+ ERR ("i array not present") ;
+ }
+
+ if (xtype != CHOLMOD_PATTERN && Tx == NULL)
+ {
+ ERR ("x array not present") ;
+ }
+ if (xtype == CHOLMOD_ZOMPLEX && Tz == NULL)
+ {
+ ERR ("z array not present") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check and print each entry */
+ /* ---------------------------------------------------------------------- */
+
+ init_print = print ;
+ ETC_START (count, 8) ;
+
+ for (p = 0 ; p < nz ; p++)
+ {
+ ETC (p >= nz-4, count, -1) ;
+ i = Ti [p] ;
+ P4 (" "I8":", p) ;
+ P4 (" "I_8"", i) ;
+ if (i < 0 || i >= nrow)
+ {
+ ERR ("row index out of range") ;
+ }
+ j = Tj [p] ;
+ P4 (" "I_8"", j) ;
+ if (j < 0 || j >= ncol)
+ {
+ ERR ("column index out of range") ;
+ }
+
+ print_value (print, xtype, Tx, Tz, p, Common) ;
+
+ P4 ("%s", "\n") ;
+ }
+
+ /* triplet matrix is valid */
+ P3 ("%s", " OK\n") ;
+ return (TRUE) ;
+}
+
+
+
+int CHOLMOD(check_triplet)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_triplet (0, NULL, T, Common)) ;
+}
+
+
+int CHOLMOD(print_triplet)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to print */
+ char *name, /* printed name of triplet matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_triplet (Common->print, name, T, Common)) ;
+}
+
+
+
+/* ========================================================================== */
+/* === CHOLMOD debugging routines =========================================== */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+/* The global variables present only when debugging enabled. */
+int CHOLMOD(dump) = 0 ;
+int CHOLMOD(dump_malloc) = -1 ;
+
+/* workspace: no debug routines use workspace in Common */
+
+/* ========================================================================== */
+/* === cholmod_dump_init ==================================================== */
+/* ========================================================================== */
+
+void CHOLMOD(dump_init) (char *s, cholmod_common *Common)
+{
+ FILE *f ;
+ f = fopen ("debug", "r") ;
+ if (f == NULL)
+ {
+ CHOLMOD(dump) = 0 ;
+ }
+ else
+ {
+ fscanf (f, "%d", &CHOLMOD(dump)) ;
+ fclose (f) ;
+ }
+ PRINT1 (("%s: cholmod_dump_init, D = %d\n", s, CHOLMOD(dump))) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_sparse ================================================== */
+/* ========================================================================== */
+
+UF_long CHOLMOD(dump_sparse) /* returns nnz (diag (A)) or EMPTY if error */
+(
+ cholmod_sparse *A,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int *Wi ;
+ UF_long nnzdiag ;
+ Int ok ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (0) ;
+ }
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ Wi = malloc (MAX (1, A->nrow) * sizeof (Int)) ;
+ ok = check_sparse (Wi, CHOLMOD(dump), name, A, &nnzdiag, Common) ;
+ if (Wi != NULL) free (Wi) ;
+ return (ok ? nnzdiag : EMPTY) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_factor ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_factor)
+(
+ cholmod_factor *L,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int *Wi ;
+ int ok ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ Wi = malloc (MAX (1, L->n) * sizeof (Int)) ;
+ ok = check_factor (Wi, CHOLMOD(dump), name, L, Common) ;
+ if (Wi != NULL) free (Wi) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_perm ==================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_perm)
+(
+ Int *Perm,
+ size_t len,
+ size_t n,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int *Wi ;
+ int ok ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Wi = malloc (MAX (1, n) * sizeof (Int)) ;
+ ok = check_perm (Wi, CHOLMOD(dump), name, Perm, len, n,Common) ;
+ if (Wi != NULL) free (Wi) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_dense =================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_dense)
+(
+ cholmod_dense *X,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_dense (CHOLMOD(dump), name, X, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_triplet ================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(dump_triplet)
+(
+ cholmod_triplet *T,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_triplet (CHOLMOD(dump), name, T, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_subset ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_subset)
+(
+ Int *S,
+ size_t len,
+ size_t n,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_subset (S, len, n, CHOLMOD(dump), name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_parent ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_parent)
+(
+ Int *Parent,
+ size_t n,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_parent (Parent, n, CHOLMOD(dump), name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_real ==================================================== */
+/* ========================================================================== */
+
+void CHOLMOD(dump_real)
+(
+ char *name, Real *X, UF_long nrow, UF_long ncol, int lower, int xentry,
+ cholmod_common *Common
+)
+{
+ /* dump an nrow-by-ncol real dense matrix */
+ UF_long i, j ;
+ double x, z ;
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return ;
+ }
+ PRINT1 (("%s: dump_real, nrow: %ld ncol: %ld lower: %d\n",
+ name, nrow, ncol, lower)) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ PRINT2 ((" col %ld\n", j)) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ /* X is stored in column-major form */
+ if (lower && i < j)
+ {
+ PRINT2 ((" %5ld: -", i)) ;
+ }
+ else
+ {
+ x = *X ;
+ PRINT2 ((" %5ld: %e", i, x)) ;
+ if (xentry == 2)
+ {
+ z = *(X+1) ;
+ PRINT2 ((", %e", z)) ;
+ }
+ }
+ PRINT2 (("\n")) ;
+ X += xentry ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_super =================================================== */
+/* ========================================================================== */
+
+void CHOLMOD(dump_super)
+(
+ UF_long s,
+ Int *Super, Int *Lpi, Int *Ls, Int *Lpx, double *Lx,
+ int xentry,
+ cholmod_common *Common
+)
+{
+ Int k1, k2, do_values, psi, psx, nsrow, nscol, psend, ilast, p, i ;
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return ;
+ }
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ nscol = k2 - k1 ;
+ do_values = (Lpx != NULL) && (Lx != NULL) ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ nsrow = psend - psi ;
+ PRINT1 (("\nSuper %ld, columns "ID" to "ID", "ID" rows "ID" cols\n",
+ s, k1, k2-1, nsrow, nscol)) ;
+ ilast = -1 ;
+ for (p = psi ; p < psend ; p++)
+ {
+ i = Ls [p] ;
+ PRINT2 ((" "ID" : p-psi "ID"\n", i, p-psi)) ;
+ ASSERT (IMPLIES (p-psi < nscol, i == k1 + (p-psi))) ;
+ if (p-psi == nscol-1) PRINT2 (("------\n")) ;
+ ASSERT (i > ilast) ;
+ ilast = i ;
+ }
+ if (do_values)
+ {
+ psx = Lpx [s] ;
+ CHOLMOD(dump_real) ("Supernode", Lx + xentry*psx, nsrow, nscol, TRUE,
+ xentry, Common) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_mem ===================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_mem) (char *where, UF_long should, cholmod_common *Common)
+{
+ UF_long diff = should - Common->memory_inuse ;
+ if (diff != 0)
+ {
+ PRINT0 (("mem: %-15s peak %10g inuse %10g should %10g\n",
+ where, (double) Common->memory_usage, (double) Common->memory_inuse,
+ (double) should)) ;
+ PRINT0 (("mem: %s diff %ld !\n", where, diff)) ;
+ }
+ return (diff == 0) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_partition =============================================== */
+/* ========================================================================== */
+
+/* make sure we have a proper separator (for debugging only)
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(dump_partition)
+(
+ UF_long n,
+ Int *Cp,
+ Int *Ci,
+ Int *Cnw,
+ Int *Part,
+ UF_long sepsize,
+ cholmod_common *Common
+)
+{
+ Int chek [3], which, ok, i, j, p ;
+ PRINT1 (("bisect sepsize %ld\n", sepsize)) ;
+ ok = TRUE ;
+ chek [0] = 0 ;
+ chek [1] = 0 ;
+ chek [2] = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT2 (("--------j "ID" in part "ID" nw "ID"\n", j, Part [j], Cnw[j]));
+ which = Part [j] ;
+ for (p = Cp [j] ; p < Cp [j+1] ; p++)
+ {
+ i = Ci [p] ;
+ PRINT3 (("i "ID", part "ID"\n", i, Part [i])) ;
+ if (which == 0)
+ {
+ if (Part [i] == 1)
+ {
+ PRINT0 (("Error! "ID" "ID"\n", i, j)) ;
+ ok = FALSE ;
+ }
+ }
+ else if (which == 1)
+ {
+ if (Part [i] == 0)
+ {
+ PRINT0 (("Error! "ID" "ID"\n", i, j)) ;
+ ok = FALSE ;
+ }
+ }
+ }
+ if (which < 0 || which > 2)
+ {
+ PRINT0 (("Part out of range\n")) ;
+ ok = FALSE ;
+ }
+ chek [which] += Cnw [j] ;
+ }
+ PRINT1 (("sepsize %ld check "ID" "ID" "ID"\n",
+ sepsize, chek[0], chek[1],chek[2]));
+ if (sepsize != chek[2])
+ {
+ PRINT0 (("mismatch!\n")) ;
+ ok = FALSE ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_work ==================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_work) (int flag, int head, UF_long wsize,
+ cholmod_common *Common)
+{
+ double *W ;
+ Int *Flag, *Head ;
+ Int k, nrow, mark ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ Head = Common->Head ;
+ W = Common->Xwork ;
+ mark = Common->mark ;
+
+ if (wsize < 0)
+ {
+ /* check all of Xwork */
+ wsize = Common->xworksize ;
+ }
+ else
+ {
+ /* check on the first wsize doubles in Xwork */
+ wsize = MIN (wsize, (Int) (Common->xworksize)) ;
+ }
+
+ if (flag)
+ {
+ for (k = 0 ; k < nrow ; k++)
+ {
+ if (Flag [k] >= mark)
+ {
+ PRINT0 (("Flag invalid, Flag ["ID"] = "ID", mark = "ID"\n",
+ k, Flag [k], mark)) ;
+ ASSERT (0) ;
+ return (FALSE) ;
+ }
+ }
+ }
+
+ if (head)
+ {
+ for (k = 0 ; k < nrow ; k++)
+ {
+ if (Head [k] != EMPTY)
+ {
+ PRINT0 (("Head invalid, Head ["ID"] = "ID"\n", k, Head [k])) ;
+ ASSERT (0) ;
+ return (FALSE) ;
+ }
+ }
+ }
+
+ for (k = 0 ; k < wsize ; k++)
+ {
+ if (W [k] != 0.)
+ {
+ PRINT0 (("W invalid, W ["ID"] = %g\n", k, W [k])) ;
+ ASSERT (0) ;
+ return (FALSE) ;
+ }
+ }
+
+ return (TRUE) ;
+}
+#endif
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Check/cholmod_read.c b/src/C/SuiteSparse/CHOLMOD/Check/cholmod_read.c
new file mode 100644
index 0000000..afdbddf
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Check/cholmod_read.c
@@ -0,0 +1,1319 @@
+/* ========================================================================== */
+/* === Check/cholmod_read =================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis.
+ * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Read a sparse matrix in triplet or dense form. A triplet matrix can be
+ * returned as compressed-column sparse matrix. The file format is compatible
+ * with all variations of the Matrix Market "coordinate" and "array" format
+ * (http://www.nist.gov/MatrixMarket). The format supported by these routines
+ * also allow other formats, where the Matrix Market header is optional.
+ *
+ * Although the Matrix Market header is optional, I recommend that users stick
+ * with the strict Matrix Market format. The optional format appears here to
+ * support the reading of symmetric matrices stored with just their upper
+ * triangular parts present, for testing and development of the A->stype > 0
+ * format in CHOLMOD. That format is not included in the Matrix Market format.
+ *
+ * If the first line of the file starts with %%MatrixMarket, then it is
+ * interpretted as a file in Matrix Market format. This line must have
+ * the following format:
+ *
+ * %%MatrixMarket matrix <fmt> <type> <storage>
+ *
+ * <fmt> is one of: coordinate or array. The former is a sparse matrix in
+ * triplet form. The latter is a dense matrix in column-major form.
+ *
+ * <type> is one of: real, complex, pattern, or integer.
+ * The functions here convert the "integer" and "pattern" types to real.
+ *
+ * <storage> is one of: general, hermitian, symmetric, or skew-symmetric
+ *
+ * The strings are case-insensitive. Only the first character is
+ * significant (or the first two for skew-symmetric).
+ *
+ * <type> is ignored for all matrices; the actual type (real, complex,
+ * or pattern) is inferred from the number of tokens in each line of the
+ * file. For a "coordinate" matrix: 2: pattern, 3: real, 4: complex; for
+ * a dense "array" matrix: 1: real, 2: complex. This is compatible with
+ * the Matrix Market format, since pattern matrices must have two tokens
+ * per line, real matrices must have 3, and complex matrices must have 4.
+ * A storage of "general" implies an stype of zero (see below).
+ * "symmetric" and "hermitian" imply an stype of -1. Skew-symmetric and
+ * complex symmetric matrices are always returned with both upper and lower
+ * triangular parts present, with an stype of zero, since CHOLMOD does not
+ * have a method for representing skew-symmetric and complex symmetric
+ * matrices. Real symmetric and complex Hermitian matrices may optionally
+ * be returned with both parts present.
+ *
+ * Any other lines starting with "%" are treated as comments, and are ignored.
+ * Blank lines are ignored. The Matrix Market header is optional in this
+ * routine (it is not optional in the Matrix Market format).
+ *
+ * Note that complex matrices are always returned in CHOLMOD_COMPLEX format,
+ * not CHOLMOD_ZOMPLEX.
+ *
+ * -----------------------------------------------------------------------------
+ * Triplet matrices:
+ * -----------------------------------------------------------------------------
+ *
+ * The first data line of a triplet matrix contains 3 or 4 integers:
+ *
+ * nrow ncol nnz stype
+ *
+ * where stype is optional (stype does not appear in the Matrix Market format).
+ * The matrix is nrow-by-ncol. The following nnz lines (excluding comments
+ * and blank lines) each contain a single entry. Duplicates are permitted,
+ * and are summed in the output matrix.
+ *
+ * The stype is first derived from the Matrix Market header. If the stype
+ * appears as the fourth integer in the first data line, it is determined from
+ * that line.
+ *
+ * If stype is present, it denotes the storage format for the matrix.
+ * stype = 0 denotes an unsymmetric matrix (same as Matrix Market "general").
+ * stype = -1 denotes a real symmetric or complex Hermitian matrix whose lower
+ * triangular entries are stored. Entries may be present in the upper
+ * triangular part, but these are ignored (same as Matrix Market
+ * "real symmetric" and "complex Hermitian").
+ * stype = 1 denotes a real symmetric or complex Hermitian matrix whose upper
+ * triangular entries are stored. Entries may be present in the lower
+ * triangular part, but these are ignored. This option is not present
+ * in the Matrix Market format.
+ *
+ * If stype is not present (no Matrix Market header and not in the first data
+ * line) it is inferred from the rest of the data. If the matrix is
+ * rectangular, or has entries in both the upper and lower triangular parts,
+ * then it is assumed to be unsymmetric (stype=0). If only entries in the
+ * lower triangular part are present, the matrix is assumed to have stype = -1.
+ * If only entries in the upper triangular part are present, the matrix is
+ * assumed to have stype = 1.
+ *
+ * After the first data line (with nrow, ncol, nnz, and optionally stype),
+ * each nonzero consists of one line with 2, 3, or 4 entries. All lines must
+ * have the same number of entries. The first two entries are the row and
+ * column indices of the nonzero. If 3 entries are present, the 3rd entry is
+ * the numerical value, and the matrix is real. If 4 entries are present,
+ * the 3rd and 4th entries in the line are the real and imaginary parts of
+ * a complex value.
+ *
+ * The matrix can be either 0-based or 1-based. It is first assumed to be
+ * one-based (all matrices in the Matrix Market are one-based), with row indices
+ * in the range 1 to ncol and column indices in the range 1 to nrow. If a row
+ * or column index of zero is found, the matrix is assumed to be zero-based
+ * (with row indices in the range 0 to ncol-1 and column indices in the range 0
+ * to nrow-1).
+ *
+ * If Common->prefer_binary is set to its default value of FALSE, then
+ * for symmetric pattern-only matrices, the kth diagonal (if present) is set to
+ * one plus the degree of the row/column k, and the off-diagonal entries are set
+ * to -1. A symmetric pattern-only matrix with a zero-free diagonal is thus
+ * converted into a symmetric positive definite matrix. All entries are set to
+ * one for an unsymmetric pattern-only matrix. This differs from the
+ * Matrix Market format (A = mmread ('file') returns a binary pattern for A for
+ * symmetric pattern-only matrices). If Common->prefer_binary is TRUE, then
+ * this function returns a binary matrix (just like mmread('file')).
+ *
+ * -----------------------------------------------------------------------------
+ * Dense matrices:
+ * -----------------------------------------------------------------------------
+ *
+ * A dense matrix is specified by the Matrix Market "array" format. The
+ * Matrix Market header is optional; if not present, the matrix is assumed to
+ * be in the Matrix Market "general" format. The first data line contains just
+ * two integers:
+ *
+ * nrow ncol
+ *
+ * The <type> can be real, integer, or complex (not pattern). These functions
+ * convert an integer type to real. The entries in the matrix are stored in
+ * column-major format, with one line per entry. Two entries are present in
+ * each line for complex matrices, one for real and integer matrices. In
+ * rectangular and unsymmetric matrices, all entries are present. For real
+ * symmetric or complex Hermitian matrices, only entries in the lower triangular
+ * part appear. For skew-symmetric matrices, only entries in the strictly
+ * lower triangular part appear.
+ *
+ * Since CHOLMOD does not have a data structure for presenting dense symmetric/
+ * Hermitian matrices, these functions always return a dense matrix in its
+ * general form, with both upper and lower parts present.
+ */
+
+#ifndef NCHECK
+
+#include "cholmod_internal.h"
+#include "cholmod_check.h"
+#include <string.h>
+#include <ctype.h>
+
+/* The MatrixMarket format specificies a maximum line length of 1024 */
+#define MAXLINE 1030
+
+/* ========================================================================== */
+/* === get_line ============================================================= */
+/* ========================================================================== */
+
+/* Read one line of the file, return TRUE if successful, FALSE if EOF. */
+
+static int get_line (FILE *f, char *buf)
+{
+ buf [0] = '\0' ;
+ buf [1] = '\0' ;
+ buf [MAXLINE] = '\0' ;
+ return (fgets (buf, MAXLINE, f) != NULL) ;
+}
+
+/* ========================================================================== */
+/* === fix_inf ============================================================== */
+/* ========================================================================== */
+
+/* Replace huge values with +/- Inf's, since scanf and printf don't deal
+ * with Inf's properly.
+ */
+
+static double fix_inf (double x)
+{
+ if ((x >= HUGE_DOUBLE) || (x <= -HUGE_DOUBLE))
+ {
+ /* treat this as +/- Inf (assume 2*x leads to overflow) */
+ x = 2*x ;
+ }
+ return (x) ;
+}
+
+/* ========================================================================== */
+/* === is_blank_line ======================================================== */
+/* ========================================================================== */
+
+/* TRUE if s is a blank line or comment, FALSE otherwise */
+
+static int is_blank_line
+(
+ char *s
+)
+{
+ int c, k ;
+ if (s [0] == '%')
+ {
+ /* a comment line */
+ return (TRUE) ;
+ }
+ for (k = 0 ; k <= MAXLINE ; k++)
+ {
+ c = s [k] ;
+ if (c == '\0')
+ {
+ /* end of line */
+ break ;
+ }
+ if (!isspace (c))
+ {
+ /* non-space character */
+ return (FALSE) ;
+ }
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === read_header ========================================================== */
+/* ========================================================================== */
+
+/* Read the header. This consists of zero or more comment lines (blank, or
+ * starting with a "%" in the first column), followed by a single data line
+ * containing up to four numerical values.
+ *
+ * The first line may optionally be a Matrix Market header line, of the form
+ *
+ * %%MatrixMarket matrix <fmt> <type> <storage>
+ *
+ * The first data line of a sparse matrix in triplet form consists of 3 or 4
+ * numerical values:
+ *
+ * nrow ncol nnz stype
+ *
+ * where stype is optional (it does not appear in the Matrix Market file
+ * format). The first line of a dense matrix in column-major form consists of
+ * two numerical values:
+ *
+ * nrow ncol
+ *
+ * The stype of the matrix is determine either from the Matrix Market header,
+ * or (optionally) from the first data line. stypes of 0 to -3 directly
+ * correlate with the Matrix Market format; stype = 1 is an extension to that
+ * format.
+ *
+ * 999: unknown (will be inferred from the data)
+ * 1: real symmetric or complex Hermitian with upper part stored
+ * (not in the Matrix Market format)
+ * 0: unsymmetric (same as Matrix Market "general")
+ * -1: real symmetric or complex Hermitian, with lower part stored
+ * (Matrix Market "real symmetric" or "complex hermitian")
+ * -2: real or complex skew symmetric (lower part stored, can only be
+ * specified by Matrix Market header)
+ * -3: complex symmetric (lower part stored)
+ * specified by Matrix Market header)
+ *
+ * The Matrix Market header is optional. If stype appears in the first data
+ * line, it is determine by that data line. Otherwise, if the Matrix Market
+ * header appears, stype is determined from that header. If stype does not
+ * appear, it is set to "unknown" (999).
+ */
+
+#define STYPE_UNKNOWN 999
+#define STYPE_SYMMETRIC_UPPER 1
+#define STYPE_UNSYMMETRIC 0
+#define STYPE_SYMMETRIC_LOWER -1
+#define STYPE_SKEW_SYMMETRIC -2
+#define STYPE_COMPLEX_SYMMETRIC_LOWER -3
+
+static int read_header /* returns TRUE if successful, FALSE on error */
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from */
+ /* ---- output --- */
+ char *buf, /* a character array of size MAXLINE+1 */
+ int *mtype, /* CHOLMOD_TRIPLET or CHOLMOD_DENSE */
+ size_t *nrow, /* number of rows in the matrix */
+ size_t *ncol, /* number of columns in the matrix */
+ size_t *nnz, /* number of entries in a triplet matrix (0 for dense)*/
+ int *stype /* stype (see above) */
+)
+{
+ char *p ;
+ int first = TRUE, got_mm_header = FALSE, c, c2, is_complex, nitems ;
+ double l1, l2, l3, l4 ;
+
+ *mtype = CHOLMOD_TRIPLET ;
+ *nrow = 0 ;
+ *ncol = 0 ;
+ *nnz = 0 ;
+ *stype = STYPE_UNKNOWN ;
+
+ for ( ; ; )
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the next line */
+ /* ------------------------------------------------------------------ */
+
+ if (!get_line (f, buf))
+ {
+ /* premature end of file */
+ return (FALSE) ;
+ }
+
+ if (first && (strncmp (buf, "%%MatrixMarket", 14) == 0))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* read a Matrix Market header */
+ /* -------------------------------------------------------------- */
+
+ got_mm_header = TRUE ;
+ p = buf ;
+
+ /* -------------------------------------------------------------- */
+ /* get "matrix" token */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ if (c != 'm')
+ {
+ /* bad format */
+ return (FALSE) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* get the fmt token ("coord" or "array") */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ if (c == 'c')
+ {
+ *mtype = CHOLMOD_TRIPLET ;
+ }
+ else if (c == 'a')
+ {
+ *mtype = CHOLMOD_DENSE ;
+ }
+ else
+ {
+ /* bad format, neither "coordinate" nor "array" */
+ return (FALSE) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* get type token (real, pattern, complex, integer) */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ if (!(c == 'r' || c == 'p' || c == 'c' || c == 'i'))
+ {
+ /* bad format */
+ return (FALSE) ;
+ }
+ is_complex = (c == 'c') ;
+
+ /* -------------------------------------------------------------- */
+ /* get storage token (general, hermitian, symmetric, skew) */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ c2 = tolower (*(p+1)) ;
+ if (c == 'g')
+ {
+ /* "general" storage (unsymmetric matrix), both parts present */
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ else if (c == 's' && c2 == 'y')
+ {
+ /* "symmetric" */
+ if (is_complex)
+ {
+ /* complex symmetric, lower triangular part present */
+ *stype = STYPE_COMPLEX_SYMMETRIC_LOWER ;
+ }
+ else
+ {
+ /* real symmetric, lower triangular part present */
+ *stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ }
+ else if (c == 'h')
+ {
+ /* "hermitian" matrix, lower triangular part present */
+ *stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ else if (c == 's' && c2 == 'k')
+ {
+ /* "skew-symmetric" (real or complex), lower part present */
+ *stype = STYPE_SKEW_SYMMETRIC ;
+ }
+ else
+ {
+ /* bad format */
+ return (FALSE) ;
+ }
+
+ }
+ else if (is_blank_line (buf))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* blank line or comment line */
+ /* -------------------------------------------------------------- */
+
+ continue ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* read the first data line and return */
+ /* -------------------------------------------------------------- */
+
+ /* format: nrow ncol nnz stype */
+ l1 = EMPTY ;
+ l2 = EMPTY ;
+ l3 = 0 ;
+ l4 = 0 ;
+ nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &l3, &l4) ;
+ if (nitems < 2 || nitems > 4 || l1 > Int_max || l2 > Int_max)
+ {
+ /* invalid matrix */
+ return (FALSE) ;
+ }
+ *nrow = l1 ;
+ *ncol = l2 ;
+ if (nitems == 2)
+ {
+ /* a dense matrix */
+ if (!got_mm_header)
+ {
+ *mtype = CHOLMOD_DENSE ;
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ }
+ if (nitems == 3 || nitems == 4)
+ {
+ /* a sparse triplet matrix */
+ *nnz = l3 ;
+ if (!got_mm_header)
+ {
+ *mtype = CHOLMOD_TRIPLET ;
+ }
+ }
+ if (nitems == 4)
+ {
+ /* an stype specified here can only be 1, 0, or -1 */
+ if (l4 < 0)
+ {
+ *stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ else if (l4 > 0)
+ {
+ *stype = STYPE_SYMMETRIC_UPPER ;
+ }
+ else
+ {
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ }
+ if (*nrow != *ncol)
+ {
+ /* a rectangular matrix must be unsymmetric */
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ return (TRUE) ;
+ }
+
+ first = FALSE ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === read_triplet ========================================================= */
+/* ========================================================================== */
+
+/* Header has already been read in, including first line (nrow ncol nnz stype).
+ * Read the triplets. */
+
+static cholmod_triplet *read_triplet
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ size_t nrow, /* number of rows */
+ size_t ncol, /* number of columns */
+ size_t nnz, /* number of triplets in file to read */
+ int stype, /* stype from header, or "unknown" */
+ int prefer_unsym, /* if TRUE, always return T->stype of zero */
+ /* ---- workspace */
+ char *buf, /* of size MAXLINE+1 */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ double *Tx ;
+ Int *Ti, *Tj, *Rdeg, *Cdeg ;
+ cholmod_triplet *T ;
+ double l1, l2 ;
+ Int nitems, xtype, unknown, k, nshould, is_lower, is_upper, one_based, i, j,
+ imax, jmax, ignore, skew_symmetric, p, complex_symmetric ;
+ size_t s, nnz2, extra ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return for empty matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == 0 || ncol == 0 || nnz == 0)
+ {
+ /* return an empty matrix */
+ return (CHOLMOD(allocate_triplet) (nrow, ncol, 0, 0, CHOLMOD_REAL,
+ Common)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* special stype cases: unknown, skew symmetric, and complex symmetric */
+ /* ---------------------------------------------------------------------- */
+
+ unknown = (stype == STYPE_UNKNOWN) ;
+ skew_symmetric = (stype == STYPE_SKEW_SYMMETRIC) ;
+ complex_symmetric = (stype == STYPE_COMPLEX_SYMMETRIC_LOWER) ;
+
+ extra = 0 ;
+ if (stype < STYPE_SYMMETRIC_LOWER
+ || (prefer_unsym && stype != STYPE_UNSYMMETRIC))
+ {
+ /* 999: unknown might be converted to unsymmetric */
+ /* 1: symmetric upper converted to unsym. if prefer_unsym is TRUE */
+ /* -1: symmetric lower converted to unsym. if prefer_unsym is TRUE */
+ /* -2: real or complex skew symmetric converted to unsymmetric */
+ /* -3: complex symmetric converted to unsymmetric */
+ stype = STYPE_UNSYMMETRIC ;
+ extra = nnz ;
+ }
+ nnz2 = CHOLMOD(add_size_t) (nnz, extra, &ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = nrow + ncol */
+ s = CHOLMOD(add_size_t) (nrow, ncol, &ok) ;
+ if (!ok || nrow > Int_max || ncol > Int_max || nnz > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ Rdeg = Common->Iwork ; /* size nrow */
+ Cdeg = Rdeg + nrow ; /* size ncol */
+
+ /* ---------------------------------------------------------------------- */
+ /* read the triplets */
+ /* ---------------------------------------------------------------------- */
+
+ is_lower = TRUE ;
+ is_upper = TRUE ;
+ one_based = TRUE ;
+ imax = 0 ;
+ jmax = 0 ;
+
+ Tx = NULL ;
+ Ti = NULL ;
+ Tj = NULL ;
+ xtype = 999 ;
+ nshould = 0 ;
+
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the next triplet, skipping blank lines and comment lines */
+ /* ------------------------------------------------------------------ */
+
+ l1 = EMPTY ;
+ l2 = EMPTY ;
+ x = 0 ;
+ z = 0 ;
+
+ for ( ; ; )
+ {
+ if (!get_line (f, buf))
+ {
+ /* premature end of file - not enough triplets read in */
+ ERROR (CHOLMOD_INVALID, "premature EOF") ;
+ return (NULL) ;
+ }
+ if (is_blank_line (buf))
+ {
+ /* blank line or comment */
+ continue ;
+ }
+ nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &x, &z) ;
+ x = fix_inf (x) ;
+ z = fix_inf (z) ;
+ break ;
+ }
+
+ nitems = (nitems == EOF) ? 0 : nitems ;
+ i = l1 ;
+ j = l2 ;
+
+ /* ------------------------------------------------------------------ */
+ /* for first triplet: determine type and allocate triplet matrix */
+ /* ------------------------------------------------------------------ */
+
+ if (k == 0)
+ {
+ if (nitems < 2 || nitems > 4)
+ {
+ /* invalid matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+ else if (nitems == 2)
+ {
+ /* this will be converted into a real matrix later */
+ xtype = CHOLMOD_PATTERN ;
+ }
+ else if (nitems == 3)
+ {
+ xtype = CHOLMOD_REAL ;
+ }
+ else if (nitems == 4)
+ {
+ xtype = CHOLMOD_COMPLEX ;
+ }
+
+ /* the rest of the lines should have the same number of entries */
+ nshould = nitems ;
+
+ /* allocate triplet matrix */
+ T = CHOLMOD(allocate_triplet) (nrow, ncol, nnz2, stype,
+ (xtype == CHOLMOD_PATTERN ? CHOLMOD_REAL : xtype), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ T->nnz = nnz ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* save the entry in the triplet matrix */
+ /* ------------------------------------------------------------------ */
+
+ if (nitems != nshould || i < 0 || j < 0)
+ {
+ /* wrong format, premature end-of-file, or negative indices */
+ CHOLMOD(free_triplet) (&T, Common) ;
+ ERROR (CHOLMOD_INVALID, "invalid matrix file") ;
+ return (NULL) ;
+ }
+
+ Ti [k] = i ;
+ Tj [k] = j ;
+
+ if (i < j)
+ {
+ /* this entry is in the upper triangular part */
+ is_lower = FALSE ;
+ }
+ if (i > j)
+ {
+ /* this entry is in the lower triangular part */
+ is_upper = FALSE ;
+ }
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ Tx [k] = x ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Tx [2*k ] = x ; /* real part */
+ Tx [2*k+1] = z ; /* imaginary part */
+ }
+
+ if (i == 0 || j == 0)
+ {
+ one_based = FALSE ;
+ }
+
+ imax = MAX (i, imax) ;
+ jmax = MAX (j, jmax) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to zero-based */
+ /* ---------------------------------------------------------------------- */
+
+ if (one_based)
+ {
+ /* input matrix is one-based; convert matrix to zero-based */
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ Ti [k]-- ;
+ Tj [k]-- ;
+ }
+ }
+
+ if (one_based ?
+ (imax > (Int) nrow || jmax > (Int) ncol) :
+ (imax >= (Int) nrow || jmax >= (Int) ncol))
+ {
+ /* indices out of range */
+ CHOLMOD(free_triplet) (&T, Common) ;
+ ERROR (CHOLMOD_INVALID, "indices out of range") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the stype, if not yet known */
+ /* ---------------------------------------------------------------------- */
+
+ if (unknown)
+ {
+ if (is_lower && is_upper)
+ {
+ /* diagonal matrix, symmetric with upper part present */
+ stype = STYPE_SYMMETRIC_UPPER ;
+ }
+ else if (is_lower && !is_upper)
+ {
+ /* symmetric, lower triangular part present */
+ stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ else if (!is_lower && is_upper)
+ {
+ /* symmetric, upper triangular part present */
+ stype = STYPE_SYMMETRIC_UPPER ;
+ }
+ else
+ {
+ /* unsymmetric */
+ stype = STYPE_UNSYMMETRIC ;
+ extra = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* add the remainder of symmetric, skew-symmetric or Hermitian matrices */
+ /* ---------------------------------------------------------------------- */
+
+ /* note that this step is not done for real symmetric or complex Hermitian
+ * matrices, unless prefer_unsym is TRUE */
+ if (extra > 0)
+ {
+ p = nnz ;
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i != j)
+ {
+ Ti [p] = j ;
+ Tj [p] = i ;
+ if (xtype == CHOLMOD_REAL)
+ {
+ if (skew_symmetric)
+ {
+ Tx [p] = -Tx [k] ;
+ }
+ else
+ {
+ Tx [p] = Tx [k] ;
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ if (skew_symmetric)
+ {
+ Tx [2*p ] = -Tx [2*k ] ;
+ Tx [2*p+1] = -Tx [2*k+1] ;
+ }
+ else if (complex_symmetric)
+ {
+ Tx [2*p ] = Tx [2*k ] ;
+ Tx [2*p+1] = Tx [2*k+1] ;
+ }
+ else /* Hermitian */
+ {
+ Tx [2*p ] = Tx [2*k ] ;
+ Tx [2*p+1] = -Tx [2*k+1] ;
+ }
+ }
+ p++ ;
+ }
+ }
+ T->nnz = p ;
+ nnz = p ;
+ }
+
+ T->stype = stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create values for a pattern-only matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (xtype == CHOLMOD_PATTERN)
+ {
+ if (stype == STYPE_UNSYMMETRIC || Common->prefer_binary)
+ {
+ /* unsymmetric case, or binary case */
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ Tx [k] = 1 ;
+ }
+ }
+ else
+ {
+ /* compute the row and columm degrees (excluding the diagonal) */
+ for (i = 0 ; i < (Int) nrow ; i++)
+ {
+ Rdeg [i] = 0 ;
+ }
+ for (j = 0 ; j < (Int) ncol ; j++)
+ {
+ Cdeg [j] = 0 ;
+ }
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if ((stype < 0 && i > j) || (stype > 0 && i < j))
+ {
+ /* both a(i,j) and a(j,i) appear in the matrix */
+ Rdeg [i]++ ;
+ Cdeg [j]++ ;
+ Rdeg [j]++ ;
+ Cdeg [i]++ ;
+ }
+ }
+ /* assign the numerical values */
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ Tx [k] = (i == j) ? (1 + MAX (Rdeg [i], Cdeg [j])) : (-1) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the new triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === read_dense =========================================================== */
+/* ========================================================================== */
+
+/* Header has already been read in, including first line (nrow ncol).
+ * Read a dense matrix. */
+
+static cholmod_dense *read_dense
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ size_t nrow, /* number of rows */
+ size_t ncol, /* number of columns */
+ int stype, /* stype from header */
+ /* ---- workspace */
+ char *buf, /* of size MAXLINE+1 */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ double *Xx ;
+ cholmod_dense *X ;
+ Int nitems, xtype, nshould, i, j, k, kup, first ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return for empty matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == 0 || ncol == 0)
+ {
+ /* return an empty dense matrix */
+ return (CHOLMOD(zeros) (nrow, ncol, CHOLMOD_REAL, Common)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the entries */
+ /* ---------------------------------------------------------------------- */
+
+ first = TRUE ;
+
+ for (j = 0 ; j < (Int) ncol ; j++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the row index of the first entry in the file for column j */
+ /* ------------------------------------------------------------------ */
+
+ if (stype == STYPE_UNSYMMETRIC)
+ {
+ i = 0 ;
+ }
+ else if (stype == STYPE_SKEW_SYMMETRIC)
+ {
+ i = j+1 ;
+ }
+ else /* real symmetric or complex Hermitian lower */
+ {
+ i = j ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* get column j */
+ /* ------------------------------------------------------------------ */
+
+ for ( ; i < (Int) nrow ; i++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* get the next entry, skipping blank lines and comment lines */
+ /* -------------------------------------------------------------- */
+
+ x = 0 ;
+ z = 0 ;
+ for ( ; ; )
+ {
+
+ if (!get_line (f, buf))
+ {
+ /* premature end of file - not enough entries read in */
+ ERROR (CHOLMOD_INVALID, "premature EOF") ;
+ return (NULL) ;
+ }
+
+ if (is_blank_line (buf))
+ {
+ /* blank line or comment */
+ continue ;
+ }
+ nitems = sscanf (buf, "%lg %lg\n", &x, &z) ;
+ x = fix_inf (x) ;
+ z = fix_inf (z) ;
+ break ;
+ }
+
+ nitems = (nitems == EOF) ? 0 : nitems ;
+
+ /* -------------------------------------------------------------- */
+ /* for first entry: determine type and allocate dense matrix */
+ /* -------------------------------------------------------------- */
+
+ if (first)
+ {
+ first = FALSE ;
+
+ if (nitems < 1 || nitems > 2)
+ {
+ /* invalid matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+ else if (nitems == 1)
+ {
+ /* a real matrix */
+ xtype = CHOLMOD_REAL ;
+ }
+ else if (nitems == 2)
+ {
+ /* a complex matrix */
+ xtype = CHOLMOD_COMPLEX ;
+ }
+
+ /* the rest of the lines should have same number of entries */
+ nshould = nitems ;
+
+ /* allocate the result */
+ X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ Xx = X->x ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* save the entry in the dense matrix */
+ /* -------------------------------------------------------------- */
+
+ if (nitems != nshould)
+ {
+ /* wrong format or premature end-of-file */
+ CHOLMOD(free_dense) (&X, Common) ;
+ ERROR (CHOLMOD_INVALID, "invalid matrix file") ;
+ return (NULL) ;
+ }
+
+ k = i + j*nrow ;
+ kup = j + i*nrow ;
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ /* real matrix */
+ Xx [k] = x ;
+ if (k != kup)
+ {
+ if (stype == STYPE_SYMMETRIC_LOWER)
+ {
+ /* real symmetric matrix */
+ Xx [kup] = x ;
+ }
+ else if (stype == STYPE_SKEW_SYMMETRIC)
+ {
+ /* real skew symmetric matrix */
+ Xx [kup] = -x ;
+ }
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Xx [2*k ] = x ; /* real part */
+ Xx [2*k+1] = z ; /* imaginary part */
+ if (k != kup)
+ {
+ if (stype == STYPE_SYMMETRIC_LOWER)
+ {
+ /* complex Hermitian */
+ Xx [2*kup ] = x ; /* real part */
+ Xx [2*kup+1] = -z ; /* imaginary part */
+ }
+ else if (stype == STYPE_SKEW_SYMMETRIC)
+ {
+ /* complex skew symmetric */
+ Xx [2*kup ] = -x ; /* real part */
+ Xx [2*kup+1] = -z ; /* imaginary part */
+ }
+ if (stype == STYPE_COMPLEX_SYMMETRIC_LOWER)
+ {
+ /* complex symmetric */
+ Xx [2*kup ] = x ; /* real part */
+ Xx [2*kup+1] = z ; /* imaginary part */
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the new dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_triplet ================================================= */
+/* ========================================================================== */
+
+/* Read in a triplet matrix from a file. */
+
+cholmod_triplet *CHOLMOD(read_triplet)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ char buf [MAXLINE+1] ;
+ size_t nrow, ncol, nnz ;
+ int stype, mtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read the header and first data line */
+ /* ---------------------------------------------------------------------- */
+
+ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) ||
+ mtype != CHOLMOD_TRIPLET)
+ {
+ /* invalid matrix - this function can only read in a triplet matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (read_triplet (f, nrow, ncol, nnz, stype, FALSE, buf, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_sparse ================================================== */
+/* ========================================================================== */
+
+/* Read a sparse matrix from a file. See cholmod_read_triplet for a discussion
+ * of the file format.
+ *
+ * If Common->prefer_upper is TRUE (the default case), a symmetric matrix is
+ * returned stored in upper-triangular form (A->stype == 1).
+ */
+
+cholmod_sparse *CHOLMOD(read_sparse)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A, *A2 ;
+ cholmod_triplet *T ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to a sparse matrix in compressed-column form */
+ /* ---------------------------------------------------------------------- */
+
+ T = CHOLMOD(read_triplet) (f, Common) ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ;
+ CHOLMOD(free_triplet) (&T, Common) ;
+
+ if (Common->prefer_upper && A != NULL && A->stype == -1)
+ {
+ /* A=A' */
+ A2 = CHOLMOD(transpose) (A, 2, Common) ;
+ CHOLMOD(free_sparse) (&A, Common) ;
+ A = A2 ;
+ }
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_dense =================================================== */
+/* ========================================================================== */
+
+/* Read a dense matrix from a file. */
+
+cholmod_dense *CHOLMOD(read_dense)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ char buf [MAXLINE+1] ;
+ size_t nrow, ncol, nnz ;
+ int stype, mtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read the header and first data line */
+ /* ---------------------------------------------------------------------- */
+
+ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) ||
+ mtype != CHOLMOD_DENSE)
+ {
+ /* invalid matrix - this function can only read in a dense matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (read_dense (f, nrow, ncol, stype, buf, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_matrix ================================================== */
+/* ========================================================================== */
+
+/* Read a triplet matrix, sparse matrix or a dense matrix from a file. Returns
+ * a void pointer to either a cholmod_triplet, cholmod_sparse, or cholmod_dense
+ * object. The type of object is passed back to the caller as the mtype
+ * argument. */
+
+void *CHOLMOD(read_matrix)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ int prefer, /* If 0, a sparse matrix is always return as a
+ * cholmod_triplet form. It can have any stype
+ * (symmetric-lower, unsymmetric, or
+ * symmetric-upper).
+ * If 1, a sparse matrix is returned as an unsymmetric
+ * cholmod_sparse form (A->stype == 0), with both
+ * upper and lower triangular parts present.
+ * This is what the MATLAB mread mexFunction does,
+ * since MATLAB does not have an stype.
+ * If 2, a sparse matrix is returned with an stype of 0
+ * or 1 (unsymmetric, or symmetric with upper part
+ * stored).
+ * This argument has no effect for dense matrices.
+ */
+ /* ---- output---- */
+ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ void *G = NULL ;
+ cholmod_sparse *A, *A2 ;
+ cholmod_triplet *T ;
+ char buf [MAXLINE+1] ;
+ size_t nrow, ncol, nnz ;
+ int stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ RETURN_IF_NULL (mtype, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read the header to determine the mtype */
+ /* ---------------------------------------------------------------------- */
+
+ if (!read_header (f, buf, mtype, &nrow, &ncol, &nnz, &stype))
+ {
+ /* invalid matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read a matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (*mtype == CHOLMOD_TRIPLET)
+ {
+ /* read in the triplet matrix */
+ T = read_triplet (f, nrow, ncol, nnz, stype, prefer == 1, buf, Common) ;
+ if (prefer == 0)
+ {
+ /* return matrix in its original triplet form */
+ G = T ;
+ }
+ else
+ {
+ /* return matrix in a compressed-column form */
+ A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ;
+ CHOLMOD(free_triplet) (&T, Common) ;
+ if (A != NULL && prefer == 2 && A->stype == -1)
+ {
+ /* convert A from symmetric-lower to symmetric-upper */
+ A2 = CHOLMOD(transpose) (A, 2, Common) ;
+ CHOLMOD(free_sparse) (&A, Common) ;
+ A = A2 ;
+ }
+ *mtype = CHOLMOD_SPARSE ;
+ G = A ;
+ }
+ }
+ else if (*mtype == CHOLMOD_DENSE)
+ {
+ /* return a dense matrix */
+ G = read_dense (f, nrow, ncol, stype, buf, Common) ;
+ }
+ return (G) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Check/cholmod_write.c b/src/C/SuiteSparse/CHOLMOD/Check/cholmod_write.c
new file mode 100644
index 0000000..dc461ba
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Check/cholmod_write.c
@@ -0,0 +1,742 @@
+/* ========================================================================== */
+/* === Check/cholmod_write ================================================== */
+/* ========================================================================== */
+
+/* Write a matrix to a file in Matrix Market form.
+ *
+ * A can be sparse or full.
+ *
+ * If present and non-empty, A and Z must have the same dimension. Z contains
+ * the explicit zero entries in the matrix (which MATLAB drops). The entries
+ * of Z appear as explicit zeros in the output file. Z is optional. If it is
+ * an empty matrix it is ignored. Z must be sparse or empty, if present.
+ * It is ignored if A is full.
+ *
+ * filename is the name of the output file. comments is file whose
+ * contents are include after the Matrix Market header and before the first
+ * data line. Ignored if an empty string or not present.
+ *
+ * Except for the workspace used by cholmod_symmetry (ncol integers) for
+ * the sparse case, these routines use no workspace at all.
+ */
+
+#ifndef NCHECK
+
+#include "cholmod_internal.h"
+#include "cholmod_check.h"
+#include <string.h>
+#include <ctype.h>
+
+#define MMLEN 1024
+#define MAXLINE MMLEN+6
+
+/* ========================================================================== */
+/* === include_comments ===================================================== */
+/* ========================================================================== */
+
+/* Read in the comments file, if it exists, and copy it to the Matrix Market
+ * file. A "%" is prepended to each line. Returns TRUE if successful, FALSE
+ * otherwise.
+ */
+
+static int include_comments (FILE *f, char *comments)
+{
+ FILE *cf = NULL ;
+ char buffer [MAXLINE] ;
+ int ok = TRUE ;
+ if (comments != NULL && comments [0] != '\0')
+ {
+ cf = fopen (comments, "r") ;
+ if (cf == NULL)
+ {
+ return (FALSE) ;
+ }
+ while (ok && fgets (buffer, MAXLINE, cf) != NULL)
+ {
+ /* ensure the line is not too long */
+ buffer [MMLEN-1] = '\0' ;
+ buffer [MMLEN-2] = '\n' ;
+ ok = ok && (fprintf (f, "%%%s", buffer) > 0) ;
+ }
+ fclose (cf) ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === get_value ============================================================ */
+/* ========================================================================== */
+
+/* Get the pth value in the matrix. */
+
+static void get_value
+(
+ double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */
+ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */
+ Int p, /* get the pth entry */
+ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */
+ double *x, /* the real part */
+ double *z /* the imaginary part */
+)
+{
+ switch (xtype)
+ {
+ case CHOLMOD_PATTERN:
+ *x = 1 ;
+ *z = 0 ;
+ break ;
+
+ case CHOLMOD_REAL:
+ *x = Ax [p] ;
+ *z = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *x = Ax [2*p] ;
+ *z = Ax [2*p+1] ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *x = Ax [p] ;
+ *z = Az [p] ;
+ break ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === print_value ========================================================== */
+/* ========================================================================== */
+
+/* Print a numeric value to the file, using the shortest format that ensures
+ * the value is written precisely. Returns TRUE if successful, FALSE otherwise.
+ */
+
+static int print_value
+(
+ FILE *f, /* file to print to */
+ double x, /* value to print */
+ Int is_integer /* TRUE if printing as an integer */
+)
+{
+ double y, z ;
+ char s [MAXLINE], *p ;
+ Int width, i, c, dest, src ;
+ int ok ;
+
+ if (is_integer)
+ {
+ i = (Int) x ;
+ ok = (fprintf (f, ID, i) > 0) ;
+ return (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* handle Inf and NaN */
+ /* ---------------------------------------------------------------------- */
+
+ /* change -inf to -HUGE_DOUBLE, and change +inf and nan to +HUGE_DOUBLE */
+ if (CHOLMOD_IS_NAN (x) || x >= HUGE_DOUBLE)
+ {
+ x = HUGE_DOUBLE ;
+ }
+ else if (x <= -HUGE_DOUBLE)
+ {
+ x = -HUGE_DOUBLE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the smallest acceptable precision */
+ /* ---------------------------------------------------------------------- */
+
+ for (width = 6 ; width < 20 ; width++)
+ {
+ sprintf (s, "%.*g", width, x) ;
+ sscanf (s, "%lg", &y) ;
+ if (x == y) break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* shorten the string */
+ /* ---------------------------------------------------------------------- */
+
+ /* change "e+0" to "e", change "e+" to "e", and change "e-0" to "e-" */
+ for (i = 0 ; i < MAXLINE && s [i] != '\0' ; i++)
+ {
+ if (s [i] == 'e')
+ {
+ if (s [i+1] == '+')
+ {
+ dest = i+1 ;
+ if (s [i+2] == '0')
+ {
+ /* delete characters s[i+1] and s[i+2] */
+ src = i+3 ;
+ }
+ else
+ {
+ /* delete characters s[i+1] */
+ src = i+2 ;
+ }
+ }
+ else if (s [i+1] == '-')
+ {
+ dest = i+2 ;
+ if (s [i+2] == '0')
+ {
+ /* delete character s[i+2] */
+ src = i+3 ;
+ }
+ else
+ {
+ /* no change */
+ break ;
+ }
+ }
+ while (s [src] != '\0')
+ {
+ s [dest++] = s [src++] ;
+ }
+ s [dest] = '\0' ;
+ break ;
+ }
+ }
+
+ /* delete the leading "0" if present and not necessary */
+ p = s ;
+ s [MAXLINE-1] = '\0' ;
+ i = strlen (s) ;
+ if (i > 2 && s [0] == '0' && s [1] == '.')
+ {
+ /* change "0.x" to ".x" */
+ p = s + 1 ;
+ }
+ else if (i > 3 && s [0] == '-' && s [1] == '0' && s [2] == '.')
+ {
+ /* change "-0.x" to "-.x" */
+ s [1] = '-' ;
+ p = s + 1 ;
+ }
+
+#if 0
+ /* double-check */
+ i = sscanf (p, "%lg", &z) ;
+ if (i != 1 || y != z)
+ {
+ /* oops! something went wrong in the "e+0" edit, above. */
+ /* this "cannot" happen */
+ sprintf (s, "%.*g", width, x) ;
+ p = s ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print the value to the file */
+ /* ---------------------------------------------------------------------- */
+
+ ok = (fprintf (f, "%s", p) > 0) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === print_triplet ======================================================== */
+/* ========================================================================== */
+
+/* Print a triplet, converting it to one-based. Returns TRUE if successful,
+ * FALSE otherwise.
+ */
+
+static int print_triplet
+(
+ FILE *f, /* file to print to */
+ Int is_binary, /* TRUE if file is "pattern" */
+ Int is_complex, /* TRUE if file is "complex" */
+ Int is_integer, /* TRUE if file is "integer" */
+ Int i, /* row index (zero-based) */
+ Int j, /* column index (zero-based) */
+ double x, /* real part */
+ double z /* imaginary part */
+)
+{
+ int ok ;
+ ok = (fprintf (f, ID " " ID, 1+i, 1+j) > 0) ;
+ if (!is_binary)
+ {
+ fprintf (f, " ") ;
+ ok = ok && print_value (f, x, is_integer) ;
+ if (is_complex)
+ {
+ fprintf (f, " ") ;
+ ok = ok && print_value (f, z, is_integer) ;
+ }
+ }
+ ok = ok && (fprintf (f, "\n") > 0) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === ntriplets ============================================================ */
+/* ========================================================================== */
+
+/* Compute the number of triplets that will be printed to the file
+ * from the matrix A. */
+
+static Int ntriplets
+(
+ cholmod_sparse *A, /* matrix that will be printed */
+ Int is_sym /* TRUE if the file is symmetric (lower part only)*/
+)
+{
+ Int *Ap, *Ai, *Anz, packed, i, j, p, pend, ncol, stype, nz = 0 ;
+ if (A == NULL)
+ {
+ /* the Z matrix is NULL */
+ return (0) ;
+ }
+ stype = A->stype ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ ncol = A->ncol ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym)))
+ {
+ /* CHOLMOD matrix is symmetric-lower (and so is the file);
+ * or CHOLMOD matrix is unsymmetric and either A(i,j) is in
+ * the lower part or the file is unsymmetric. */
+ nz++ ;
+ }
+ else if (stype > 0 && i <= j)
+ {
+ /* CHOLMOD matrix is symmetric-upper, but the file is
+ * symmetric-lower. Need to transpose the entry. */
+ nz++ ;
+ }
+ }
+ }
+ return (nz) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_write_sparse ================================================= */
+/* ========================================================================== */
+
+/* Write a sparse matrix to a file in Matrix Market format. Optionally include
+ * comments, and print explicit zero entries given by the pattern of the Z
+ * matrix. If not NULL, the Z matrix must have the same dimensions and stype
+ * as A.
+ *
+ * Returns the symmetry in which the matrix was printed (1 to 7, see the
+ * CHOLMOD_MM_* codes in CHOLMOD/Include/cholmod_core.h), or -1 on failure.
+ *
+ * If A and Z are sorted on input, and either unsymmetric (stype = 0) or
+ * symmetric-lower (stype < 0), and if A and Z do not overlap, then the triplets
+ * are sorted, first by column and then by row index within each column, with
+ * no duplicate entries. If all the above holds except stype > 0, then the
+ * triplets are sorted by row first and then column.
+ */
+
+int CHOLMOD(write_sparse)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_sparse *A, /* matrix to print */
+ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ double *Ax, *Az ;
+ Int *Ap, *Ai, *Anz, *Zp, *Zi, *Znz ;
+ Int nrow, ncol, is_complex, symmetry, i, j, q, iz, p, nz, is_binary, stype,
+ is_integer, asym, is_sym, xtype, apacked, zpacked, pend, qend, k, zsym ;
+ int ok ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (f, EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ if (Z != NULL && (Z->nrow == 0 || Z->ncol == 0))
+ {
+ /* Z is non-NULL but empty, so treat it as a NULL matrix */
+ Z = NULL ;
+ }
+ if (Z != NULL)
+ {
+ RETURN_IF_XTYPE_INVALID (Z, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ if (Z->nrow != A->nrow || Z->ncol != A->ncol || Z->stype != A->stype)
+ {
+ ERROR (CHOLMOD_INVALID, "dimension or type of A and Z mismatch") ;
+ return (EMPTY) ;
+ }
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the A matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ xtype = A->xtype ;
+ apacked = A->packed ;
+
+ if (xtype == CHOLMOD_PATTERN)
+ {
+ /* a CHOLMOD pattern matrix is printed as "pattern" in the file */
+ is_binary = TRUE ;
+ is_integer = FALSE ;
+ is_complex = FALSE ;
+ }
+ else if (xtype == CHOLMOD_REAL)
+ {
+ /* determine if a real matrix is in fact binary or integer */
+ is_binary = TRUE ;
+ is_integer = TRUE ;
+ is_complex = FALSE ;
+ for (j = 0 ; (is_binary || is_integer) && j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (apacked) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; (is_binary || is_integer) && p < pend ; p++)
+ {
+ x = Ax [p] ;
+ if (x != 1)
+ {
+ is_binary = FALSE ;
+ }
+ /* convert to Int and then back to double */
+ i = (Int) x ;
+ z = (double) i ;
+ if (z != x)
+ {
+ is_integer = FALSE ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* a CHOLMOD complex matrix is printed as "complex" in the file */
+ is_binary = FALSE ;
+ is_integer = FALSE ;
+ is_complex = TRUE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the Z matrix (only consider the pattern) */
+ /* ---------------------------------------------------------------------- */
+
+ Zp = NULL ;
+ Zi = NULL ;
+ Znz = NULL ;
+ zpacked = TRUE ;
+ if (Z != NULL)
+ {
+ Zp = Z->p ;
+ Zi = Z->i ;
+ Znz = Z->nz ;
+ zpacked = Z->packed ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the symmetry of A and Z */
+ /* ---------------------------------------------------------------------- */
+
+ stype = A->stype ;
+ if (A->nrow != A->ncol)
+ {
+ asym = CHOLMOD_MM_RECTANGULAR ;
+ }
+ else if (stype != 0)
+ {
+ /* CHOLMOD's A and Z matrices have a symmetric (and matching) stype.
+ * Note that the diagonal is not checked. */
+ asym = is_complex ? CHOLMOD_MM_HERMITIAN : CHOLMOD_MM_SYMMETRIC ;
+ }
+ else if (!A->sorted)
+ {
+ /* A is in unsymmetric storage, but unsorted */
+ asym = CHOLMOD_MM_UNSYMMETRIC ;
+ }
+ else
+ {
+ /* CHOLMOD's stype is zero (stored in unsymmetric form) */
+ asym = EMPTY ;
+ zsym = EMPTY ;
+
+#ifndef NMATRIXOPS
+ /* determine if the matrices are in fact symmetric or Hermitian */
+ asym = CHOLMOD(symmetry) (A, 1, NULL, NULL, NULL, NULL, Common) ;
+ zsym = (Z == NULL) ? 999 :
+ CHOLMOD(symmetry) (Z, 1, NULL, NULL, NULL, NULL, Common) ;
+#endif
+
+ if (asym == EMPTY || zsym <= CHOLMOD_MM_UNSYMMETRIC)
+ {
+ /* not computed, out of memory, or Z is unsymmetric */
+ asym = CHOLMOD_MM_UNSYMMETRIC ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* write the Matrix Market header */
+ /* ---------------------------------------------------------------------- */
+
+ ok = fprintf (f, "%%%%MatrixMarket matrix coordinate") > 0 ;
+
+ if (is_complex)
+ {
+ ok = ok && (fprintf (f, " complex") > 0) ;
+ }
+ else if (is_binary)
+ {
+ ok = ok && (fprintf (f, " pattern") > 0) ;
+ }
+ else if (is_integer)
+ {
+ ok = ok && (fprintf (f, " integer") > 0) ;
+ }
+ else
+ {
+ ok = ok && (fprintf (f, " real") > 0) ;
+ }
+
+ switch (asym)
+ {
+ case CHOLMOD_MM_RECTANGULAR:
+ case CHOLMOD_MM_UNSYMMETRIC:
+ /* A is rectangular or unsymmetric */
+ ok = ok && (fprintf (f, " general\n") > 0) ;
+ is_sym = FALSE ;
+ symmetry = CHOLMOD_MM_UNSYMMETRIC ;
+ break ;
+
+ case CHOLMOD_MM_SYMMETRIC:
+ case CHOLMOD_MM_SYMMETRIC_POSDIAG:
+ /* A is symmetric */
+ ok = ok && (fprintf (f, " symmetric\n") > 0) ;
+ is_sym = TRUE ;
+ symmetry = CHOLMOD_MM_SYMMETRIC ;
+ break ;
+
+ case CHOLMOD_MM_HERMITIAN:
+ case CHOLMOD_MM_HERMITIAN_POSDIAG:
+ /* A is Hermitian */
+ ok = ok && (fprintf (f, " Hermitian\n") > 0) ;
+ is_sym = TRUE ;
+ symmetry = CHOLMOD_MM_HERMITIAN ;
+ break ;
+
+ case CHOLMOD_MM_SKEW_SYMMETRIC:
+ /* A is skew symmetric */
+ ok = ok && (fprintf (f, " skew-symmetric\n") > 0) ;
+ is_sym = TRUE ;
+ symmetry = CHOLMOD_MM_SKEW_SYMMETRIC ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* include the comments if present */
+ /* ---------------------------------------------------------------------- */
+
+ ok = ok && include_comments (f, comments) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write a sparse matrix (A and Z) */
+ /* ---------------------------------------------------------------------- */
+
+ nz = ntriplets (A, is_sym) + ntriplets (Z, is_sym) ;
+
+ /* write the first data line, with nrow, ncol, and # of triplets */
+ ok = ok && (fprintf (f, ID " " ID " " ID "\n", nrow, ncol, nz) > 0) ;
+
+ for (j = 0 ; ok && j < ncol ; j++)
+ {
+ /* merge column of A and Z */
+ p = Ap [j] ;
+ pend = (apacked) ? Ap [j+1] : p + Anz [j] ;
+ q = (Z == NULL) ? 0 : Zp [j] ;
+ qend = (Z == NULL) ? 0 : ((zpacked) ? Zp [j+1] : q + Znz [j]) ;
+ while (ok)
+ {
+ /* get the next row index from A and Z */
+ i = (p < pend) ? Ai [p] : (nrow+1) ;
+ iz = (q < qend) ? Zi [q] : (nrow+2) ;
+ if (i <= iz)
+ {
+ /* get A(i,j), or quit if both A and Z are exhausted */
+ if (i == nrow+1) break ;
+ get_value (Ax, Az, p, xtype, &x, &z) ;
+ p++ ;
+ }
+ else
+ {
+ /* get Z(i,j) */
+ i = iz ;
+ x = 0 ;
+ z = 0 ;
+ q++ ;
+ }
+ if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym)))
+ {
+ /* CHOLMOD matrix is symmetric-lower (and so is the file);
+ * or CHOLMOD matrix is unsymmetric and either A(i,j) is in
+ * the lower part or the file is unsymmetric. */
+ ok = ok && print_triplet (f, is_binary, is_complex, is_integer,
+ i,j, x,z) ;
+ }
+ else if (stype > 0 && i <= j)
+ {
+ /* CHOLMOD matrix is symmetric-upper, but the file is
+ * symmetric-lower. Need to transpose the entry. If the
+ * matrix is real, the complex part is ignored. If the matrix
+ * is complex, it Hermitian.
+ */
+ ASSERT (IMPLIES (is_complex, asym == CHOLMOD_MM_HERMITIAN)) ;
+ if (z != 0)
+ {
+ z = -z ;
+ }
+ ok = ok && print_triplet (f, is_binary, is_complex, is_integer,
+ j,i, x,z) ;
+ }
+ }
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_INVALID, "error reading/writing file") ;
+ return (EMPTY) ;
+ }
+
+ return (asym) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_write_dense ================================================== */
+/* ========================================================================== */
+
+/* Write a dense matrix to a file in Matrix Market format. Optionally include
+ * comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if
+ * square). Future versions may return 1 to 7 on success (a CHOLMOD_MM_* code,
+ * just as cholmod_write_sparse does).
+ *
+ * A dense matrix is written in "general" format; symmetric formats in the
+ * Matrix Market standard are not exploited.
+ */
+
+int CHOLMOD(write_dense)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_dense *X, /* matrix to print */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ FILE *cf ;
+ double *Xx, *Xz ;
+ Int nrow, ncol, is_complex, i, j, nz, xtype, p ;
+ int ok ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (f, EMPTY) ;
+ RETURN_IF_NULL (X, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the X matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Xx = X->x ;
+ Xz = X->z ;
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ xtype = X->xtype ;
+ is_complex = (xtype == CHOLMOD_COMPLEX) || (xtype == CHOLMOD_ZOMPLEX) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write the Matrix Market header */
+ /* ---------------------------------------------------------------------- */
+
+ ok = (fprintf (f, "%%%%MatrixMarket matrix array") > 0) ;
+ if (is_complex)
+ {
+ ok = ok && (fprintf (f, " complex general\n") > 0) ;
+ }
+ else
+ {
+ ok = ok && (fprintf (f, " real general\n") > 0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* include the comments if present */
+ /* ---------------------------------------------------------------------- */
+
+ ok = ok && include_comments (f, comments) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write a dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* write the first data line, with nrow and ncol */
+ ok = ok && (fprintf (f, ID " " ID "\n", nrow, ncol) > 0) ;
+
+ Xx = X->x ;
+ Xz = X->z ;
+ for (j = 0 ; ok && j < ncol ; j++)
+ {
+ for (i = 0 ; ok && i < nrow ; i++)
+ {
+ p = i + j*nrow ;
+ get_value (Xx, Xz, p, xtype, &x, &z) ;
+ ok = ok && print_value (f, x, FALSE) ;
+ if (is_complex)
+ {
+ ok = ok && (fprintf (f, " ") > 0) ;
+ ok = ok && print_value (f, z, FALSE) ;
+ }
+ ok = ok && (fprintf (f, "\n") > 0) ;
+ }
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_INVALID, "error reading/writing file") ;
+ return (EMPTY) ;
+ }
+
+ return ((nrow == ncol) ? CHOLMOD_MM_UNSYMMETRIC : CHOLMOD_MM_RECTANGULAR) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Check/lesser.txt b/src/C/SuiteSparse/CHOLMOD/Check/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Check/lesser.txt
@@ -0,0 +1,504 @@
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diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/License.txt b/src/C/SuiteSparse/CHOLMOD/Cholesky/License.txt
new file mode 100644
index 0000000..b444856
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Cholesky module, Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Cholesky module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_amd.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_amd.c
new file mode 100644
index 0000000..09f8ec1
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_amd.c
@@ -0,0 +1,212 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_amd ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the AMD ordering routine. Orders A if the matrix is
+ * symmetric. On output, Perm [k] = i if row/column i of A is the kth
+ * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation.
+ *
+ * If A is unsymmetric, cholmod_amd orders A*A'. On output, Perm [k] = i if
+ * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to
+ * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is
+ * ordered.
+ *
+ * Computes the flop count for a subsequent LL' factorization, the number
+ * of nonzeros in L, and the number of nonzeros in the matrix ordered (A,
+ * A*A' or A(:,f)*A(:,f)').
+ *
+ * workspace: Iwork (6*nrow). Head (nrow).
+ *
+ * Allocates a temporary copy of A+A' or A*A' (with
+ * both upper and lower triangular parts) as input to AMD.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "amd.h"
+#include "cholmod_cholesky.h"
+
+#if (!defined (AMD_VERSION) || (AMD_VERSION < AMD_VERSION_CODE (2,0)))
+#error "AMD v2.0 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === cholmod_amd ========================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(amd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double Info [AMD_INFO], Control2 [AMD_CONTROL], *Control ;
+ Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Iwork, *Next ;
+ cholmod_sparse *C ;
+ Int j, n, cnz ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ n = A->nrow ;
+
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ if (n == 0)
+ {
+ /* nothing to do */
+ Common->fl = 0 ;
+ Common->lnz = 0 ;
+ Common->anz = 0 ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: this is less than the space used in cholmod_analyze, so if
+ * cholmod_amd is being called by that routine, no space will be
+ * allocated.
+ */
+
+ /* s = MAX (6*n, A->ncol) */
+ s = CHOLMOD(mult_size_t) (n, 6, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+ s = MAX (s, A->ncol) ;
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ Iwork = Common->Iwork ;
+ Degree = Iwork ; /* size n */
+ Wi = Iwork + n ; /* size n */
+ Len = Iwork + 2*((size_t) n) ; /* size n */
+ Nv = Iwork + 3*((size_t) n) ; /* size n */
+ Next = Iwork + 4*((size_t) n) ; /* size n */
+ Elen = Iwork + 5*((size_t) n) ; /* size n */
+
+ Head = Common->Head ; /* size n+1, but only n is used */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the input matrix for AMD */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */
+ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ;
+ }
+ else
+ {
+ /* C = A+A', but use only the upper triangular part of A if A->stype = 1
+ * and only the lower part of A if A->stype = -1. Add extra space of
+ * nnz(C)/2+n to C. */
+ C = CHOLMOD(copy) (A, 0, -2, Common) ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, fset invalid, or other error */
+ return (FALSE) ;
+ }
+
+ Cp = C->p ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Len [j] = Cp [j+1] - Cp [j] ;
+ }
+
+ /* C does not include the diagonal, and both upper and lower parts.
+ * Common->anz includes the diagonal, and just the lower part of C */
+ cnz = Cp [n] ;
+ Common->anz = cnz / 2 + n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order C using AMD */
+ /* ---------------------------------------------------------------------- */
+
+ /* get parameters */
+ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
+ {
+ /* use AMD defaults */
+ Control = NULL ;
+ }
+ else
+ {
+ Control = Control2 ;
+ Control [AMD_DENSE] = Common->method [Common->current].prune_dense ;
+ Control [AMD_AGGRESSIVE] = Common->method [Common->current].aggressive ;
+ }
+
+ /* AMD_2 does not use amd_malloc and amd_free, but set these pointers just
+ * be safe. */
+ amd_malloc = Common->malloc_memory ;
+ amd_free = Common->free_memory ;
+ amd_calloc = Common->calloc_memory ;
+ amd_realloc = Common->realloc_memory ;
+
+ /* AMD_2 doesn't print anything either, but future versions might,
+ * so set the amd_printf pointer too. */
+ amd_printf = Common->print_function ;
+
+#ifdef LONG
+ amd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
+ Degree, Wi, Control, Info) ;
+#else
+ amd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
+ Degree, Wi, Control, Info) ;
+#endif
+
+ /* LL' flop count. Need to subtract n for LL' flop count. Note that this
+ * is a slight upper bound which is often exact (see AMD/Source/amd_2.c for
+ * details). cholmod_analyze computes an exact flop count and fill-in. */
+ Common->fl = Info [AMD_NDIV] + 2 * Info [AMD_NMULTSUBS_LDL] + n ;
+
+ /* Info [AMD_LNZ] excludes the diagonal */
+ Common->lnz = n + Info [AMD_LNZ] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the AMD workspace and clear the persistent workspace in Common */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (IMPLIES (Common->status == CHOLMOD_OK,
+ CHOLMOD(dump_perm) (Perm, n, n, "AMD2 perm", Common))) ;
+ CHOLMOD(free_sparse) (&C, Common) ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ Head [j] = EMPTY ;
+ }
+ return (TRUE) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_analyze.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_analyze.c
new file mode 100644
index 0000000..19ce5b4
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_analyze.c
@@ -0,0 +1,896 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_analyze ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Order and analyze a matrix (either simplicial or supernodal), in prepartion
+ * for numerical factorization via cholmod_factorize or via the "expert"
+ * routines cholmod_rowfac and cholmod_super_numeric.
+ *
+ * symmetric case: A or A(p,p)
+ * unsymmetric case: AA', A(p,:)*A(p,:)', A(:,f)*A(:,f)', or A(p,f)*A(p,f)'
+ *
+ * For the symmetric case, only the upper or lower triangular part of A is
+ * accessed (depending on the type of A). LL'=A (or permuted A) is analzed.
+ * For the unsymmetric case (LL'=AA' or permuted A).
+ *
+ * There can be no duplicate entries in p or f. p is of length m if A is
+ * m-by-n. f can be length 0 to n.
+ *
+ * In both cases, the columns of A need not be sorted. A can be in packed
+ * or unpacked form.
+ *
+ * Ordering options include:
+ *
+ * natural: A is not permuted to reduce fill-in
+ * given: a permutation can be provided to this routine (UserPerm)
+ * AMD: approximate minumum degree (AMD for the symmetric case,
+ * COLAMD for the AA' case).
+ * METIS: nested dissection with METIS_NodeND
+ * NESDIS: nested dissection using METIS_NodeComputeSeparator,
+ * typically followed by a constrained minimum degree
+ * (CAMD for the symmetric case, CCOLAMD for the AA' case).
+ *
+ * Multiple ordering options can be tried (up to 9 of them), and the best one
+ * is selected (the one that gives the smallest number of nonzeros in the
+ * simplicial factor L). If one method fails, cholmod_analyze keeps going, and
+ * picks the best among the methods that succeeded. This routine fails (and
+ * returns NULL) if either initial memory allocation fails, all ordering methods
+ * fail, or the supernodal analysis (if requested) fails. By default, the 9
+ * methods available are:
+ *
+ * 1) given permutation (skipped if UserPerm is NULL)
+ * 2) AMD (symmetric case) or COLAMD (unsymmetric case)
+ * 3) METIS with default parameters
+ * 4) NESDIS with default parameters (stopping the partitioning when
+ * the graph is of size nd_small = 200 or less, remove nodes with
+ * more than max (16, prune_dense * sqrt (n)) nodes where
+ * prune_dense = 10, and follow partitioning with CCOLAMD, a
+ * constrained minimum degree ordering).
+ * 5) natural
+ * 6) NESDIS, nd_small = 20000, prune_dense = 10
+ * 7) NESDIS, nd_small = 4, prune_dense = 10, no min degree
+ * 8) NESDIS, nd_small = 200, prune_dense = 0
+ * 9) COLAMD for A*A' or AMD for A
+ *
+ * By default, the first two are tried, and METIS is tried if AMD reports a high
+ * flop count and fill-in. Let fl denote the flop count for the AMD, ordering,
+ * nnz(L) the # of nonzeros in L, and nnz(tril(A)) (or A*A'). If
+ * fl/nnz(L) >= 500 and nnz(L)/nnz(tril(A)) >= 5, then METIS is attempted. The
+ * best ordering is used (UserPerm if given, AMD, and METIS if attempted). If
+ * you do not have METIS, only the first two will be tried (user permutation,
+ * if provided, and AMD/COLAMD). This default behavior is obtained when
+ * Common->nmethods is zero. In this case, methods 0, 1, and 2 in
+ * Common->method [..] are reset to User-provided, AMD, and METIS (or NESDIS
+ * if Common->default_nesdis is set to the non-default value of TRUE),
+ * respectively.
+ *
+ * You can modify these 9 methods and the number of methods tried by changing
+ * parameters in the Common argument. If you know the best ordering for your
+ * matrix, set Common->nmethods to 1 and set Common->method[0].ordering to the
+ * requested ordering method. Parameters for each method can also be modified
+ * (refer to cholmod.h for details).
+ *
+ * Note that it is possible for METIS to terminate your program if it runs out
+ * of memory. This is not the case for any CHOLMOD or minimum degree ordering
+ * routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD). Since NESDIS relies on
+ * METIS, it too can terminate your program.
+ *
+ * The factor L is returned as simplicial symbolic (L->is_super FALSE) if
+ * Common->supernodal <= CHOLMOD_SIMPLICIAL (0) or as supernodal symbolic if
+ * Common->supernodal >= CHOLMOD_SUPERNODAL (2). If Common->supernodal is
+ * equal to CHOLMOD_AUTO (1), then L is simplicial if the flop count per
+ * nonzero in L is less than Common->supernodal_switch (default: 40), and
+ * is returned as a supernodal factor otherwise.
+ *
+ * In both cases, L->xtype is CHOLMOD_PATTERN.
+ * A subsequent call to cholmod_factorize will perform a
+ * simplicial or supernodal factorization, depending on the type of L.
+ *
+ * For the simplicial case, L contains the fill-reducing permutation (L->Perm)
+ * and the counts of nonzeros in each column of L (L->ColCount). For the
+ * supernodal case, L also contains the nonzero pattern of each supernode.
+ *
+ * workspace: Flag (nrow), Head (nrow+1)
+ * if symmetric: Iwork (6*nrow)
+ * if unsymmetric: Iwork (6*nrow+ncol).
+ * calls various ordering routines, which typically allocate O(nnz(A))
+ * temporary workspace ((2 to 3)*nnz(A) * sizeof (Int) is typical, but it
+ * can be much higher if A*A' must be explicitly formed for METIS). Also
+ * allocates up to 2 temporary (permuted/transpose) copies of the nonzero
+ * pattern of A, and up to 3*n*sizeof(Int) additional workspace.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+#ifndef NPARTITION
+#include "cholmod_partition.h"
+#endif
+
+
+/* ========================================================================== */
+/* === cholmod_analyze ====================================================== */
+/* ========================================================================== */
+
+/* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor
+ * that can later be passed to cholmod_factorize. */
+
+cholmod_factor *CHOLMOD(analyze)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(analyze_p) (A, NULL, NULL, 0, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === permute_matrices ===================================================== */
+/* ========================================================================== */
+
+/* Permute and transpose a matrix. Allocates the A1 and A2 matrices, if needed,
+ * or returns them as NULL if not needed.
+ */
+
+static int permute_matrices
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to permute */
+ Int ordering, /* ordering method used */
+ Int *Perm, /* fill-reducing permutation */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ Int do_rowcolcounts,/* if TRUE, compute both S and F. If FALSE, only
+ * S is needed for the symmetric case, and only F for
+ * the unsymmetric case */
+ /* ---- output --- */
+ cholmod_sparse **A1_handle, /* see comments below for A1, A2, S, F */
+ cholmod_sparse **A2_handle,
+ cholmod_sparse **S_handle,
+ cholmod_sparse **F_handle,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A1, *A2, *S, *F ;
+
+ *A1_handle = NULL ;
+ *A2_handle = NULL ;
+ *S_handle = NULL ;
+ *F_handle = NULL ;
+ A1 = NULL ;
+ A2 = NULL ;
+
+ if (ordering == CHOLMOD_NATURAL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* natural ordering of A */
+ /* ------------------------------------------------------------------ */
+
+ if (A->stype < 0)
+ {
+ /* symmetric lower case: A already in lower form, so S=A' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ;
+ F = A ;
+ S = A2 ;
+ }
+ else if (A->stype > 0)
+ {
+ /* symmetric upper case: F = pattern of triu (A)', S = A */
+ /* workspace: Iwork (nrow) */
+ if (do_rowcolcounts)
+ {
+ /* F not needed for symmetric case if do_rowcolcounts FALSE */
+ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ;
+ }
+ F = A1 ;
+ S = A ;
+ }
+ else
+ {
+ /* unsymmetric case: F = pattern of A (:,f)', S = A */
+ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */
+ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ;
+ F = A1 ;
+ S = A ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A is permuted */
+ /* ------------------------------------------------------------------ */
+
+ if (A->stype < 0)
+ {
+ /* symmetric lower case: S = tril (A (p,p))' and F = S' */
+ /* workspace: Iwork (2*nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ;
+ S = A2 ;
+ /* workspace: Iwork (nrow) */
+ if (do_rowcolcounts)
+ {
+ /* F not needed for symmetric case if do_rowcolcounts FALSE */
+ A1 = CHOLMOD(ptranspose) (A2, 0, NULL, NULL, 0, Common) ;
+ }
+ F = A1 ;
+ }
+ else if (A->stype > 0)
+ {
+ /* symmetric upper case: F = triu (A (p,p))' and S = F' */
+ /* workspace: Iwork (2*nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ;
+ F = A1 ;
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ;
+ S = A2 ;
+ }
+ else
+ {
+ /* unsymmetric case: F = A (p,f)' and S = F' */
+ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */
+ A1 = CHOLMOD(ptranspose) (A, 0, Perm, fset, fsize, Common) ;
+ F = A1 ;
+ if (do_rowcolcounts)
+ {
+ /* S not needed for unsymmetric case if do_rowcolcounts FALSE */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ;
+ }
+ S = A2 ;
+ }
+ }
+
+ /* If any cholmod_*transpose fails, one or more matrices will be NULL */
+ *A1_handle = A1 ;
+ *A2_handle = A2 ;
+ *S_handle = S ;
+ *F_handle = F ;
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_analyze_ordering ============================================= */
+/* ========================================================================== */
+
+/* Given a matrix A and its fill-reducing permutation, compute the elimination
+ * tree, its (non-weighted) postordering, and the number of nonzeros in each
+ * column of L. Also computes the flop count, the total nonzeros in L, and
+ * the nonzeros in A (Common->fl, Common->lnz, and Common->anz).
+ *
+ * The column counts of L, flop count, and other statistics from
+ * cholmod_rowcolcounts are not computed if ColCount is NULL.
+ *
+ * workspace: Iwork (2*nrow if symmetric, 2*nrow+ncol if unsymmetric),
+ * Flag (nrow), Head (nrow+1)
+ */
+
+int CHOLMOD(analyze_ordering)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int ordering, /* ordering method used */
+ Int *Perm, /* size n, fill-reducing permutation to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ Int *Parent, /* size n, elimination tree */
+ Int *Post, /* size n, postordering of elimination tree */
+ Int *ColCount, /* size n, nnz in each column of L */
+ /* ---- workspace */
+ Int *First, /* size nworkspace for cholmod_postorder */
+ Int *Level, /* size n workspace for cholmod_postorder */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A1, *A2, *S, *F ;
+ Int n, ok, do_rowcolcounts ;
+
+ /* check inputs */
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+
+ n = A->nrow ;
+
+ do_rowcolcounts = (ColCount != NULL) ;
+
+ /* permute A according to Perm and fset */
+ ok = permute_matrices (A, ordering, Perm, fset, fsize, do_rowcolcounts,
+ &A1, &A2, &S, &F, Common) ;
+
+ /* find etree of S (symmetric upper/lower case) or F (unsym case) */
+ /* workspace: symmmetric: Iwork (nrow), unsym: Iwork (nrow+ncol) */
+ ok = ok && CHOLMOD(etree) (A->stype ? S:F, Parent, Common) ;
+
+ /* postorder the etree (required by cholmod_rowcolcounts) */
+ /* workspace: Iwork (2*nrow) */
+ ok = ok && (CHOLMOD(postorder) (Parent, n, NULL, Post, Common) == n) ;
+
+ /* cholmod_postorder doesn't set Common->status if it returns < n */
+ Common->status = (!ok && Common->status == CHOLMOD_OK) ?
+ CHOLMOD_INVALID : Common->status ;
+
+ /* analyze LL'=S or SS' or S(:,f)*S(:,f)' */
+ /* workspace:
+ * if symmetric: Flag (nrow), Iwork (2*nrow)
+ * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1)
+ */
+ if (do_rowcolcounts)
+ {
+ ok = ok && CHOLMOD(rowcolcounts) (A->stype ? F:S, fset, fsize, Parent,
+ Post, NULL, ColCount, First, Level, Common) ;
+ }
+
+ /* free temporary matrices and return result */
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === Free workspace and return L ========================================== */
+/* ========================================================================== */
+
+#define FREE_WORKSPACE_AND_RETURN \
+{ \
+ Common->no_workspace_reallocate = FALSE ; \
+ CHOLMOD(free) (n, sizeof (Int), Lparent, Common) ; \
+ CHOLMOD(free) (n, sizeof (Int), Perm, Common) ; \
+ CHOLMOD(free) (n, sizeof (Int), ColCount, Common) ; \
+ if (Common->status < CHOLMOD_OK) \
+ { \
+ CHOLMOD(free_factor) (&L, Common) ; \
+ } \
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \
+ return (L) ; \
+}
+
+
+/* ========================================================================== */
+/* === cholmod_analyze_p ==================================================== */
+/* ========================================================================== */
+
+/* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a
+ * symbolic factor that can later be passed to cholmod_factorize, where
+ * F = A(:,fset) if fset is not NULL and A->stype is zero.
+ * UserPerm is tried if non-NULL. */
+
+cholmod_factor *CHOLMOD(analyze_p)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ Int *UserPerm, /* user-provided permutation, size A->nrow */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double lnz_best ;
+ Int *First, *Level, *Work4n, *Cmember, *CParent, *ColCount, *Lperm, *Parent,
+ *Post, *Perm, *Lparent, *Lcolcount ;
+ cholmod_factor *L ;
+ Int k, n, ordering, method, nmethods, status, default_strategy, ncol, uncol,
+ skip_analysis, skip_best ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ status = CHOLMOD_OK ;
+ Common->selected = EMPTY ;
+ Common->called_nd = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ ncol = A->ncol ;
+ uncol = (A->stype == 0) ? (A->ncol) : 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* set the default strategy */
+ /* ---------------------------------------------------------------------- */
+
+ lnz_best = (double) EMPTY ;
+ skip_best = FALSE ;
+ nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ;
+ nmethods = MAX (0, nmethods) ;
+ PRINT1 (("nmethods "ID"\n", nmethods)) ;
+
+ default_strategy = (nmethods == 0) ;
+ if (default_strategy)
+ {
+ /* default strategy: try UserPerm, if given. Try AMD for A, or COLAMD
+ * to order A*A'. Try METIS for the symmetric case only if AMD reports
+ * a high degree of fill-in and flop count. Always try METIS for the
+ * unsymmetric case. METIS is not tried if the Partition Module
+ * isn't installed. If Common->default_nesdis is TRUE, then NESDIS
+ * is used as the 3rd ordering instead. */
+ Common->method [0].ordering = CHOLMOD_GIVEN ;/* skip if UserPerm NULL */
+ Common->method [1].ordering = CHOLMOD_AMD ;
+ Common->method [2].ordering =
+ (Common->default_nesdis ? CHOLMOD_NESDIS : CHOLMOD_METIS) ;
+#ifndef NPARTITION
+ nmethods = 3 ;
+#else
+ nmethods = 2 ;
+#endif
+ }
+
+#ifdef NSUPERNODAL
+ /* CHOLMOD Supernodal module not installed, just do simplicial analysis */
+ Common->supernodal = CHOLMOD_SIMPLICIAL ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: enough space needs to be allocated here so that routines called by
+ * cholmod_analyze do not reallocate the space.
+ */
+
+ /* s = 6*n + uncol */
+ s = CHOLMOD(mult_size_t) (n, 6, &ok) ;
+ s = CHOLMOD(add_size_t) (s, uncol, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ensure that subsequent routines, called by cholmod_analyze, do not
+ * reallocate any workspace. This is set back to FALSE in the
+ * FREE_WORKSPACE_AND_RETURN macro, which is the only way this function
+ * returns to its caller. */
+ Common->no_workspace_reallocate = TRUE ;
+
+ /* Use the last 4*n Int's in Iwork for Parent, First, Level, and Post, since
+ * other CHOLMOD routines will use the first 2n+uncol space. The ordering
+ * routines (cholmod_amd, cholmod_colamd, cholmod_ccolamd, cholmod_metis)
+ * are an exception. They can use all 6n + ncol space, since the contents
+ * of Parent, First, Level, and Post are not needed across calls to those
+ * routines. */
+ Work4n = Common->Iwork ;
+ Work4n += 2*((size_t) n) + uncol ;
+ Parent = Work4n ;
+ First = Work4n + n ;
+ Level = Work4n + 2*((size_t) n) ;
+ Post = Work4n + 3*((size_t) n) ;
+
+ /* note that this assignment means that cholmod_nested_dissection,
+ * cholmod_ccolamd, and cholmod_camd can use only the first 4n+uncol
+ * space in Common->Iwork */
+ Cmember = Post ;
+ CParent = Level ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate more workspace, and an empty simplicial symbolic factor */
+ /* ---------------------------------------------------------------------- */
+
+ L = CHOLMOD(allocate_factor) (n, Common) ;
+ Lparent = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ FREE_WORKSPACE_AND_RETURN ;
+ }
+ Lperm = L->Perm ;
+ Lcolcount = L->ColCount ;
+ Common->anz = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* try all the requested ordering options and backup to AMD if needed */
+ /* ---------------------------------------------------------------------- */
+
+ /* turn off error handling [ */
+ Common->try_catch = TRUE ;
+
+ for (method = 0 ; method <= nmethods ; method++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* determine the method to try */
+ /* ------------------------------------------------------------------ */
+
+ Common->fl = EMPTY ;
+ Common->lnz = EMPTY ;
+ skip_analysis = FALSE ;
+
+ if (method == nmethods)
+ {
+ /* All methods failed: backup to AMD */
+ if (Common->selected == EMPTY && !default_strategy)
+ {
+ PRINT1 (("All methods requested failed: backup to AMD\n")) ;
+ ordering = CHOLMOD_AMD ;
+ }
+ else
+ {
+ break ;
+ }
+ }
+ else
+ {
+ ordering = Common->method [method].ordering ;
+ }
+ Common->current = method ;
+ PRINT1 (("method "ID": Try method: "ID"\n", method, ordering)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the fill-reducing permutation */
+ /* ------------------------------------------------------------------ */
+
+ if (ordering == CHOLMOD_NATURAL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* natural ordering */
+ /* -------------------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = k ;
+ }
+
+ }
+ else if (ordering == CHOLMOD_GIVEN)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use given ordering of A, if provided */
+ /* -------------------------------------------------------------- */
+
+ if (UserPerm == NULL)
+ {
+ /* this is not an error condition */
+ PRINT1 (("skip, no user perm given\n")) ;
+ continue ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ /* UserPerm is checked in cholmod_ptranspose */
+ Perm [k] = UserPerm [k] ;
+ }
+
+ }
+ else if (ordering == CHOLMOD_AMD)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* AMD ordering of A, A*A', or A(:,f)*A(:,f)' */
+ /* -------------------------------------------------------------- */
+
+ CHOLMOD(amd) (A, fset, fsize, Perm, Common) ;
+ skip_analysis = TRUE ;
+
+ }
+ else if (ordering == CHOLMOD_COLAMD)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* AMD for symmetric case, COLAMD for A*A' or A(:,f)*A(:,f)' */
+ /* -------------------------------------------------------------- */
+
+ if (A->stype)
+ {
+ CHOLMOD(amd) (A, fset, fsize, Perm, Common) ;
+ skip_analysis = TRUE ;
+ }
+ else
+ {
+ /* Alternative:
+ CHOLMOD(ccolamd) (A, fset, fsize, NULL, Perm, Common) ;
+ */
+ /* do not postorder, it is done later, below */
+ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1)*/
+ CHOLMOD(colamd) (A, fset, fsize, FALSE, Perm, Common) ;
+ }
+
+ }
+ else if (ordering == CHOLMOD_METIS)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use METIS_NodeND directly (via a CHOLMOD wrapper) */
+ /* -------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ /* postorder parameter is false, because it will be later, below */
+ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1) */
+ Common->called_nd = TRUE ;
+ CHOLMOD(metis) (A, fset, fsize, FALSE, Perm, Common) ;
+#else
+ Common->status = CHOLMOD_NOT_INSTALLED ;
+#endif
+
+ }
+ else if (ordering == CHOLMOD_NESDIS)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use CHOLMOD's nested dissection */
+ /* -------------------------------------------------------------- */
+
+ /* this method is based on METIS' node bissection routine
+ * (METIS_NodeComputeSeparator). In contrast to METIS_NodeND,
+ * it calls CAMD or CCOLAMD on the whole graph, instead of MMD
+ * on just the leaves. */
+#ifndef NPARTITION
+ /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow) */
+ Common->called_nd = TRUE ;
+ CHOLMOD(nested_dissection) (A, fset, fsize, Perm, CParent, Cmember,
+ Common) ;
+#else
+ Common->status = CHOLMOD_NOT_INSTALLED ;
+#endif
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* invalid ordering method */
+ /* -------------------------------------------------------------- */
+
+ Common->status = CHOLMOD_INVALID ;
+ PRINT1 (("No such ordering: "ID"\n", ordering)) ;
+ }
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, or method failed */
+ status = MIN (status, Common->status) ;
+ Common->status = CHOLMOD_OK ;
+ continue ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* analyze the ordering */
+ /* ------------------------------------------------------------------ */
+
+ if (!skip_analysis)
+ {
+ if (!CHOLMOD(analyze_ordering) (A, ordering, Perm, fset, fsize,
+ Parent, Post, ColCount, First, Level, Common))
+ {
+ /* ordering method failed; clear status and try next method */
+ status = MIN (status, Common->status) ;
+ Common->status = CHOLMOD_OK ;
+ continue ;
+ }
+ }
+
+ ASSERT (Common->fl >= 0 && Common->lnz >= 0) ;
+ Common->method [method].fl = Common->fl ;
+ Common->method [method].lnz = Common->lnz ;
+ PRINT1 (("lnz %g fl %g\n", Common->lnz, Common->fl)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* pick the best method */
+ /* ------------------------------------------------------------------ */
+
+ /* fl.pt. compare, but lnz can never be NaN */
+ if (Common->selected == EMPTY || Common->lnz < lnz_best)
+ {
+ Common->selected = method ;
+ PRINT1 (("this is best so far, method "ID"\n", method)) ;
+ L->ordering = ordering ;
+ lnz_best = Common->lnz ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Lperm [k] = Perm [k] ;
+ }
+ /* save the results of cholmod_analyze_ordering, if it was called */
+ skip_best = skip_analysis ;
+ if (!skip_analysis)
+ {
+ /* save the column count; becomes permanent part of L */
+ for (k = 0 ; k < n ; k++)
+ {
+ Lcolcount [k] = ColCount [k] ;
+ }
+ /* Parent is needed for weighted postordering and for supernodal
+ * analysis. Does not become a permanent part of L */
+ for (k = 0 ; k < n ; k++)
+ {
+ Lparent [k] = Parent [k] ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* determine if METIS is to be skipped */
+ /* ------------------------------------------------------------------ */
+
+ if (default_strategy && ordering == CHOLMOD_AMD)
+ {
+ if ((Common->fl < 500 * Common->lnz) ||
+ (Common->lnz < 5 * Common->anz))
+ {
+ /* AMD found an ordering with less than 500 flops per nonzero in
+ * L, or one with a fill-in ratio (nnz(L)/nnz(A)) of less than
+ * 5. This is pretty good, and it's unlikely that METIS will do
+ * better (this heuristic is based on tests on all symmetric
+ * positive definite matrices in the UF sparse matrix
+ * collection, and it works well across a wide range of
+ * problems). METIS can take much more time and AMD. */
+ break ;
+ }
+ }
+ }
+
+ /* turn error printing back on ] */
+ Common->try_catch = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return if no ordering method succeeded */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->selected == EMPTY)
+ {
+ /* All methods failed.
+ * If two or more methods failed, they may have failed for different
+ * reasons. Both would clear Common->status and skip to the next
+ * method. Common->status needs to be restored here to the worst error
+ * obtained in any of the methods. CHOLMOD_INVALID is worse
+ * than CHOLMOD_OUT_OF_MEMORY, since the former implies something may
+ * be wrong with the user's input. CHOLMOD_OUT_OF_MEMORY is simply an
+ * indication of lack of resources. */
+ ASSERT (status < CHOLMOD_OK) ;
+ ERROR (status, "all methods failed") ;
+ FREE_WORKSPACE_AND_RETURN ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* do the analysis for AMD, if skipped */
+ /* ---------------------------------------------------------------------- */
+
+ Common->fl = Common->method [Common->selected].fl ;
+ Common->lnz = Common->method [Common->selected].lnz ;
+ ASSERT (Common->lnz >= 0) ;
+
+ if (skip_best)
+ {
+ if (!CHOLMOD(analyze_ordering) (A, L->ordering, Lperm, fset, fsize,
+ Lparent, Post, Lcolcount, First, Level, Common))
+ {
+ /* out of memory, or method failed */
+ FREE_WORKSPACE_AND_RETURN ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* postorder the etree, weighted by the column counts */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->postorder)
+ {
+ /* combine the fill-reducing ordering with the weighted postorder */
+ /* workspace: Iwork (2*nrow) */
+ if (CHOLMOD(postorder) (Lparent, n, Lcolcount, Post, Common) == n)
+ {
+ /* use First and Level as workspace [ */
+ Int *Wi = First, *InvPost = Level ;
+ Int newchild, oldchild, newparent, oldparent ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Wi [k] = Lperm [Post [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Lperm [k] = Wi [k] ;
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Wi [k] = Lcolcount [Post [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Lcolcount [k] = Wi [k] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ InvPost [Post [k]] = k ;
+ }
+
+ /* updated Lparent needed only for supernodal case */
+ for (newchild = 0 ; newchild < n ; newchild++)
+ {
+ oldchild = Post [newchild] ;
+ oldparent = Lparent [oldchild] ;
+ newparent = (oldparent == EMPTY) ? EMPTY : InvPost [oldparent] ;
+ Wi [newchild] = newparent ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Lparent [k] = Wi [k] ;
+ }
+ /* done using Iwork as workspace ] */
+
+ /* L is now postordered, no longer in natural ordering */
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ L->ordering = CHOLMOD_POSTORDERED ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal analysis, if requested or if selected automatically */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NSUPERNODAL
+ if (Common->supernodal > CHOLMOD_AUTO
+ || (Common->supernodal == CHOLMOD_AUTO &&
+ Common->lnz > 0 &&
+ (Common->fl / Common->lnz) >= Common->supernodal_switch))
+ {
+ cholmod_sparse *S, *F, *A2, *A1 ;
+
+ permute_matrices (A, L->ordering, Lperm, fset, fsize, TRUE,
+ &A1, &A2, &S, &F, Common) ;
+
+ /* workspace: Flag (nrow), Head (nrow), Iwork (5*nrow) */
+ CHOLMOD(super_symbolic) (S, F, Lparent, L, Common) ;
+ PRINT1 (("status %d\n", Common->status)) ;
+
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* free temporary matrices and workspace, and return result L */
+ /* ---------------------------------------------------------------------- */
+
+ FREE_WORKSPACE_AND_RETURN ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_colamd.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_colamd.c
new file mode 100644
index 0000000..1f20101
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_colamd.c
@@ -0,0 +1,210 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_colamd ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the COLAMD ordering routine (version 2.4 or later).
+ * Finds a permutation p such that the Cholesky factorization of PAA'P' is
+ * sparser than AA' using colamd. If the postorder input parameter is TRUE,
+ * the column etree is found and postordered, and the colamd ordering is then
+ * combined with its postordering. A must be unsymmetric.
+ *
+ * There can be no duplicate entries in f.
+ * f can be length 0 to n if A is m-by-n.
+ *
+ * workspace: Iwork (4*nrow+ncol), Head (nrow+1), Flag (nrow)
+ * Allocates a copy of its input matrix, which
+ * is then used as CCOLAMD's workspace.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "colamd.h"
+#include "cholmod_cholesky.h"
+
+#if (!defined (COLAMD_VERSION) || (COLAMD_VERSION < COLAMD_VERSION_CODE (2,5)))
+#error "COLAMD v2.5 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === cholmod_colamd ======================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(colamd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with a coletree postorder */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double knobs [COLAMD_KNOBS] ;
+ cholmod_sparse *C ;
+ Int *NewPerm, *Parent, *Post, *Work2n ;
+ Int k, nrow, ncol ;
+ size_t s, alen ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->stype != 0)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: this is less than the space used in cholmod_analyze, so if
+ * cholmod_colamd is being called by that routine, no space will be
+ * allocated.
+ */
+
+ /* s = 4*nrow + ncol */
+ s = CHOLMOD(mult_size_t) (nrow, 4, &ok) ;
+ s = CHOLMOD(add_size_t) (s, ncol, &ok) ;
+
+#ifdef LONG
+ alen = colamd_l_recommended (A->nzmax, ncol, nrow) ;
+ colamd_l_set_defaults (knobs) ;
+#else
+ alen = colamd_recommended (A->nzmax, ncol, nrow) ;
+ colamd_set_defaults (knobs) ;
+#endif
+
+ if (!ok || alen == 0)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate COLAMD workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* colamd_printf is only available in colamd v2.4 or later */
+ colamd_printf = Common->print_function ;
+
+ C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy (and transpose) the input matrix A into the colamd workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* C = A (:,f)', which also packs A if needed. */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset) */
+ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix (destroys the contents of C->i and C->p) */
+ /* ---------------------------------------------------------------------- */
+
+ /* get parameters */
+ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
+ {
+ /* this is the CHOLMOD default, not the COLAMD default */
+ knobs [COLAMD_DENSE_ROW] = -1 ;
+ }
+ else
+ {
+ /* get the knobs from the Common parameters */
+ knobs [COLAMD_DENSE_COL] = Common->method[Common->current].prune_dense ;
+ knobs [COLAMD_DENSE_ROW] = Common->method[Common->current].prune_dense2;
+ knobs [COLAMD_AGGRESSIVE] = Common->method[Common->current].aggressive ;
+ }
+
+ if (ok)
+ {
+ Int *Cp ;
+ Int stats [COLAMD_STATS] ;
+ Cp = C->p ;
+
+#ifdef LONG
+ colamd_l (ncol, nrow, alen, C->i, Cp, knobs, stats) ;
+#else
+ colamd (ncol, nrow, alen, C->i, Cp, knobs, stats) ;
+#endif
+
+ ok = stats [COLAMD_STATUS] ;
+ ok = (ok == COLAMD_OK || ok == COLAMD_OK_BUT_JUMBLED) ;
+ /* permutation returned in C->p, if the ordering succeeded */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Perm [k] = Cp [k] ;
+ }
+ }
+
+ CHOLMOD(free_sparse) (&C, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* column etree postordering */
+ /* ---------------------------------------------------------------------- */
+
+ if (postorder)
+ {
+ /* use the last 2*n space in Iwork for Parent and Post */
+ Work2n = Common->Iwork ;
+ Work2n += 2*((size_t) nrow) + ncol ;
+ Parent = Work2n ; /* size nrow (i/i/l) */
+ Post = Work2n + nrow ; /* size nrow (i/i/l) */
+
+ /* workspace: Iwork (2*nrow+ncol), Flag (nrow), Head (nrow+1) */
+ ok = ok && CHOLMOD(analyze_ordering) (A, CHOLMOD_COLAMD, Perm, fset,
+ fsize, Parent, Post, NULL, NULL, NULL, Common) ;
+
+ /* combine the colamd permutation with its postordering */
+ if (ok)
+ {
+ NewPerm = Common->Iwork ; /* size nrow (i/i/l) */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ NewPerm [k] = Perm [Post [k]] ;
+ }
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Perm [k] = NewPerm [k] ;
+ }
+ }
+ }
+
+ return (ok) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_etree.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_etree.c
new file mode 100644
index 0000000..592cba8
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_etree.c
@@ -0,0 +1,227 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_etree =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Compute the elimination tree of A or A'*A
+ *
+ * In the symmetric case, the upper triangular part of A is used. Entries not
+ * in this part of the matrix are ignored. Computing the etree of a symmetric
+ * matrix from just its lower triangular entries is not supported.
+ *
+ * In the unsymmetric case, all of A is used, and the etree of A'*A is computed.
+ *
+ * References:
+ *
+ * J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans.
+ * Math. Software, vol 12, 1986, pp. 127-148.
+ *
+ * J. Liu, "The role of elimination trees in sparse factorization", SIAM J.
+ * Matrix Analysis & Applic., vol 11, 1990, pp. 134-172.
+ *
+ * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for
+ * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710.
+ *
+ * workspace: symmetric: Iwork (nrow), unsymmetric: Iwork (nrow+ncol)
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === update_etree ========================================================= */
+/* ========================================================================== */
+
+static void update_etree
+(
+ /* inputs, not modified */
+ Int k, /* process the edge (k,i) in the input graph */
+ Int i,
+ /* inputs, modified on output */
+ Int Parent [ ], /* Parent [t] = p if p is the parent of t */
+ Int Ancestor [ ] /* Ancestor [t] is the ancestor of node t in the
+ partially-constructed etree */
+)
+{
+ Int a ;
+ for ( ; ; ) /* traverse the path from k to the root of the tree */
+ {
+ a = Ancestor [k] ;
+ if (a == i)
+ {
+ /* final ancestor reached; no change to tree */
+ return ;
+ }
+ /* perform path compression */
+ Ancestor [k] = i ;
+ if (a == EMPTY)
+ {
+ /* final ancestor undefined; this is a new edge in the tree */
+ Parent [k] = i ;
+ return ;
+ }
+ /* traverse up to the ancestor of k */
+ k = a ;
+ }
+}
+
+/* ========================================================================== */
+/* === cholmod_etree ======================================================== */
+/* ========================================================================== */
+
+/* Find the elimination tree of A or A'*A */
+
+int CHOLMOD(etree)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* ---- output --- */
+ Int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Ai, *Anz, *Ancestor, *Prev, *Iwork ;
+ Int i, j, jprev, p, pend, nrow, ncol, packed, stype ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ stype = A->stype ;
+
+ /* s = A->nrow + (stype ? 0 : A->ncol) */
+ s = CHOLMOD(add_size_t) (A->nrow, (stype ? 0 : A->ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "etree", Common) >= 0) ;
+ Iwork = Common->Iwork ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ; /* the number of columns of A */
+ nrow = A->nrow ; /* the number of rows of A */
+ Ap = A->p ; /* size ncol+1, column pointers for A */
+ Ai = A->i ; /* the row indices of A */
+ Anz = A->nz ; /* number of nonzeros in each column of A */
+ packed = A->packed ;
+ Ancestor = Iwork ; /* size ncol (i/i/l) */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Parent [j] = EMPTY ;
+ Ancestor [j] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the etree */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric (upper) case: compute etree (A) */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* for each row i in column j of triu(A), excluding the diagonal */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i < j)
+ {
+ update_etree (i, j, Parent, Ancestor) ;
+ }
+ }
+ }
+
+ }
+ else if (stype == 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* unsymmetric case: compute etree (A'*A) */
+ /* ------------------------------------------------------------------ */
+
+ Prev = Iwork + ncol ; /* size nrow (i/i/l) */
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Prev [i] = EMPTY ;
+ }
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* for each row i in column j of A */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* a graph is constructed dynamically with one path per row
+ * of A. If the ith row of A contains column indices
+ * (j1,j2,j3,j4) then the new graph has edges (j1,j2), (j2,j3),
+ * and (j3,j4). When at node i of this path-graph, all edges
+ * (jprev,j) are considered, where jprev<j */
+ i = Ai [p] ;
+ jprev = Prev [i] ;
+ if (jprev != EMPTY)
+ {
+ update_etree (jprev, j, Parent, Ancestor) ;
+ }
+ Prev [i] = j ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric case with lower triangular part not supported */
+ /* ------------------------------------------------------------------ */
+
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+
+ ASSERT (CHOLMOD(dump_parent) (Parent, ncol, "Parent", Common)) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_factorize.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_factorize.c
new file mode 100644
index 0000000..15544d3
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_factorize.c
@@ -0,0 +1,429 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_factorize =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Computes the numerical factorization of a symmetric matrix. The primary
+ * inputs to this routine are a sparse matrix A and the symbolic factor L from
+ * cholmod_analyze or a prior numerical factor L. If A is symmetric, this
+ * routine factorizes A(p,p)+beta*I (beta can be zero), where p is the
+ * fill-reducing permutation (L->Perm). If A is unsymmetric, either
+ * A(p,:)*A(p,:)'+beta*I or A(p,f)*A(p,f)'+beta*I is factorized. The set f and
+ * the nonzero pattern of the matrix A must be the same as the matrix passed to
+ * cholmod_analyze for the supernodal case. For the simplicial case, it can
+ * be different, but it should be the same for best performance. beta is real.
+ *
+ * A simplicial factorization or supernodal factorization is chosen, based on
+ * the type of the factor L. If L->is_super is TRUE, a supernodal LL'
+ * factorization is computed. Otherwise, a simplicial numeric factorization
+ * is computed, either LL' or LDL', depending on Common->final_ll.
+ *
+ * Once the factorization is complete, it can be left as is or optionally
+ * converted into any simplicial numeric type, depending on the
+ * Common->final_* parameters. If converted from a supernodal to simplicial
+ * type, and the Common->final_resymbol parameter is true, then numerically
+ * zero entries in L due to relaxed supernodal amalgamation are removed from
+ * the simplicial factor (they are always left in the supernodal form of L).
+ * Entries that are numerically zero but present in the simplicial symbolic
+ * pattern of L are left in place (that is, the graph of L remains chordal).
+ * This is required for the update/downdate/rowadd/rowdel routines to work
+ * properly.
+ *
+ * workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow+2*nsuper)
+ * if unsymmetric: Iwork (2*nrow+MAX(2*nsuper,ncol))
+ * where nsuper is 0 if simplicial, or the # of relaxed supernodes in
+ * L otherwise (nsuper <= nrow).
+ * if simplicial: W (nrow).
+ * Allocates up to two temporary copies of its input matrix (including
+ * both pattern and numerical values).
+ *
+ * If the matrix is not positive definite the routine returns TRUE, but
+ * sets Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the
+ * column at which the failure occurred. Columns L->minor to L->n-1 are
+ * set to zero.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex), except that the
+ * input matrix A cannot be pattern-only. If L is simplicial, its numeric
+ * xtype matches A on output. If L is supernodal, its xtype is real if A is
+ * real, or complex if A is complex or zomplex.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+
+/* ========================================================================== */
+/* === cholmod_factorize ==================================================== */
+/* ========================================================================== */
+
+/* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained
+ * from cholmod_analyze. The analysis can be re-used simply by calling this
+ * routine a second time with another matrix. A must have the same nonzero
+ * pattern as that passed to cholmod_analyze. */
+
+int CHOLMOD(factorize)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double zero [2] ;
+ zero [0] = 0 ;
+ zero [1] = 0 ;
+ return (CHOLMOD(factorize_p) (A, zero, NULL, 0, L, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_factorize_p ================================================== */
+/* ========================================================================== */
+
+/* Same as cholmod_factorize, but with more options. */
+
+int CHOLMOD(factorize_p)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *S, *F, *A1, *A2 ;
+ Int nrow, ncol, stype, convert, n, nsuper, grow2, status ;
+ size_t s, t, uncol ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ n = L->n ;
+ stype = A->stype ;
+ if (L->n != A->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+ if (stype != 0 && nrow != ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (FALSE) ;
+ }
+ DEBUG (CHOLMOD(dump_sparse) (A, "A for cholmod_factorize", Common)) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = (L->is_super ? L->nsuper : 0) ;
+ uncol = ((stype != 0) ? 0 : ncol) ;
+
+ /* s = 2*nrow + MAX (uncol, 2*nsuper) */
+ s = CHOLMOD(mult_size_t) (nsuper, 2, &ok) ;
+ s = MAX (uncol, s) ;
+ t = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ s = CHOLMOD(add_size_t) (s, t, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ S = NULL ;
+ F = NULL ;
+ A1 = NULL ;
+ A2 = NULL ;
+
+ /* convert to another form when done, if requested */
+ convert = !(Common->final_asis) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* perform supernodal LL' or simplicial LDL' factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->is_super)
+ {
+
+#ifndef NSUPERNODAL
+
+ /* ------------------------------------------------------------------ */
+ /* supernodal factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* natural ordering */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* S = tril (A'), F not needed */
+ /* workspace: Iwork (nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ;
+ S = A1 ;
+ }
+ else if (stype < 0)
+ {
+ /* This is the fastest option for the natural ordering */
+ /* S = A; F not needed */
+ S = A ;
+ }
+ else
+ {
+ /* F = A(:,f)' */
+ /* workspace: Iwork (nrow) */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ;
+ F = A1 ;
+ /* S = A */
+ S = A ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* permute the input matrix before factorization */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* This is the fastest option for factoring a permuted matrix */
+ /* S = tril (PAP'); F not needed */
+ /* workspace: Iwork (2*nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ S = A1 ;
+ }
+ else if (stype < 0)
+ {
+ /* A2 = triu (PAP') */
+ /* workspace: Iwork (2*nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ /* S = tril (A2'); F not needed */
+ /* workspace: Iwork (nrow) */
+ A1 = CHOLMOD(ptranspose) (A2, 2, NULL, NULL, 0, Common) ;
+ S = A1 ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ ASSERT (A2 == NULL) ;
+ }
+ else
+ {
+ /* F = A(p,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ;
+ F = A1 ;
+ /* S = F' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ;
+ S = A2 ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* supernodal factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow+2*nsuper) */
+ if (Common->status == CHOLMOD_OK)
+ {
+ CHOLMOD(super_numeric) (S, F, beta, L, Common) ;
+ }
+ status = Common->status ;
+ ASSERT (IMPLIES (status >= CHOLMOD_OK, L->xtype != CHOLMOD_PATTERN)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* convert to final form, if requested */
+ /* ------------------------------------------------------------------ */
+
+ if (Common->status >= CHOLMOD_OK && convert)
+ {
+ /* workspace: none */
+ ok = CHOLMOD(change_factor) (L->xtype, Common->final_ll,
+ Common->final_super, Common->final_pack,
+ Common->final_monotonic, L, Common) ;
+ if (ok && Common->final_resymbol && !(L->is_super))
+ {
+ /* workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow)
+ * if unsymmetric: Iwork (2*nrow+ncol) */
+ CHOLMOD(resymbol_noperm) (S, fset, fsize, Common->final_pack,
+ L, Common) ;
+ }
+ }
+
+#else
+
+ /* ------------------------------------------------------------------ */
+ /* CHOLMOD Supernodal module not installed */
+ /* ------------------------------------------------------------------ */
+
+ status = CHOLMOD_NOT_INSTALLED ;
+ ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ;
+
+#endif
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* simplicial LDL' factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* Permute the input matrix A if necessary. cholmod_rowfac requires
+ * triu(A) in column form for the symmetric case, and A in column form
+ * for the unsymmetric case (the matrix S). The unsymmetric case
+ * requires A in row form, or equivalently A' in column form (the
+ * matrix F).
+ */
+
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* natural ordering */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* F is not needed, S = A */
+ S = A ;
+ }
+ else if (stype < 0)
+ {
+ /* F is not needed, S = A' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ;
+ S = A2 ;
+ }
+ else
+ {
+ /* F = A (:,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ;
+ F = A1 ;
+ S = A ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* permute the input matrix before factorization */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* F = tril (A (p,p)') */
+ /* workspace: Iwork (2*nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ /* A2 = triu (F') */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A1, 2, NULL, NULL, 0, Common) ;
+ /* the symmetric case does not need F, free it and set to NULL*/
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ }
+ else if (stype < 0)
+ {
+ /* A2 = triu (A (p,p)'), F not needed. This is the fastest
+ * way to factorize a matrix using the simplicial routine
+ * (cholmod_rowfac). */
+ /* workspace: Iwork (2*nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ }
+ else
+ {
+ /* F = A (p,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ;
+ F = A1 ;
+ /* A2 = F' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ;
+ }
+ S = A2 ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* simplicial LDL' or LL' factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* factorize beta*I+S (symmetric) or beta*I+F*F' (unsymmetric) */
+ /* workspace: Flag (nrow), W (nrow), Iwork (2*nrow) */
+ if (Common->status == CHOLMOD_OK)
+ {
+ grow2 = Common->grow2 ;
+ L->is_ll = BOOLEAN (Common->final_ll) ;
+ if (L->xtype == CHOLMOD_PATTERN && Common->final_pack)
+ {
+ /* allocate a factor with exactly the space required */
+ Common->grow2 = 0 ;
+ }
+ CHOLMOD(rowfac) (S, F, beta, 0, nrow, L, Common) ;
+ Common->grow2 = grow2 ;
+ }
+ status = Common->status ;
+
+ /* ------------------------------------------------------------------ */
+ /* convert to final form, if requested */
+ /* ------------------------------------------------------------------ */
+
+ if (Common->status >= CHOLMOD_OK && convert)
+ {
+ /* workspace: none */
+ CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE,
+ Common->final_pack, Common->final_monotonic, L, Common) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free A1 and A2 if they exist */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ Common->status = MAX (Common->status, status) ;
+ return (Common->status >= CHOLMOD_OK) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_postorder.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_postorder.c
new file mode 100644
index 0000000..d9b44c5
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_postorder.c
@@ -0,0 +1,292 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_postorder =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Compute the postorder of a tree. */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+
+/* ========================================================================== */
+/* === dfs ================================================================== */
+/* ========================================================================== */
+
+/* The code below includes both a recursive and non-recursive depth-first-search
+ * of a tree. The recursive code is simpler, but can lead to stack overflow.
+ * It is left here for reference, to understand what the non-recursive code
+ * is computing. To try the recursive version, uncomment the following
+ * #define, or compile the code with -DRECURSIVE. Be aware that stack
+ * overflow may occur.
+#define RECURSIVE
+ */
+
+#ifdef RECURSIVE
+
+/* recursive version: a working code for reference only, not actual use */
+
+static Int dfs /* return the new value of k */
+(
+ Int p, /* start a DFS at node p */
+ Int k, /* start the node numbering at k */
+ Int Post [ ], /* Post ordering, modified on output */
+ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */
+ Int Next [ ], /* Next [j] = sibling of j; unmodified */
+ Int Pstack [ ] /* unused */
+)
+{
+ Int j ;
+ /* start a DFS at each child of node p */
+ for (j = Head [p] ; j != EMPTY ; j = Next [j])
+ {
+ /* start a DFS at child node j */
+ k = dfs (j, k, Post, Head, Next, Pstack) ;
+ }
+ Post [k++] = p ; /* order node p as the kth node */
+ Head [p] = EMPTY ; /* link list p no longer needed */
+ return (k) ; /* the next node will be numbered k */
+}
+
+#else
+
+/* non-recursive version for actual use */
+
+static Int dfs /* return the new value of k */
+(
+ Int p, /* start the DFS at a root node p */
+ Int k, /* start the node numbering at k */
+ Int Post [ ], /* Post ordering, modified on output */
+ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */
+ Int Next [ ], /* Next [j] = sibling of j; unmodified */
+ Int Pstack [ ] /* workspace of size n, undefined on input or output */
+)
+{
+ Int j, phead ;
+
+ /* put the root node on the stack */
+ Pstack [0] = p ;
+ phead = 0 ;
+
+ /* while the stack is not empty, do: */
+ while (phead >= 0)
+ {
+ /* grab the node p from top of the stack and get its youngest child j */
+ p = Pstack [phead] ;
+ j = Head [p] ;
+ if (j == EMPTY)
+ {
+ /* all children of p ordered. remove p from stack and order it */
+ phead-- ;
+ Post [k++] = p ; /* order node p as the kth node */
+ }
+ else
+ {
+ /* leave p on the stack. Start a DFS at child node j by putting
+ * j on the stack and removing j from the list of children of p. */
+ Head [p] = Next [j] ;
+ Pstack [++phead] = j ;
+ }
+ }
+ return (k) ; /* the next node will be numbered k */
+}
+
+#endif
+
+/* ========================================================================== */
+/* === cholmod_postorder ==================================================== */
+/* ========================================================================== */
+
+/* Postorder a tree. The tree is either an elimination tree (the output from
+ * from cholmod_etree) or a component tree (from cholmod_nested_dissection).
+ *
+ * An elimination tree is a complete tree of n nodes with Parent [j] > j or
+ * Parent [j] = EMPTY if j is a root. On output Post [0..n-1] is a complete
+ * permutation vector.
+ *
+ * A component tree is a subset of 0..n-1. Parent [j] = -2 if node j is not
+ * in the component tree. Parent [j] = EMPTY if j is a root of the component
+ * tree, and Parent [j] is in the range 0 to n-1 if j is in the component
+ * tree but not a root. On output, Post [k] is defined only for nodes in
+ * the component tree. Post [k] = j if node j is the kth node in the
+ * postordered component tree, where k is in the range 0 to the number of
+ * components minus 1.
+ *
+ * Node j is ignored and not included in the postorder if Parent [j] < EMPTY.
+ *
+ * As a result, check_parent (Parent, n,...) may fail on input, since
+ * cholmod_check_parent assumes Parent is an elimination tree. Similarly,
+ * cholmod_check_perm (Post, ...) may fail on output, since Post is a partial
+ * permutation if Parent is a component tree.
+ *
+ * An optional node weight can be given. When starting a postorder at node j,
+ * the children of j are ordered in decreasing order of their weight.
+ * If no weights are given (Weight is NULL) then children are ordered in
+ * decreasing order of their node number. The weight of a node must be in the
+ * range 0 to n-1. Weights outside that range are silently converted to that
+ * range (weights < 0 are treated as zero, and weights >= n are treated as n-1).
+ *
+ *
+ * workspace: Head (n), Iwork (2*n)
+ */
+
+UF_long CHOLMOD(postorder) /* return # of nodes postordered */
+(
+ /* ---- input ---- */
+ Int *Parent, /* size n. Parent [j] = p if p is the parent of j */
+ size_t n,
+ Int *Weight, /* size n, optional. Weight [j] is weight of node j */
+ /* ---- output --- */
+ Int *Post, /* size n. Post [k] = j is kth in postordered tree */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Head, *Next, *Pstack, *Iwork ;
+ Int j, p, k, w, nextj ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (Parent, EMPTY) ;
+ RETURN_IF_NULL (Post, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 2*n */
+ s = CHOLMOD(mult_size_t) (n, 2, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (EMPTY) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Head = Common->Head ; /* size n+1, initially all EMPTY */
+ Iwork = Common->Iwork ;
+ Next = Iwork ; /* size n (i/i/l) */
+ Pstack = Iwork + n ; /* size n (i/i/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct a link list of children for each node */
+ /* ---------------------------------------------------------------------- */
+
+ if (Weight == NULL)
+ {
+
+ /* in reverse order so children are in ascending order in each list */
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ p = Parent [j] ;
+ if (p >= 0 && p < ((Int) n))
+ {
+ /* add j to the list of children for node p */
+ Next [j] = Head [p] ;
+ Head [p] = j ;
+ }
+ }
+
+ /* Head [p] = j if j is the youngest (least-numbered) child of p */
+ /* Next [j1] = j2 if j2 is the next-oldest sibling of j1 */
+
+ }
+ else
+ {
+
+ /* First, construct a set of link lists according to Weight.
+ *
+ * Whead [w] = j if node j is the first node in bucket w.
+ * Next [j1] = j2 if node j2 follows j1 in a link list.
+ */
+
+ Int *Whead = Pstack ; /* use Pstack as workspace for Whead [ */
+
+ for (w = 0 ; w < ((Int) n) ; w++)
+ {
+ Whead [w] = EMPTY ;
+ }
+ /* do in forward order, so nodes that ties are ordered by node index */
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ p = Parent [j] ;
+ if (p >= 0 && p < ((Int) n))
+ {
+ w = Weight [j] ;
+ w = MAX (0, w) ;
+ w = MIN (w, ((Int) n) - 1) ;
+ /* place node j at the head of link list for weight w */
+ Next [j] = Whead [w] ;
+ Whead [w] = j ;
+ }
+ }
+
+ /* traverse weight buckets, placing each node in its parent's list */
+ for (w = n-1 ; w >= 0 ; w--)
+ {
+ for (j = Whead [w] ; j != EMPTY ; j = nextj)
+ {
+ nextj = Next [j] ;
+ /* put node j in the link list of its parent */
+ p = Parent [j] ;
+ ASSERT (p >= 0 && p < ((Int) n)) ;
+ Next [j] = Head [p] ;
+ Head [p] = j ;
+ }
+ }
+
+ /* Whead no longer needed ] */
+ /* Head [p] = j if j is the lightest child of p */
+ /* Next [j1] = j2 if j2 is the next-heaviest sibling of j1 */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* start a DFS at each root node of the etree */
+ /* ---------------------------------------------------------------------- */
+
+ k = 0 ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ if (Parent [j] == EMPTY)
+ {
+ /* j is the root of a tree; start a DFS here */
+ k = dfs (j, k, Post, Head, Next, Pstack) ;
+ }
+ }
+
+ /* this would normally be EMPTY already, unless Parent is invalid */
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ Head [j] = EMPTY ;
+ }
+
+ PRINT1 (("postordered "ID" nodes\n", k)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (k) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rcond.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rcond.c
new file mode 100644
index 0000000..69f7412
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rcond.c
@@ -0,0 +1,161 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_rcond =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Return a rough estimate of the reciprocal of the condition number:
+ * the minimum entry on the diagonal of L (or absolute entry of D for an LDL'
+ * factorization) divided by the maximum entry (squared for LL'). L can be
+ * real, complex, or zomplex. Returns -1 on error, 0 if the matrix is singular
+ * or has a zero entry on the diagonal of L, 1 if the matrix is 0-by-0, or
+ * min(diag(L))/max(diag(L)) otherwise. Never returns NaN; if L has a NaN on
+ * the diagonal it returns zero instead.
+ *
+ * For an LL' factorization, (min(diag(L))/max(diag(L)))^2 is returned.
+ * For an LDL' factorization, (min(diag(D))/max(diag(D))) is returned.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === LMINMAX ============================================================== */
+/* ========================================================================== */
+
+/* Update lmin and lmax for one entry L(j,j) */
+
+#define FIRST_LMINMAX(Ljj,lmin,lmax) \
+{ \
+ double ljj = Ljj ; \
+ if (IS_NAN (ljj)) \
+ { \
+ return (0) ; \
+ } \
+ lmin = ljj ; \
+ lmax = ljj ; \
+}
+
+#define LMINMAX(Ljj,lmin,lmax) \
+{ \
+ double ljj = Ljj ; \
+ if (IS_NAN (ljj)) \
+ { \
+ return (0) ; \
+ } \
+ if (ljj < lmin) \
+ { \
+ lmin = ljj ; \
+ } \
+ else if (ljj > lmax) \
+ { \
+ lmax = ljj ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === cholmod_rcond ======================================================== */
+/* ========================================================================== */
+
+double CHOLMOD(rcond) /* return min(diag(L)) / max(diag(L)) */
+(
+ /* ---- input ---- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double lmin, lmax, rcond ;
+ double *Lx ;
+ Int *Lpi, *Lpx, *Super, *Lp ;
+ Int n, e, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol, jj, j ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (L, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ n = L->n ;
+ if (n == 0)
+ {
+ return (1) ;
+ }
+ if (L->minor < L->n)
+ {
+ return (0) ;
+ }
+
+ e = (L->xtype == CHOLMOD_COMPLEX) ? 2 : 1 ;
+
+ if (L->is_super)
+ {
+ /* L is supernodal */
+ nsuper = L->nsuper ; /* number of supernodes in L */
+ Lpi = L->pi ; /* column pointers for integer pattern */
+ Lpx = L->px ; /* column pointers for numeric values */
+ Super = L->super ; /* supernode sizes */
+ Lx = L->x ; /* numeric values */
+ FIRST_LMINMAX (Lx [0], lmin, lmax) ; /* first diagonal entry of L */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ; /* first column in supernode s */
+ k2 = Super [s+1] ; /* last column in supernode is k2-1 */
+ psi = Lpi [s] ; /* first row index is L->s [psi] */
+ psend = Lpi [s+1] ; /* last row index is L->s [psend-1] */
+ psx = Lpx [s] ; /* first numeric entry is Lx [psx] */
+ nsrow = psend - psi ; /* supernode is nsrow-by-nscol */
+ nscol = k2 - k1 ;
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ LMINMAX (Lx [e * (psx + jj + jj*nsrow)], lmin, lmax) ;
+ }
+ }
+ }
+ else
+ {
+ /* L is simplicial */
+ Lp = L->p ;
+ Lx = L->x ;
+ if (L->is_ll)
+ {
+ /* LL' factorization */
+ FIRST_LMINMAX (Lx [Lp [0]], lmin, lmax) ;
+ for (j = 1 ; j < n ; j++)
+ {
+ LMINMAX (Lx [e * Lp [j]], lmin, lmax) ;
+ }
+ }
+ else
+ {
+ /* LDL' factorization, the diagonal might be negative */
+ FIRST_LMINMAX (fabs (Lx [Lp [0]]), lmin, lmax) ;
+ for (j = 1 ; j < n ; j++)
+ {
+ LMINMAX (fabs (Lx [e * Lp [j]]), lmin, lmax) ;
+ }
+ }
+ }
+ rcond = lmin / lmax ;
+ if (L->is_ll)
+ {
+ rcond = rcond*rcond ;
+ }
+ return (rcond) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_resymbol.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_resymbol.c
new file mode 100644
index 0000000..a25f771
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_resymbol.c
@@ -0,0 +1,604 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_resymbol ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Recompute the symbolic pattern of L. Entries not in the symbolic pattern
+ * are dropped. L->Perm can be used (or not) to permute the input matrix A.
+ *
+ * These routines are used after a supernodal factorization is converted into
+ * a simplicial one, to remove zero entries that were added due to relaxed
+ * supernode amalgamation. They can also be used after a series of downdates
+ * to remove entries that would no longer be present if the matrix were
+ * factorized from scratch. A downdate (cholmod_updown) does not remove any
+ * entries from L.
+ *
+ * workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow)
+ * if unsymmetric: Iwork (2*nrow+ncol).
+ * Allocates up to 2 copies of its input matrix A (pattern only).
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === cholmod_resymbol ===================================================== */
+/* ========================================================================== */
+
+/* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P',
+ * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not).
+ *
+ * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it
+ * first permutes A according to L->Perm. A can be upper/lower/unsymmetric,
+ * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */
+
+int CHOLMOD(resymbol)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *H, *F, *G ;
+ Int stype, nrow, ncol ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ if (L->is_super)
+ {
+ /* cannot operate on a supernodal factorization */
+ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ;
+ return (FALSE) ;
+ }
+ if (L->n != A->nrow)
+ {
+ /* dimensions must agree */
+ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ stype = A->stype ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ /* s = 2*nrow + (stype ? 0 : ncol) */
+ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ s = CHOLMOD(add_size_t) (s, (stype ? 0 : ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* permute the input matrix if necessary */
+ /* ---------------------------------------------------------------------- */
+
+ H = NULL ;
+ G = NULL ;
+
+ if (stype > 0)
+ {
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ /* F = triu(A)' */
+ /* workspace: Iwork (nrow) */
+ G = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ;
+ }
+ else
+ {
+ /* F = triu(A(p,p))' */
+ /* workspace: Iwork (2*nrow) */
+ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ;
+ }
+ F = G ;
+ }
+ else if (stype < 0)
+ {
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ F = A ;
+ }
+ else
+ {
+ /* G = triu(A(p,p))' */
+ /* workspace: Iwork (2*nrow) */
+ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ;
+ /* H = G' */
+ /* workspace: Iwork (nrow) */
+ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ;
+ F = H ;
+ }
+ }
+ else
+ {
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ F = A ;
+ }
+ else
+ {
+ /* G = A(p,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ G = CHOLMOD(ptranspose) (A, 0, L->Perm, fset, fsize, Common) ;
+ /* H = G' */
+ /* workspace: Iwork (ncol) */
+ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ;
+ F = H ;
+ }
+ }
+
+ /* No need to check for failure here. cholmod_resymbol_noperm will return
+ * FALSE if F is NULL. */
+
+ /* ---------------------------------------------------------------------- */
+ /* resymbol */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(resymbol_noperm) (F, fset, fsize, pack, L, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the temporary matrices, if they exist */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&H, Common) ;
+ CHOLMOD(free_sparse) (&G, Common) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_resymbol_noperm ============================================== */
+/* ========================================================================== */
+
+/* Redo symbolic LDL' or LL' factorization of I + F*F' or I+A, where F=A(:,f).
+ *
+ * L already exists, but is a superset of the true dynamic pattern (simple
+ * column downdates and row deletions haven't pruned anything). Just redo the
+ * symbolic factorization and drop entries that are no longer there. The
+ * diagonal is not modified. The number of nonzeros in column j of L
+ * (L->nz[j]) can decrease. The column pointers (L->p[j]) remain unchanged if
+ * pack is FALSE or if L is not monotonic. Otherwise, the columns of L are
+ * packed in place.
+ *
+ * For the symmetric case, the columns of the lower triangular part of A
+ * are accessed by column. NOTE that this the transpose of the general case.
+ *
+ * For the unsymmetric case, F=A(:,f) is accessed by column.
+ *
+ * A need not be sorted, and can be packed or unpacked. If L->Perm is not
+ * identity, then A must already be permuted according to the permutation used
+ * to factorize L. The advantage of using this routine is that it does not
+ * need to create permuted copies of A first.
+ *
+ * This routine can be called if L is only partially factored via cholmod_rowfac
+ * since all it does is prune. If an entry is in F*F' or A, but not in L, it
+ * isn't added to L.
+ *
+ * L must be simplicial LDL' or LL'; it cannot be supernodal or symbolic.
+ *
+ * The set f is held in fset and fsize.
+ * fset = NULL means ":" in MATLAB. fset is ignored.
+ * fset != NULL means f = fset [0..fset-1].
+ * fset != NULL and fsize = 0 means f is the empty set.
+ * There can be no duplicates in fset.
+ * Common->status is set to CHOLMOD_INVALID if fset is invalid.
+ *
+ * workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow)
+ * if unsymmetric: Iwork (2*nrow+ncol).
+ * Unlike cholmod_resymbol, this routine does not allocate any temporary
+ * copies of its input matrix.
+ */
+
+int CHOLMOD(resymbol_noperm)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Lz ;
+ Int i, j, k, row, parent, p, pend, pdest, ncol, apacked, sorted, nrow, nf,
+ use_fset, mark, jj, stype, xtype ;
+ Int *Ap, *Ai, *Anz, *Li, *Lp, *Lnz, *Flag, *Head, *Link, *Anext, *Iwork ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ stype = A->stype ;
+ ASSERT (IMPLIES (stype != 0, nrow == ncol)) ;
+ if (stype > 0)
+ {
+ /* symmetric, with upper triangular part, not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric upper not supported ") ;
+ return (FALSE) ;
+ }
+ if (L->is_super)
+ {
+ /* cannot operate on a supernodal or symbolic factorization */
+ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ;
+ return (FALSE) ;
+ }
+ if (L->n != A->nrow)
+ {
+ /* dimensions must agree */
+ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 2*nrow + (stype ? 0 : ncol) */
+ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ if (stype != 0)
+ {
+ s = CHOLMOD(add_size_t) (s, ncol, &ok) ;
+ }
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ai = A->i ;
+ Ap = A->p ;
+ Anz = A->nz ;
+ apacked = A->packed ;
+ sorted = A->sorted ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+ xtype = L->xtype ;
+
+ /* If L is monotonic on input, then it can be packed or
+ * unpacked on output, depending on the pack input parameter. */
+
+ /* cannot pack a non-monotonic matrix */
+ if (!(L->is_monotonic))
+ {
+ pack = FALSE ;
+ }
+
+ ASSERT (L->nzmax >= (size_t) (Lp [L->n])) ;
+
+ pdest = 0 ;
+
+ PRINT1 (("\n\n===================== Resymbol pack %d Apacked %d\n",
+ pack, A->packed)) ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "ReSymbol A:", Common) >= 0) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol initial L (i, x):", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size nrow */
+ Head = Common->Head ; /* size nrow+1 */
+ Iwork = Common->Iwork ;
+ Link = Iwork ; /* size nrow (i/i/l) [ */
+ Lnz = Iwork + nrow ; /* size nrow (i/i/l), if L not packed */
+ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l), unsym. only */
+ for (j = 0 ; j < nrow ; j++)
+ {
+ Link [j] = EMPTY ;
+ }
+
+ /* use Lnz in L itself */
+ Lnz = L->nz ;
+ ASSERT (Lnz != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* for the unsymmetric case, queue each column of A (:,f) */
+ /* ---------------------------------------------------------------------- */
+
+ /* place each column of the basis set on the link list corresponding to */
+ /* the smallest row index in that column */
+
+ if (stype == 0)
+ {
+ use_fset = (fset != NULL) ;
+ if (use_fset)
+ {
+ nf = fsize ;
+ /* This is the only O(ncol) loop in cholmod_resymbol.
+ * It is required only to check the fset. */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Anext [j] = -2 ;
+ }
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = fset [jj] ;
+ if (j < 0 || j > ncol || Anext [j] != -2)
+ {
+ /* out-of-range or duplicate entry in fset */
+ ERROR (CHOLMOD_INVALID, "fset invalid") ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (FALSE) ;
+ }
+ /* flag column j as having been seen */
+ Anext [j] = EMPTY ;
+ }
+ /* the fset is now valid */
+ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ;
+ }
+ else
+ {
+ nf = ncol ;
+ }
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = (use_fset) ? (fset [jj]) : jj ;
+ /* column j is the fset; find the smallest row (if any) */
+ p = Ap [j] ;
+ pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ if (pend > p)
+ {
+ k = Ai [p] ;
+ if (!sorted)
+ {
+ for ( ; p < pend ; p++)
+ {
+ k = MIN (k, Ai [p]) ;
+ }
+ }
+ /* place column j on link list k */
+ ASSERT (k >= 0 && k < nrow) ;
+ Anext [j] = Head [k] ;
+ Head [k] = j ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* recompute symbolic LDL' factorization */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < nrow ; k++)
+ {
+
+#ifndef NDEBUG
+ PRINT1 (("\n\n================== Initial column k = "ID"\n", k)) ;
+ for (p = Lp [k] ; p < Lp [k] + Lnz [k] ; p++)
+ {
+ PRINT1 ((" row: "ID" value: ", Li [p])) ;
+ PRINT1 (("\n")) ;
+ }
+ PRINT1 (("Recomputing LDL, column k = "ID"\n", k)) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* compute column k of I+F*F' or I+A */
+ /* ------------------------------------------------------------------ */
+
+ /* flag the diagonal entry */
+ mark = CHOLMOD(clear_flag) (Common) ;
+ Flag [k] = mark ;
+ PRINT1 ((" row: "ID" (diagonal)\n", k)) ;
+
+ if (stype != 0)
+ {
+ /* merge column k of A into Flag (lower triangular part only) */
+ p = Ap [k] ;
+ pend = (apacked) ? (Ap [k+1]) : (p + Anz [k]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > k)
+ {
+ Flag [i] = mark ;
+ }
+ }
+ }
+ else
+ {
+ /* for each column j whos first row index is in row k */
+ for (j = Head [k] ; j != EMPTY ; j = Anext [j])
+ {
+ /* merge column j of A into Flag */
+ PRINT1 ((" ---- A column "ID"\n", j)) ;
+ p = Ap [j] ;
+ pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ PRINT1 ((" length "ID" adding\n", pend-p)) ;
+ for ( ; p < pend ; p++)
+ {
+#ifndef NDEBUG
+ ASSERT (Ai [p] >= k && Ai [p] < nrow) ;
+ if (Flag [Ai [p]] < mark) PRINT1 ((" row "ID"\n", Ai [p])) ;
+#endif
+ Flag [Ai [p]] = mark ;
+ }
+ }
+ /* clear the kth link list */
+ Head [k] = EMPTY ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* compute pruned pattern of kth column of L = union of children */
+ /* ------------------------------------------------------------------ */
+
+ /* for each column j of L whose parent is k */
+ for (j = Link [k] ; j != EMPTY ; j = Link [j])
+ {
+ /* merge column j of L into Flag */
+ PRINT1 ((" ---- L column "ID"\n", k)) ;
+ ASSERT (j < k) ;
+ ASSERT (Lnz [j] > 0) ;
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ ASSERT (Li [p] == j && Li [p+1] == k) ;
+ p++ ; /* skip past the diagonal entry */
+ for ( ; p < pend ; p++)
+ {
+ /* add to pattern */
+ ASSERT (Li [p] >= k && Li [p] < nrow) ;
+ Flag [Li [p]] = mark ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* prune the kth column of L */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("Final column of L:\n")) ;
+ p = Lp [k] ;
+ pend = p + Lnz [k] ;
+
+ if (pack)
+ {
+ /* shift column k upwards */
+ Lp [k] = pdest ;
+ }
+ else
+ {
+ /* leave column k in place, just reduce Lnz [k] */
+ pdest = p ;
+ }
+
+ for ( ; p < pend ; p++)
+ {
+ ASSERT (pdest < pend) ;
+ ASSERT (pdest <= p) ;
+ row = Li [p] ;
+ ASSERT (row >= k && row < nrow) ;
+ if (Flag [row] == mark)
+ {
+ /* keep this entry */
+ Li [pdest] = row ;
+ if (xtype == CHOLMOD_REAL)
+ {
+ Lx [pdest] = Lx [p] ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Lx [2*pdest ] = Lx [2*p ] ;
+ Lx [2*pdest+1] = Lx [2*p+1] ;
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ Lx [pdest] = Lx [p] ;
+ Lz [pdest] = Lz [p] ;
+ }
+ pdest++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* prepare this column for its parent */
+ /* ------------------------------------------------------------------ */
+
+ Lnz [k] = pdest - Lp [k] ;
+
+ PRINT1 ((" L("ID") length "ID"\n", k, Lnz [k])) ;
+ ASSERT (Lnz [k] > 0) ;
+
+ /* parent is the first entry in the column after the diagonal */
+ parent = (Lnz [k] > 1) ? (Li [Lp [k] + 1]) : EMPTY ;
+
+ PRINT1 (("parent ("ID") = "ID"\n", k, parent)) ;
+ ASSERT ((parent > k && parent < nrow) || (parent == EMPTY)) ;
+
+ if (parent != EMPTY)
+ {
+ Link [k] = Link [parent] ;
+ Link [parent] = k ;
+ }
+ }
+
+ /* done using Iwork for Link, Lnz (if needed), and Anext ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to packed, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (pack)
+ {
+ /* finalize Lp */
+ Lp [nrow] = pdest ;
+ /* Shrink L to be just large enough. It cannot fail. */
+ /* workspace: none */
+ ASSERT ((size_t) (Lp [nrow]) <= L->nzmax) ;
+ CHOLMOD(reallocate_factor) (Lp [nrow], L, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(clear_flag) (Common) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol final L (i, x):", Common)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rowcolcounts.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rowcolcounts.c
new file mode 100644
index 0000000..7965868
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rowcolcounts.c
@@ -0,0 +1,535 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_rowcolcounts ======================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Compute the row and column counts of the Cholesky factor L of the matrix
+ * A or A*A'. The etree and its postordering must already be computed (see
+ * cholmod_etree and cholmod_postorder) and given as inputs to this routine.
+ *
+ * For the symmetric case (LL'=A), A is accessed by column. Only the lower
+ * triangular part of A is used. Entries not in this part of the matrix are
+ * ignored. This is the same as storing the upper triangular part of A by
+ * rows, with entries in the lower triangular part being ignored. NOTE: this
+ * representation is the TRANSPOSE of the input to cholmod_etree.
+ *
+ * For the unsymmetric case (LL'=AA'), A is accessed by column. Equivalently,
+ * if A is viewed as a matrix in compressed-row form, this routine computes
+ * the row and column counts for L where LL'=A'A. If the input vector f is
+ * present, then F*F' is analyzed instead, where F = A(:,f).
+ *
+ * The set f is held in fset and fsize.
+ * fset = NULL means ":" in MATLAB. fset is ignored.
+ * fset != NULL means f = fset [0..fset-1].
+ * fset != NULL and fsize = 0 means f is the empty set.
+ * Common->status is set to CHOLMOD_INVALID if fset is invalid.
+ *
+ * In both cases, the columns of A need not be sorted.
+ * A can be packed or unpacked.
+ *
+ * References:
+ * J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and
+ * column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis &
+ * Applic., vol 15, 1994, pp. 1075-1091.
+ *
+ * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for
+ * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710.
+ *
+ * workspace:
+ * if symmetric: Flag (nrow), Iwork (2*nrow)
+ * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1)
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === initialize_node ====================================================== */
+/* ========================================================================== */
+
+static int initialize_node /* initial work for kth node in postordered etree */
+(
+ Int k, /* at the kth step of the algorithm (and kth node) */
+ Int Post [ ], /* Post [k] = i, the kth node in postordered etree */
+ Int Parent [ ], /* Parent [i] is the parent of i in the etree */
+ Int ColCount [ ], /* ColCount [c] is the current weight of node c */
+ Int PrevNbr [ ] /* PrevNbr [u] = k if u was last considered at step k */
+)
+{
+ Int p, parent ;
+ /* determine p, the kth node in the postordered etree */
+ p = Post [k] ;
+ /* adjust the weight if p is not a root of the etree */
+ parent = Parent [p] ;
+ if (parent != EMPTY)
+ {
+ ColCount [parent]-- ;
+ }
+ /* flag node p to exclude self edges (p,p) */
+ PrevNbr [p] = k ;
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === process_edge ========================================================= */
+/* ========================================================================== */
+
+/* edge (p,u) is being processed. p < u is a descendant of its ancestor u in
+ * the etree. node p is the kth node in the postordered etree. */
+
+static void process_edge
+(
+ Int p, /* process edge (p,u) of the matrix */
+ Int u,
+ Int k, /* we are at the kth node in the postordered etree */
+ Int First [ ], /* First [i] = k if the postordering of first
+ * descendent of node i is k */
+ Int PrevNbr [ ], /* u was last considered at step k = PrevNbr [u] */
+ Int ColCount [ ], /* ColCount [c] is the current weight of node c */
+ Int PrevLeaf [ ], /* s = PrevLeaf [u] means that s was the last leaf
+ * seen in the subtree rooted at u. */
+ Int RowCount [ ], /* RowCount [i] is # of nonzeros in row i of L,
+ * including the diagonal. Not computed if NULL. */
+ Int SetParent [ ], /* the FIND/UNION data structure, which forms a set
+ * of trees. A root i has i = SetParent [i]. Following
+ * a path from i to the root q of the subtree containing
+ * i means that q is the SetParent representative of i.
+ * All nodes in the tree could have their SetParent
+ * equal to the root q; the tree representation is used
+ * to save time. When a path is traced from i to its
+ * root q, the path is re-traversed to set the SetParent
+ * of the whole path to be the root q. */
+ Int Level [ ] /* Level [i] = length of path from node i to root */
+)
+{
+ Int prevleaf, q, s, sparent ;
+ if (First [p] > PrevNbr [u])
+ {
+ /* p is a leaf of the subtree of u */
+ ColCount [p]++ ;
+ prevleaf = PrevLeaf [u] ;
+ if (prevleaf == EMPTY)
+ {
+ /* p is the first leaf of subtree of u; RowCount will be incremented
+ * by the length of the path in the etree from p up to u. */
+ q = u ;
+ }
+ else
+ {
+ /* q = FIND (prevleaf): find the root q of the
+ * SetParent tree containing prevleaf */
+ for (q = prevleaf ; q != SetParent [q] ; q = SetParent [q])
+ {
+ ;
+ }
+ /* the root q has been found; re-traverse the path and
+ * perform path compression */
+ s = prevleaf ;
+ for (s = prevleaf ; s != q ; s = sparent)
+ {
+ sparent = SetParent [s] ;
+ SetParent [s] = q ;
+ }
+ /* adjust the RowCount and ColCount; RowCount will be incremented by
+ * the length of the path from p to the SetParent root q, and
+ * decrement the ColCount of q by one. */
+ ColCount [q]-- ;
+ }
+ if (RowCount != NULL)
+ {
+ /* if RowCount is being computed, increment it by the length of
+ * the path from p to q */
+ RowCount [u] += (Level [p] - Level [q]) ;
+ }
+ /* p is a leaf of the subtree of u, so mark PrevLeaf [u] to be p */
+ PrevLeaf [u] = p ;
+ }
+ /* flag u has having been processed at step k */
+ PrevNbr [u] = k ;
+}
+
+
+/* ========================================================================== */
+/* === finalize_node ======================================================== */
+/* ========================================================================== */
+
+static void finalize_node /* compute UNION (p, Parent [p]) */
+(
+ Int p,
+ Int Parent [ ], /* Parent [p] is the parent of p in the etree */
+ Int SetParent [ ] /* see process_edge, above */
+)
+{
+ /* all nodes in the SetParent tree rooted at p now have as their final
+ * root the node Parent [p]. This computes UNION (p, Parent [p]) */
+ if (Parent [p] != EMPTY)
+ {
+ SetParent [p] = Parent [p] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowcolcounts ================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(rowcolcounts)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ Int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */
+ Int *Post, /* size nrow. Post [k] = i if i is the kth node in
+ * the postordered etree. */
+ /* ---- output --- */
+ Int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of
+ * L, including the diagonal. */
+ Int *ColCount, /* size nrow. ColCount [i] = # entries in the ith
+ * column of L, including the diagonal. */
+ Int *First, /* size nrow. First [i] = k is the least postordering
+ * of any descendant of i. */
+ Int *Level, /* size nrow. Level [i] is the length of the path from
+ * i to the root, with Level [root] = 0. */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double fl, ff ;
+ Int *Ap, *Ai, *Anz, *PrevNbr, *SetParent, *Head, *PrevLeaf, *Anext, *Ipost,
+ *Iwork ;
+ Int i, j, r, k, len, s, p, pend, inew, stype, nf, anz, inode, parent,
+ nrow, ncol, packed, use_fset, jj ;
+ size_t w ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_NULL (Post, FALSE) ;
+ RETURN_IF_NULL (ColCount, FALSE) ;
+ RETURN_IF_NULL (First, FALSE) ;
+ RETURN_IF_NULL (Level, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype > 0)
+ {
+ /* symmetric with upper triangular part not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric upper not supported") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ; /* the number of rows of A */
+ ncol = A->ncol ; /* the number of columns of A */
+
+ /* w = 2*nrow + (stype ? 0 : ncol) */
+ w = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ w = CHOLMOD(add_size_t) (w, (stype ? 0 : ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, w, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ ASSERT (CHOLMOD(dump_perm) (Post, nrow, nrow, "Post", Common)) ;
+ ASSERT (CHOLMOD(dump_parent) (Parent, nrow, "Parent", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ; /* size ncol+1, column pointers for A */
+ Ai = A->i ; /* the row indices of A, of size nz=Ap[ncol+1] */
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ SetParent = Iwork ; /* size nrow (i/i/l) */
+ PrevNbr = Iwork + nrow ; /* size nrow (i/i/l) */
+ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l) (unsym only) */
+ PrevLeaf = Common->Flag ; /* size nrow */
+ Head = Common->Head ; /* size nrow+1 (unsym only)*/
+
+ /* ---------------------------------------------------------------------- */
+ /* find the first descendant and level of each node in the tree */
+ /* ---------------------------------------------------------------------- */
+
+ /* First [i] = k if the postordering of first descendent of node i is k */
+ /* Level [i] = length of path from node i to the root (Level [root] = 0) */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ First [i] = EMPTY ;
+ }
+
+ /* postorder traversal of the etree */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ /* node i of the etree is the kth node in the postordered etree */
+ i = Post [k] ;
+
+ /* i is a leaf if First [i] is still EMPTY */
+ /* ColCount [i] starts at 1 if i is a leaf, zero otherwise */
+ ColCount [i] = (First [i] == EMPTY) ? 1 : 0 ;
+
+ /* traverse the path from node i to the root, stopping if we find a
+ * node r whose First [r] is already defined. */
+ len = 0 ;
+ for (r = i ; (r != EMPTY) && (First [r] == EMPTY) ; r = Parent [r])
+ {
+ First [r] = k ;
+ len++ ;
+ }
+ if (r == EMPTY)
+ {
+ /* we hit a root node, the level of which is zero */
+ len-- ;
+ }
+ else
+ {
+ /* we stopped at node r, where Level [r] is already defined */
+ len += Level [r] ;
+ }
+ /* re-traverse the path from node i to r; set the level of each node */
+ for (s = i ; s != r ; s = Parent [s])
+ {
+ Level [s] = len-- ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* AA' case: sort columns of A according to first postordered row index */
+ /* ---------------------------------------------------------------------- */
+
+ fl = 0.0 ;
+ if (stype == 0)
+ {
+ /* [ use PrevNbr [0..nrow-1] as workspace for Ipost */
+ Ipost = PrevNbr ;
+ /* Ipost [i] = k if i is the kth node in the postordered etree. */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Ipost [Post [k]] = k ;
+ }
+ use_fset = (fset != NULL) ;
+ if (use_fset)
+ {
+ nf = fsize ;
+ /* clear Anext to check fset */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Anext [j] = -2 ;
+ }
+ /* find the first postordered row in each column of A (post,f)
+ * and place the column in the corresponding link list */
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = fset [jj] ;
+ if (j < 0 || j > ncol || Anext [j] != -2)
+ {
+ /* out-of-range or duplicate entry in fset */
+ ERROR (CHOLMOD_INVALID, "fset invalid") ;
+ return (FALSE) ;
+ }
+ /* flag column j as having been seen */
+ Anext [j] = EMPTY ;
+ }
+ /* fset is now valid */
+ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ;
+ }
+ else
+ {
+ nf = ncol ;
+ }
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = (use_fset) ? (fset [jj]) : jj ;
+ /* column j is in the fset; find the smallest row (if any) */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ ff = (double) MAX (0, pend - p) ;
+ fl += ff*ff + ff ;
+ if (pend > p)
+ {
+ k = Ipost [Ai [p]] ;
+ for ( ; p < pend ; p++)
+ {
+ inew = Ipost [Ai [p]] ;
+ k = MIN (k, inew) ;
+ }
+ /* place column j in link list k */
+ ASSERT (k >= 0 && k < nrow) ;
+ Anext [j] = Head [k] ;
+ Head [k] = j ;
+ }
+ }
+ /* Ipost no longer needed for inverse postordering ]
+ * Head [k] contains a link list of all columns whose first
+ * postordered row index is equal to k, for k = 0 to nrow-1. */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row counts and node weights */
+ /* ---------------------------------------------------------------------- */
+
+ if (RowCount != NULL)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ RowCount [i] = 1 ;
+ }
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ PrevLeaf [i] = EMPTY ;
+ PrevNbr [i] = EMPTY ;
+ SetParent [i] = i ; /* every node is in its own set, by itself */
+ }
+
+ if (stype != 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric case: LL' = A */
+ /* ------------------------------------------------------------------ */
+
+ /* also determine the number of entries in triu(A) */
+ anz = nrow ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ /* j is the kth node in the postordered etree */
+ j = initialize_node (k, Post, Parent, ColCount, PrevNbr) ;
+
+ /* for all nonzeros A(i,j) below the diagonal, in column j of A */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > j)
+ {
+ /* j is a descendant of i in etree(A) */
+ anz++ ;
+ process_edge (j, i, k, First, PrevNbr, ColCount,
+ PrevLeaf, RowCount, SetParent, Level) ;
+ }
+ }
+ /* update SetParent: UNION (j, Parent [j]) */
+ finalize_node (j, Parent, SetParent) ;
+ }
+ Common->anz = anz ;
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* unsymmetric case: LL' = AA' */
+ /* ------------------------------------------------------------------ */
+
+ for (k = 0 ; k < nrow ; k++)
+ {
+ /* inode is the kth node in the postordered etree */
+ inode = initialize_node (k, Post, Parent, ColCount, PrevNbr) ;
+
+ /* for all cols j whose first postordered row is k: */
+ for (j = Head [k] ; j != EMPTY ; j = Anext [j])
+ {
+ /* k is the first postordered row in column j of A */
+ /* for all rows i in column j: */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* has i already been considered at this step k */
+ if (PrevNbr [i] < k)
+ {
+ /* inode is a descendant of i in etree(AA') */
+ /* process edge (inode,i) and set PrevNbr[i] to k */
+ process_edge (inode, i, k, First, PrevNbr, ColCount,
+ PrevLeaf, RowCount, SetParent, Level) ;
+ }
+ }
+ }
+ /* clear link list k */
+ Head [k] = EMPTY ;
+ /* update SetParent: UNION (inode, Parent [inode]) */
+ finalize_node (inode, Parent, SetParent) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finish computing the column counts */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j < nrow ; j++)
+ {
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ /* add the ColCount of j to its parent */
+ ColCount [parent] += ColCount [j] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Common->mark = EMPTY ;
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* flop count and nnz(L) for subsequent LL' numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* use double to avoid integer overflow. lnz cannot be NaN. */
+ Common->aatfl = fl ;
+ Common->lnz = 0. ;
+ fl = 0 ;
+ for (j = 0 ; j < nrow ; j++)
+ {
+ ff = (double) (ColCount [j]) ;
+ Common->lnz += ff ;
+ fl += ff*ff ;
+ }
+
+ Common->fl = fl ;
+ PRINT1 (("rowcol fl %g lnz %g\n", Common->fl, Common->lnz)) ;
+
+ return (TRUE) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rowfac.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rowfac.c
new file mode 100644
index 0000000..f0be0e9
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_rowfac.c
@@ -0,0 +1,677 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_rowfac ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Full or incremental numerical LDL' or LL' factorization (simplicial, not
+ * supernodal) cholmod_factorize is the "easy" wrapper for this code, but it
+ * does not provide access to incremental factorization.
+ *
+ * cholmod_rowfac computes the full or incremental LDL' or LL' factorization of
+ * A+beta*I (where A is symmetric) or A*F+beta*I (where A and F are unsymmetric
+ * and only the upper triangular part of A*F+beta*I is used). It computes
+ * L (and D, for LDL') one row at a time. beta is real.
+ *
+ * A is nrow-by-ncol or nrow-by-nrow. In "packed" form it is a conventional
+ * column-oriented sparse matrix. Row indices of column j are in
+ * Ai [Ap [j] ... Ap [j+1]-1] and values in the same locations of Ax.
+ * will be faster if A has sorted columns. In "unpacked" form the column
+ * of A ends at Ap [j] + Anz [j] - 1 instead of Ap [j+1] - 1.
+ *
+ * Row indices in each column of A can be sorted or unsorted, but the routine
+ * routine works fastest if A is sorted, or if only triu(A) is provided
+ * for the symmetric case.
+ *
+ * The unit-diagonal nrow-by-nrow output matrix L is returned in "unpacked"
+ * column form, with row indices of column j in Li [Lp [j] ...
+ * Lp [j] + Lnz [j] - 1] and values in the same location in Lx. The row
+ * indices in each column of L are in sorted order. The unit diagonal of L
+ * is not stored.
+ *
+ * L can be a simplicial symbolic or numeric (L->is_super must be FALSE).
+ * A symbolic factor is converted immediately into a numeric factor containing
+ * the identity matrix.
+ *
+ * For a full factorization, kstart = 0 and kend = nrow. The existing nonzero
+ * entries (numerical values in L->x and L->z for the zomplex case, and indices
+ * in L->i), if any, are overwritten.
+ *
+ * To compute an incremental factorization, select kstart and kend as the range
+ * of rows of L you wish to compute. A correct factorization will be computed
+ * only if all descendants of all nodes k = kstart to kend-1 in the etree have
+ * been factorized by a prior call to this routine, and if rows kstart to kend-1
+ * have not been factorized. This condition is NOT checked on input.
+ *
+ * ---------------
+ * Symmetric case:
+ * ---------------
+ *
+ * The factorization (in MATLAB notation) is:
+ *
+ * S = beta*I + A
+ * S = triu (S) + triu (S,1)'
+ * L*D*L' = S, or L*L' = S
+ *
+ * A is a conventional sparse matrix in compressed column form. Only the
+ * diagonal and upper triangular part of A is accessed; the lower
+ * triangular part is ignored and assumed to be equal to the upper
+ * triangular part. For an incremental factorization, only columns kstart
+ * to kend-1 of A are accessed. F is not used.
+ *
+ * ---------------
+ * Unsymmetric case:
+ * ---------------
+ *
+ * The factorization (in MATLAB notation) is:
+ *
+ * S = beta*I + A*F
+ * S = triu (S) + triu (S,1)'
+ * L*D*L' = S, or L*L' = S
+ *
+ * The typical case is F=A'. Alternatively, if F=A(:,f)', then this
+ * routine factorizes S = beta*I + A(:,f)*A(:,f)'.
+ *
+ * All of A and F are accessed, but only the upper triangular part of A*F
+ * is used. F must be of size A->ncol by A->nrow. F is used for the
+ * unsymmetric case only. F can be packed or unpacked and it need not be
+ * sorted.
+ *
+ * For a complete factorization of beta*I + A*A',
+ * this routine performs a number of flops exactly equal to:
+ *
+ * sum (for each column j of A) of (Anz (j)^2 + Anz (j)), to form S
+ * +
+ * sum (for each column j of L) of (Lnz (j)^2 + 3*Lnz (j)), to factorize S
+ *
+ * where Anz (j) is the number of nonzeros in column j of A, and Lnz (j)
+ * is the number of nonzero in column j of L below the diagonal.
+ *
+ *
+ * workspace: Flag (nrow), W (nrow if real, 2*nrow if complex/zomplex),
+ * Iwork (nrow)
+ *
+ * Supports any xtype, except a pattern-only input matrix A cannot be
+ * factorized.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === subtree ============================================================== */
+/* ========================================================================== */
+
+/* Compute the nonzero pattern of the sparse triangular solve Lx=b, where L in
+ * this case is L(0:k-1,0:k-1), and b is a column of A. This is done by
+ * traversing the kth row-subtree of the elimination tree of L, starting from
+ * each nonzero entry in b. The pattern is returned postordered, and is valid
+ * for a subsequent numerical triangular solve of Lx=b. The elimination tree
+ * can be provided in a Parent array, or extracted from the pattern of L itself.
+ *
+ * The pattern of x = inv(L)*b is returned in Stack [top...].
+ * Also scatters b, or a multiple of b, into the work vector W.
+ *
+ * The SCATTER macro is defines how the numerical values of A or A*A' are to be
+ * scattered.
+ *
+ * PARENT(i) is a macro the defines how the etree is accessed. It is either:
+ * #define PARENT(i) Parent [i]
+ * #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY
+ */
+
+#define SUBTREE \
+ for ( ; p < pend ; p++) \
+ { \
+ i = Ai [p] ; \
+ if (i <= k) \
+ { \
+ /* scatter the column of A, or A*A' into Wx and Wz */ \
+ SCATTER ; \
+ /* start at node i and traverse up the subtree, stop at node k */ \
+ for (len = 0 ; i < k && i != EMPTY && Flag [i] < mark ; i = parent) \
+ { \
+ /* L(k,i) is nonzero, and seen for the first time */ \
+ Stack [len++] = i ; /* place i on the stack */ \
+ Flag [i] = mark ; /* mark i as visited */ \
+ parent = PARENT (i) ; /* traverse up the etree to the parent */ \
+ } \
+ /* move the path down to the bottom of the stack */ \
+ while (len > 0) \
+ { \
+ Stack [--top] = Stack [--len] ; \
+ } \
+ } \
+ else if (sorted) \
+ { \
+ break ; \
+ } \
+ }
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_rowfac.c"
+#define COMPLEX
+#include "t_cholmod_rowfac.c"
+#define ZOMPLEX
+#include "t_cholmod_rowfac.c"
+
+#define MASK
+#define REAL
+#include "t_cholmod_rowfac.c"
+#define COMPLEX
+#include "t_cholmod_rowfac.c"
+#define ZOMPLEX
+#include "t_cholmod_rowfac.c"
+#undef MASK
+
+
+/* ========================================================================== */
+/* === cholmod_row_subtree ================================================== */
+/* ========================================================================== */
+
+/* Compute the nonzero pattern of the solution to the lower triangular system
+ * L(0:k-1,0:k-1) * x = A (0:k-1,k) if A is symmetric, or
+ * L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)' if A is unsymmetric.
+ * This gives the nonzero pattern of row k of L (excluding the diagonal).
+ * The pattern is returned postordered.
+ *
+ * The symmetric case requires A to be in symmetric-upper form.
+ *
+ * The result is returned in R, a pre-allocated sparse matrix of size nrow-by-1,
+ * with R->nzmax >= nrow. R is assumed to be packed (Rnz [0] is not updated);
+ * the number of entries in R is given by Rp [0].
+ *
+ * FUTURE WORK: a very minor change to this routine could allow it to compute
+ * the nonzero pattern of x for any system Lx=b. The SUBTREE macro would need
+ * to change, to eliminate its dependence on k.
+ *
+ * workspace: Flag (nrow)
+ */
+
+int CHOLMOD(row_subtree)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ size_t krow, /* row k of L */
+ Int *Parent, /* elimination tree */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Fp, *Fi, *Fnz ;
+ Int p, pend, parent, t, stype, nrow, k, pf, pfend, Fpacked, packed,
+ sorted, top, len, i, mark ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (R, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype == 0)
+ {
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ }
+ if (krow >= A->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "subtree: k invalid") ;
+ return (FALSE) ;
+ }
+ if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax)
+ {
+ ERROR (CHOLMOD_INVALID, "subtree: R invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* symmetric upper case: F is not needed. It may be NULL */
+ Fp = NULL ;
+ Fi = NULL ;
+ Fnz = NULL ;
+ Fpacked = TRUE ;
+ }
+ else if (stype == 0)
+ {
+ /* unsymmetric case: F is required. */
+ Fp = F->p ;
+ Fi = F->i ;
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ }
+ else
+ {
+ /* symmetric lower triangular form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ sorted = A->sorted ;
+
+ k = krow ;
+ Stack = R->i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the pattern of L(k,:) */
+ /* ---------------------------------------------------------------------- */
+
+ top = nrow ; /* Stack is empty */
+ Flag [k] = mark ; /* do not include diagonal entry in Stack */
+
+#define SCATTER /* do not scatter numerical values */
+#define PARENT(i) Parent [i] /* use Parent for etree */
+
+ if (stype != 0)
+ {
+ /* scatter kth col of triu (A), get pattern L(k,:) */
+ p = Ap [k] ;
+ pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ;
+ SUBTREE ;
+ }
+ else
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ pf = Fp [k] ;
+ pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ;
+ for ( ; pf < pfend ; pf++)
+ {
+ /* get nonzero entry F (t,k) */
+ t = Fi [pf] ;
+ p = Ap [t] ;
+ pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ;
+ SUBTREE ;
+ }
+ }
+
+#undef SCATTER
+#undef PARENT
+
+ /* shift the stack upwards, to the first part of R */
+ len = nrow - top ;
+ for (i = 0 ; i < len ; i++)
+ {
+ Stack [i] = Stack [top + i] ;
+ }
+
+ Rp = R->p ;
+ Rp [0] = 0 ;
+ Rp [1] = len ;
+ R->sorted = FALSE ;
+
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_row_lsubtree ================================================= */
+/* ========================================================================== */
+
+/* Identical to cholmod_row_subtree, except that the elimination tree is
+ * obtained from L itself, as the first off-diagonal entry in each column.
+ * L must be simplicial, not supernodal */
+
+int CHOLMOD(row_lsubtree)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required
+ * for the symmetric case. Need not be sorted. */
+ size_t krow, /* row k of L */
+ cholmod_factor *L, /* the factor L from which parent(i) is derived */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Lp, *Li, *Lnz ;
+ Int p, pend, parent, t, stype, nrow, k, pf, packed, sorted, top, len, i,
+ mark ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (R, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype == 0)
+ {
+ RETURN_IF_NULL (Fi, FALSE) ;
+ }
+ if (krow >= A->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "lsubtree: k invalid") ;
+ return (FALSE) ;
+ }
+ if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax)
+ {
+ ERROR (CHOLMOD_INVALID, "lsubtree: R invalid") ;
+ return (FALSE) ;
+ }
+ if (L->is_super)
+ {
+ ERROR (CHOLMOD_INVALID, "lsubtree: L invalid (cannot be supernodal)") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype < 0)
+ {
+ /* symmetric lower triangular form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ sorted = A->sorted ;
+
+ k = krow ;
+ Stack = R->i ;
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lnz = L->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the pattern of L(k,:) */
+ /* ---------------------------------------------------------------------- */
+
+ top = nrow ; /* Stack is empty */
+ Flag [k] = mark ; /* do not include diagonal entry in Stack */
+
+#define SCATTER /* do not scatter numerical values */
+#define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY
+
+ if (stype != 0)
+ {
+ /* scatter kth col of triu (A), get pattern L(k,:) */
+ p = Ap [k] ;
+ pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ;
+ SUBTREE ;
+ }
+ else
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ for (pf = 0 ; pf < (Int) fnz ; pf++)
+ {
+ /* get nonzero entry F (t,k) */
+ t = Fi [pf] ;
+ p = Ap [t] ;
+ pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ;
+ SUBTREE ;
+ }
+ }
+
+#undef SCATTER
+#undef PARENT
+
+ /* shift the stack upwards, to the first part of R */
+ len = nrow - top ;
+ for (i = 0 ; i < len ; i++)
+ {
+ Stack [i] = Stack [top + i] ;
+ }
+
+ Rp = R->p ;
+ Rp [0] = 0 ;
+ Rp [1] = len ;
+ R->sorted = FALSE ;
+
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowfac ======================================================= */
+/* ========================================================================== */
+
+/* This is the incremental factorization for general purpose usage. */
+
+int CHOLMOD(rowfac)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ double beta [2], /* factorize beta*I+A or beta*I+AA' */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(rowfac_mask) (A, F, beta, kstart, kend, NULL, NULL, L,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowfac_mask ================================================== */
+/* ========================================================================== */
+
+/* This is meant for use in LPDASA only. */
+
+int CHOLMOD(rowfac_mask)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ double beta [2], /* factorize beta*I+A or beta*I+AA' */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ Int *mask, /* size A->nrow. if mask[i] >= 0 row i is set to zero */
+ Int *RLinkUp, /* size A->nrow. link list of rows to compute */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int n ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (L->xtype != CHOLMOD_PATTERN && A->xtype != L->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype of A and L do not match") ;
+ return (FALSE) ;
+ }
+ if (L->is_super)
+ {
+ ERROR (CHOLMOD_INVALID, "can only do simplicial factorization");
+ return (FALSE) ;
+ }
+ if (A->stype == 0)
+ {
+ RETURN_IF_NULL (F, FALSE) ;
+ if (A->xtype != F->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype of A and F do not match") ;
+ return (FALSE) ;
+ }
+ }
+ if (A->stype < 0)
+ {
+ /* symmetric lower triangular form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+ if (kend > L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "kend invalid") ;
+ return (FALSE) ;
+ }
+ if (A->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "dimensions of A and L do not match") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ Common->rowfacfl = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Xwork is of size n for the real case, 2*n for complex/zomplex */
+ n = L->n ;
+
+ /* s = ((A->xtype != CHOLMOD_REAL) ? 2:1)*n */
+ s = CHOLMOD(mult_size_t) (n, ((A->xtype != CHOLMOD_REAL) ? 2:1), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, n, s, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, A->nrow, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ if (RLinkUp == NULL)
+ {
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ ok = r_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ ok = z_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ;
+ break ;
+ }
+
+ }
+ else
+ {
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ ok = r_cholmod_rowfac_mask (A, F, beta, kstart, kend,
+ mask, RLinkUp, L, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_rowfac_mask (A, F, beta, kstart, kend,
+ mask, RLinkUp, L, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ ok = z_cholmod_rowfac_mask (A, F, beta, kstart, kend,
+ mask, RLinkUp, L, Common) ;
+ break ;
+ }
+ }
+
+ return (ok) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_solve.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_solve.c
new file mode 100644
index 0000000..f8ab992
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_solve.c
@@ -0,0 +1,1195 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_solve =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Solve one of the following systems:
+ *
+ * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm
+ * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm
+ * LDx=b 2: CHOLMOD_LD
+ * DL'x=b 3: CHOLMOD_DLt
+ * Lx=b 4: CHOLMOD_L
+ * L'x=b 5: CHOLMOD_Lt
+ * Dx=b 6: CHOLMOD_D
+ * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm)
+ * x=P'b 8: CHOLMOD_Pt apply an inverse permutation
+ *
+ * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'.
+ * For an LL' factorization, D is the identity matrix. Thus CHOLMOD_LD and
+ * CHOLMOD_L solve the same system if an LL' factorization was performed,
+ * for example.
+ *
+ * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm,
+ * or their complex counterparts ztrsv, zgemv, ztrsm, and zgemm.
+ *
+ * If both L and B are real, then X is returned real. If either is complex
+ * or zomplex, X is returned as either complex or zomplex, depending on the
+ * Common->prefer_zomplex parameter.
+ *
+ * Supports any numeric xtype (pattern-only matrices not supported).
+ *
+ * This routine does not check to see if the diagonal of L or D is zero,
+ * because sometimes a partial solve can be done with indefinite or singular
+ * matrix. If you wish to check in your own code, test L->minor. If
+ * L->minor == L->n, then the matrix has no zero diagonal entries.
+ * If k = L->minor < L->n, then L(k,k) is zero for an LL' factorization, or
+ * D(k,k) is zero for an LDL' factorization.
+ *
+ * This routine returns X as NULL only if it runs out of memory. If L is
+ * indefinite or singular, then X may contain Inf's or NaN's, but it will
+ * exist on output.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_solve.c"
+
+#define COMPLEX
+#include "t_cholmod_solve.c"
+
+#define ZOMPLEX
+#include "t_cholmod_solve.c"
+
+/* ========================================================================== */
+/* === Permutation macro ==================================================== */
+/* ========================================================================== */
+
+/* If Perm is NULL, it is interpretted as the identity permutation */
+
+#define P(k) ((Perm == NULL) ? (k) : Perm [k])
+
+
+/* ========================================================================== */
+/* === perm ================================================================= */
+/* ========================================================================== */
+
+/* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1) where B is nrow-by-ncol.
+ *
+ * Creates a permuted copy of a contiguous set of columns of B.
+ * Y is already allocated on input. Y must be of sufficient size. Let nk be
+ * the number of columns accessed in B. Y->xtype determines the complexity of
+ * the result.
+ *
+ * If B is real and Y is complex (or zomplex), only the real part of B is
+ * copied into Y. The imaginary part of Y is set to zero.
+ *
+ * If B is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of B are returned in Y. Y is returned as nrow-by-2*nk. The even
+ * columns of Y contain the real part of B and the odd columns contain the
+ * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * returned as nrow-by-nk with leading dimension nrow. Y->nzmax must be >=
+ * nrow*nk.
+ *
+ * The case where the input (B) is real and the output (Y) is zomplex is
+ * not used.
+ */
+
+static void perm
+(
+ /* ---- input ---- */
+ cholmod_dense *B, /* input matrix B */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of B to copy */
+ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *Y /* output matrix Y, already allocated */
+)
+{
+ double *Yx, *Yz, *Bx, *Bz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = B->ncol ;
+ nrow = B->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ;
+ d = B->d ;
+ Bx = B->x ;
+ Bz = B->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ Y->nrow = nrow ;
+ Y->ncol = dual*nk ;
+ Y->d = nrow ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = B (P (1:nrow), k1:k2-1) */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2] = Bx [p] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, B complex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2 ] = Bx [2*p ] ; /* real */
+ Yx [k + j2 + nrow] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, B zomplex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2 ] = Bx [p] ; /* real */
+ Yx [k + j2 + nrow] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y complex, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [2*k + j2] = Bx [p] ; /* real */
+ Yx [2*k+1 + j2] = 0 ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [2*k + j2] = Bx [2*p ] ; /* real */
+ Yx [2*k+1 + j2] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [2*k + j2] = Bx [p] ; /* real */
+ Yx [2*k+1 + j2] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (B->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2] = Bx [2*p ] ; /* real */
+ Yz [k + j2] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2] = Bx [p] ; /* real */
+ Yz [k + j2] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === iperm ================================================================ */
+/* ========================================================================== */
+
+/* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y where X is nrow-by-ncol.
+ *
+ * Copies and permutes Y into a contiguous set of columns of X. X is already
+ * allocated on input. Y must be of sufficient size. Let nk be the number
+ * of columns accessed in X. X->xtype determines the complexity of the result.
+ *
+ * If X is real and Y is complex (or zomplex), only the real part of B is
+ * copied into X. The imaginary part of Y is ignored.
+ *
+ * If X is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of Y are returned in X. Y is nrow-by-2*nk. The even
+ * columns of Y contain the real part of B and the odd columns contain the
+ * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * nrow-by-nk with leading dimension nrow. Y->nzmax must be >= nrow*nk.
+ *
+ * The case where the input (Y) is complex and the output (X) is real,
+ * and the case where the input (Y) is zomplex and the output (X) is real,
+ * are not used.
+ */
+
+static void iperm
+(
+ /* ---- input ---- */
+ cholmod_dense *Y, /* input matrix Y */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of B to copy */
+ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *X /* output matrix X, already allocated */
+)
+{
+ double *Yx, *Yz, *Xx, *Xz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = X->ncol ;
+ nrow = X->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*
+ ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* X (P (1:nrow), k1:k2-1) = Y */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (X->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, X real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [k + j2] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, X complex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [k + j2 ] ; /* real */
+ Xx [2*p+1] = Yx [k + j2 + nrow] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, X zomplex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [k + j2 ] ; /* real */
+ Xz [p] = Yx [k + j2 + nrow] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [2*k + j2] ; /* real */
+ Xx [2*p+1] = Yx [2*k+1 + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [2*k + j2] ; /* real */
+ Xz [p] = Yx [2*k+1 + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [k + j2] ; /* real */
+ Xx [2*p+1] = Yz [k + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [k + j2] ; /* real */
+ Xz [p] = Yz [k + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === ptrans =============================================================== */
+/* ========================================================================== */
+
+/* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1)' where B is nrow-by-ncol.
+ *
+ * Creates a permuted and transposed copy of a contiguous set of columns of B.
+ * Y is already allocated on input. Y must be of sufficient size. Let nk be
+ * the number of columns accessed in B. Y->xtype determines the complexity of
+ * the result.
+ *
+ * If B is real and Y is complex (or zomplex), only the real part of B is
+ * copied into Y. The imaginary part of Y is set to zero.
+ *
+ * If B is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of B are returned in Y. Y is returned as 2*nk-by-nrow. The even
+ * rows of Y contain the real part of B and the odd rows contain the
+ * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * returned as nk-by-nrow with leading dimension nk. Y->nzmax must be >=
+ * nrow*nk.
+ *
+ * The array transpose is performed, not the complex conjugate transpose.
+ */
+
+static void ptrans
+(
+ /* ---- input ---- */
+ cholmod_dense *B, /* input matrix B */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of B to copy */
+ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *Y /* output matrix Y, already allocated */
+)
+{
+ double *Yx, *Yz, *Bx, *Bz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = B->ncol ;
+ nrow = B->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ;
+ d = B->d ;
+ Bx = B->x ;
+ Bz = B->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ Y->nrow = dual*nk ;
+ Y->ncol = nrow ;
+ Y->d = dual*nk ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = B (P (1:nrow), k1:k2-1)' */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [p] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, B complex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, B zomplex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [p] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y complex, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [p] ; /* real */
+ Yx [j2+1 + k*2*nk] = 0 ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [p] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y zomplex, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [p] ; /* real */
+ Yz [j2 + k*nk] = 0 ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [2*p ] ; /* real */
+ Yz [j2 + k*nk] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [p] ; /* real */
+ Yz [j2 + k*nk] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === iptrans ============================================================== */
+/* ========================================================================== */
+
+/* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y' where X is nrow-by-ncol.
+ *
+ * Copies into a permuted and transposed contiguous set of columns of X.
+ * X is already allocated on input. Y must be of sufficient size. Let nk be
+ * the number of columns accessed in X. X->xtype determines the complexity of
+ * the result.
+ *
+ * If X is real and Y is complex (or zomplex), only the real part of Y is
+ * copied into X. The imaginary part of Y is ignored.
+ *
+ * If X is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of X are returned in Y. Y is 2*nk-by-nrow. The even
+ * rows of Y contain the real part of X and the odd rows contain the
+ * imaginary part of X. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * nk-by-nrow with leading dimension nk. Y->nzmax must be >= nrow*nk.
+ *
+ * The case where Y is complex or zomplex, and X is real, is not used.
+ *
+ * The array transpose is performed, not the complex conjugate transpose.
+ */
+
+static void iptrans
+(
+ /* ---- input ---- */
+ cholmod_dense *Y, /* input matrix Y */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of X to copy into */
+ Int ncols, /* last column to copy is min(k1+ncols,X->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *X /* output matrix X, already allocated */
+)
+{
+ double *Yx, *Yz, *Xx, *Xz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = X->ncol ;
+ nrow = X->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*
+ ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* X (P (1:nrow), k1:k2-1) = Y' */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (X->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, X real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*nk] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, X complex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */
+ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, X zomplex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*2*nk] ; /* real */
+ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */
+ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*2*nk] ; /* real */
+ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [j2 + k*nk] ; /* real */
+ Xx [2*p+1] = Yz [j2 + k*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*nk] ; /* real */
+ Xz [p] = Yz [j2 + k*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_solve ======================================================== */
+/* ========================================================================== */
+
+/* Solve a linear system.
+ *
+ * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'.
+ * The Dx=b solve returns silently for the LL' factorizations (it is implicitly
+ * identity).
+ */
+
+cholmod_dense *CHOLMOD(solve)
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_dense *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *Y = NULL, *X = NULL ;
+ Int *Perm ;
+ Int n, nrhs, ncols, ctype, xtype, k1, nr, ytype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ if (sys < CHOLMOD_A || sys > CHOLMOD_Pt)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid system") ;
+ return (NULL) ;
+ }
+ if (B->d < L->n || B->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ;
+ return (NULL) ;
+ }
+ DEBUG (CHOLMOD(dump_factor) (L, "L", Common)) ;
+ DEBUG (CHOLMOD(dump_dense) (B, "B", Common)) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if ((sys == CHOLMOD_P || sys == CHOLMOD_Pt || sys == CHOLMOD_A)
+ && L->ordering != CHOLMOD_NATURAL)
+ {
+ Perm = L->Perm ;
+ }
+ else
+ {
+ /* do not use L->Perm; use the identity permutation instead */
+ Perm = NULL ;
+ }
+
+ nrhs = B->ncol ;
+ n = L->n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the result X */
+ /* ---------------------------------------------------------------------- */
+
+ ctype = (Common->prefer_zomplex) ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX ;
+
+ if (sys == CHOLMOD_P || sys == CHOLMOD_Pt)
+ {
+ /* x=Pb and x=P'b return X real if B is real; X is the preferred
+ * complex/zcomplex type if B is complex or zomplex */
+ xtype = (B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : ctype ;
+ }
+ else if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL)
+ {
+ /* X is real if both L and B are real */
+ xtype = CHOLMOD_REAL ;
+ }
+ else
+ {
+ /* X is complex, use the preferred complex/zomplex type */
+ xtype = ctype ;
+ }
+
+ X = CHOLMOD(allocate_dense) (n, nrhs, n, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve using L, D, L', P, or some combination */
+ /* ---------------------------------------------------------------------- */
+
+ if (sys == CHOLMOD_P)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* x = P*b */
+ /* ------------------------------------------------------------------ */
+
+ perm (B, Perm, 0, nrhs, X) ;
+
+ }
+ else if (sys == CHOLMOD_Pt)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* x = P'*b */
+ /* ------------------------------------------------------------------ */
+
+ iperm (B, Perm, 0, nrhs, X) ;
+
+ }
+ else if (L->is_super)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve using a supernodal LL' factorization */
+ /* ------------------------------------------------------------------ */
+
+#ifndef NSUPERNODAL
+ Int ok ;
+
+ /* allocate workspace */
+ cholmod_dense *E ;
+ Int dual ;
+ dual = (L->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ;
+ Y = CHOLMOD(allocate_dense) (n, dual*nrhs, n, L->xtype, Common) ;
+ E = CHOLMOD(allocate_dense) (dual*nrhs, L->maxesize, dual*nrhs,
+ L->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_dense) (&X, Common) ;
+ CHOLMOD(free_dense) (&Y, Common) ;
+ CHOLMOD(free_dense) (&E, Common) ;
+ return (NULL) ;
+ }
+
+ perm (B, Perm, 0, nrhs, Y) ; /* Y = P*B */
+
+ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt)
+ {
+ ok = CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */
+ ok = ok && CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/
+ }
+ else if (sys == CHOLMOD_L || sys == CHOLMOD_LD)
+ {
+ ok = CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */
+ }
+ else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt)
+ {
+ ok = CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/
+ }
+ CHOLMOD(free_dense) (&E, Common) ;
+
+ iperm (Y, Perm, 0, nrhs, X) ; /* X = P'*Y */
+
+ if (CHECK_BLAS_INT && !ok)
+ {
+ /* integer overflow in the BLAS */
+ CHOLMOD(free_dense) (&X, Common) ;
+ }
+
+#else
+ /* CHOLMOD Supernodal module not installed */
+ ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ;
+#endif
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve using a simplicial LL' or LDL' factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL)
+ {
+ /* L, B, and Y are all real */
+ /* solve with up to 4 columns of B at a time */
+ ncols = 4 ;
+ nr = MAX (4, nrhs) ;
+ ytype = CHOLMOD_REAL ;
+ }
+ else if (L->xtype == CHOLMOD_REAL)
+ {
+ /* solve with one column of B (real/imag), at a time */
+ ncols = 1 ;
+ nr = 2 ;
+ ytype = CHOLMOD_REAL ;
+ }
+ else
+ {
+ /* L is complex or zomplex, B is real/complex/zomplex, Y has the
+ * same complexity as L. Solve with one column of B at a time. */
+ ncols = 1 ;
+ nr = 1 ;
+ ytype = L->xtype ;
+ }
+
+ Y = CHOLMOD(allocate_dense) (nr, n, nr, ytype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_dense) (&X, Common) ;
+ CHOLMOD(free_dense) (&Y, Common) ;
+ return (NULL) ;
+ }
+
+ for (k1 = 0 ; k1 < nrhs ; k1 += ncols)
+ {
+ /* -------------------------------------------------------------- */
+ /* Y = B (P, k1:k1+ncols-1)' = (P * B (:,...))' */
+ /* -------------------------------------------------------------- */
+
+ ptrans (B, Perm, k1, ncols, Y) ;
+
+ /* -------------------------------------------------------------- */
+ /* solve Y = (L' \ (L \ Y'))', or other system, with template */
+ /* -------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+ case CHOLMOD_REAL:
+ r_simplicial_solver (sys, L, Y) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_simplicial_solver (sys, L, Y) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_simplicial_solver (sys, L, Y) ;
+ break ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* X (P, k1:k2+ncols-1) = Y' */
+ /* -------------------------------------------------------------- */
+
+ iptrans (Y, Perm, k1, ncols, X) ;
+ }
+ }
+
+ CHOLMOD(free_dense) (&Y, Common) ;
+ DEBUG (CHOLMOD(dump_dense) (X, "X result", Common)) ;
+ return (X) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_spsolve.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_spsolve.c
new file mode 100644
index 0000000..9ae0a93
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/cholmod_spsolve.c
@@ -0,0 +1,397 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_spsolve ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Given an LL' or LDL' factorization of A, solve one of the following systems:
+ *
+ * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm
+ * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm
+ * LDx=b 2: CHOLMOD_LD
+ * DL'x=b 3: CHOLMOD_DLt
+ * Lx=b 4: CHOLMOD_L
+ * L'x=b 5: CHOLMOD_Lt
+ * Dx=b 6: CHOLMOD_D
+ * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm)
+ * x=P'b 8: CHOLMOD_Pt apply an inverse permutation
+ *
+ * where b and x are sparse. If L and b are real, then x is real. Otherwise,
+ * x is complex or zomplex, depending on the Common->prefer_zomplex parameter.
+ * All xtypes of x and b are supported (real, complex, and zomplex).
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === EXPAND_AS_NEEDED ===================================================== */
+/* ========================================================================== */
+
+/* Double the size of the sparse matrix X, if we have run out of space. */
+
+#define EXPAND_AS_NEEDED \
+if (xnz >= nzmax) \
+{ \
+ nzmax *= 2 ; \
+ CHOLMOD(reallocate_sparse) (nzmax, X, Common) ; \
+ if (Common->status < CHOLMOD_OK) \
+ { \
+ CHOLMOD(free_sparse) (&X, Common) ; \
+ CHOLMOD(free_dense) (&X4, Common) ; \
+ CHOLMOD(free_dense) (&B4, Common) ; \
+ return (NULL) ; \
+ } \
+ Xi = X->i ; \
+ Xx = X->x ; \
+ Xz = X->z ; \
+}
+
+
+/* ========================================================================== */
+/* === cholmod_spolve ======================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(spsolve) /* returns the sparse solution X */
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_sparse *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ cholmod_dense *X4, *B4 ;
+ cholmod_sparse *X ;
+ double *Bx, *Bz, *Xx, *Xz, *B4x, *B4z, *X4x, *X4z ;
+ Int *Bi, *Bp, *Xp, *Xi, *Bnz ;
+ Int n, nrhs, q, p, i, j, j1, j2, packed, block, pend, jn, xtype ;
+ size_t xnz, nzmax ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ if (L->n != B->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ;
+ return (NULL) ;
+ }
+ if (B->stype)
+ {
+ ERROR (CHOLMOD_INVALID, "B cannot be stored in symmetric mode") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace B4 and initial result X */
+ /* ---------------------------------------------------------------------- */
+
+ n = L->n ;
+ nrhs = B->ncol ;
+
+ /* X is real if both L and B are real, complex/zomplex otherwise */
+ xtype = (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) ?
+ CHOLMOD_REAL :
+ (Common->prefer_zomplex ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX) ;
+
+ /* solve up to 4 columns at a time */
+ block = MIN (nrhs, 4) ;
+
+ /* initial size of X is at most 4*n */
+ nzmax = n*block ;
+
+ X = CHOLMOD(spzeros) (n, nrhs, nzmax, xtype, Common) ;
+ B4 = CHOLMOD(zeros) (n, block, B->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&X, Common) ;
+ CHOLMOD(free_dense) (&B4, Common) ;
+ return (NULL) ;
+ }
+
+ Bp = B->p ;
+ Bi = B->i ;
+ Bx = B->x ;
+ Bz = B->z ;
+ Bnz = B->nz ;
+ packed = B->packed ;
+
+ Xp = X->p ;
+ Xi = X->i ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ xnz = 0 ;
+
+ B4x = B4->x ;
+ B4z = B4->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve in chunks of 4 columns at a time */
+ /* ---------------------------------------------------------------------- */
+
+ for (j1 = 0 ; j1 < nrhs ; j1 += block)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* adjust the number of columns of B4 */
+ /* ------------------------------------------------------------------ */
+
+ j2 = MIN (nrhs, j1 + block) ;
+ B4->ncol = j2 - j1 ;
+
+ /* ------------------------------------------------------------------ */
+ /* scatter B(j1:j2-1) into B4 */
+ /* ------------------------------------------------------------------ */
+
+ for (j = j1 ; j < j2 ; j++)
+ {
+ p = Bp [j] ;
+ pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ;
+ jn = (j-j1)*n ;
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for ( ; p < pend ; p++)
+ {
+ B4x [Bi [p] + jn] = Bx [p] ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + jn ;
+ B4x [2*q ] = Bx [2*p ] ;
+ B4x [2*q+1] = Bx [2*p+1] ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + jn ;
+ B4x [q] = Bx [p] ;
+ B4z [q] = Bz [p] ;
+ }
+ break ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* solve the system (X4 = A\B4 or other system) */
+ /* ------------------------------------------------------------------ */
+
+ X4 = CHOLMOD(solve) (sys, L, B4, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&X, Common) ;
+ CHOLMOD(free_dense) (&B4, Common) ;
+ CHOLMOD(free_dense) (&X4, Common) ;
+ return (NULL) ;
+ }
+ ASSERT (X4->xtype == xtype) ;
+ X4x = X4->x ;
+ X4z = X4->z ;
+
+ /* ------------------------------------------------------------------ */
+ /* append the solution onto X */
+ /* ------------------------------------------------------------------ */
+
+ for (j = j1 ; j < j2 ; j++)
+ {
+ Xp [j] = xnz ;
+ jn = (j-j1)*n ;
+ if ( xnz + n <= nzmax)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* X is guaranteed to be large enough */
+ /* ---------------------------------------------------------- */
+
+ switch (xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + jn] ;
+ if (IS_NONZERO (x))
+ {
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [2*(i + jn) ] ;
+ z = X4x [2*(i + jn)+1] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ Xi [xnz] = i ;
+ Xx [2*xnz ] = x ;
+ Xx [2*xnz+1] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + jn] ;
+ z = X4z [i + jn] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ Xz [xnz] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* X may need to increase in size */
+ /* ---------------------------------------------------------- */
+
+ switch (xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + jn] ;
+ if (IS_NONZERO (x))
+ {
+ EXPAND_AS_NEEDED ;
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [2*(i + jn) ] ;
+ z = X4x [2*(i + jn)+1] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ EXPAND_AS_NEEDED ;
+ Xi [xnz] = i ;
+ Xx [2*xnz ] = x ;
+ Xx [2*xnz+1] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + jn] ;
+ z = X4z [i + jn] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ EXPAND_AS_NEEDED ;
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ Xz [xnz] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+ }
+
+ }
+ }
+ CHOLMOD(free_dense) (&X4, Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* clear B4 for next iteration */
+ /* ------------------------------------------------------------------ */
+
+ if (j2 < nrhs)
+ {
+
+ for (j = j1 ; j < j2 ; j++)
+ {
+ p = Bp [j] ;
+ pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ;
+ jn = (j-j1)*n ;
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for ( ; p < pend ; p++)
+ {
+ B4x [Bi [p] + jn] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + jn ;
+ B4x [2*q ] = 0 ;
+ B4x [2*q+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + jn ;
+ B4x [q] = 0 ;
+ B4z [q] = 0 ;
+ }
+ break ;
+ }
+ }
+ }
+ }
+
+ Xp [nrhs] = xnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce X in size, free workspace, and return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (xnz <= X->nzmax) ;
+ CHOLMOD(reallocate_sparse) (xnz, X, Common) ;
+ ASSERT (Common->status == CHOLMOD_OK) ;
+ CHOLMOD(free_dense) (&B4, Common) ;
+ return (X) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/lesser.txt b/src/C/SuiteSparse/CHOLMOD/Cholesky/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/lesser.txt
@@ -0,0 +1,504 @@
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+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the library, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the
+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_lsolve.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_lsolve.c
new file mode 100644
index 0000000..1ab79b9
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_lsolve.c
@@ -0,0 +1,843 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_lsolve ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine to solve Lx=b with unit or non-unit diagonal, or
+ * solve LDx=b.
+ *
+ * The numeric xtype of L and Y must match. Y contains b on input and x on
+ * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the
+ * complex or zomplex cases, and nrow <= 4 for the real case.
+ *
+ * This file is not compiled separately. It is included in t_cholmod_solve.c
+ * instead. It contains no user-callable routines.
+ *
+ * workspace: none
+ *
+ * Supports real, complex, and zomplex factors.
+ */
+
+/* undefine all prior definitions */
+#undef FORM_NAME
+#undef LSOLVE
+
+/* -------------------------------------------------------------------------- */
+/* define the method */
+/* -------------------------------------------------------------------------- */
+
+#ifdef LL
+/* LL': solve Lx=b with non-unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ll_lsolve_ ## rank
+
+#elif defined (LD)
+/* LDL': solve LDx=b */
+#define FORM_NAME(prefix,rank) prefix ## ldl_ldsolve_ ## rank
+
+#else
+/* LDL': solve Lx=b with unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ldl_lsolve_ ## rank
+
+#endif
+
+/* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */
+
+#define LSOLVE(prefix,rank) FORM_NAME(prefix,rank)
+
+#ifdef REAL
+
+/* ========================================================================== */
+/* === LSOLVE (1) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 1 column */
+
+static void LSOLVE (PREFIX,1)
+(
+ cholmod_factor *L,
+ double X [ ] /* n-by-1 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y = X [j] ;
+#ifdef LL
+ y /= Lx [p] ;
+ X [j] = y ;
+#elif defined (LD)
+ X [j] = y / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ X [Li [p]] -= Lx [p] * y ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2] ;
+ Int q = Lp [j+1] ;
+#ifdef LL
+ y [0] = X [j] / Lx [p] ;
+ y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ;
+ X [j ] = y [0] ;
+ X [j+1] = y [1] ;
+#elif defined (LD)
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ X [j ] = y [0] / Lx [p] ;
+ X [j+1] = y [1] / Lx [q] ;
+#else
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ X [j+1] = y [1] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+#ifdef LL
+ y [0] = X [j] / Lx [p] ;
+ y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ;
+ y [2] = (X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1]) / Lx [r] ;
+ X [j ] = y [0] ;
+ X [j+1] = y [1] ;
+ X [j+2] = y [2] ;
+#elif defined (LD)
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ;
+ X [j ] = y [0] / Lx [p] ;
+ X [j+1] = y [1] / Lx [q] ;
+ X [j+2] = y [2] / Lx [r] ;
+#else
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ;
+ X [j+1] = y [1] ;
+ X [j+2] = y [2] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] + Lx [r] * y [2] ;
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (2) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 2 columns */
+
+static void LSOLVE (PREFIX,2)
+(
+ cholmod_factor *L,
+ double X [ ][2] /* n-by-2 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2] ;
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+#ifdef LL
+ y [0] /= Lx [p] ;
+ y [1] /= Lx [p] ;
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+#elif defined (LD)
+ X [j][0] = y [0] / Lx [p] ;
+ X [j][1] = y [1] / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ X [i][0] -= Lx [p] * y [0] ;
+ X [i][1] -= Lx [p] * y [1] ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][2] ;
+ Int q = Lp [j+1] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ;
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ X [i][0] -= Lx [p] * y [0][0] + Lx [q] * y [1][0] ;
+ X [i][1] -= Lx [p] * y [0][1] + Lx [q] * y [1][1] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][2] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ;
+ y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r];
+ y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r];
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+2][0] = y [2][0] / Lx [r] ;
+ X [j+2][1] = y [2][1] / Lx [r] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ X[i][0] -= Lx[p] * y[0][0] + Lx[q] * y[1][0] + Lx[r] * y[2][0] ;
+ X[i][1] -= Lx[p] * y[0][1] + Lx[q] * y[1][1] + Lx[r] * y[2][1] ;
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (3) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 3 columns */
+
+static void LSOLVE (PREFIX,3)
+(
+ cholmod_factor *L,
+ double X [ ][3] /* n-by-3 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3] ;
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+#ifdef LL
+ y [0] /= Lx [p] ;
+ y [1] /= Lx [p] ;
+ y [2] /= Lx [p] ;
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+#elif defined (LD)
+ X [j][0] = y [0] / Lx [p] ;
+ X [j][1] = y [1] / Lx [p] ;
+ X [j][2] = y [2] / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ double lx = Lx [p] ;
+ X [i][0] -= lx * y [0] ;
+ X [i][1] -= lx * y [1] ;
+ X [i][2] -= lx * y [2] ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][3] ;
+ Int q = Lp [j+1] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ;
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ double lx [2] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ;
+ X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ;
+ X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][3] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ;
+ y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r];
+ y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r];
+ y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r];
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+ X [j+2][0] = y [2][0] / Lx [r] ;
+ X [j+2][1] = y [2][1] / Lx [r] ;
+ X [j+2][2] = y [2][2] / Lx [r] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ double lx [3] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ lx [2] = Lx [r] ;
+ X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0];
+ X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1];
+ X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2];
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (4) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 4 columns */
+
+static void LSOLVE (PREFIX,4)
+(
+ cholmod_factor *L,
+ double X [ ][4] /* n-by-4 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [4] ;
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+ y [3] = X [j][3] ;
+#ifdef LL
+ y [0] /= Lx [p] ;
+ y [1] /= Lx [p] ;
+ y [2] /= Lx [p] ;
+ y [3] /= Lx [p] ;
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+ X [j][3] = y [3] ;
+#elif defined (LD)
+ X [j][0] = y [0] / Lx [p] ;
+ X [j][1] = y [1] / Lx [p] ;
+ X [j][2] = y [2] / Lx [p] ;
+ X [j][3] = y [3] / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ double lx = Lx [p] ;
+ X [i][0] -= lx * y [0] ;
+ X [i][1] -= lx * y [1] ;
+ X [i][2] -= lx * y [2] ;
+ X [i][3] -= lx * y [3] ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][4] ;
+ Int q = Lp [j+1] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+ y [0][3] = X [j][3] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [0][3] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ;
+ y [1][3] = (X [j+1][3] - Lx [p+1] * y [0][3]) / Lx [q] ;
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j ][3] = y [0][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j ][3] = y [0][3] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+ X [j+1][3] = y [1][3] / Lx [q] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ double lx [2] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ;
+ X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ;
+ X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ;
+ X [i][3] -= lx [0] * y [0][3] + lx [1] * y [1][3] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][4] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+ y [0][3] = X [j][3] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [0][3] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ;
+ y [1][3] = (X [j+1][3] - Lx[p+1] * y[0][3]) / Lx [q] ;
+ y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r];
+ y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r];
+ y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r];
+ y [2][3] = (X [j+2][3] - Lx[p+2] * y[0][3] - Lx[q+1]*y[1][3])/Lx[r];
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j ][3] = y [0][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+ X [j+2][3] = y [2][3] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j ][3] = y [0][3] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+ X [j+1][3] = y [1][3] / Lx [q] ;
+ X [j+2][0] = y [2][0] / Lx [r] ;
+ X [j+2][1] = y [2][1] / Lx [r] ;
+ X [j+2][2] = y [2][2] / Lx [r] ;
+ X [j+2][3] = y [2][3] / Lx [r] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+ X [j+2][3] = y [2][3] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ double lx [3] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ lx [2] = Lx [r] ;
+ X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0];
+ X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1];
+ X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2];
+ X [i][3] -= lx[0] * y[0][3] + lx[1] * y[1][3] + lx[2] * y[2][3];
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+#endif
+
+
+/* ========================================================================== */
+/* === LSOLVE (k) =========================================================== */
+/* ========================================================================== */
+
+static void LSOLVE (PREFIX,k)
+(
+ cholmod_factor *L,
+ cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */
+)
+{
+
+#ifndef REAL
+ double yx [2] ;
+#ifdef ZOMPLEX
+ double yz [1] ;
+ double *Lz = L->z ;
+ double *Xz = Y->z ;
+#endif
+ double *Lx = L->x ;
+ double *Xx = Y->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int i, j, n = L->n ;
+#endif
+
+ ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
+ ASSERT (L->n == Y->ncol) ; /* dimensions must match */
+ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
+ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */
+
+#ifdef REAL
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow <= 4) ;
+
+ switch (Y->nrow)
+ {
+ case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ;
+ case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ;
+ case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ;
+ case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ;
+ }
+
+#else
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a complex linear system, with just one right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow == 1) ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* y = X [j] ; */
+ ASSIGN (yx,yz,0, Xx,Xz,j) ;
+
+#ifdef LL
+ /* y /= Lx [p] ; */
+ /* X [j] = y ; */
+ DIV_REAL (yx,yz,0, yx,yz,0, Lx,p) ;
+ ASSIGN (Xx,Xz,j, yx,yz,0) ;
+#elif defined (LD)
+ /* X [j] = y / Lx [p] ; */
+ DIV_REAL (Xx,Xz,j, yx,yz,0, Lx,p) ;
+#endif
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* X [Li [p]] -= Lx [p] * y ; */
+ i = Li [p] ;
+ MULTSUB (Xx,Xz,i, Lx,Lz,p, yx,yz,0) ;
+ }
+ }
+
+#endif
+}
+
+/* prepare for the next inclusion of this file in cholmod_solve.c */
+#undef LL
+#undef LD
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_ltsolve.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_ltsolve.c
new file mode 100644
index 0000000..e58d1cd
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_ltsolve.c
@@ -0,0 +1,841 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_ltsolve =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine to solve L'x=b with unit or non-unit diagonal, or
+ * solve DL'x=b.
+ *
+ * The numeric xtype of L and Y must match. Y contains b on input and x on
+ * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the
+ * complex or zomplex cases, and nrow <= 4 for the real case.
+ *
+ * This file is not compiled separately. It is included in t_cholmod_solve.c
+ * instead. It contains no user-callable routines.
+ *
+ * workspace: none
+ *
+ * Supports real, complex, and zomplex factors.
+ */
+
+/* undefine all prior definitions */
+#undef FORM_NAME
+#undef LSOLVE
+#undef DIAG
+
+/* -------------------------------------------------------------------------- */
+/* define the method */
+/* -------------------------------------------------------------------------- */
+
+#ifdef LL
+/* LL': solve Lx=b with non-unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ll_ltsolve_ ## rank
+#define DIAG
+
+#elif defined (LD)
+/* LDL': solve LDx=b */
+#define FORM_NAME(prefix,rank) prefix ## ldl_dltsolve_ ## rank
+#define DIAG
+
+#else
+/* LDL': solve Lx=b with unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ldl_ltsolve_ ## rank
+
+#endif
+
+/* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */
+#define LSOLVE(prefix,rank) FORM_NAME(prefix,rank)
+
+#ifdef REAL
+
+/* ========================================================================== */
+/* === LSOLVE (1) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 1 column */
+
+static void LSOLVE (PREFIX,1)
+(
+ cholmod_factor *L,
+ double X [ ] /* n-by-1 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y = X [j] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y /= d ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ y -= Lx [p] * X [Li [p]] ;
+ }
+#ifdef LL
+ X [j] = y / d ;
+#else
+ X [j] = y ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0] = X [j ] / d [0] ;
+ y [1] = X [j-1] / d [1] ;
+#else
+ y [0] = X [j ] ;
+ y [1] = X [j-1] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i] ;
+ y [1] -= Lx [q] * X [i] ;
+ }
+#ifdef LL
+ y [0] /= d [0] ;
+ y [1] = (y [1] - t * y [0]) / d [1] ;
+#else
+ y [1] -= t * y [0] ;
+#endif
+ X [j ] = y [0] ;
+ X [j-1] = y [1] ;
+ j -= 2 ; /* advance to the next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3], t [3] ;
+ Int q = Lp [j-1] ;
+ Int r = Lp [j-2] ;
+#ifdef DIAG
+ double d [3] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+ d [2] = Lx [r] ;
+#endif
+ t [0] = Lx [q+1] ;
+ t [1] = Lx [r+1] ;
+ t [2] = Lx [r+2] ;
+#ifdef LD
+ y [0] = X [j] / d [0] ;
+ y [1] = X [j-1] / d [1] ;
+ y [2] = X [j-2] / d [2] ;
+#else
+ y [0] = X [j] ;
+ y [1] = X [j-1] ;
+ y [2] = X [j-2] ;
+#endif
+ for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i] ;
+ y [1] -= Lx [q] * X [i] ;
+ y [2] -= Lx [r] * X [i] ;
+ }
+#ifdef LL
+ y [0] /= d [0] ;
+ y [1] = (y [1] - t [0] * y [0]) / d [1] ;
+ y [2] = (y [2] - t [2] * y [0] - t [1] * y [1]) / d [2] ;
+#else
+ y [1] -= t [0] * y [0] ;
+ y [2] -= t [2] * y [0] + t [1] * y [1] ;
+#endif
+ X [j-2] = y [2] ;
+ X [j-1] = y [1] ;
+ X [j ] = y [0] ;
+ j -= 3 ; /* advance to the next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (2) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 2 columns */
+
+static void LSOLVE (PREFIX,2)
+(
+ cholmod_factor *L,
+ double X [ ][2] /* n-by-2 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y [0] = X [j][0] / d ;
+ y [1] = X [j][1] / d ;
+#else
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i][0] ;
+ y [1] -= Lx [p] * X [i][1] ;
+ }
+#ifdef LL
+ X [j][0] = y [0] / d ;
+ X [j][1] = y [1] / d ;
+#else
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][2], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
+#else
+ y [1][0] -= t * y [0][0] ;
+ y [1][1] -= t * y [0][1] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ j -= 2 ; /* advance to the next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][2], t [3] ;
+ Int q = Lp [j-1] ;
+ Int r = Lp [j-2] ;
+#ifdef DIAG
+ double d [3] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+ d [2] = Lx [r] ;
+#endif
+ t [0] = Lx [q+1] ;
+ t [1] = Lx [r+1] ;
+ t [2] = Lx [r+2] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [2][0] = X [j-2][0] / d [2] ;
+ y [2][1] = X [j-2][1] / d [2] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [2][0] = X [j-2][0] ;
+ y [2][1] = X [j-2][1] ;
+#endif
+ for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [2][0] -= Lx [r] * X [i][0] ;
+ y [2][1] -= Lx [r] * X [i][1] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ;
+ y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2];
+ y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2];
+#else
+ y [1][0] -= t [0] * y [0][0] ;
+ y [1][1] -= t [0] * y [0][1] ;
+ y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ;
+ y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-2][0] = y [2][0] ;
+ X [j-2][1] = y [2][1] ;
+ j -= 3 ; /* advance to the next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (3) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 3 columns */
+
+static void LSOLVE (PREFIX,3)
+(
+ cholmod_factor *L,
+ double X [ ][3] /* n-by-3 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y [0] = X [j][0] / d ;
+ y [1] = X [j][1] / d ;
+ y [2] = X [j][2] / d ;
+#else
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i][0] ;
+ y [1] -= Lx [p] * X [i][1] ;
+ y [2] -= Lx [p] * X [i][2] ;
+ }
+#ifdef LL
+ X [j][0] = y [0] / d ;
+ X [j][1] = y [1] / d ;
+ X [j][2] = y [2] / d ;
+#else
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][3], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [0][2] = X [j ][2] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [1][2] = X [j-1][2] / d [1] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [0][2] = X [j ][2] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [1][2] = X [j-1][2] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [0][2] -= Lx [p] * X [i][2] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [1][2] -= Lx [q] * X [i][2] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [0][2] /= d [0] ;
+ y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
+ y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ;
+#else
+ y [1][0] -= t * y [0][0] ;
+ y [1][1] -= t * y [0][1] ;
+ y [1][2] -= t * y [0][2] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-1][2] = y [1][2] ;
+ j -= 2 ; /* advance to the next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][3], t [3] ;
+ Int q = Lp [j-1] ;
+ Int r = Lp [j-2] ;
+#ifdef DIAG
+ double d [3] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+ d [2] = Lx [r] ;
+#endif
+ t [0] = Lx [q+1] ;
+ t [1] = Lx [r+1] ;
+ t [2] = Lx [r+2] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [0][2] = X [j ][2] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [1][2] = X [j-1][2] / d [1] ;
+ y [2][0] = X [j-2][0] / d [2] ;
+ y [2][1] = X [j-2][1] / d [2] ;
+ y [2][2] = X [j-2][2] / d [2] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [0][2] = X [j ][2] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [1][2] = X [j-1][2] ;
+ y [2][0] = X [j-2][0] ;
+ y [2][1] = X [j-2][1] ;
+ y [2][2] = X [j-2][2] ;
+#endif
+ for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [0][2] -= Lx [p] * X [i][2] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [1][2] -= Lx [q] * X [i][2] ;
+ y [2][0] -= Lx [r] * X [i][0] ;
+ y [2][1] -= Lx [r] * X [i][1] ;
+ y [2][2] -= Lx [r] * X [i][2] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [0][2] /= d [0] ;
+ y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ;
+ y [1][2] = (y [1][2] - t [0] * y [0][2]) / d [1] ;
+ y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2];
+ y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2];
+ y [2][2] = (y [2][2] - t [2] * y [0][2] - t [1] * y [1][2]) / d [2];
+#else
+ y [1][0] -= t [0] * y [0][0] ;
+ y [1][1] -= t [0] * y [0][1] ;
+ y [1][2] -= t [0] * y [0][2] ;
+ y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ;
+ y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ;
+ y [2][2] -= t [2] * y [0][2] + t [1] * y [1][2] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-1][2] = y [1][2] ;
+ X [j-2][0] = y [2][0] ;
+ X [j-2][1] = y [2][1] ;
+ X [j-2][2] = y [2][2] ;
+ j -= 3 ; /* advance to the next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (4) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 4 columns */
+
+static void LSOLVE (PREFIX,4)
+(
+ cholmod_factor *L,
+ double X [ ][4] /* n-by-4 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [4] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y [0] = X [j][0] / d ;
+ y [1] = X [j][1] / d ;
+ y [2] = X [j][2] / d ;
+ y [3] = X [j][3] / d ;
+#else
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+ y [3] = X [j][3] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i][0] ;
+ y [1] -= Lx [p] * X [i][1] ;
+ y [2] -= Lx [p] * X [i][2] ;
+ y [3] -= Lx [p] * X [i][3] ;
+ }
+#ifdef LL
+ X [j][0] = y [0] / d ;
+ X [j][1] = y [1] / d ;
+ X [j][2] = y [2] / d ;
+ X [j][3] = y [3] / d ;
+#else
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+ X [j][3] = y [3] ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else /* if (j == 1 || lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) */
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][4], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [0][2] = X [j ][2] / d [0] ;
+ y [0][3] = X [j ][3] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [1][2] = X [j-1][2] / d [1] ;
+ y [1][3] = X [j-1][3] / d [1] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [0][2] = X [j ][2] ;
+ y [0][3] = X [j ][3] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [1][2] = X [j-1][2] ;
+ y [1][3] = X [j-1][3] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [0][2] -= Lx [p] * X [i][2] ;
+ y [0][3] -= Lx [p] * X [i][3] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [1][2] -= Lx [q] * X [i][2] ;
+ y [1][3] -= Lx [q] * X [i][3] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [0][2] /= d [0] ;
+ y [0][3] /= d [0] ;
+ y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
+ y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ;
+ y [1][3] = (y [1][3] - t * y [0][3]) / d [1] ;
+#else
+ y [1][0] -= t * y [0][0] ;
+ y [1][1] -= t * y [0][1] ;
+ y [1][2] -= t * y [0][2] ;
+ y [1][3] -= t * y [0][3] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j ][3] = y [0][3] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-1][2] = y [1][2] ;
+ X [j-1][3] = y [1][3] ;
+ j -= 2 ; /* advance to the next column of L */
+ }
+
+ /* NOTE: with 4 right-hand-sides, it suffices to exploit dynamic
+ * supernodes of just size 1 and 2. 3-column supernodes are not
+ * needed. */
+ }
+}
+
+#endif
+
+/* ========================================================================== */
+/* === LSOLVE (k) =========================================================== */
+/* ========================================================================== */
+
+static void LSOLVE (PREFIX,k)
+(
+ cholmod_factor *L,
+ cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */
+)
+{
+
+#ifndef REAL
+#ifdef DIAG
+ double d [1] ;
+#endif
+ double yx [2] ;
+#ifdef ZOMPLEX
+ double yz [1] ;
+ double *Lz = L->z ;
+ double *Xz = Y->z ;
+#endif
+ double *Lx = L->x ;
+ double *Xx = Y->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int i, j, n = L->n ;
+#endif
+
+ ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
+ ASSERT (L->n == Y->ncol) ; /* dimensions must match */
+ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
+ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */
+
+#ifdef REAL
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow <= 4) ;
+ switch (Y->nrow)
+ {
+ case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ;
+ case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ;
+ case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ;
+ case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ;
+ }
+
+#else
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a complex linear system, with just one right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow == 1) ;
+
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* y = X [j] ; */
+ ASSIGN (yx,yz,0, Xx,Xz,j) ;
+
+#ifdef DIAG
+ /* d = Lx [p] ; */
+ ASSIGN_REAL (d,0, Lx,p) ;
+#endif
+#ifdef LD
+ /* y /= d ; */
+ DIV_REAL (yx,yz,0, yx,yz,0, d,0) ;
+#endif
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* y -= conj (Lx [p]) * X [Li [p]] ; */
+ i = Li [p] ;
+ MULTSUBCONJ (yx,yz,0, Lx,Lz,p, Xx,Xz,i) ;
+ }
+
+#ifdef LL
+ /* X [j] = y / d ; */
+ DIV_REAL (Xx,Xz,j, yx,yz,0, d,0) ;
+#else
+ /* X [j] = y ; */
+ ASSIGN (Xx,Xz,j, yx,yz,0) ;
+#endif
+
+ }
+
+#endif
+}
+
+/* prepare for the next inclusion of this file in cholmod_solve.c */
+#undef LL
+#undef LD
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_rowfac.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_rowfac.c
new file mode 100644
index 0000000..57f0f33
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_rowfac.c
@@ -0,0 +1,456 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_rowfac ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_rowfac. Supports any numeric xtype
+ * (real, complex, or zomplex).
+ *
+ * workspace: Iwork (n), Flag (n), Xwork (n if real, 2*n if complex)
+ */
+
+#include "cholmod_template.h"
+
+#ifdef MASK
+static int TEMPLATE (cholmod_rowfac_mask)
+#else
+static int TEMPLATE (cholmod_rowfac)
+#endif
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ double beta [2], /* factorize beta*I+A or beta*I+AA' (beta [0] only) */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+#ifdef MASK
+ /* These inputs are used for cholmod_rowfac_mask only */
+ Int *mask, /* size A->nrow. if mask[i] then W(i) is set to zero */
+ Int *RLinkUp, /* size A->nrow. link list of rows to compute */
+#endif
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double yx [2], lx [2], fx [2], dk [1], di [1], fl = 0 ;
+#ifdef ZOMPLEX
+ double yz [1], lz [1], fz [1] ;
+#endif
+ double *Ax, *Az, *Lx, *Lz, *Wx, *Wz, *Fx, *Fz ;
+ Int *Ap, *Anz, *Ai, *Lp, *Lnz, *Li, *Lnext, *Flag, *Stack, *Fp, *Fi, *Fnz,
+ *Iwork ;
+ Int i, p, k, t, pf, pfend, top, s, mark, pend, n, lnz, is_ll, multadds,
+ use_dbound, packed, stype, Fpacked, sorted, nzmax, len, parent ;
+#ifndef REAL
+ Int dk_imaginary ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT1 (("\nin cholmod_rowfac, kstart %d kend %d stype %d\n",
+ kstart, kend, A->stype)) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "Initial L", Common)) ;
+
+ n = A->nrow ;
+ stype = A->stype ;
+
+ if (stype > 0)
+ {
+ /* symmetric upper case: F is not needed. It may be NULL */
+ Fp = NULL ;
+ Fi = NULL ;
+ Fx = NULL ;
+ Fz = NULL ;
+ Fnz = NULL ;
+ Fpacked = TRUE ;
+ }
+ else
+ {
+ /* unsymmetric case: F is required. */
+ Fp = F->p ;
+ Fi = F->i ;
+ Fx = F->x ;
+ Fz = F->z ;
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ }
+
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Ax = A->x ; /* size nz, numeric values of A */
+ Az = A->z ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ sorted = A->sorted ;
+
+ use_dbound = IS_GT_ZERO (Common->dbound) ;
+
+ /* get the current factors L (and D for LDL'); allocate space if needed */
+ is_ll = L->is_ll ;
+ if (L->xtype == CHOLMOD_PATTERN)
+ {
+ /* ------------------------------------------------------------------ */
+ /* L is symbolic only; allocate and initialize L (and D for LDL') */
+ /* ------------------------------------------------------------------ */
+
+ /* workspace: none */
+ CHOLMOD(change_factor) (A->xtype, is_ll, FALSE, FALSE, TRUE, L, Common);
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (FALSE) ;
+ }
+ ASSERT (L->minor == (size_t) n) ;
+ }
+ else if (kstart == 0 && kend == (size_t) n)
+ {
+ /* ------------------------------------------------------------------ */
+ /* refactorization; reset L->nz and L->minor to restart factorization */
+ /* ------------------------------------------------------------------ */
+
+ L->minor = n ;
+ Lnz = L->nz ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Lnz [k] = 1 ;
+ }
+ }
+
+ ASSERT (is_ll == L->is_ll) ;
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "L ready", Common)) ;
+ DEBUG (CHOLMOD(dump_sparse) (A, "A ready", Common)) ;
+ DEBUG (if (stype == 0) CHOLMOD(dump_sparse) (F, "F ready", Common)) ;
+
+ /* inputs, can be modified on output: */
+ Lp = L->p ; /* size n+1 */
+ ASSERT (Lp != NULL) ;
+
+ /* outputs, contents defined on input for incremental case only: */
+ Lnz = L->nz ; /* size n */
+ Lnext = L->next ; /* size n+2 */
+ Li = L->i ; /* size L->nzmax, can change in size */
+ Lx = L->x ; /* size L->nzmax or 2*L->nzmax, can change in size */
+ Lz = L->z ; /* size L->nzmax for zomplex case, can change in size */
+ nzmax = L->nzmax ;
+ ASSERT (Lnz != NULL && Li != NULL && Lx != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Stack = Iwork ; /* size n (i/i/l) */
+ Flag = Common->Flag ; /* size n, Flag [i] < mark must hold */
+ Wx = Common->Xwork ; /* size n if real, 2*n if complex or
+ * zomplex. Xwork [i] == 0 must hold. */
+ Wz = Wx + n ; /* size n for zomplex case only */
+ mark = Common->mark ;
+ ASSERT ((Int) Common->xworksize >= (L->xtype == CHOLMOD_REAL ? 1:2)*n) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute LDL' or LL' factorization by rows */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef MASK
+#define NEXT(k) k = RLinkUp [k]
+#else
+#define NEXT(k) k++
+#endif
+
+ for (k = kstart ; k < ((Int) kend) ; NEXT(k))
+ {
+ PRINT1 (("\n===============K "ID" Lnz [k] "ID"\n", k, Lnz [k])) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute pattern of kth row of L and scatter kth input column */
+ /* ------------------------------------------------------------------ */
+
+ /* column k of L is currently empty */
+ ASSERT (Lnz [k] == 1) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ;
+
+ top = n ; /* Stack is empty */
+ Flag [k] = mark ; /* do not include diagonal entry in Stack */
+
+ /* use Li [Lp [i]+1] for etree */
+#define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY
+
+ if (stype > 0)
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ p = Ap [k] ;
+ pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ;
+ /* W [i] = Ax [i] ; scatter column of A */
+#define SCATTER ASSIGN(Wx,Wz,i, Ax,Az,p)
+ SUBTREE ;
+#undef SCATTER
+ }
+ else
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ pf = Fp [k] ;
+ pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ;
+ for ( ; pf < pfend ; pf++)
+ {
+ /* get nonzero entry F (t,k) */
+ t = Fi [pf] ;
+ /* fk = Fx [pf] */
+ ASSIGN (fx, fz, 0, Fx, Fz, pf) ;
+ p = Ap [t] ;
+ pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ;
+ multadds = 0 ;
+ /* W [i] += Ax [p] * fx ; scatter column of A*A' */
+#define SCATTER MULTADD (Wx,Wz,i, Ax,Az,p, fx,fz,0) ; multadds++ ;
+ SUBTREE ;
+#undef SCATTER
+#ifdef REAL
+ fl += 2 * ((double) multadds) ;
+#else
+ fl += 8 * ((double) multadds) ;
+#endif
+ }
+ }
+
+#undef PARENT
+
+ /* ------------------------------------------------------------------ */
+ /* if mask is present, set the corresponding entries in W to zero */
+ /* ------------------------------------------------------------------ */
+
+#ifdef MASK
+ /* remove the dead element of Wx */
+ if (mask != NULL)
+ {
+
+#if 0
+ /* older version */
+ for (p = n; p > top;)
+ {
+ i = Stack [--p] ;
+ if ( mask [i] >= 0 )
+ {
+ CLEAR (Wx,Wz,i) ; /* set W(i) to zero */
+ }
+ }
+#endif
+
+ for (s = top ; s < n ; s++)
+ {
+ i = Stack [s] ;
+ if (mask [i] >= 0)
+ {
+ CLEAR (Wx,Wz,i) ; /* set W(i) to zero */
+ }
+ }
+
+ }
+#endif
+
+ /* nonzero pattern of kth row of L is now in Stack [top..n-1].
+ * Flag [Stack [top..n-1]] is equal to mark, but no longer needed */
+
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute kth row of L and store in column form */
+ /* ------------------------------------------------------------------ */
+
+ /* Solve L (0:k-1, 0:k-1) * y (0:k-1) = b (0:k-1) where
+ * b (0:k) = A (0:k,k) or A(0:k,:) * F(:,k) is in W and Stack.
+ *
+ * For LDL' factorization:
+ * L (k, 0:k-1) = y (0:k-1) ./ D (0:k-1)
+ * D (k) = b (k) - L (k, 0:k-1) * y (0:k-1)
+ *
+ * For LL' factorization:
+ * L (k, 0:k-1) = y (0:k-1)
+ * L (k,k) = sqrt (b (k) - L (k, 0:k-1) * L (0:k-1, k))
+ */
+
+ /* dk = W [k] + beta */
+ ADD_REAL (dk,0, Wx,k, beta,0) ;
+
+#ifndef REAL
+ /* In the unsymmetric case, the imaginary part of W[k] must be real,
+ * since F is assumed to be the complex conjugate transpose of A. In
+ * the symmetric case, W[k] is the diagonal of A. If the imaginary part
+ * of W[k] is nonzero, then the Cholesky factorization cannot be
+ * computed; A is not positive definite */
+ dk_imaginary = (stype > 0) ? (IMAG_IS_NONZERO (Wx,Wz,k)) : FALSE ;
+#endif
+
+ /* W [k] = 0.0 ; */
+ CLEAR (Wx,Wz,k) ;
+
+ for (s = top ; s < n ; s++)
+ {
+ /* get i for each nonzero entry L(k,i) */
+ i = Stack [s] ;
+
+ /* y = W [i] ; */
+ ASSIGN (yx,yz,0, Wx,Wz,i) ;
+
+ /* W [i] = 0.0 ; */
+ CLEAR (Wx,Wz,i) ;
+
+ lnz = Lnz [i] ;
+ p = Lp [i] ;
+ ASSERT (lnz > 0 && Li [p] == i) ;
+ pend = p + lnz ;
+
+ /* di = Lx [p] ; the diagonal entry L or D(i,i), which is real */
+ ASSIGN_REAL (di,0, Lx,p) ;
+
+ if (i >= (Int) L->minor || IS_ZERO (di [0]))
+ {
+ /* For the LL' factorization, L(i,i) is zero. For the LDL',
+ * D(i,i) is zero. Skip column i of L, and set L(k,i) = 0. */
+ CLEAR (lx,lz,0) ;
+ p = pend ;
+ }
+ else if (is_ll)
+ {
+#ifdef REAL
+ fl += 2 * ((double) (pend - p - 1)) + 3 ;
+#else
+ fl += 8 * ((double) (pend - p - 1)) + 6 ;
+#endif
+ /* forward solve using L (i:(k-1),i) */
+ /* divide by L(i,i), which must be real and nonzero */
+ /* y /= di [0] */
+ DIV_REAL (yx,yz,0, yx,yz,0, di,0) ;
+ for (p++ ; p < pend ; p++)
+ {
+ /* W [Li [p]] -= Lx [p] * y ; */
+ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ;
+ }
+ /* do not scale L; compute dot product for L(k,k) */
+ /* L(k,i) = conj(y) ; */
+ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ;
+ /* d -= conj(y) * y ; */
+ LLDOT (dk,0, yx,yz,0) ;
+ }
+ else
+ {
+#ifdef REAL
+ fl += 2 * ((double) (pend - p - 1)) + 3 ;
+#else
+ fl += 8 * ((double) (pend - p - 1)) + 6 ;
+#endif
+ /* forward solve using D (i,i) and L ((i+1):(k-1),i) */
+ for (p++ ; p < pend ; p++)
+ {
+ /* W [Li [p]] -= Lx [p] * y ; */
+ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ;
+ }
+ /* Scale L (k,0:k-1) for LDL' factorization, compute D (k,k)*/
+#ifdef REAL
+ /* L(k,i) = y/d */
+ lx [0] = yx [0] / di [0] ;
+ /* d -= L(k,i) * y */
+ dk [0] -= lx [0] * yx [0] ;
+#else
+ /* L(k,i) = conj(y) ; */
+ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ;
+ /* L(k,i) /= di ; */
+ DIV_REAL (lx,lz,0, lx,lz,0, di,0) ;
+ /* d -= conj(y) * y / di */
+ LDLDOT (dk,0, yx,yz,0, di,0) ;
+#endif
+ }
+
+ /* determine if column i of L can hold the new L(k,i) entry */
+ if (p >= Lp [Lnext [i]])
+ {
+ /* column i needs to grow */
+ PRINT1 (("Factor Colrealloc "ID", old Lnz "ID"\n", i, Lnz [i]));
+ if (!CHOLMOD(reallocate_column) (i, lnz + 1, L, Common))
+ {
+ /* out of memory, L is now simplicial symbolic */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = 0 ; */
+ CLEAR (Wx,Wz,i) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ;
+ return (FALSE) ;
+ }
+ Li = L->i ; /* L->i, L->x, L->z may have moved */
+ Lx = L->x ;
+ Lz = L->z ;
+ p = Lp [i] + lnz ; /* contents of L->p changed */
+ ASSERT (p < Lp [Lnext [i]]) ;
+ }
+
+ /* store L (k,i) in the column form matrix of L */
+ Li [p] = k ;
+ /* Lx [p] = L(k,i) ; */
+ ASSIGN (Lx,Lz,p, lx,lz,0) ;
+ Lnz [i]++ ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* ensure abs (d) >= dbound if dbound is given, and store it in L */
+ /* ------------------------------------------------------------------ */
+
+ p = Lp [k] ;
+ Li [p] = k ;
+
+ if (k >= (Int) L->minor)
+ {
+ /* the matrix is already not positive definite */
+ dk [0] = 0 ;
+ }
+ else if (use_dbound)
+ {
+ /* modify the diagonal to force LL' or LDL' to exist */
+ dk [0] = CHOLMOD(dbound) (is_ll ? fabs (dk [0]) : dk [0], Common) ;
+ }
+ else if ((is_ll ? (IS_LE_ZERO (dk [0])) : (IS_ZERO (dk [0])))
+#ifndef REAL
+ || dk_imaginary
+#endif
+ )
+ {
+ /* the matrix has just been found to be not positive definite */
+ dk [0] = 0 ;
+ L->minor = k ;
+ ERROR (CHOLMOD_NOT_POSDEF, "not positive definite") ;
+ }
+
+ if (is_ll)
+ {
+ /* this is counted as one flop, below */
+ dk [0] = sqrt (dk [0]) ;
+ }
+
+ /* Lx [p] = D(k,k) = d ; real part only */
+ ASSIGN_REAL (Lx,p, dk,0) ;
+ CLEAR_IMAG (Lx,Lz,p) ;
+ }
+
+#undef NEXT
+
+ if (is_ll) fl += MAX ((Int) kend - (Int) kstart, 0) ; /* count sqrt's */
+ Common->rowfacfl = fl ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "final cholmod_rowfac", Common)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ;
+ return (TRUE) ;
+}
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_solve.c b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_solve.c
new file mode 100644
index 0000000..a70594a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Cholesky/t_cholmod_solve.c
@@ -0,0 +1,164 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_solve ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_solve. Supports any numeric xtype (real,
+ * complex, or zomplex). The xtypes of all matrices (L and Y) must match.
+ */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === simplicial template solvers ========================================== */
+/* ========================================================================== */
+
+/* LL': solve Lx=b with non-unit diagonal */
+#define LL
+#include "t_cholmod_lsolve.c"
+
+/* LDL': solve LDx=b */
+#define LD
+#include "t_cholmod_lsolve.c"
+
+/* LDL': solve Lx=b with unit diagonal */
+#include "t_cholmod_lsolve.c"
+
+/* LL': solve L'x=b with non-unit diagonal */
+#define LL
+#include "t_cholmod_ltsolve.c"
+
+/* LDL': solve DL'x=b */
+#define LD
+#include "t_cholmod_ltsolve.c"
+
+/* LDL': solve L'x=b with unit diagonal */
+#include "t_cholmod_ltsolve.c"
+
+
+/* ========================================================================== */
+/* === t_ldl_dsolve ========================================================= */
+/* ========================================================================== */
+
+/* Solve Dx=b for an LDL' factorization, where Y holds b' on input and x' on
+ * output. */
+
+static void TEMPLATE (ldl_dsolve)
+(
+ cholmod_factor *L,
+ cholmod_dense *Y /* nr-by-n with leading dimension nr */
+)
+{
+ double d [1] ;
+ double *Lx, *Yx, *Yz ;
+ Int *Lp ;
+ Int n, nrhs, k, p, k1, k2 ;
+
+ ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
+ ASSERT (L->n == Y->ncol) ; /* dimensions must match */
+ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
+ ASSERT (!(L->is_super) && !(L->is_ll)) ; /* L is simplicial LDL' */
+
+ nrhs = Y->nrow ;
+ n = L->n ;
+ Lp = L->p ;
+ Lx = L->x ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ for (k = 0 ; k < n ; k++)
+ {
+ k1 = k*nrhs ;
+ k2 = (k+1)*nrhs ;
+ ASSIGN_REAL (d,0, Lx,Lp[k]) ;
+ for (p = k1 ; p < k2 ; p++)
+ {
+ DIV_REAL (Yx,Yz,p, Yx,Yz,p, d,0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === t_simplicial_solver ================================================== */
+/* ========================================================================== */
+
+/* Solve a linear system, where Y' contains the (array-transposed) right-hand
+ * side on input, and the solution on output. No permutations are applied;
+ * these must have already been applied to Y on input. */
+
+static void TEMPLATE (simplicial_solver)
+(
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factor to use, a simplicial LL' or LDL' */
+ cholmod_dense *Y /* right-hand-side on input, solution on output */
+)
+{
+ if (L->is_ll)
+ {
+ /* The factorization is LL' */
+ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt)
+ {
+ /* Solve Ax=b or LL'x=b */
+ TEMPLATE (ll_lsolve_k) (L, Y) ;
+ TEMPLATE (ll_ltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_L || sys == CHOLMOD_LD)
+ {
+ /* Solve Lx=b */
+ TEMPLATE (ll_lsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt)
+ {
+ /* Solve L'x=b */
+ TEMPLATE (ll_ltsolve_k) (L, Y) ;
+ }
+ }
+ else
+ {
+ /* The factorization is LDL' */
+ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt)
+ {
+ /* Solve Ax=b or LDL'x=b */
+ TEMPLATE (ldl_lsolve_k) (L, Y) ;
+ TEMPLATE (ldl_dltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_LD)
+ {
+ /* Solve LDx=b */
+ TEMPLATE (ldl_ldsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_L)
+ {
+ /* Solve Lx=b */
+ TEMPLATE (ldl_lsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_Lt)
+ {
+ /* Solve L'x=b */
+ TEMPLATE (ldl_ltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_DLt)
+ {
+ /* Solve DL'x=b */
+ TEMPLATE (ldl_dltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_D)
+ {
+ /* Solve Dx=b */
+ TEMPLATE (ldl_dsolve) (L, Y) ;
+ }
+ }
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/License.txt b/src/C/SuiteSparse/CHOLMOD/Core/License.txt
new file mode 100644
index 0000000..51b795e
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/Core Module. Copyright (C) 2005-2006, Univ. of Florida.
+Author: Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Core module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_aat.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_aat.c
new file mode 100644
index 0000000..0b2b75b
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_aat.c
@@ -0,0 +1,300 @@
+/* ========================================================================== */
+/* === Core/cholmod_aat ===================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = A*A' or C = A(:,f)*A(:,f)'
+ *
+ * A can be packed or unpacked, sorted or unsorted, but must be stored with
+ * both upper and lower parts (A->stype of zero). C is returned as packed,
+ * C->stype of zero (both upper and lower parts present), and unsorted. See
+ * cholmod_ssmult in the MatrixOps Module for a more general matrix-matrix
+ * multiply.
+ *
+ * You can trivially convert C into a symmetric upper/lower matrix by
+ * changing C->stype = 1 or -1 after calling this routine.
+ *
+ * workspace:
+ * Flag (A->nrow),
+ * Iwork (max (A->nrow, A->ncol)) if fset present,
+ * Iwork (A->nrow) if no fset,
+ * W (A->nrow) if mode > 0,
+ * allocates temporary copy for A'.
+ *
+ * A can be pattern or real. Complex or zomplex cases are supported only
+ * if the mode is <= 0 (in which case the numerical values are ignored).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+cholmod_sparse *CHOLMOD(aat)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag)
+ * -2: pattern only, no diagonal, add 50% + n extra
+ * space to C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double fjt ;
+ double *Ax, *Fx, *Cx, *W ;
+ Int *Ap, *Anz, *Ai, *Fp, *Fi, *Cp, *Ci, *Flag ;
+ cholmod_sparse *C, *F ;
+ Int packed, j, i, pa, paend, pf, pfend, n, mark, cnz, t, p, values, diag,
+ extra ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix cannot be symmetric") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ diag = (mode >= 0) ;
+ n = A->nrow ;
+ CHOLMOD(allocate_work) (n, MAX (A->ncol, A->nrow), values ? n : 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+
+ /* get the A matrix */
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ packed = A->packed ;
+
+ /* get workspace */
+ W = Common->Xwork ; /* size n, unused if values is FALSE */
+ Flag = Common->Flag ; /* size n, Flag [0..n-1] < mark on input*/
+
+ /* ---------------------------------------------------------------------- */
+ /* F = A' or A(:,f)' */
+ /* ---------------------------------------------------------------------- */
+
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ F = CHOLMOD(ptranspose) (A, values, NULL, fset, fsize, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ Fp = F->p ;
+ Fi = F->i ;
+ Fx = F->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the number of entries in the result C */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* exclude the diagonal, if requested */
+ if (!diag)
+ {
+ Flag [j] = mark ;
+ }
+
+ /* for each nonzero F(t,j) in column j, do: */
+ pfend = Fp [j+1] ;
+ for (pf = Fp [j] ; pf < pfend ; pf++)
+ {
+ /* F(t,j) is nonzero */
+ t = Fi [pf] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */
+ pa = Ap [t] ;
+ paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ cnz++ ;
+ }
+ }
+ }
+ if (cnz < 0)
+ {
+ break ; /* integer overflow case */
+ }
+ }
+
+ extra = (mode == -2) ? (cnz/2 + n) : 0 ;
+
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for integer overflow */
+ /* ---------------------------------------------------------------------- */
+
+ if (cnz < 0 || (cnz + extra) < 0)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ CHOLMOD(clear_flag) (Common) ;
+ CHOLMOD(free_sparse) (&F, Common) ;
+ return (NULL) ; /* problem too large */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (n, n, cnz + extra, FALSE, TRUE, 0,
+ values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&F, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = A*A' */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = 0 ;
+
+ if (values)
+ {
+
+ /* pattern and values */
+ for (j = 0 ; j < n ; j++)
+ {
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* start column j of C */
+ Cp [j] = cnz ;
+
+ /* for each nonzero F(t,j) in column j, do: */
+ pfend = Fp [j+1] ;
+ for (pf = Fp [j] ; pf < pfend ; pf++)
+ {
+ /* F(t,j) is nonzero */
+ t = Fi [pf] ;
+ fjt = Fx [pf] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j)
+ * and scatter the values into W */
+ pa = Ap [t] ;
+ paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ Ci [cnz++] = i ;
+ }
+ W [i] += Ax [pa] * fjt ;
+ }
+ }
+
+ /* gather the values into C(:,j) */
+ for (p = Cp [j] ; p < cnz ; p++)
+ {
+ i = Ci [p] ;
+ Cx [p] = W [i] ;
+ W [i] = 0 ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* pattern only */
+ for (j = 0 ; j < n ; j++)
+ {
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* exclude the diagonal, if requested */
+ if (!diag)
+ {
+ Flag [j] = mark ;
+ }
+
+ /* start column j of C */
+ Cp [j] = cnz ;
+
+ /* for each nonzero F(t,j) in column j, do: */
+ pfend = Fp [j+1] ;
+ for (pf = Fp [j] ; pf < pfend ; pf++)
+ {
+ /* F(t,j) is nonzero */
+ t = Fi [pf] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */
+ pa = Ap [t] ;
+ paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ Ci [cnz++] = i ;
+ }
+ }
+ }
+ }
+ }
+
+ Cp [n] = cnz ;
+ ASSERT (IMPLIES (mode != -2, MAX (1,cnz) == C->nzmax)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace and free temporary matrices and return result */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&F, Common) ;
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ;
+ DEBUG (i = CHOLMOD(dump_sparse) (C, "aat", Common)) ;
+ ASSERT (IMPLIES (mode < 0, i == 0)) ;
+ return (C) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_add.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_add.c
new file mode 100644
index 0000000..c7fbba5
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_add.c
@@ -0,0 +1,278 @@
+/* ========================================================================== */
+/* === Core/cholmod_add ===================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = alpha*A + beta*B, or spones(A+B). Result is packed, with sorted or
+ * unsorted columns. This routine is much faster and takes less memory if C
+ * is allowed to have unsorted columns.
+ *
+ * If A and B are both symmetric (in upper form) then C is the same. Likewise,
+ * if A and B are both symmetric (in lower form) then C is the same.
+ * Otherwise, C is unsymmetric. A and B must have the same dimension.
+ *
+ * workspace: Flag (nrow), W (nrow) if values, Iwork (max (nrow,ncol)).
+ * allocates temporary copies for A and B if they are symmetric.
+ * allocates temporary copy of C if it is to be returned sorted.
+ *
+ * A and B can have an xtype of pattern or real. Complex or zomplex cases
+ * are supported only if the "values" input parameter is FALSE.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+cholmod_sparse *CHOLMOD(add)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to add */
+ cholmod_sparse *B, /* matrix to add */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for B */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE, sort columns of C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Bx, *Cx, *W ;
+ Int apacked, up, lo, nrow, ncol, bpacked, nzmax, pa, paend, pb, pbend, i,
+ j, p, mark, nz ;
+ Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Flag, *Cp, *Ci ;
+ cholmod_sparse *A2, *B2, *C ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ values = values &&
+ (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->nrow != B->nrow || A->ncol != B->ncol)
+ {
+ /* A and B must have the same dimensions */
+ ERROR (CHOLMOD_INVALID, "A and B dimesions do not match") ;
+ return (NULL) ;
+ }
+ /* A and B must have the same numerical type if values is TRUE (both must
+ * be CHOLMOD_REAL, this is implicitly checked above) */
+
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ CHOLMOD(allocate_work) (nrow, MAX (nrow,ncol), values ? nrow : 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow <= 1)
+ {
+ /* C will be implicitly sorted, so no need to sort it here */
+ sorted = FALSE ;
+ }
+
+ /* convert A or B to unsymmetric, if necessary */
+ A2 = NULL ;
+ B2 = NULL ;
+
+ if (A->stype != B->stype)
+ {
+ if (A->stype)
+ {
+ /* workspace: Iwork (max (nrow,ncol)) */
+ A2 = CHOLMOD(copy) (A, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ A = A2 ;
+ }
+ if (B->stype)
+ {
+ /* workspace: Iwork (max (nrow,ncol)) */
+ B2 = CHOLMOD(copy) (B, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+ B = B2 ;
+ }
+ }
+
+ /* get the A matrix */
+ ASSERT (A->stype == B->stype) ;
+ up = (A->stype > 0) ;
+ lo = (A->stype < 0) ;
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ apacked = A->packed ;
+
+ /* get the B matrix */
+ Bp = B->p ;
+ Bnz = B->nz ;
+ Bi = B->i ;
+ Bx = B->x ;
+ bpacked = B->packed ;
+
+ /* get workspace */
+ W = Common->Xwork ; /* size nrow, used if values is TRUE */
+ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input */
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the result C */
+ /* ---------------------------------------------------------------------- */
+
+ /* If integer overflow occurs, nzmax < 0 and the allocate fails properly
+ * (likewise in most other matrix manipulation routines). */
+ nzmax = A->nzmax + B->nzmax ;
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, FALSE, TRUE,
+ SIGN (A->stype), values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute C = alpha*A + beta*B */
+ /* ---------------------------------------------------------------------- */
+
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cp [j] = nz ;
+
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* scatter B into W */
+ pb = Bp [j] ;
+ pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ;
+ for (p = pb ; p < pbend ; p++)
+ {
+ i = Bi [p] ;
+ if ((up && i > j) || (lo && i < j))
+ {
+ continue ;
+ }
+ Flag [i] = mark ;
+ if (values)
+ {
+ W [i] = beta [0] * Bx [p] ;
+ }
+ }
+
+ /* add A and gather from W into C(:,j) */
+ pa = Ap [j] ;
+ paend = (apacked) ? (Ap [j+1]) : (pa + Anz [j]) ;
+ for (p = pa ; p < paend ; p++)
+ {
+ i = Ai [p] ;
+ if ((up && i > j) || (lo && i < j))
+ {
+ continue ;
+ }
+ Flag [i] = EMPTY ;
+ Ci [nz] = i ;
+ if (values)
+ {
+ Cx [nz] = W [i] + alpha [0] * Ax [p] ;
+ W [i] = 0 ;
+ }
+ nz++ ;
+ }
+
+ /* gather remaining entries into C(:,j), using pattern of B */
+ for (p = pb ; p < pbend ; p++)
+ {
+ i = Bi [p] ;
+ if ((up && i > j) || (lo && i < j))
+ {
+ continue ;
+ }
+ if (Flag [i] == mark)
+ {
+ Ci [nz] = i ;
+ if (values)
+ {
+ Cx [nz] = W [i] ;
+ W [i] = 0 ;
+ }
+ nz++ ;
+ }
+ }
+ }
+
+ Cp [ncol] = nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce C in size and free temporary matrices */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (MAX (1,nz) <= C->nzmax) ;
+ CHOLMOD(reallocate_sparse) (nz, C, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sort C, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (sorted)
+ {
+ /* workspace: Iwork (max (nrow,ncol)) */
+ if (!CHOLMOD(sort) (C, Common))
+ {
+ CHOLMOD(free_sparse) (&C, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C, "add", Common) >= 0) ;
+ return (C) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_band.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_band.c
new file mode 100644
index 0000000..2e5f0ac
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_band.c
@@ -0,0 +1,374 @@
+/* ========================================================================== */
+/* === Core/cholmod_band ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = tril (triu (A,k1), k2)
+ *
+ * C is a matrix consisting of the diagonals of A from k1 to k2.
+ *
+ * k=0 is the main diagonal of A, k=1 is the superdiagonal, k=-1 is the
+ * subdiagonal, and so on. If A is m-by-n, then:
+ *
+ * k1=-m C = tril (A,k2)
+ * k2=n C = triu (A,k1)
+ * k1=0 and k2=0 C = diag(A), except C is a matrix, not a vector
+ *
+ * Values of k1 and k2 less than -m are treated as -m, and values greater
+ * than n are treated as n.
+ *
+ * A can be of any symmetry (upper, lower, or unsymmetric); C is returned in
+ * the same form, and packed. If A->stype > 0, entries in the lower
+ * triangular part of A are ignored, and the opposite is true if
+ * A->stype < 0. If A has sorted columns, then so does C.
+ * C has the same size as A.
+ *
+ * If inplace is TRUE, then the matrix A is modified in place.
+ * Only packed matrices can be converted in place.
+ *
+ * C can be returned as a numerical valued matrix (if A has numerical values
+ * and mode > 0), as a pattern-only (mode == 0), or as a pattern-only but with
+ * the diagonal entries removed (mode < 0).
+ *
+ * workspace: none
+ *
+ * A can have an xtype of pattern or real. Complex and zomplex cases supported
+ * only if mode <= 0 (in which case the numerical values are ignored).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+static cholmod_sparse *band /* returns C, or NULL if failure */
+(
+ /* ---- input or in/out if inplace is TRUE --- */
+ cholmod_sparse *A,
+ /* ---- input ---- */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diagonal) */
+ int inplace, /* if TRUE, then convert A in place */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Cx ;
+ Int packed, nz, j, p, pend, i, ncol, nrow, jlo, jhi, ilo, ihi, sorted,
+ values, diag ;
+ Int *Ap, *Anz, *Ai, *Cp, *Ci ;
+ cholmod_sparse *C ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ packed = A->packed ;
+ diag = (mode >= 0) ;
+ if (inplace && !packed)
+ {
+ /* cannot operate on an unpacked matrix in place */
+ ERROR (CHOLMOD_INVALID, "cannot operate on unpacked matrix in-place") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+
+ PRINT1 (("k1 %ld k2 %ld\n", k1, k2)) ;
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ sorted = A->sorted ;
+
+
+ if (A->stype > 0)
+ {
+ /* ignore any entries in strictly lower triangular part of A */
+ k1 = MAX (k1, 0) ;
+ }
+ if (A->stype < 0)
+ {
+ /* ignore any entries in strictly upper triangular part of A */
+ k2 = MIN (k2, 0) ;
+ }
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+
+ /* ensure k1 and k2 are in the range -nrow to +ncol to
+ * avoid possible integer overflow if k1 and k2 are huge */
+ k1 = MAX (-nrow, k1) ;
+ k1 = MIN (k1, ncol) ;
+ k2 = MAX (-nrow, k2) ;
+ k2 = MIN (k2, ncol) ;
+
+ /* consider columns jlo to jhi. columns outside this range are empty */
+ jlo = MAX (k1, 0) ;
+ jhi = MIN (k2+nrow, ncol) ;
+
+ if (k1 > k2)
+ {
+ /* nothing to do */
+ jlo = ncol ;
+ jhi = ncol ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C, or operate on A in place */
+ /* ---------------------------------------------------------------------- */
+
+ if (inplace)
+ {
+ /* convert A in place */
+ C = A ;
+ }
+ else
+ {
+ /* count the number of entries in the result C */
+ nz = 0 ;
+ if (sorted)
+ {
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > ihi)
+ {
+ break ;
+ }
+ if (i >= ilo && (diag || i != j))
+ {
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= ilo && i <= ihi && (diag || i != j))
+ {
+ nz++ ;
+ }
+ }
+ }
+ }
+ /* allocate C; A will not be modified. C is sorted if A is sorted */
+ C = CHOLMOD(allocate_sparse) (A->nrow, ncol, nz, sorted, TRUE,
+ A->stype, values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct C */
+ /* ---------------------------------------------------------------------- */
+
+ /* columns 0 to jlo-1 are empty */
+ for (j = 0 ; j < jlo ; j++)
+ {
+ Cp [j] = 0 ;
+ }
+
+ nz = 0 ;
+ if (sorted)
+ {
+ if (values)
+ {
+ /* pattern and values */
+ ASSERT (diag) ;
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > ihi)
+ {
+ break ;
+ }
+ if (i >= ilo)
+ {
+ Ci [nz] = i ;
+ Cx [nz] = Ax [p] ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* pattern only, perhaps with no diagonal */
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > ihi)
+ {
+ break ;
+ }
+ if (i >= ilo && (diag || i != j))
+ {
+ Ci [nz++] = i ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (values)
+ {
+ /* pattern and values */
+ ASSERT (diag) ;
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= ilo && i <= ihi)
+ {
+ Ci [nz] = i ;
+ Cx [nz] = Ax [p] ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* pattern only, perhaps with no diagonal */
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= ilo && i <= ihi && (diag || i != j))
+ {
+ Ci [nz++] = i ;
+ }
+ }
+ }
+ }
+ }
+
+ /* columns jhi to ncol-1 are empty */
+ for (j = jhi ; j <= ncol ; j++)
+ {
+ Cp [j] = nz ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce A in size if done in place */
+ /* ---------------------------------------------------------------------- */
+
+ if (inplace)
+ {
+ /* free the unused parts of A, and reduce A->i and A->x in size */
+ ASSERT (MAX (1,nz) <= A->nzmax) ;
+ CHOLMOD(reallocate_sparse) (nz, A, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result C */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (i = CHOLMOD(dump_sparse) (C, "band", Common)) ;
+ ASSERT (IMPLIES (mode < 0, i == 0)) ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_band ========================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(band)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to extract band matrix from */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (band (A, k1, k2, mode, FALSE, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_band_inplace ================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(band_inplace)
+(
+ /* ---- input ---- */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix from which entries not in band are removed */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (band (A, k1, k2, mode, TRUE, Common) != NULL) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_change_factor.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_change_factor.c
new file mode 100644
index 0000000..cc90b0e
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_change_factor.c
@@ -0,0 +1,1227 @@
+/* ========================================================================== */
+/* === Core/cholmod_change_factor =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Change the numeric/symbolic, LL/LDL, simplicial/super, packed/unpacked,
+ * monotonic/non-monotonic status of a cholmod_factor object.
+ *
+ * There are four basic classes of factor types:
+ *
+ * (1) simplicial symbolic: Consists of two size-n arrays: the fill-reducing
+ * permutation (L->Perm) and the nonzero count for each column of L
+ * (L->ColCount). All other factor types also include this information.
+ * L->ColCount may be exact (obtained from the analysis routines), or
+ * it may be a guess. During factorization, and certainly after update/
+ * downdate, the columns of L can have a different number of nonzeros.
+ * L->ColCount is used to allocate space. L->ColCount is exact for the
+ * supernodal factorizations. The nonzero pattern of L is not kept.
+ *
+ * (2) simplicial numeric: These represent L in a compressed column form. The
+ * variants of this type are:
+ *
+ * LDL': L is unit diagonal. Row indices in column j are located in
+ * L->i [L->p [j] ... L->p [j] + L->nz [j]], and corresponding numeric
+ * values are in the same locations in L->x. The total number of
+ * entries is the sum of L->nz [j]. The unit diagonal is not stored;
+ * D is stored on the diagonal of L instead. L->p may or may not be
+ * monotonic. The order of storage of the columns in L->i and L->x is
+ * given by a doubly-linked list (L->prev and L->next). L->p is of
+ * size n+1, but only the first n entries are used (it is used if L
+ * is converted to a sparse matrix via cholmod_factor_to_sparse).
+ *
+ * For the complex case, L->x is stored interleaved with real/imag
+ * parts, and is of size 2*lnz*sizeof(double). For the zomplex case,
+ * L->x is of size lnz*sizeof(double) and holds the real part; L->z
+ * is the same size and holds the imaginary part.
+ *
+ * LL': This is identical to the LDL' form, except that the non-unit
+ * diagonal of L is stored as the first entry in each column of L.
+ *
+ * (3) supernodal symbolic: A representation of the nonzero pattern of the
+ * supernodes for a supernodal factorization. There are L->nsuper
+ * supernodes. Columns L->super [k] to L->super [k+1]-1 are in the kth
+ * supernode. The row indices for the kth supernode are in
+ * L->s [L->pi [k] ... L->pi [k+1]-1]. The numerical values are not
+ * allocated (L->x), but when they are they will be located in
+ * L->x [L->px [k] ... L->px [k+1]-1], and the L->px array is defined
+ * in this factor type.
+ *
+ * For the complex case, L->x is stored interleaved with real/imag parts,
+ * and is of size 2*L->xsize*sizeof(double). The zomplex supernodal case
+ * is not supported, since it is not compatible with LAPACK and the BLAS.
+ *
+ * (4) supernodal numeric: Always an LL' factorization. L is non-unit
+ * diagonal. L->x contains the numerical values of the supernodes, as
+ * described above for the supernodal symbolic factor.
+ * For the complex case, L->x is stored interleaved, and is of size
+ * 2*L->xsize*sizeof(double). The zomplex supernodal case is not
+ * supported, since it is not compatible with LAPACK and the BLAS.
+ *
+ * FUTURE WORK: support a supernodal LDL' factor.
+ *
+ *
+ * In all cases, the row indices in each column (L->i for simplicial L and
+ * L->s for supernodal L) are kept sorted from low indices to high indices.
+ * This means the diagonal of L (or D for LDL' factors) is always kept as the
+ * first entry in each column.
+ *
+ * The cholmod_change_factor routine can do almost all possible conversions.
+ * It cannot do the following conversions:
+ *
+ * (1) Simplicial numeric types cannot be converted to a supernodal
+ * symbolic type. This would simultaneously deallocate the
+ * simplicial pattern and numeric values and reallocate uninitialized
+ * space for the supernodal pattern. This isn't useful for the user,
+ * and not needed by CHOLMOD's own routines either.
+ *
+ * (2) Only a symbolic factor (simplicial to supernodal) can be converted
+ * to a supernodal numeric factor.
+ *
+ * Some conversions are meant only to be used internally by other CHOLMOD
+ * routines, and should not be performed by the end user. They allocate space
+ * whose contents are undefined:
+ *
+ * (1) converting from simplicial symbolic to supernodal symbolic.
+ * (2) converting any factor to supernodal numeric.
+ *
+ * workspace: no conversion routine uses workspace in Common. No temporary
+ * workspace is allocated.
+ *
+ * Supports all xtypes, except that there is no supernodal zomplex L.
+ *
+ * The to_xtype parameter is used only when converting from symbolic to numeric
+ * or numeric to symbolic. It cannot be used to convert a numeric xtype (real,
+ * complex, or zomplex) to a different numeric xtype. For that conversion,
+ * use cholmod_factor_xtype instead.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+static void natural_list (cholmod_factor *L) ;
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_change_factor.c"
+#define COMPLEX
+#include "t_cholmod_change_factor.c"
+#define ZOMPLEX
+#include "t_cholmod_change_factor.c"
+
+
+/* ========================================================================== */
+/* === L_is_packed ========================================================== */
+/* ========================================================================== */
+
+/* Return TRUE if the columns of L are packed, FALSE otherwise. For debugging
+ * only. */
+
+#ifndef NDEBUG
+static int L_is_packed (cholmod_factor *L, cholmod_common *Common)
+{
+ Int j ;
+ Int *Lnz = L->nz ;
+ Int *Lp = L->p ;
+ Int n = L->n ;
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super)
+ {
+ return (TRUE) ;
+ }
+
+ if (Lnz == NULL || Lp == NULL)
+ {
+ return (TRUE) ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT3 (("j: "ID" Lnz "ID" Lp[j+1] "ID" Lp[j] "ID"\n", j, Lnz [j],
+ Lp [j+1], Lp [j])) ;
+ if (Lnz [j] != (Lp [j+1] - Lp [j]))
+ {
+ PRINT2 (("L is not packed\n")) ;
+ return (FALSE) ;
+ }
+ }
+ return (TRUE) ;
+}
+#endif
+
+
+/* ========================================================================== */
+/* === natural_list ========================================================= */
+/* ========================================================================== */
+
+/* Create a naturally-ordered doubly-linked list of columns. */
+
+static void natural_list (cholmod_factor *L)
+{
+ Int head, tail, n, j ;
+ Int *Lnext, *Lprev ;
+ Lnext = L->next ;
+ Lprev = L->prev ;
+ ASSERT (Lprev != NULL && Lnext != NULL) ;
+ n = L->n ;
+ head = n+1 ;
+ tail = n ;
+ Lnext [head] = 0 ;
+ Lprev [head] = EMPTY ;
+ Lnext [tail] = EMPTY ;
+ Lprev [tail] = n-1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnext [j] = j+1 ;
+ Lprev [j] = j-1 ;
+ }
+ Lprev [0] = head ;
+ L->is_monotonic = TRUE ;
+}
+
+
+/* ========================================================================== */
+/* === allocate_simplicial_numeric ========================================== */
+/* ========================================================================== */
+
+/* Allocate O(n) arrays for simplicial numeric factorization. Initializes
+ * the link lists only. Does not allocate the L->i, L->x, or L->z arrays. */
+
+static int allocate_simplicial_numeric
+(
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ Int n ;
+ Int *Lp, *Lnz, *Lprev, *Lnext ;
+ size_t n1, n2 ;
+
+ PRINT1 (("Allocate simplicial\n")) ;
+
+ ASSERT (L->xtype == CHOLMOD_PATTERN || L->is_super) ;
+ ASSERT (L->p == NULL) ;
+ ASSERT (L->nz == NULL) ;
+ ASSERT (L->prev == NULL) ;
+ ASSERT (L->next == NULL) ;
+
+ n = L->n ;
+
+ /* this cannot cause size_t overflow */
+ n1 = ((size_t) n) + 1 ;
+ n2 = ((size_t) n) + 2 ;
+
+ Lp = CHOLMOD(malloc) (n1, sizeof (Int), Common) ;
+ Lnz = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ Lprev = CHOLMOD(malloc) (n2, sizeof (Int), Common) ;
+ Lnext = CHOLMOD(malloc) (n2, sizeof (Int), Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (n1, sizeof (Int), Lp, Common) ;
+ CHOLMOD(free) (n, sizeof (Int), Lnz, Common) ;
+ CHOLMOD(free) (n2, sizeof (Int), Lprev, Common) ;
+ CHOLMOD(free) (n2, sizeof (Int), Lnext, Common) ;
+ PRINT1 (("Allocate simplicial failed\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ L->p = Lp ;
+ L->nz = Lnz ;
+ L->prev = Lprev ;
+ L->next = Lnext ;
+ /* initialize a doubly linked list for columns in natural order */
+ natural_list (L) ;
+ PRINT1 (("Allocate simplicial done\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === simplicial_symbolic_to_super_symbolic ================================ */
+/* ========================================================================== */
+
+/* Convert a simplicial symbolic factor supernodal symbolic factor. Does not
+ * initialize the new space. */
+
+static int simplicial_symbolic_to_super_symbolic
+(
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ Int nsuper, xsize, ssize ;
+ Int *Lsuper, *Lpi, *Lpx, *Ls ;
+ size_t nsuper1 ;
+
+ ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ;
+
+ xsize = L->xsize ;
+ ssize = L->ssize ;
+ nsuper = L->nsuper ;
+ nsuper1 = ((size_t) nsuper) + 1 ;
+
+ PRINT1 (("simple sym to super sym: ssize "ID" xsize "ID" nsuper "ID""
+ " status %d\n", ssize, xsize, nsuper, Common->status)) ;
+
+ /* O(nsuper) arrays, where nsuper <= n */
+ Lsuper = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ;
+ Lpi = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ;
+ Lpx = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ;
+
+ /* O(ssize) array, where ssize <= nnz(L), and usually much smaller */
+ Ls = CHOLMOD(malloc) (ssize, sizeof (Int), Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nsuper1, sizeof (Int), Lsuper, Common) ;
+ CHOLMOD(free) (nsuper1, sizeof (Int), Lpi, Common) ;
+ CHOLMOD(free) (nsuper1, sizeof (Int), Lpx, Common) ;
+ CHOLMOD(free) (ssize, sizeof (Int), Ls, Common) ;
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ ASSERT (Lsuper != NULL && Lpi != NULL && Lpx != NULL && Ls != NULL) ;
+
+ L->maxcsize = 0 ;
+ L->maxesize = 0 ;
+
+ L->super = Lsuper ;
+ L->pi = Lpi ;
+ L->px = Lpx ;
+ L->s = Ls ;
+ Ls [0] = EMPTY ; /* supernodal pattern undefined */
+
+ L->is_super = TRUE ;
+ L->is_ll = TRUE ; /* supernodal LDL' not supported */
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+ L->minor = L->n ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === any_to_simplicial_symbolic =========================================== */
+/* ========================================================================== */
+
+/* Convert any factor L to a simplicial symbolic factor, leaving only L->Perm
+ * and L->ColCount. Cannot fail. Any of the components of L (except Perm and
+ * ColCount) may already be free'd. */
+
+static void any_to_simplicial_symbolic
+(
+ cholmod_factor *L,
+ int to_ll,
+ cholmod_common *Common
+)
+{
+ Int n, lnz, xs, ss, s, e ;
+ size_t n1, n2 ;
+
+ /* ============================================== commit the changes to L */
+
+ n = L->n ;
+ lnz = L->nzmax ;
+ s = L->nsuper + 1 ;
+ xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ;
+ e = (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) ;
+ ss = L->ssize ;
+
+ /* this cannot cause size_t overflow */
+ n1 = ((size_t) n) + 1 ;
+ n2 = ((size_t) n) + 2 ;
+
+ /* free all but the symbolic analysis (Perm and ColCount) */
+ L->p = CHOLMOD(free) (n1, sizeof (Int), L->p, Common) ;
+ L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ;
+ L->x = CHOLMOD(free) (xs, e*sizeof (double), L->x, Common) ;
+ L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ;
+ L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ;
+ L->next = CHOLMOD(free) (n2, sizeof (Int), L->next, Common) ;
+ L->prev = CHOLMOD(free) (n2, sizeof (Int), L->prev, Common) ;
+ L->super = CHOLMOD(free) (s, sizeof (Int), L->super, Common) ;
+ L->pi = CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ;
+ L->px = CHOLMOD(free) (s, sizeof (Int), L->px, Common) ;
+ L->s = CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ;
+ L->nzmax = 0 ;
+ L->is_super = FALSE ;
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+ L->minor = n ;
+ L->is_ll = to_ll ;
+}
+
+
+/* ========================================================================== */
+/* === ll_super_to_super_symbolic =========================================== */
+/* ========================================================================== */
+
+/* Convert a numerical supernodal L to symbolic supernodal. Cannot fail. */
+
+static void ll_super_to_super_symbolic
+(
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+
+ /* ============================================== commit the changes to L */
+
+ /* free all but the supernodal numerical factor */
+ ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_super && L->is_ll) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start to super symbolic", Common)) ;
+ L->x = CHOLMOD(free) (L->xsize,
+ (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) * sizeof (double), L->x,
+ Common) ;
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+ L->minor = L->n ;
+ L->is_ll = TRUE ; /* supernodal LDL' not supported */
+ DEBUG (CHOLMOD(dump_factor) (L, "done to super symbolic", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === simplicial_symbolic_to_simplicial_numeric ============================ */
+/* ========================================================================== */
+
+/* Convert a simplicial symbolic L to a simplicial numeric L; allocate space
+ * for L using L->ColCount from symbolic analysis, and set L to identity.
+ *
+ * If packed < 0, then this routine is creating a copy of another factor
+ * (via cholmod_copy_factor). In this case, the space is not initialized. */
+
+static void simplicial_symbolic_to_simplicial_numeric
+(
+ cholmod_factor *L,
+ int to_ll,
+ int packed,
+ int to_xtype,
+ cholmod_common *Common
+)
+{
+ double grow0, grow1, xlen, xlnz ;
+ double *Lx, *Lz ;
+ Int *Li, *Lp, *Lnz, *ColCount ;
+ Int n, grow, grow2, p, j, lnz, len, ok, e ;
+
+ ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ;
+ if (!allocate_simplicial_numeric (L, Common))
+ {
+ PRINT1 (("out of memory, allocate simplicial numeric\n")) ;
+ return ; /* out of memory */
+ }
+ ASSERT (L->ColCount != NULL && L->nz != NULL && L->p != NULL) ;
+ ASSERT (L->x == NULL && L->z == NULL && L->i == NULL) ;
+
+ ColCount = L->ColCount ;
+ Lnz = L->nz ;
+ Lp = L->p ;
+ ok = TRUE ;
+ n = L->n ;
+
+ if (packed < 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* used by cholmod_copy_factor to allocate a copy of a factor object */
+ /* ------------------------------------------------------------------ */
+
+ lnz = L->nzmax ;
+ L->nzmax = 0 ;
+
+ }
+ else if (packed)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* LDL' or LL' packed */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("convert to packed LL' or LDL'\n")) ;
+ lnz = 0 ;
+ for (j = 0 ; ok && j < n ; j++)
+ {
+ /* ensure len is in the range 1 to n-j */
+ len = ColCount [j] ;
+ len = MAX (1, len) ;
+ len = MIN (len, n-j) ;
+ lnz += len ;
+ ok = (lnz >= 0) ;
+ }
+ for (j = 0 ; j <= n ; j++)
+ {
+ Lp [j] = j ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnz [j] = 1 ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* LDL' unpacked */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("convert to unpacked\n")) ;
+ /* compute new lnzmax */
+ /* if any parameter is NaN, grow is false */
+ grow0 = Common->grow0 ;
+ grow1 = Common->grow1 ;
+ grow2 = Common->grow2 ;
+ grow0 = IS_NAN (grow0) ? 1 : grow0 ;
+ grow1 = IS_NAN (grow1) ? 1 : grow1 ;
+ /* fl.pt. compare, but no NaN's: */
+ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ;
+ PRINT1 (("init, grow1 %g grow2 "ID"\n", grow1, grow2)) ;
+ /* initialize Lp and Lnz for each column */
+ lnz = 0 ;
+ for (j = 0 ; ok && j < n ; j++)
+ {
+ Lp [j] = lnz ;
+ Lnz [j] = 1 ;
+
+ /* ensure len is in the range 1 to n-j */
+ len = ColCount [j] ;
+ len = MAX (1, len) ;
+ len = MIN (len, n-j) ;
+
+ /* compute len in double to avoid integer overflow */
+ PRINT1 (("ColCount ["ID"] = "ID"\n", j, len)) ;
+ if (grow)
+ {
+ xlen = (double) len ;
+ xlen = grow1 * xlen + grow2 ;
+ xlen = MIN (xlen, n-j) ;
+ len = (Int) xlen ;
+ }
+ ASSERT (len >= 1 && len <= n-j) ;
+ lnz += len ;
+ ok = (lnz >= 0) ;
+ }
+ if (ok)
+ {
+ Lp [n] = lnz ;
+ if (grow)
+ {
+ /* add extra space */
+ xlnz = (double) lnz ;
+ xlnz *= grow0 ;
+ xlnz = MIN (xlnz, Size_max) ;
+ xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ;
+ lnz = (Int) xlnz ;
+ }
+ }
+ }
+
+ lnz = MAX (1, lnz) ;
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ }
+
+ /* allocate L->i, L->x, and L->z */
+ PRINT1 (("resizing from zero size to lnz "ID"\n", lnz)) ;
+ ASSERT (L->nzmax == 0) ;
+ e = (to_xtype == CHOLMOD_COMPLEX ? 2 : 1) ;
+ if (!ok || !CHOLMOD(realloc_multiple) (lnz, 1, to_xtype, &(L->i), NULL,
+ &(L->x), &(L->z), &(L->nzmax), Common))
+ {
+ L->p = CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ;
+ L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ;
+ L->prev = CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ;
+ L->next = CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ;
+ L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ;
+ L->x = CHOLMOD(free) (lnz, e*sizeof (double), L->x, Common) ;
+ L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ;
+ PRINT1 (("cannot realloc simplicial numeric\n")) ;
+ return ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ /* initialize L to be the identity matrix */
+ L->xtype = to_xtype ;
+ L->dtype = DTYPE ;
+ L->minor = n ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+
+#if 0
+ if (lnz == 1)
+ {
+ /* the user won't expect to access this entry, but some CHOLMOD
+ * routines may. Set it to zero so that valgrind doesn't complain. */
+ switch (to_xtype)
+ {
+ case CHOLMOD_REAL:
+ Lx [0] = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ Lx [0] = 0 ;
+ Lx [1] = 0 ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ Lx [0] = 0 ;
+ Lz [0] = 0 ;
+ break ;
+ }
+ }
+#endif
+
+ if (packed >= 0)
+ {
+ /* create the unit diagonal for either the LL' or LDL' case */
+
+ switch (L->xtype)
+ {
+ case CHOLMOD_REAL:
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Lp [j] < Lp [j+1]) ;
+ p = Lp [j] ;
+ Li [p] = j ;
+ Lx [p] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Lp [j] < Lp [j+1]) ;
+ p = Lp [j] ;
+ Li [p] = j ;
+ Lx [2*p ] = 1 ;
+ Lx [2*p+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Lp [j] < Lp [j+1]) ;
+ p = Lp [j] ;
+ Li [p] = j ;
+ Lx [p] = 1 ;
+ Lz [p] = 0 ;
+ }
+ break ;
+ }
+ }
+
+ L->is_ll = to_ll ;
+
+ PRINT1 (("done convert simplicial symbolic to numeric\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === change_simplicial_numeric ============================================ */
+/* ========================================================================== */
+
+/* Change LL' to LDL', LDL' to LL', or leave as-is.
+ *
+ * If to_packed is TRUE, then the columns of L are packed and made monotonic
+ * (to_monotonic is ignored; it is implicitly TRUE).
+ *
+ * If to_monotonic is TRUE but to_packed is FALSE, the columns of L are made
+ * monotonic but not packed.
+ *
+ * If both to_packed and to_monotonic are FALSE, then the columns of L are
+ * left as-is, and the conversion is done in place.
+ *
+ * If L is already monotonic, or if it is to be left non-monotonic, then this
+ * conversion always succeeds.
+ *
+ * When converting an LDL' to LL' factorization, any column with a negative
+ * or zero diagonal entry is not modified so that conversion back to LDL' will
+ * succeed. This can result in a matrix L with a negative entry on the diagonal
+ * If the kth entry on the diagonal of D is negative, it and the kth column of
+ * L are left unchanged. A subsequent conversion back to an LDL' form will also
+ * leave the column unchanged, so the correct LDL' factorization will be
+ * restored. L->minor is set to the smallest k for which D (k,k) is negative.
+ */
+
+static void change_simplicial_numeric
+(
+ cholmod_factor *L,
+ int to_ll,
+ int to_packed,
+ int to_monotonic,
+ cholmod_common *Common
+)
+{
+ double grow0, grow1, xlen, xlnz ;
+ void *newLi, *newLx, *newLz ;
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz ;
+ Int make_monotonic, grow2, n, j, lnz, len, grow, ok, make_ll, make_ldl ;
+ size_t nzmax0 ;
+
+ PRINT1 (("\n===Change simplicial numeric: %d %d %d\n",
+ to_ll, to_packed, to_monotonic)) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "change simplicial numeric", Common)) ;
+ ASSERT (L->xtype != CHOLMOD_PATTERN && !(L->is_super)) ;
+
+ make_monotonic = ((to_packed || to_monotonic) && !(L->is_monotonic)) ;
+ make_ll = (to_ll && !(L->is_ll)) ;
+ make_ldl = (!to_ll && L->is_ll) ;
+
+ n = L->n ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+
+ grow = FALSE ;
+ grow0 = Common->grow0 ;
+ grow1 = Common->grow1 ;
+ grow2 = Common->grow2 ;
+ grow0 = IS_NAN (grow0) ? 1 : grow0 ;
+ grow1 = IS_NAN (grow1) ? 1 : grow1 ;
+ ok = TRUE ;
+ newLi = NULL ;
+ newLx = NULL ;
+ newLz = NULL ;
+ lnz = 0 ;
+
+ if (make_monotonic)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Columns out of order, but will be reordered and optionally packed. */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("L is non-monotonic\n")) ;
+
+ /* compute new L->nzmax */
+ if (!to_packed)
+ {
+ /* if any parameter is NaN, grow is false */
+ /* fl.pt. comparisons below are false if any parameter is NaN */
+ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ;
+ }
+ for (j = 0 ; ok && j < n ; j++)
+ {
+ len = Lnz [j] ;
+ ASSERT (len >= 1 && len <= n-j) ;
+
+ /* compute len in double to avoid integer overflow */
+ if (grow)
+ {
+ xlen = (double) len ;
+ xlen = grow1 * xlen + grow2 ;
+ xlen = MIN (xlen, n-j) ;
+ len = (Int) xlen ;
+ }
+ ASSERT (len >= Lnz [j] && len <= n-j) ;
+
+ PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n",
+ j, Lnz [j], len, lnz)) ;
+
+ lnz += len ;
+ ok = (lnz >= 0) ;
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return ;
+ }
+
+ if (grow)
+ {
+ xlnz = (double) lnz ;
+ xlnz *= grow0 ;
+ xlnz = MIN (xlnz, Size_max) ;
+ xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ;
+ lnz = (Int) xlnz ;
+ }
+
+ lnz = MAX (1, lnz) ;
+ PRINT1 (("final lnz "ID"\n", lnz)) ;
+ nzmax0 = 0 ;
+
+ CHOLMOD(realloc_multiple) (lnz, 1, L->xtype, &newLi, NULL,
+ &newLx, &newLz, &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return ; /* out of memory */
+ }
+ }
+
+ /* ============================================== commit the changes to L */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the simplicial L, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ r_change_simplicial_numeric (L, to_ll, to_packed,
+ newLi, newLx, newLz, lnz, grow, grow1, grow2,
+ make_ll, make_monotonic, make_ldl, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_change_simplicial_numeric (L, to_ll, to_packed,
+ newLi, newLx, newLz, lnz, grow, grow1, grow2,
+ make_ll, make_monotonic, make_ldl, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_change_simplicial_numeric (L, to_ll, to_packed,
+ newLi, newLx, newLz, lnz, grow, grow1, grow2,
+ make_ll, make_monotonic, make_ldl, Common) ;
+ break ;
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "L simplicial changed", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === ll_super_to_simplicial_numeric ======================================= */
+/* ========================================================================== */
+
+/* Convert a supernodal numeric factorization to any simplicial numeric one.
+ * Leaves L->xtype unchanged (real or complex, not zomplex since there is
+ * no supernodal zomplex L). */
+
+static void ll_super_to_simplicial_numeric
+(
+ cholmod_factor *L,
+ int to_packed,
+ int to_ll,
+ cholmod_common *Common
+)
+{
+ Int *Ls, *Lpi, *Lpx, *Super, *Li ;
+ Int n, lnz, s, nsuper, psi, psend, nsrow, nscol, k1, k2, erows ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "start LL super to simplicial", Common)) ;
+ PRINT1 (("super -> simplicial (%d %d)\n", to_packed, to_ll)) ;
+ ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_ll && L->is_super) ;
+ ASSERT (L->x != NULL && L->i == NULL) ;
+
+ n = L->n ;
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+
+ /* Int overflow cannot occur since supernodal L already exists */
+
+ if (to_packed)
+ {
+ /* count the number of nonzeros in L. Each supernode is of the form
+ *
+ * l . . . For this example, nscol = 4 (# columns). nsrow = 9.
+ * l l . . The "." entries are allocated in the supernodal
+ * l l l . factor, but not used. They are not copied to the
+ * l l l l simplicial factor. Some "l" and "e" entries may be
+ * e e e e numerically zero and even symbolically zero if a
+ * e e e e tight simplicial factorization or resymbol were
+ * e e e e done, because of numerical cancellation and relaxed
+ * e e e e supernode amalgamation, respectively.
+ * e e e e
+ */
+ lnz = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ ASSERT (nsrow >= nscol) ;
+ erows = nsrow - nscol ;
+
+ /* lower triangular part, including the diagonal,
+ * counting the "l" terms in the figure above. */
+ lnz += nscol * (nscol+1) / 2 ;
+
+ /* rectangular part, below the diagonal block (the "e" terms) */
+ lnz += nscol * erows ;
+ }
+ ASSERT (lnz <= (Int) (L->xsize)) ;
+ }
+ else
+ {
+ /* Li will be the same size as Lx */
+ lnz = L->xsize ;
+ }
+ ASSERT (lnz >= 0) ;
+ PRINT1 (("simplicial lnz = "ID" to_packed: %d to_ll: %d L->xsize %g\n",
+ lnz, to_ll, to_packed, (double) L->xsize)) ;
+
+ Li = CHOLMOD(malloc) (lnz, sizeof (Int), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return ; /* out of memory */
+ }
+
+ if (!allocate_simplicial_numeric (L, Common))
+ {
+ CHOLMOD(free) (lnz, sizeof (Int), Li, Common) ;
+ return ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ L->i = Li ;
+ L->nzmax = lnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the supernodal L, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ r_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free unused parts of L */
+ /* ---------------------------------------------------------------------- */
+
+ L->super = CHOLMOD(free) (nsuper+1, sizeof (Int), L->super, Common) ;
+ L->pi = CHOLMOD(free) (nsuper+1, sizeof (Int), L->pi, Common) ;
+ L->px = CHOLMOD(free) (nsuper+1, sizeof (Int), L->px, Common) ;
+ L->s = CHOLMOD(free) (L->ssize, sizeof (Int), L->s, Common) ;
+
+ L->ssize = 0 ;
+ L->xsize = 0 ;
+ L->nsuper = 0 ;
+ L->maxesize = 0 ;
+ L->maxcsize = 0 ;
+
+ L->is_super = FALSE ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "done LL super to simplicial", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === super_symbolic_to_ll_super =========================================== */
+/* ========================================================================== */
+
+/* Convert a supernodal symbolic factorization to a supernodal numeric
+ * factorization by allocating L->x. Contents of L->x are undefined.
+ */
+
+static int super_symbolic_to_ll_super
+(
+ int to_xtype,
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ double *Lx ;
+ Int wentry = (to_xtype == CHOLMOD_REAL) ? 1 : 2 ;
+ PRINT1 (("convert super sym to num\n")) ;
+ ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_super) ;
+ Lx = CHOLMOD(malloc) (L->xsize, wentry * sizeof (double), Common) ;
+ PRINT1 (("xsize %g\n", (double) L->xsize)) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ if (L->xsize == 1)
+ {
+ /* the caller won't expect to access this entry, but some CHOLMOD
+ * routines may. Set it to zero so that valgrind doesn't complain. */
+ switch (to_xtype)
+ {
+ case CHOLMOD_REAL:
+ Lx [0] = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ Lx [0] = 0 ;
+ Lx [1] = 0 ;
+ break ;
+ }
+ }
+
+ L->x = Lx ;
+ L->xtype = to_xtype ;
+ L->dtype = DTYPE ;
+ L->minor = L->n ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_change_factor ================================================ */
+/* ========================================================================== */
+
+/* Convert a factor L. Some conversions simply allocate uninitialized space
+ * that meant to be filled later.
+ *
+ * If the conversion fails, the factor is left in its original form, with one
+ * exception. Converting a supernodal symbolic factor to a simplicial numeric
+ * one (with L=D=I) may leave the factor in simplicial symbolic form.
+ *
+ * Memory allocated for each conversion is listed below.
+ */
+
+int CHOLMOD(change_factor)
+(
+ /* ---- input ---- */
+ int to_xtype, /* convert to CHOLMOD_PATTERN, _REAL, _COMPLEX, or
+ * _ZOMPLEX */
+ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */
+ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */
+ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */
+ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (to_xtype < CHOLMOD_PATTERN || to_xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ PRINT1 (("-----convert from (%d,%d,%d,%d,%d) to (%d,%d,%d,%d,%d)\n",
+ L->xtype, L->is_ll, L->is_super, L_is_packed (L, Common), L->is_monotonic,
+ to_xtype, to_ll, to_super, to_packed, to_monotonic)) ;
+
+ /* ensure all parameters are TRUE/FALSE */
+ to_ll = BOOLEAN (to_ll) ;
+ to_super = BOOLEAN (to_super) ;
+
+ ASSERT (BOOLEAN (L->is_ll) == L->is_ll) ;
+ ASSERT (BOOLEAN (L->is_super) == L->is_super) ;
+
+ if (to_super && to_xtype == CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "supernodal zomplex L not supported") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert */
+ /* ---------------------------------------------------------------------- */
+
+ if (to_xtype == CHOLMOD_PATTERN)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert to symbolic */
+ /* ------------------------------------------------------------------ */
+
+ if (!to_super)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert any factor into a simplicial symbolic factor */
+ /* -------------------------------------------------------------- */
+
+ any_to_simplicial_symbolic (L, to_ll, Common) ; /* cannot fail */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert to a supernodal symbolic factor */
+ /* -------------------------------------------------------------- */
+
+ if (L->xtype != CHOLMOD_PATTERN && L->is_super)
+ {
+ /* convert from supernodal numeric to supernodal symbolic.
+ * this preserves symbolic pattern of L, discards numeric
+ * values */
+ ll_super_to_super_symbolic (L, Common) ; /* cannot fail */
+ }
+ else if (L->xtype == CHOLMOD_PATTERN && !(L->is_super))
+ {
+ /* convert from simplicial symbolic to supernodal symbolic.
+ * contents of supernodal pattern are uninitialized. Not meant
+ * for the end user. */
+ simplicial_symbolic_to_super_symbolic (L, Common) ;
+ }
+ else
+ {
+ /* cannot convert from simplicial numeric to supernodal
+ * symbolic */
+ ERROR (CHOLMOD_INVALID,
+ "cannot convert L to supernodal symbolic") ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert to numeric */
+ /* ------------------------------------------------------------------ */
+
+ if (to_super)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert to supernodal numeric factor */
+ /* -------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN)
+ {
+ if (L->is_super)
+ {
+ /* Convert supernodal symbolic to supernodal numeric.
+ * Contents of supernodal numeric values are uninitialized.
+ * This is used by cholmod_super_numeric. Not meant for
+ * the end user. */
+ super_symbolic_to_ll_super (to_xtype, L, Common) ;
+ }
+ else
+ {
+ /* Convert simplicial symbolic to supernodal numeric.
+ * Contents not defined. This is used by
+ * Core/cholmod_copy_factor only. Not meant for the end
+ * user. */
+ if (!simplicial_symbolic_to_super_symbolic (L, Common))
+ {
+ /* failure, convert back to simplicial symbolic */
+ any_to_simplicial_symbolic (L, to_ll, Common) ;
+ }
+ else
+ {
+ /* conversion to super symbolic OK, allocate numeric
+ * part */
+ super_symbolic_to_ll_super (to_xtype, L, Common) ;
+ }
+ }
+ }
+ else
+ {
+ /* nothing to do if L is already in supernodal numeric form */
+ if (!(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID,
+ "cannot convert simplicial L to supernodal") ;
+ }
+ /* FUTURE WORK: convert to/from supernodal LL' and LDL' */
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert any factor to simplicial numeric */
+ /* -------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super))
+ {
+
+ /* ---------------------------------------------------------- */
+ /* convert simplicial symbolic to simplicial numeric (L=I,D=I)*/
+ /* ---------------------------------------------------------- */
+
+ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed,
+ to_xtype, Common) ;
+
+ }
+ else if (L->xtype != CHOLMOD_PATTERN && L->is_super)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* convert a supernodal LL' to simplicial numeric */
+ /* ---------------------------------------------------------- */
+
+ ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ;
+
+ }
+ else if (L->xtype == CHOLMOD_PATTERN && L->is_super)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* convert a supernodal symbolic to simplicial numeric (L=D=I)*/
+ /* ---------------------------------------------------------- */
+
+ any_to_simplicial_symbolic (L, to_ll, Common) ;
+ /* if the following fails, it leaves the factor in simplicial
+ * symbolic form */
+ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed,
+ to_xtype, Common) ;
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* change a simplicial numeric factor */
+ /* ---------------------------------------------------------- */
+
+ /* change LL' to LDL', LDL' to LL', or leave as-is. pack the
+ * columns of L, or leave as-is. Ensure the columns are
+ * monotonic, or leave as-is. */
+
+ change_simplicial_numeric (L, to_ll, to_packed, to_monotonic,
+ Common) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ return (Common->status >= CHOLMOD_OK) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_common.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_common.c
new file mode 100644
index 0000000..d954024
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_common.c
@@ -0,0 +1,657 @@
+/* ========================================================================== */
+/* === Core/cholmod_common ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_common object:
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_start the first call to CHOLMOD
+ * cholmod_finish the last call to CHOLMOD
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_defaults restore (most) default control parameters
+ * cholmod_allocate_work allocate (or reallocate) workspace in Common
+ * cholmod_free_work free workspace in Common
+ * cholmod_clear_flag clear Common->Flag in workspace
+ * cholmod_maxrank column dimension of Common->Xwork workspace
+ *
+ * The Common object is unique. It cannot be allocated or deallocated by
+ * CHOLMOD, since it contains the definition of the memory management routines
+ * used (pointers to malloc, free, realloc, and calloc, or their equivalent).
+ * The Common object contains workspace that is used between calls to
+ * CHOLMOD routines. This workspace allocated by CHOLMOD as needed, by
+ * cholmod_allocate_work and cholmod_free_work.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === cholmod_start ======================================================== */
+/* ========================================================================== */
+
+/* Initialize Common default parameters and statistics. Sets workspace
+ * pointers to NULL.
+ *
+ * This routine must be called just once, prior to calling any other CHOLMOD
+ * routine. Do not call this routine after any other CHOLMOD routine (except
+ * cholmod_finish, to start a new CHOLMOD session), or a memory leak will
+ * occur.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(start)
+(
+ cholmod_common *Common
+)
+{
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* user error handling routine */
+ /* ---------------------------------------------------------------------- */
+
+ Common->error_handler = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* integer and numerical types */
+ /* ---------------------------------------------------------------------- */
+
+ Common->itype = ITYPE ;
+ Common->dtype = DTYPE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* default control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(defaults) (Common) ;
+ Common->try_catch = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* memory management routines */
+ /* ---------------------------------------------------------------------- */
+
+ /* The user can replace cholmod's memory management routines by redefining
+ * these function pointers. */
+
+#ifndef NMALLOC
+ /* stand-alone ANSI C program */
+ Common->malloc_memory = malloc ;
+ Common->free_memory = free ;
+ Common->realloc_memory = realloc ;
+ Common->calloc_memory = calloc ;
+#else
+ /* no memory manager defined at compile-time; MUST define one at run-time */
+ Common->malloc_memory = NULL ;
+ Common->free_memory = NULL ;
+ Common->realloc_memory = NULL ;
+ Common->calloc_memory = NULL ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* complex arithmetic routines */
+ /* ---------------------------------------------------------------------- */
+
+ Common->complex_divide = CHOLMOD(divcomplex) ;
+ Common->hypotenuse = CHOLMOD(hypot) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print routine */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPRINT
+ /* stand-alone ANSI C program */
+ Common->print_function = printf ;
+#else
+ /* printing disabled */
+ Common->print_function = NULL ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* This code assumes the workspace held in Common is not initialized. If
+ * it is, then a memory leak will occur because the pointers are
+ * overwritten with NULL. */
+
+ Common->nrow = 0 ;
+ Common->mark = EMPTY ;
+ Common->xworksize = 0 ;
+ Common->iworksize = 0 ;
+ Common->Flag = NULL ;
+ Common->Head = NULL ;
+ Common->Iwork = NULL ;
+ Common->Xwork = NULL ;
+ Common->no_workspace_reallocate = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics */
+ /* ---------------------------------------------------------------------- */
+
+ /* fl and lnz are computed in cholmod_analyze and cholmod_rowcolcounts */
+ Common->fl = EMPTY ;
+ Common->lnz = EMPTY ;
+
+ /* modfl is computed in cholmod_updown, cholmod_rowadd, and cholmod_rowdel*/
+ Common->modfl = EMPTY ;
+
+ /* all routines use status as their error-report code */
+ Common->status = CHOLMOD_OK ;
+
+ Common->malloc_count = 0 ; /* # calls to malloc minus # calls to free */
+ Common->memory_usage = 0 ; /* peak memory usage (in bytes) */
+ Common->memory_inuse = 0 ; /* current memory in use (in bytes) */
+
+ Common->nrealloc_col = 0 ;
+ Common->nrealloc_factor = 0 ;
+ Common->ndbounds_hit = 0 ;
+ Common->rowfacfl = 0 ;
+ Common->aatfl = EMPTY ;
+
+ /* Common->called_nd is TRUE if cholmod_analyze called or NESDIS */
+ Common->called_nd = FALSE ;
+
+ DEBUG_INIT ("cholmod start") ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_defaults ===================================================== */
+/* ========================================================================== */
+
+/* Set Common default parameters, except for the function pointers.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(defaults)
+(
+ cholmod_common *Common
+)
+{
+ Int i ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* default control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Common->dbound = 0.0 ;
+ Common->grow0 = 1.2 ;
+ Common->grow1 = 1.2 ;
+ Common->grow2 = 5 ;
+ Common->maxrank = 8 ;
+
+ Common->final_asis = TRUE ;
+ Common->final_super = TRUE ;
+ Common->final_ll = FALSE ;
+ Common->final_pack = TRUE ;
+ Common->final_monotonic = TRUE ;
+ Common->final_resymbol = FALSE ;
+
+ /* use simplicial factorization if flop/nnz(L) < 40, supernodal otherwise */
+ Common->supernodal = CHOLMOD_AUTO ;
+ Common->supernodal_switch = 40 ;
+
+ Common->nrelax [0] = 4 ;
+ Common->nrelax [1] = 16 ;
+ Common->nrelax [2] = 48 ;
+ Common->zrelax [0] = 0.8 ;
+ Common->zrelax [1] = 0.1 ;
+ Common->zrelax [2] = 0.05 ;
+
+ Common->prefer_zomplex = FALSE ;
+ Common->prefer_upper = TRUE ;
+ Common->prefer_binary = FALSE ;
+ Common->quick_return_if_not_posdef = FALSE ;
+
+ /* METIS workarounds */
+ Common->metis_memory = 0.0 ; /* > 0 for memory guard (2 is reasonable) */
+ Common->metis_nswitch = 3000 ;
+ Common->metis_dswitch = 0.66 ;
+
+ Common->print = 3 ;
+ Common->precise = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* default ordering methods */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that if the Partition module is not installed, the CHOLMOD_METIS
+ * and CHOLMOD_NESDIS methods will not be available. cholmod_analyze will
+ * report the CHOLMOD_NOT_INSTALLED error, and safely skip over them.
+ */
+
+#if (CHOLMOD_MAXMETHODS < 9)
+#error "CHOLMOD_MAXMETHODS must be 9 or more (defined in cholmod_core.h)."
+#endif
+
+ /* default strategy: try given, AMD, and then METIS if AMD reports high
+ * fill-in. NESDIS can be used instead, if Common->default_nesdis is TRUE.
+ */
+ Common->nmethods = 0 ; /* use default strategy */
+ Common->default_nesdis = FALSE ; /* use METIS in default strategy */
+
+ Common->current = 0 ; /* current method being tried */
+ Common->selected = 0 ; /* the best method selected */
+
+ /* first, fill each method with default parameters */
+ for (i = 0 ; i <= CHOLMOD_MAXMETHODS ; i++)
+ {
+ /* CHOLMOD's default method is AMD for A or AA' */
+ Common->method [i].ordering = CHOLMOD_AMD ;
+
+ /* CHOLMOD nested dissection and minimum degree parameter */
+ Common->method [i].prune_dense = 10.0 ; /* dense row/col control */
+
+ /* min degree parameters (AMD, COLAMD, SYMAMD, CAMD, CCOLAMD, CSYMAMD)*/
+ Common->method [i].prune_dense2 = -1 ; /* COLAMD dense row control */
+ Common->method [i].aggressive = TRUE ; /* aggressive absorption */
+ Common->method [i].order_for_lu = FALSE ;/* order for Cholesky not LU */
+
+ /* CHOLMOD's nested dissection (METIS + constrained AMD) */
+ Common->method [i].nd_small = 200 ; /* small graphs aren't cut */
+ Common->method [i].nd_compress = TRUE ; /* compress graph & subgraphs */
+ Common->method [i].nd_camd = 1 ; /* use CAMD */
+ Common->method [i].nd_components = FALSE ; /* lump connected comp. */
+ Common->method [i].nd_oksep = 1.0 ; /* sep ok if < oksep*n */
+
+ /* statistics for each method are not yet computed */
+ Common->method [i].fl = EMPTY ;
+ Common->method [i].lnz = EMPTY ;
+ }
+
+ Common->postorder = TRUE ; /* follow ordering with weighted postorder */
+
+ /* Next, define some methods. The first five use default parameters. */
+ Common->method [0].ordering = CHOLMOD_GIVEN ; /* skip if UserPerm NULL */
+ Common->method [1].ordering = CHOLMOD_AMD ;
+ Common->method [2].ordering = CHOLMOD_METIS ;
+ Common->method [3].ordering = CHOLMOD_NESDIS ;
+ Common->method [4].ordering = CHOLMOD_NATURAL ;
+
+ /* CHOLMOD's nested dissection with large leaves of separator tree */
+ Common->method [5].ordering = CHOLMOD_NESDIS ;
+ Common->method [5].nd_small = 20000 ;
+
+ /* CHOLMOD's nested dissection with tiny leaves, and no AMD ordering */
+ Common->method [6].ordering = CHOLMOD_NESDIS ;
+ Common->method [6].nd_small = 4 ;
+ Common->method [6].nd_camd = 0 ; /* no CSYMAMD or CAMD */
+
+ /* CHOLMOD's nested dissection with no dense node removal */
+ Common->method [7].ordering = CHOLMOD_NESDIS ;
+ Common->method [7].prune_dense = -1. ;
+
+ /* COLAMD for A*A', AMD for A */
+ Common->method [8].ordering = CHOLMOD_COLAMD ;
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_finish ======================================================= */
+/* ========================================================================== */
+
+/* The last call to CHOLMOD must be cholmod_finish. You may call this routine
+ * more than once, and can safely call any other CHOLMOD routine after calling
+ * it (including cholmod_start).
+ *
+ * The statistics and parameter settings in Common are preserved. The
+ * workspace in Common is freed. This routine is just another name for
+ * cholmod_free_work.
+ */
+
+int CHOLMOD(finish)
+(
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(free_work) (Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_work ================================================ */
+/* ========================================================================== */
+
+/* Allocate and initialize workspace for CHOLMOD routines, or increase the size
+ * of already-allocated workspace. If enough workspace is already allocated,
+ * then nothing happens.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), Iwork (iworksize), Xwork (xworksize)
+ */
+
+int CHOLMOD(allocate_work)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows in the matrix A */
+ size_t iworksize, /* size of Iwork */
+ size_t xworksize, /* size of Xwork */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *W ;
+ Int *Head ;
+ Int i ;
+ size_t nrow1 ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Allocate Flag (nrow) and Head (nrow+1) */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = MAX (1, nrow) ;
+
+ /* nrow1 = nrow + 1 */
+ nrow1 = CHOLMOD(add_size_t) (nrow, 1, &ok) ;
+ if (!ok)
+ {
+ /* nrow+1 causes size_t overflow ; problem is too large */
+ Common->status = CHOLMOD_TOO_LARGE ;
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ if (nrow > Common->nrow)
+ {
+
+ if (Common->no_workspace_reallocate)
+ {
+ /* CHOLMOD is not allowed to change the workspace here */
+ Common->status = CHOLMOD_INVALID ;
+ return (FALSE) ;
+ }
+
+ /* free the old workspace (if any) and allocate new space */
+ Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int), Common->Flag,
+ Common) ;
+ Common->Head = CHOLMOD(free) (Common->nrow+1,sizeof (Int), Common->Head,
+ Common) ;
+ Common->Flag = CHOLMOD(malloc) (nrow, sizeof (Int), Common) ;
+ Common->Head = CHOLMOD(malloc) (nrow1, sizeof (Int), Common) ;
+
+ /* record the new size of Flag and Head */
+ Common->nrow = nrow ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ /* initialize Flag and Head */
+ Common->mark = EMPTY ;
+ CHOLMOD(clear_flag) (Common) ;
+ Head = Common->Head ;
+ for (i = 0 ; i <= (Int) (nrow) ; i++)
+ {
+ Head [i] = EMPTY ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Allocate Iwork (iworksize) */
+ /* ---------------------------------------------------------------------- */
+
+ iworksize = MAX (1, iworksize) ;
+ if (iworksize > Common->iworksize)
+ {
+
+ if (Common->no_workspace_reallocate)
+ {
+ /* CHOLMOD is not allowed to change the workspace here */
+ Common->status = CHOLMOD_INVALID ;
+ return (FALSE) ;
+ }
+
+ /* free the old workspace (if any) and allocate new space.
+ * integer overflow safely detected in cholmod_malloc */
+ CHOLMOD(free) (Common->iworksize, sizeof (Int), Common->Iwork, Common) ;
+ Common->Iwork = CHOLMOD(malloc) (iworksize, sizeof (Int), Common) ;
+
+ /* record the new size of Iwork */
+ Common->iworksize = iworksize ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ /* note that Iwork does not need to be initialized */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Allocate Xwork (xworksize) and set it to ((double) 0.) */
+ /* ---------------------------------------------------------------------- */
+
+ /* make sure xworksize is >= 1 */
+ xworksize = MAX (1, xworksize) ;
+ if (xworksize > Common->xworksize)
+ {
+
+ if (Common->no_workspace_reallocate)
+ {
+ /* CHOLMOD is not allowed to change the workspace here */
+ Common->status = CHOLMOD_INVALID ;
+ return (FALSE) ;
+ }
+
+ /* free the old workspace (if any) and allocate new space */
+ CHOLMOD(free) (Common->xworksize, sizeof (double), Common->Xwork,
+ Common) ;
+ Common->Xwork = CHOLMOD(malloc) (xworksize, sizeof (double), Common) ;
+
+ /* record the new size of Xwork */
+ Common->xworksize = xworksize ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ /* initialize Xwork */
+ W = Common->Xwork ;
+ for (i = 0 ; i < (Int) xworksize ; i++)
+ {
+ W [i] = 0. ;
+ }
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_work ==================================================== */
+/* ========================================================================== */
+
+/* Deallocate the CHOLMOD workspace.
+ *
+ * workspace: deallocates all workspace in Common
+ */
+
+int CHOLMOD(free_work)
+(
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int),
+ Common->Flag, Common) ;
+ Common->Head = CHOLMOD(free) (Common->nrow+1, sizeof (Int),
+ Common->Head, Common) ;
+ Common->Iwork = CHOLMOD(free) (Common->iworksize, sizeof (Int),
+ Common->Iwork, Common) ;
+ Common->Xwork = CHOLMOD(free) (Common->xworksize, sizeof (double),
+ Common->Xwork, Common) ;
+ Common->nrow = 0 ;
+ Common->iworksize = 0 ;
+ Common->xworksize = 0 ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_clear_flag =================================================== */
+/* ========================================================================== */
+
+/* Increment mark to ensure Flag [0..nrow-1] < mark. If integer overflow
+ * occurs, or mark was initially negative, reset the entire array. This is
+ * not an error condition, but an intended function of the Flag workspace.
+ *
+ * workspace: Flag (nrow). Does not modify Flag if nrow is zero.
+ */
+
+UF_long CHOLMOD(clear_flag)
+(
+ cholmod_common *Common
+)
+{
+ Int i, nrow, *Flag ;
+
+ RETURN_IF_NULL_COMMON (-1) ;
+
+ Common->mark++ ;
+ if (Common->mark <= 0)
+ {
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ PRINT2 (("reset Flag: nrow "ID"\n", nrow)) ;
+ PRINT2 (("reset Flag: mark %ld\n", Common->mark)) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Flag [i] = EMPTY ;
+ }
+ Common->mark = 0 ;
+ }
+ return (Common->mark) ;
+}
+
+
+/* ========================================================================== */
+/* ==== cholmod_maxrank ===================================================== */
+/* ========================================================================== */
+
+/* Find a valid value of Common->maxrank. Returns 0 if error, or 2, 4, or 8
+ * if successful. */
+
+size_t CHOLMOD(maxrank) /* returns validated value of Common->maxrank */
+(
+ /* ---- input ---- */
+ size_t n, /* A and L will have n rows */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ size_t maxrank ;
+ RETURN_IF_NULL_COMMON (0) ;
+ maxrank = Common->maxrank ;
+ if (n > 0)
+ {
+ /* Ensure maxrank*n*sizeof(double) does not result in integer overflow.
+ * If n is so large that 2*n*sizeof(double) results in integer overflow
+ * (n = 268,435,455 if an Int is 32 bits), then maxrank will be 0 or 1,
+ * but maxrank will be set to 2 below. 2*n will not result in integer
+ * overflow, and CHOLMOD will run out of memory or safely detect integer
+ * overflow elsewhere.
+ */
+ maxrank = MIN (maxrank, Size_max / (n * sizeof (double))) ;
+ }
+ if (maxrank <= 2)
+ {
+ maxrank = 2 ;
+ }
+ else if (maxrank <= 4)
+ {
+ maxrank = 4 ;
+ }
+ else
+ {
+ maxrank = 8 ;
+ }
+ return (maxrank) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dbound ======================================================= */
+/* ========================================================================== */
+
+/* Ensure the absolute value of a diagonal entry, D (j,j), is greater than
+ * Common->dbound. This routine is not meant for the user to call. It is used
+ * by the various LDL' factorization and update/downdate routines. The
+ * default value of Common->dbound is zero, and in that case this routine is not
+ * called at all. No change is made if D (j,j) is NaN. CHOLMOD does not call
+ * this routine if Common->dbound is NaN.
+ */
+
+double CHOLMOD(dbound) /* returns modified diagonal entry of D */
+(
+ /* ---- input ---- */
+ double dj, /* diagonal entry of D, for LDL' factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double dbound ;
+ RETURN_IF_NULL_COMMON (0) ;
+ if (!IS_NAN (dj))
+ {
+ dbound = Common->dbound ;
+ if (dj < 0)
+ {
+ if (dj > -dbound)
+ {
+ dj = -dbound ;
+ Common->ndbounds_hit++ ;
+ if (Common->status == CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ;
+ }
+ }
+ }
+ else
+ {
+ if (dj < dbound)
+ {
+ dj = dbound ;
+ Common->ndbounds_hit++ ;
+ if (Common->status == CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ;
+ }
+ }
+ }
+ }
+ return (dj) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_complex.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_complex.c
new file mode 100644
index 0000000..8bef584
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_complex.c
@@ -0,0 +1,547 @@
+/* ========================================================================== */
+/* === Core/cholmod_complex ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* If you convert a matrix that contains uninitialized data, valgrind will
+ * complain. This can occur in a factor L which has gaps (a partial
+ * factorization, or after updates that change the nonzero pattern), an
+ * unpacked sparse matrix, a dense matrix with leading dimension d > # of rows,
+ * or any matrix (dense, sparse, triplet, or factor) with more space allocated
+ * than is used. You can safely ignore any of these complaints by valgrind. */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === cholmod_hypot ======================================================== */
+/* ========================================================================== */
+
+/* There is an equivalent routine called hypot in <math.h>, which conforms
+ * to ANSI C99. However, CHOLMOD does not assume that ANSI C99 is available.
+ * You can use the ANSI C99 hypot routine with:
+ *
+ * #include <math.h>
+ * Common->hypotenuse = hypot ;
+ *
+ * Default value of the Common->hypotenuse pointer is cholmod_hypot.
+ *
+ * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately.
+ * The NaN cases for the double relops x >= y and x+y == x are safely ignored.
+ */
+
+double CHOLMOD(hypot) (double x, double y)
+{
+ double s, r ;
+ x = fabs (x) ;
+ y = fabs (y) ;
+ if (x >= y)
+ {
+ if (x + y == x)
+ {
+ s = x ;
+ }
+ else
+ {
+ r = y / x ;
+ s = x * sqrt (1.0 + r*r) ;
+ }
+ }
+ else
+ {
+ if (y + x == y)
+ {
+ s = y ;
+ }
+ else
+ {
+ r = x / y ;
+ s = y * sqrt (1.0 + r*r) ;
+ }
+ }
+ return (s) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_divcomplex =================================================== */
+/* ========================================================================== */
+
+/* c = a/b where c, a, and b are complex. The real and imaginary parts are
+ * passed as separate arguments to this routine. The NaN case is ignored
+ * for the double relop br >= bi. Returns 1 if the denominator is zero,
+ * 0 otherwise. Note that this return value is the single exception to the
+ * rule that all CHOLMOD routines that return int return TRUE if successful
+ * or FALSE otherise.
+ *
+ * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid
+ * underflow and overflow.
+ *
+ * c can be the same variable as a or b.
+ *
+ * Default value of the Common->complex_divide pointer is cholmod_divcomplex.
+ */
+
+int CHOLMOD(divcomplex)
+(
+ double ar, double ai, /* real and imaginary parts of a */
+ double br, double bi, /* real and imaginary parts of b */
+ double *cr, double *ci /* real and imaginary parts of c */
+)
+{
+ double tr, ti, r, den ;
+ if (fabs (br) >= fabs (bi))
+ {
+ r = bi / br ;
+ den = br + r * bi ;
+ tr = (ar + ai * r) / den ;
+ ti = (ai - ar * r) / den ;
+ }
+ else
+ {
+ r = br / bi ;
+ den = r * br + bi ;
+ tr = (ar * r + ai) / den ;
+ ti = (ai * r - ar) / den ;
+ }
+ *cr = tr ;
+ *ci = ti ;
+ return (IS_ZERO (den)) ;
+}
+
+
+/* ========================================================================== */
+/* === change_complexity ==================================================== */
+/* ========================================================================== */
+
+/* X and Z represent an array of size nz, with numeric xtype given by xtype_in.
+ *
+ * If xtype_in is:
+ * CHOLMOD_PATTERN: X and Z must be NULL.
+ * CHOLMOD_REAL: X is of size nz, Z must be NULL.
+ * CHOLMOD_COMPLEX: X is of size 2*nz, Z must be NULL.
+ * CHOLMOD_ZOMPLEX: X is of size nz, Z is of size nz.
+ *
+ * The array is changed into the numeric xtype given by xtype_out, with the
+ * same definitions of X and Z above. Note that the input conditions, above,
+ * are not checked. These are checked in the caller routine.
+ *
+ * Returns TRUE if successful, FALSE otherwise. X and Z are not modified if
+ * not successful.
+ */
+
+static int change_complexity
+(
+ /* ---- input ---- */
+ Int nz, /* size of X and/or Z */
+ int xtype_in, /* xtype of X and Z on input */
+ int xtype_out, /* requested xtype of X and Z on output */
+ int xtype1, /* xtype_out must be in the range [xtype1 .. xtype2] */
+ int xtype2,
+ /* ---- in/out --- */
+ void **XX, /* old X on input, new X on output */
+ void **ZZ, /* old Z on input, new Z on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Xold, *Zold, *Xnew, *Znew ;
+ Int k ;
+ size_t nz2 ;
+
+ if (xtype_out < xtype1 || xtype_out > xtype2)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid xtype") ;
+ return (FALSE) ;
+ }
+
+ Common->status = CHOLMOD_OK ;
+ Xold = *XX ;
+ Zold = *ZZ ;
+
+ switch (xtype_in)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* converting from pattern */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_PATTERN:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* pattern -> real */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_REAL:
+ /* allocate X and set to all ones */
+ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [k] = 1 ;
+ }
+ *XX = Xnew ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* pattern -> complex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_COMPLEX:
+ /* allocate X and set to all ones */
+ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [2*k ] = 1 ;
+ Xnew [2*k+1] = 0 ;
+ }
+ *XX = Xnew ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* pattern -> zomplex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_ZOMPLEX:
+ /* allocate X and Z and set to all ones */
+ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ;
+ CHOLMOD(free) (nz, sizeof (double), Znew, Common) ;
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [k] = 1 ;
+ Znew [k] = 0 ;
+ }
+ *XX = Xnew ;
+ *ZZ = Znew ;
+ break ;
+ }
+ break ;
+
+ /* ------------------------------------------------------------------ */
+ /* converting from real */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_REAL:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* real -> pattern */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_PATTERN:
+ /* free X */
+ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* real -> complex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_COMPLEX:
+ /* allocate a new X and copy the old X */
+ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [2*k ] = Xold [k] ;
+ Xnew [2*k+1] = 0 ;
+ }
+ CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ *XX = Xnew ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* real -> zomplex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_ZOMPLEX:
+ /* allocate a new Z and set it to zero */
+ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Znew [k] = 0 ;
+ }
+ *ZZ = Znew ;
+ break ;
+ }
+ break ;
+
+ /* ------------------------------------------------------------------ */
+ /* converting from complex */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_COMPLEX:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* complex -> pattern */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_PATTERN:
+ /* free X */
+ *XX = CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* complex -> real */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_REAL:
+ /* pack the real part of X, discarding the imaginary part */
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xold [k] = Xold [2*k] ;
+ }
+ /* shrink X in half (this cannot fail) */
+ nz2 = 2*nz ;
+ *XX = CHOLMOD(realloc) (nz, sizeof (double), *XX, &nz2,
+ Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* complex -> zomplex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_ZOMPLEX:
+ /* allocate X and Z and copy the old X into them */
+ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ;
+ CHOLMOD(free) (nz, sizeof (double), Znew, Common) ;
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [k] = Xold [2*k ] ;
+ Znew [k] = Xold [2*k+1] ;
+ }
+ CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ;
+ *XX = Xnew ;
+ *ZZ = Znew ;
+ break ;
+ }
+ break ;
+
+ /* ------------------------------------------------------------------ */
+ /* converting from zomplex */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* zomplex -> pattern */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_PATTERN:
+ /* free X and Z */
+ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* zomplex -> real */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_REAL:
+ /* free the imaginary part */
+ *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* zomplex -> complex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_COMPLEX:
+ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [2*k ] = Xold [k] ;
+ Xnew [2*k+1] = Zold [k] ;
+ }
+ CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ;
+ *XX = Xnew ;
+ *ZZ = NULL ;
+ break ;
+
+ }
+ break ;
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sparse_xtype ================================================= */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a sparse matrix. Supports any type on input
+ * and output (pattern, real, complex, or zomplex). */
+
+int CHOLMOD(sparse_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* sparse matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+
+ ok = change_complexity (A->nzmax, A->xtype, to_xtype,
+ CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(A->x), &(A->z), Common) ;
+ if (ok)
+ {
+ A->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_triplet_xtype ================================================ */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a triplet matrix. Supports any type on input
+ * and output (pattern, real, complex, or zomplex). */
+
+int CHOLMOD(triplet_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (T, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ ok = change_complexity (T->nzmax, T->xtype, to_xtype,
+ CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(T->x), &(T->z), Common) ;
+ if (ok)
+ {
+ T->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dense_xtype ================================================= */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a dense matrix. Supports real, complex or
+ * zomplex on input and output */
+
+int CHOLMOD(dense_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_dense *X, /* dense matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ ok = change_complexity (X->nzmax, X->xtype, to_xtype,
+ CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(X->x), &(X->z), Common) ;
+ if (ok)
+ {
+ X->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_factor_xtype ================================================= */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a factor. Supports real, complex or zomplex on
+ * input and output. Supernodal zomplex factors are not supported. */
+
+int CHOLMOD(factor_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (L->is_super &&
+ (L->xtype == CHOLMOD_ZOMPLEX || to_xtype == CHOLMOD_ZOMPLEX))
+ {
+ ERROR (CHOLMOD_INVALID, "invalid xtype for supernodal L") ;
+ return (FALSE) ;
+ }
+ ok = change_complexity ((L->is_super ? L->xsize : L->nzmax), L->xtype,
+ to_xtype, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(L->x), &(L->z), Common) ;
+ if (ok)
+ {
+ L->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_copy.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_copy.c
new file mode 100644
index 0000000..d4532ad
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_copy.c
@@ -0,0 +1,407 @@
+/* ========================================================================== */
+/* === Core/cholmod_copy ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = A, which allocates C and copies A into C, with possible change of
+ * stype. The diagonal can optionally be removed. The numerical entries
+ * can optionally be copied. This routine differs from cholmod_copy_sparse,
+ * which makes an exact copy of a sparse matrix.
+ *
+ * A can be of any type (packed/unpacked, upper/lower/unsymmetric). C is
+ * packed and can be of any stype (upper/lower/unsymmetric), except that if
+ * A is rectangular C can only be unsymmetric. If the stype of A and C
+ * differ, then the appropriate conversion is made.
+ *
+ * Symmetry of A (A->stype):
+ * <0: lower: assume A is symmetric with just tril(A); the rest of A is ignored
+ * 0 unsym: assume A is unsymmetric; consider all entries in A
+ * >0 upper: assume A is symmetric with just triu(A); the rest of A is ignored
+ *
+ * Symmetry of C (stype parameter):
+ * <0 lower: return just tril(C)
+ * 0 unsym: return all of C
+ * >0 upper: return just triu(C)
+ *
+ * In MATLAB: Using cholmod_copy:
+ * ---------- ----------------------------
+ * C = A ; A unsymmetric, C unsymmetric
+ * C = tril (A) ; A unsymmetric, C lower
+ * C = triu (A) ; A unsymmetric, C upper
+ * U = triu (A) ; L = tril (U',-1) ; C = L+U ; A upper, C unsymmetric
+ * C = triu (A)' ; A upper, C lower
+ * C = triu (A) ; A upper, C upper
+ * L = tril (A) ; U = triu (L',1) ; C = L+U ; A lower, C unsymmetric
+ * C = tril (A) ; A lower, C lower
+ * C = tril (A)' ; A lower, C upper
+ *
+ * workspace: Iwork (max (nrow,ncol))
+ *
+ * A can have an xtype of pattern or real. Complex and zomplex cases only
+ * supported when mode <= 0 (in which case the numerical values are ignored).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === copy_sym_to_unsym ==================================================== */
+/* ========================================================================== */
+
+/* Construct an unsymmetric copy of a symmetric sparse matrix. This does the
+ * work for as C = cholmod_copy (A, 0, mode, Common) when A is symmetric.
+ * In this case, extra space can be added to C.
+ */
+
+static cholmod_sparse *copy_sym_to_unsym
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag)
+ * -2: pattern only, no diagonal, add 50% + n extra
+ * space to C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double aij ;
+ double *Ax, *Cx ;
+ Int *Ap, *Ai, *Anz, *Cp, *Ci, *Wj, *Iwork ;
+ cholmod_sparse *C ;
+ Int nrow, ncol, nz, packed, j, p, pend, i, pc, up, lo, values, diag,
+ astype, extra ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ packed = A->packed ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ diag = (mode >= 0) ;
+
+ astype = SIGN (A->stype) ;
+ up = (astype > 0) ;
+ lo = (astype < 0) ;
+ ASSERT (astype != 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create an unsymmetric copy of a symmetric matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wj = Iwork ; /* size ncol (i/i/l) */
+
+ /* In MATLAB notation, for converting a symmetric/upper matrix:
+ * U = triu (A) ;
+ * L = tril (U',-1) ;
+ * C = L + U ;
+ *
+ * For converting a symmetric/lower matrix to unsymmetric:
+ * L = tril (A) ;
+ * U = triu (L',1) ;
+ * C = L + U ;
+ */
+ ASSERT (up || lo) ;
+ PRINT1 (("copy: convert symmetric to unsym\n")) ;
+
+ /* count the number of entries in each column of C */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wj [j] = 0 ;
+ }
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* the diagonal entry A(i,i) will appear just once
+ * (unless it is excluded with mode < 0) */
+ if (diag)
+ {
+ Wj [j]++ ;
+ }
+ }
+ else if ((up && i < j) || (lo && i > j))
+ {
+ /* upper case: A(i,j) is in the strictly upper part;
+ * A(j,i) will be added to the strictly lower part of C.
+ * lower case is the opposite. */
+ Wj [j]++ ;
+ Wj [i]++ ;
+ }
+ }
+ }
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ nz += Wj [j] ;
+ }
+
+ extra = (mode == -2) ? (nz/2 + ncol) : 0 ;
+
+ /* allocate C. C is sorted if and only if A is sorted */
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz + extra, A->sorted, TRUE, 0,
+ values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ;
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* construct the column pointers for C */
+ p = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cp [j] = p ;
+ p += Wj [j] ;
+ }
+ Cp [ncol] = p ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wj [j] = Cp [j] ;
+ }
+
+ /* construct C */
+ if (values)
+ {
+
+ /* pattern and values */
+ ASSERT (diag) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ aij = Ax [p] ;
+ if (i == j)
+ {
+ /* add diagonal entry A(i,i) to column i */
+ pc = Wj [i]++ ;
+ Ci [pc] = i ;
+ Cx [pc] = aij ;
+ }
+ else if ((up && i < j) || (lo && i > j))
+ {
+ /* add A(i,j) to column j */
+ pc = Wj [j]++ ;
+ Ci [pc] = i ;
+ Cx [pc] = aij ;
+ /* add A(j,i) to column i */
+ pc = Wj [i]++ ;
+ Ci [pc] = j ;
+ Cx [pc] = aij ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* pattern only, possibly excluding the diagonal */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* add diagonal entry A(i,i) to column i
+ * (unless it is excluded with mode < 0) */
+ if (diag)
+ {
+ Ci [Wj [i]++] = i ;
+ }
+ }
+ else if ((up && i < j) || (lo && i > j))
+ {
+ /* add A(i,j) to column j */
+ Ci [Wj [j]++] = i ;
+ /* add A(j,i) to column i */
+ Ci [Wj [i]++] = j ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (i = CHOLMOD(dump_sparse) (C, "copy_sym_to_unsym", Common)) ;
+ PRINT1 (("mode %d nnzdiag "ID"\n", mode, i)) ;
+ ASSERT (IMPLIES (mode < 0, i == 0)) ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy ========================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(copy)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ int stype, /* requested stype of C */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *C ;
+ Int nrow, ncol, up, lo, values, diag, astype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ if ((stype || A->stype) && nrow != ncol)
+ {
+ /* inputs invalid */
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ diag = (mode >= 0) ;
+ astype = SIGN (A->stype) ;
+ stype = SIGN (stype) ;
+ up = (astype > 0) ;
+ lo = (astype < 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (astype == stype)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetry of A and C are the same */
+ /* ------------------------------------------------------------------ */
+
+ /* copy A into C, keeping the same symmetry. If A is symmetric
+ * entries in the ignored part of A are not copied into C */
+ C = CHOLMOD(band) (A, -nrow, ncol, mode, Common) ;
+
+ }
+ else if (!astype)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert unsymmetric matrix A into a symmetric matrix C */
+ /* ------------------------------------------------------------------ */
+
+ if (stype > 0)
+ {
+ /* C = triu (A) */
+ C = CHOLMOD(band) (A, 0, ncol, mode, Common) ;
+ }
+ else
+ {
+ /* C = tril (A) */
+ C = CHOLMOD(band) (A, -nrow, 0, mode, Common) ;
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ C->stype = stype ;
+
+ }
+ else if (astype == -stype)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* transpose a symmetric matrix */
+ /* ------------------------------------------------------------------ */
+
+ /* converting upper to lower or lower to upper */
+ /* workspace: Iwork (nrow) */
+ C = CHOLMOD(transpose) (A, values, Common) ;
+ if (!diag)
+ {
+ /* remove diagonal, if requested */
+ CHOLMOD(band_inplace) (-nrow, ncol, -1, C, Common) ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create an unsymmetric copy of a symmetric matrix */
+ /* ------------------------------------------------------------------ */
+
+ C = copy_sym_to_unsym (A, mode, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return if error */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (diag = CHOLMOD(dump_sparse) (C, "copy", Common)) ;
+ PRINT1 (("mode %d nnzdiag "ID"\n", mode, diag)) ;
+ ASSERT (IMPLIES (mode < 0, diag == 0)) ;
+ return (C) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_dense.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_dense.c
new file mode 100644
index 0000000..57cb6de
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_dense.c
@@ -0,0 +1,640 @@
+/* ========================================================================== */
+/* === Core/cholmod_dense =================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_dense object:
+ *
+ * The solve routines and some of the MatrixOps and Modify routines use dense
+ * matrices as inputs. These are held in column-major order. With a leading
+ * dimension of d, the entry in row i and column j is held in x [i+j*d].
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_allocate_dense allocate a dense matrix
+ * cholmod_free_dense free a dense matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_zeros allocate a dense matrix of all zeros
+ * cholmod_ones allocate a dense matrix of all ones
+ * cholmod_eye allocate a dense identity matrix
+ * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix
+ * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix
+ * cholmod_copy_dense create a copy of a dense matrix
+ * cholmod_copy_dense2 copy a dense matrix (pre-allocated)
+ *
+ * All routines in this file can handle the real, complex, and zomplex cases.
+ * Pattern-only dense matrices are not supported. cholmod_sparse_to_dense can
+ * take a pattern-only input sparse matrix, however, and cholmod_dense_to_sparse
+ * can generate a pattern-only output sparse matrix.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define PATTERN
+#include "t_cholmod_dense.c"
+#define REAL
+#include "t_cholmod_dense.c"
+#define COMPLEX
+#include "t_cholmod_dense.c"
+#define ZOMPLEX
+#include "t_cholmod_dense.c"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_dense =============================================== */
+/* ========================================================================== */
+
+/* Allocate a dense matrix with leading dimension d. The space is not
+ * initialized.
+ */
+
+cholmod_dense *CHOLMOD(allocate_dense)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ size_t d, /* leading dimension */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ size_t nzmax, nzmax0 ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (d < nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "leading dimension invalid") ;
+ return (NULL) ;
+ }
+ if (xtype < CHOLMOD_REAL || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (NULL) ;
+ }
+
+ /* ensure the dimensions do not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ;
+
+ /* nzmax = MAX (1, d*ncol) ; */
+ nzmax = CHOLMOD(mult_size_t) (d, ncol, &ok) ;
+ nzmax = MAX (1, nzmax) ;
+
+ if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate header */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(malloc) (sizeof (cholmod_dense), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ PRINT1 (("cholmod_allocate_dense %d-by-%d nzmax %d xtype %d\n",
+ nrow, ncol, nzmax, xtype)) ;
+
+ X->nrow = nrow ;
+ X->ncol = ncol ;
+ X->nzmax = nzmax ;
+ X->xtype = xtype ;
+ X->dtype = DTYPE ;
+ X->x = NULL ;
+ X->z = NULL ;
+ X->d = d ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix itself */
+ /* ---------------------------------------------------------------------- */
+
+ nzmax0 = 0 ;
+ CHOLMOD(realloc_multiple) (nzmax, 0, xtype, NULL, NULL, &(X->x), &(X->z),
+ &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_dense) (&X, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_zeros ======================================================== */
+/* ========================================================================== */
+
+/* Allocate a dense matrix and set it to zero */
+
+cholmod_dense *CHOLMOD(zeros)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a dense matrix and set it to zero */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* NULL Common, out of memory, or inputs invalid */
+ }
+
+ Xx = X->x ;
+ Xz = X->z ;
+ nz = MAX (1, X->nzmax) ;
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < 2*nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xz [i] = 0 ;
+ }
+ break ;
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_ones ========================================================= */
+/* ========================================================================== */
+
+/* Allocate a dense matrix and set it to zero */
+
+cholmod_dense *CHOLMOD(ones)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a dense matrix and set it to all ones */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* NULL Common, out of memory, or inputs invalid */
+ }
+
+ Xx = X->x ;
+ Xz = X->z ;
+ nz = MAX (1, X->nzmax) ;
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [2*i ] = 1 ;
+ Xx [2*i+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 1 ;
+ }
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xz [i] = 0 ;
+ }
+ break ;
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_eye ========================================================== */
+/* ========================================================================== */
+
+/* Allocate a dense matrix and set it to the identity matrix */
+
+cholmod_dense *CHOLMOD(eye)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, n, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a dense matrix and set it to the identity matrix */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* NULL Common, out of memory, or inputs invalid */
+ }
+
+ nz = MAX (1, nrow*ncol) ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ n = MIN (nrow, ncol) ;
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i + i*nrow] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2 * (i + i*nrow)] = 1 ;
+ }
+ break ;
+ }
+
+ return (X) ;
+}
+
+/* ========================================================================== */
+/* === cholmod_free_dense =================================================== */
+/* ========================================================================== */
+
+/* free a dense matrix
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_dense)
+(
+ /* ---- in/out --- */
+ cholmod_dense **XHandle, /* dense matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (XHandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ X = *XHandle ;
+ if (X == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ X->x = CHOLMOD(free) (X->nzmax, 2*sizeof (double), X->x, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ;
+ X->z = CHOLMOD(free) (X->nzmax, sizeof (double), X->z, Common) ;
+ break ;
+ }
+
+ *XHandle = CHOLMOD(free) (1, sizeof (cholmod_dense), (*XHandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sparse_to_dense ============================================== */
+/* ========================================================================== */
+
+/* Convert a sparse matrix to a dense matrix.
+ * The output dense matrix has the same xtype as the input sparse matrix,
+ * except that a pattern-only sparse matrix A is converted into a real dense
+ * matrix X, with 1's and 0's. All xtypes are supported.
+ */
+
+cholmod_dense *CHOLMOD(sparse_to_dense)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype && A->nrow != A->ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_PATTERN:
+ X = p_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+
+ case CHOLMOD_REAL:
+ X = r_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ X = c_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ X = z_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+ }
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dense_to_sparse ============================================== */
+/* ========================================================================== */
+
+/* Convert a dense matrix to a sparse matrix, similar to the MATLAB statements:
+ *
+ * C = sparse (X) values = TRUE
+ * C = spones (sparse (X)) values = FALSE
+ *
+ * except that X must be double (it can be of many different types in MATLAB)
+ *
+ * The resulting sparse matrix C has the same numeric xtype as the input dense
+ * matrix X, unless "values" is FALSE (in which case C is real, where C(i,j)=1
+ * if (i,j) is an entry in X.
+ */
+
+cholmod_sparse *CHOLMOD(dense_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ int values, /* TRUE if values to be copied, FALSE otherwise */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *C = NULL ;
+
+ DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (X, NULL) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ if (X->d < X->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ C = r_cholmod_dense_to_sparse (X, values, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ C = c_cholmod_dense_to_sparse (X, values, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ C = z_cholmod_dense_to_sparse (X, values, Common) ;
+ break ;
+ }
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_dense2 ================================================== */
+/* ========================================================================== */
+
+/* Y = X, where X and Y are both already allocated. The leading dimensions of
+ * X and Y may differ, but both must be >= the # of rows in X and Y.
+ * Entries in rows nrow to d-1 are not copied from X, since the space might not
+ * be initialized. Y->nzmax is unchanged. X->nzmax is typically
+ * (X->d)*(X->ncol), but a user might modify that condition outside of any
+ * CHOLMOD routine.
+ *
+ * The two dense matrices X and Y must have the same numeric xtype.
+ */
+
+int CHOLMOD(copy_dense2)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* ---- output --- */
+ cholmod_dense *Y, /* copy of matrix X */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (Y, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (X->nrow != Y->nrow || X->ncol != Y->ncol || X->xtype != Y->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "X and Y must have same dimensions and xtype") ;
+ return (FALSE) ;
+ }
+ if (X->d < X->nrow || Y->d < Y->nrow
+ || (X->d * X->ncol) > X->nzmax || (Y->d * Y->ncol) > Y->nzmax)
+ {
+ ERROR (CHOLMOD_INVALID, "X and/or Y invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ r_cholmod_copy_dense2 (X, Y) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_cholmod_copy_dense2 (X, Y) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_cholmod_copy_dense2 (X, Y) ;
+ break ;
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_dense =================================================== */
+/* ========================================================================== */
+
+/* Y = X, copy a dense matrix */
+
+cholmod_dense *CHOLMOD(copy_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *Y ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (X, NULL) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate result */
+ /* ---------------------------------------------------------------------- */
+
+ Y = CHOLMOD(allocate_dense) (X->nrow, X->ncol, X->d, X->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory or X invalid */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = X */
+ /* ---------------------------------------------------------------------- */
+
+ /* This cannot fail (X and Y are allocated, and have the same nrow, ncol
+ * d, and xtype) */
+ CHOLMOD(copy_dense2) (X, Y, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ return (Y) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_error.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_error.c
new file mode 100644
index 0000000..b1e5d4c
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_error.c
@@ -0,0 +1,80 @@
+/* ========================================================================== */
+/* === Core/cholmod_error =================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD error-handling routine. */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* ==== cholmod_error ======================================================= */
+/* ========================================================================== */
+
+/* An error has occurred. Set the status, optionally print an error message,
+ * and call the user error-handling routine (if it exists). If
+ * Common->try_catch is TRUE, then CHOLMOD is inside a try/catch block.
+ * The status is set, but no message is printed and the user error handler
+ * is not called. This is not (yet) an error, since CHOLMOD may recover.
+ *
+ * In the current version, this try/catch mechanism is used internally only in
+ * cholmod_analyze, which tries multiple ordering methods and picks the best
+ * one. If one or more ordering method fails, it keeps going. Only one
+ * ordering needs to succeed for cholmod_analyze to succeed.
+ */
+
+int CHOLMOD(error)
+(
+ /* ---- input ---- */
+ int status, /* error status */
+ char *file, /* name of source code file where error occured */
+ int line, /* line number in source code file where error occured*/
+ char *message, /* error message */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ Common->status = status ;
+
+ if (!(Common->try_catch))
+ {
+
+#ifndef NPRINT
+ /* print a warning or error message */
+ if (Common->print_function != NULL)
+ {
+ if (status > 0 && Common->print > 1)
+ {
+ (Common->print_function) ("CHOLMOD warning: %s\n", message) ;
+ fflush (stdout) ;
+ fflush (stderr) ;
+ }
+ else if (Common->print > 0)
+ {
+ (Common->print_function) ("CHOLMOD error: %s\n", message) ;
+ fflush (stdout) ;
+ fflush (stderr) ;
+ }
+ }
+#endif
+
+ /* call the user error handler, if it exists */
+ if (Common->error_handler != NULL)
+ {
+ Common->error_handler (status, file, line, message) ;
+ }
+ }
+
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_factor.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_factor.c
new file mode 100644
index 0000000..8af9b38
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_factor.c
@@ -0,0 +1,935 @@
+/* ========================================================================== */
+/* === Core/cholmod_factor ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_factor object:
+ *
+ * The data structure for an LL' or LDL' factorization is too complex to
+ * describe in one sentence. This object can hold the symbolic analysis alone,
+ * or in combination with a "simplicial" (similar to a sparse matrix) or
+ * "supernodal" form of the numerical factorization. Only the routine to free
+ * a factor is primary, since a factor object is created by the factorization
+ * routine (cholmod_factorize). It must be freed with cholmod_free_factor.
+ *
+ * Primary routine:
+ * ----------------
+ * cholmod_free_factor free a factor
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_allocate_factor allocate a symbolic factor (LL' or LDL')
+ * cholmod_reallocate_factor change the # entries in a factor
+ * cholmod_change_factor change the type of factor (e.g., LDL' to LL')
+ * cholmod_pack_factor pack the columns of a factor
+ * cholmod_reallocate_column resize a single column of a factor
+ * cholmod_factor_to_sparse create a sparse matrix copy of a factor
+ * cholmod_copy_factor create a copy of a factor
+ *
+ * Note that there is no cholmod_sparse_to_factor routine to create a factor
+ * as a copy of a sparse matrix. It could be done, after a fashion, but a
+ * lower triangular sparse matrix would not necessarily have a chordal graph,
+ * which would break the many CHOLMOD routines that rely on this property.
+ *
+ * The cholmod_factor_to_sparse routine is provided so that matrix operations
+ * in the MatrixOps module may be applied to L. Those operations operate on
+ * cholmod_sparse objects, and they are not guaranteed to maintain the chordal
+ * property of L. Such a modified L cannot be safely converted back to a
+ * cholmod_factor object.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_factor ============================================== */
+/* ========================================================================== */
+
+/* Allocate a simplicial symbolic factor, with L->Perm and L->ColCount allocated
+ * and initialized to "empty" values (Perm [k] = k, and ColCount[k] = 1).
+ * The integer and numerical parts of L are not allocated. L->xtype is returned
+ * as CHOLMOD_PATTERN and L->is_super are returned as FALSE. L->is_ll is also
+ * returned FALSE, but this may be modified when the matrix is factorized.
+ *
+ * This is sufficient (but far from ideal) for input to cholmod_factorize,
+ * since the simplicial LL' or LDL' factorization (cholmod_rowfac) can
+ * reallocate the columns of L as needed. The primary purpose of this routine
+ * is to allocate space for a symbolic factorization, for the "expert" user to
+ * do his or her own symbolic analysis. The typical user should use
+ * cholmod_analyze instead of this routine.
+ *
+ * workspace: none
+ */
+
+cholmod_factor *CHOLMOD(allocate_factor)
+(
+ /* ---- input ---- */
+ size_t n, /* L is n-by-n */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int j ;
+ Int *Perm, *ColCount ;
+ cholmod_factor *L ;
+ int ok = TRUE ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ensure the dimension does not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (n, 2, &ok) ;
+ if (!ok || n > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ L = CHOLMOD(malloc) (sizeof (cholmod_factor), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ L->n = n ;
+ L->is_ll = FALSE ;
+ L->is_super = FALSE ;
+ L->is_monotonic = TRUE ;
+ L->itype = ITYPE ;
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+
+ /* allocate the purely symbolic part of L */
+ L->ordering = CHOLMOD_NATURAL ;
+ L->Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ L->ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+
+ /* simplicial part of L is empty */
+ L->nzmax = 0 ;
+ L->p = NULL ;
+ L->i = NULL ;
+ L->x = NULL ;
+ L->z = NULL ;
+ L->nz = NULL ;
+ L->next = NULL ;
+ L->prev = NULL ;
+
+ /* supernodal part of L is also empty */
+ L->nsuper = 0 ;
+ L->ssize = 0 ;
+ L->xsize = 0 ;
+ L->maxesize = 0 ;
+ L->maxcsize = 0 ;
+ L->super = NULL ;
+ L->pi = NULL ;
+ L->px = NULL ;
+ L->s = NULL ;
+
+ /* L has not been factorized */
+ L->minor = n ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_factor) (&L, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ /* initialize Perm and ColCount */
+ Perm = L->Perm ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ Perm [j] = j ;
+ }
+ ColCount = L->ColCount ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ ColCount [j] = 1 ;
+ }
+
+ return (L) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_factor ================================================== */
+/* ========================================================================== */
+
+/* Free a factor object.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_factor)
+(
+ /* ---- in/out --- */
+ cholmod_factor **LHandle, /* factor to free, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int n, lnz, xs, ss, s ;
+ cholmod_factor *L ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (LHandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ L = *LHandle ;
+ if (L == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ n = L->n ;
+ lnz = L->nzmax ;
+ s = L->nsuper + 1 ;
+ xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ;
+ ss = L->ssize ;
+
+ /* symbolic part of L */
+ CHOLMOD(free) (n, sizeof (Int), L->Perm, Common) ;
+ CHOLMOD(free) (n, sizeof (Int), L->ColCount, Common) ;
+
+ /* simplicial form of L */
+ CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ;
+ CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ;
+ CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ;
+ CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ;
+ CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ;
+
+ /* supernodal form of L */
+ CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ;
+ CHOLMOD(free) (s, sizeof (Int), L->px, Common) ;
+ CHOLMOD(free) (s, sizeof (Int), L->super, Common) ;
+ CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ;
+
+ /* numerical values for both simplicial and supernodal L */
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ CHOLMOD(free) (xs, sizeof (double), L->x, Common) ;
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ CHOLMOD(free) (xs, 2*sizeof (double), L->x, Common) ;
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ CHOLMOD(free) (xs, sizeof (double), L->x, Common) ;
+ CHOLMOD(free) (xs, sizeof (double), L->z, Common) ;
+ }
+
+ *LHandle = CHOLMOD(free) (1, sizeof (cholmod_factor), (*LHandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_factor ============================================ */
+/* ========================================================================== */
+
+/* Change the size of L->i and L->x, or allocate them if their current size
+ * is zero. L must be simplicial.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_factor)
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ PRINT1 (("realloc factor: xtype %d\n", L->xtype)) ;
+ if (L->is_super)
+ {
+ /* L must be simplicial, and not symbolic */
+ ERROR (CHOLMOD_INVALID, "L invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ PRINT1 (("realloc factor %g to %g\n", (double) L->nzmax, (double) nznew)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* resize (or allocate) the L->i and L->x components of the factor */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(realloc_multiple) (nznew, 1, L->xtype, &(L->i), NULL,
+ &(L->x), &(L->z), &(L->nzmax), Common) ;
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_column =========================================== */
+/* ========================================================================== */
+
+/* Column j needs more space, reallocate it at the end of L->i and L->x.
+ * If the reallocation fails, the factor is converted to a simplicial
+ * symbolic factor (no pattern, just L->Perm and L->ColCount).
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_column)
+(
+ /* ---- input ---- */
+ size_t j, /* the column to reallocate */
+ size_t need, /* required size of column j */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double xneed ;
+ double *Lx, *Lz ;
+ Int *Lp, *Lprev, *Lnext, *Li, *Lnz ;
+ Int n, pold, pnew, len, k, tail ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (L->is_super)
+ {
+ ERROR (CHOLMOD_INVALID, "L must be simplicial") ;
+ return (FALSE) ;
+ }
+ n = L->n ;
+ if (j >= L->n || need == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "j invalid") ;
+ return (FALSE) ; /* j out of range */
+ }
+ Common->status = CHOLMOD_OK ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "start colrealloc", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* increase the size of L if needed */
+ /* ---------------------------------------------------------------------- */
+
+ /* head = n+1 ; */
+ tail = n ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+ Lprev = L->prev ;
+ Lnext = L->next ;
+
+ ASSERT (Lnz != NULL) ;
+ ASSERT (Lnext != NULL && Lprev != NULL) ;
+ PRINT1 (("col %g need %g\n", (double) j, (double) need)) ;
+
+ /* column j cannot have more than n-j entries if all entries are present */
+ need = MIN (need, n-j) ;
+
+ /* compute need in double to avoid integer overflow */
+ if (Common->grow1 >= 1.0)
+ {
+ xneed = (double) need ;
+ xneed = Common->grow1 * xneed + Common->grow2 ;
+ xneed = MIN (xneed, n-j) ;
+ need = (Int) xneed ;
+ }
+ PRINT1 (("really new need %g current %g\n", (double) need,
+ (double) (Lp [Lnext [j]] - Lp [j]))) ;
+ ASSERT (need >= 1 && need <= n-j) ;
+
+ if (Lp [Lnext [j]] - Lp [j] >= (Int) need)
+ {
+ /* no need to reallocate the column, it's already big enough */
+ PRINT1 (("colrealloc: quick return %g %g\n",
+ (double) (Lp [Lnext [j]] - Lp [j]), (double) need)) ;
+ return (TRUE) ;
+
+ }
+
+ if (Lp [tail] + need > L->nzmax)
+ {
+ /* use double to avoid integer overflow */
+ xneed = (double) need ;
+ if (Common->grow0 < 1.2) /* fl. pt. compare, false if NaN */
+ {
+ /* if grow0 is less than 1.2 or NaN, don't use it */
+ xneed = 1.2 * (((double) L->nzmax) + xneed + 1) ;
+ }
+ else
+ {
+ xneed = Common->grow0 * (((double) L->nzmax) + xneed + 1) ;
+ }
+ if (xneed > Size_max ||
+ !CHOLMOD(reallocate_factor) ((Int) xneed, L, Common))
+ {
+ /* out of memory, convert to simplicial symbolic */
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, L->is_ll, FALSE, TRUE,
+ TRUE, L, Common) ;
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory; L now symbolic") ;
+ return (FALSE) ; /* out of memory */
+ }
+ PRINT1 (("\n=== GROW L from %g to %g\n",
+ (double) L->nzmax, (double) xneed)) ;
+ /* pack all columns so that each column has at most grow2 free space */
+ CHOLMOD(pack_factor) (L, Common) ;
+ ASSERT (Common->status == CHOLMOD_OK) ;
+ Common->nrealloc_factor++ ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reallocate the column */
+ /* ---------------------------------------------------------------------- */
+
+ Common->nrealloc_col++ ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+
+ /* remove j from its current position in the list */
+ Lnext [Lprev [j]] = Lnext [j] ;
+ Lprev [Lnext [j]] = Lprev [j] ;
+
+ /* place j at the end of the list */
+ Lnext [Lprev [tail]] = j ;
+ Lprev [j] = Lprev [tail] ;
+ Lnext [j] = n ;
+ Lprev [tail] = j ;
+
+ /* L is no longer monotonic; columns are out-of-order */
+ L->is_monotonic = FALSE ;
+
+ /* allocate space for column j */
+ pold = Lp [j] ;
+ pnew = Lp [tail] ;
+ Lp [j] = pnew ;
+ Lp [tail] += need ;
+
+ /* copy column j to the new space */
+ len = Lnz [j] ;
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ }
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ;
+ Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ Lz [pnew + k] = Lz [pold + k] ;
+ }
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "colrealloc done", Common)) ;
+
+ /* successful reallocation of column j of L */
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_pack_factor ================================================== */
+/* ========================================================================== */
+
+/* Pack the columns of a simplicial LDL' or LL' factor. This can be followed
+ * by a call to cholmod_reallocate_factor to reduce the size of L to the exact
+ * size required by the factor, if desired. Alternatively, you can leave the
+ * size of L->i and L->x the same, to allow space for future updates/rowadds.
+ *
+ * Each column is reduced in size so that it has at most Common->grow2 free
+ * space at the end of the column.
+ *
+ * Does nothing and returns silently if given any other type of factor.
+ *
+ * Does NOT force the columns of L to be monotonic. It thus differs from
+ * cholmod_change_factor (xtype, -, FALSE, TRUE, TRUE, L, Common), which
+ * packs the columns and ensures that they appear in monotonic order.
+ */
+
+int CHOLMOD(pack_factor)
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz, *Lnext ;
+ Int pnew, j, k, pold, len, n, head, tail, grow2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start pack", Common)) ;
+ PRINT1 (("PACK factor %d\n", L->is_super)) ;
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super)
+ {
+ /* nothing to do unless L is simplicial numeric */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* pack */
+ /* ---------------------------------------------------------------------- */
+
+ grow2 = Common->grow2 ;
+ PRINT1 (("\nPACK grow2 "ID"\n", grow2)) ;
+
+ pnew = 0 ;
+ n = L->n ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+
+ head = n+1 ;
+ tail = n ;
+
+ for (j = Lnext [head] ; j != tail ; j = Lnext [j])
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+ ASSERT (len > 0) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+ if (pnew < pold)
+ {
+ PRINT2 ((" pack this column\n")) ;
+
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ }
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ;
+ Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ Lz [pnew + k] = Lz [pold + k] ;
+ }
+ }
+
+ Lp [j] = pnew ;
+ }
+ len = MIN (len + grow2, n - j) ;
+ pnew = MIN (Lp [j] + len, Lp [Lnext [j]]) ;
+ }
+ PRINT2 (("final pnew = "ID"\n", pnew)) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_factor_to_sparse ============================================= */
+/* ========================================================================== */
+
+/* Constructs a column-oriented sparse matrix containing the pattern and values
+ * of a simplicial or supernodal numerical factor, and then converts the factor
+ * into a simplicial symbolic factor. If L is already packed, monotonic,
+ * and simplicial (which is the case when cholmod_factorize uses the simplicial
+ * Cholesky factorization algorithm) then this routine requires only O(1)
+ * memory and takes O(1) time.
+ *
+ * Only operates on numeric factors (real, complex, or zomplex). Does not
+ * change the numeric L->xtype (the resulting sparse matrix has the same xtype
+ * as L). If this routine fails, L is left unmodified.
+ */
+
+cholmod_sparse *CHOLMOD(factor_to_sparse)
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to copy, converted to symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *Lsparse ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start convert to matrix", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to packed, monotonic, simplicial, numeric */
+ /* ---------------------------------------------------------------------- */
+
+ /* leave as LL or LDL' */
+ if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, TRUE, TRUE, L,
+ Common))
+ {
+ ERROR (CHOLMOD_INVALID, "cannot convert L") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create Lsparse */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocate the header for Lsparse, the sparse matrix version of L */
+ Lsparse = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* transfer the contents from L to Lsparse */
+ Lsparse->nrow = L->n ;
+ Lsparse->ncol = L->n ;
+ Lsparse->p = L->p ;
+ Lsparse->i = L->i ;
+ Lsparse->x = L->x ;
+ Lsparse->z = L->z ;
+ Lsparse->nz = NULL ;
+ Lsparse->stype = 0 ;
+ Lsparse->itype = L->itype ;
+ Lsparse->xtype = L->xtype ;
+ Lsparse->dtype = L->dtype ;
+ Lsparse->sorted = TRUE ;
+ Lsparse->packed = TRUE ;
+ Lsparse->nzmax = L->nzmax ;
+ ASSERT (CHOLMOD(dump_sparse) (Lsparse, "Lsparse", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to symbolic, but do not free contents transfered to Lsparse */
+ /* ---------------------------------------------------------------------- */
+
+ L->p = NULL ;
+ L->i = NULL ;
+ L->x = NULL ;
+ L->z = NULL ;
+ L->xtype = CHOLMOD_PATTERN ;
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, FALSE, FALSE, TRUE, TRUE, L,
+ Common) ;
+
+ return (Lsparse) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_factor ================================================== */
+/* ========================================================================== */
+
+/* Create an exact copy of a factor, with one exception:
+ *
+ * Entries in unused space are not copied (they might not be initialized,
+ * and copying them would cause program checkers such as purify and
+ * valgrind to complain).
+ *
+ * Note that a supernodal L cannot be zomplex.
+ */
+
+cholmod_factor *CHOLMOD(copy_factor)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_factor *L2 ;
+ double *Lx, *L2x, *Lz, *L2z ;
+ Int *Perm, *ColCount, *Lp, *Li, *Lnz, *Lnext, *Lprev, *Lsuper, *Lpi, *Lpx,
+ *Ls, *Perm2, *ColCount2, *L2p, *L2i, *L2nz, *L2next, *L2prev, *L2super,
+ *L2pi, *L2px, *L2s ;
+ Int n, j, p, pend, s, xsize, ssize, nsuper ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start copy", Common)) ;
+
+ n = L->n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a simplicial symbolic factor */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocates L2->Perm and L2->ColCount */
+ L2 = CHOLMOD(allocate_factor) (n, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (L2->xtype == CHOLMOD_PATTERN && !(L2->is_super)) ;
+
+ Perm = L->Perm ;
+ ColCount = L->ColCount ;
+ Perm2 = L2->Perm ;
+ ColCount2 = L2->ColCount ;
+ L2->ordering = L->ordering ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Perm2 [j] = Perm [j] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ ColCount2 [j] = ColCount [j] ;
+ }
+ L2->is_ll = L->is_ll ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the rest of the factor */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype != CHOLMOD_PATTERN && !(L->super))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* allocate a simplicial numeric factor */
+ /* ------------------------------------------------------------------ */
+
+ /* allocate L2->p, L2->nz, L2->prev, L2->next, L2->i, and L2->x.
+ * packed = -1 so that cholmod_change_factor allocates space of
+ * size L2->nzmax */
+ L2->nzmax = L->nzmax ;
+ if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, -1, TRUE,
+ L2, Common))
+ {
+ CHOLMOD(free_factor) (&L2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (L->nzmax == L2->nzmax) ;
+
+ /* ------------------------------------------------------------------ */
+ /* copy the contents of a simplicial numeric factor */
+ /* ------------------------------------------------------------------ */
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+ Lprev = L->prev ;
+
+ L2p = L2->p ;
+ L2i = L2->i ;
+ L2x = L2->x ;
+ L2z = L2->z ;
+ L2nz = L2->nz ;
+ L2next = L2->next ;
+ L2prev = L2->prev ;
+ L2->xtype = L->xtype ;
+ L2->dtype = L->dtype ;
+
+ for (j = 0 ; j <= n ; j++)
+ {
+ L2p [j] = Lp [j] ;
+ }
+
+ for (j = 0 ; j < n+2 ; j++)
+ {
+ L2prev [j] = Lprev [j] ;
+ }
+
+ for (j = 0 ; j < n+2 ; j++)
+ {
+ L2next [j] = Lnext [j] ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ L2nz [j] = Lnz [j] ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ L2i [p] = Li [p] ;
+ }
+ p = Lp [j] ;
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for ( ; p < pend ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for ( ; p < pend ; p++)
+ {
+ L2x [2*p ] = Lx [2*p ] ;
+ L2x [2*p+1] = Lx [2*p+1] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for ( ; p < pend ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ L2z [p] = Lz [p] ;
+ }
+ }
+
+ }
+
+ }
+ else if (L->is_super)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy a supernodal factor */
+ /* ------------------------------------------------------------------ */
+
+ xsize = L->xsize ;
+ ssize = L->ssize ;
+ nsuper = L->nsuper ;
+
+ L2->xsize = xsize ;
+ L2->ssize = ssize ;
+ L2->nsuper = nsuper ;
+
+ /* allocate L2->super, L2->pi, L2->px, and L2->s. Allocate L2->x if
+ * L is numeric */
+ if (!CHOLMOD(change_factor) (L->xtype, TRUE, TRUE, TRUE, TRUE, L2,
+ Common))
+ {
+ CHOLMOD(free_factor) (&L2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ ASSERT (L2->s != NULL) ;
+
+ /* ------------------------------------------------------------------ */
+ /* copy the contents of a supernodal factor */
+ /* ------------------------------------------------------------------ */
+
+ Lsuper = L->super ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Lx = L->x ;
+
+ L2super = L2->super ;
+ L2pi = L2->pi ;
+ L2px = L2->px ;
+ L2s = L2->s ;
+ L2x = L2->x ;
+
+ L2->maxcsize = L->maxcsize ;
+ L2->maxesize = L->maxesize ;
+
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ L2super [s] = Lsuper [s] ;
+ }
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ L2pi [s] = Lpi [s] ;
+ }
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ L2px [s] = Lpx [s] ;
+ }
+
+ L2s [0] = 0 ;
+ for (p = 0 ; p < ssize ; p++)
+ {
+ L2s [p] = Ls [p] ;
+ }
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for (p = 0 ; p < xsize ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for (p = 0 ; p < 2*xsize ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ }
+ }
+ }
+
+ L2->minor = L->minor ;
+ L2->is_monotonic = L->is_monotonic ;
+
+ DEBUG (CHOLMOD(dump_factor) (L2, "L2 got copied", Common)) ;
+ ASSERT (L2->xtype == L->xtype && L2->is_super == L->is_super) ;
+ return (L2) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_memory.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_memory.c
new file mode 100644
index 0000000..141f006
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_memory.c
@@ -0,0 +1,565 @@
+/* ========================================================================== */
+/* === Core/cholmod_memory ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core memory management routines:
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_malloc malloc wrapper
+ * cholmod_free free wrapper
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_calloc calloc wrapper
+ * cholmod_realloc realloc wrapper
+ * cholmod_realloc_multiple realloc wrapper for multiple objects
+ *
+ * The user may make use of these, just like malloc and free. You can even
+ * malloc an object and safely free it with cholmod_free, and visa versa
+ * (except that the memory usage statistics will be corrupted). These routines
+ * do differ from malloc and free. If cholmod_free is given a NULL pointer,
+ * for example, it does nothing (unlike the ANSI free). cholmod_realloc does
+ * not return NULL if given a non-NULL pointer and a nonzero size, even if it
+ * fails (it sets an error code in Common->status instead).
+ *
+ * CHOLMOD keeps track of the amount of memory it has allocated, and so the
+ * cholmod_free routine includes as a parameter the size of the object being
+ * freed. This is only used for memory usage statistics, which are very useful
+ * in finding memory leaks in your program. If you, the user of CHOLMOD, pass
+ * the wrong size, the only consequence is that the memory usage statistics
+ * will be invalid. This will causes assertions to fail if CHOLMOD is
+ * compiled with debugging enabled, but otherwise it will cause no errors.
+ *
+ * The cholmod_free_* routines for each CHOLMOD object keep track of the size
+ * of the blocks they free, so they do not require you to pass their sizes
+ * as a parameter.
+ *
+ * If a block of size zero is requested, these routines allocate a block of
+ * size one instead.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === cholmod_add_size_t =================================================== */
+/* ========================================================================== */
+
+/* Safely compute a+b, and check for integer overflow. If overflow occurs,
+ * return 0 and set OK to FALSE. Also return 0 if OK is FALSE on input. */
+
+size_t CHOLMOD(add_size_t) (size_t a, size_t b, int *ok)
+{
+ size_t s = a + b ;
+ (*ok) = (*ok) && (s >= a) ;
+ return ((*ok) ? s : 0) ;
+}
+
+/* ========================================================================== */
+/* === cholmod_mult_size_t ================================================== */
+/* ========================================================================== */
+
+/* Safely compute a*k, where k should be small, and check for integer overflow.
+ * If overflow occurs, return 0 and set OK to FALSE. Also return 0 if OK is
+ * FALSE on input. */
+
+size_t CHOLMOD(mult_size_t) (size_t a, size_t k, int *ok)
+{
+ size_t p = 0, s ;
+ while (*ok)
+ {
+ if (k % 2)
+ {
+ p = p + a ;
+ (*ok) = (*ok) && (p >= a) ;
+ }
+ k = k / 2 ;
+ if (!k) return (p) ;
+ s = a + a ;
+ (*ok) = (*ok) && (s >= a) ;
+ a = s ;
+ }
+ return (0) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_malloc ======================================================= */
+/* ========================================================================== */
+
+/* Wrapper around malloc routine. Allocates space of size MAX(1,n)*size, where
+ * size is normally a sizeof (...).
+ *
+ * This routine, cholmod_calloc, and cholmod_realloc do not set Common->status
+ * to CHOLMOD_OK on success, so that a sequence of cholmod_malloc's, _calloc's,
+ * or _realloc's can be used. If any of them fails, the Common->status will
+ * hold the most recent error status.
+ *
+ * Usage, for a pointer to int:
+ *
+ * p = cholmod_malloc (n, sizeof (int), Common)
+ *
+ * Uses a pointer to the malloc routine (or its equivalent) defined in Common.
+ */
+
+void *CHOLMOD(malloc) /* returns pointer to the newly malloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ void *p ;
+ size_t s ;
+ int ok = TRUE ;
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (size == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ;
+ p = NULL ;
+ }
+ else if (n >= (Size_max / size) || n >= Int_max)
+ {
+ /* object is too big to allocate without causing integer overflow */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ p = NULL ;
+ }
+ else
+ {
+ /* call malloc, or its equivalent */
+ s = CHOLMOD(mult_size_t) (MAX (1,n), size, &ok) ;
+ p = ok ? ((Common->malloc_memory) (s)) : NULL ;
+ if (p == NULL)
+ {
+ /* failure: out of memory */
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ else
+ {
+ /* success: increment the count of objects allocated */
+ Common->malloc_count++ ;
+ Common->memory_inuse += (n * size) ;
+ Common->memory_usage =
+ MAX (Common->memory_usage, Common->memory_inuse) ;
+ PRINTM (("cholmod_malloc %p %d cnt: %d inuse %d\n",
+ p, n*size, Common->malloc_count, Common->memory_inuse)) ;
+ }
+ }
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free ========================================================= */
+/* ========================================================================== */
+
+/* Wrapper around free routine. Returns NULL, which can be assigned to the
+ * pointer being freed, as in:
+ *
+ * p = cholmod_free (n, sizeof (int), p, Common) ;
+ *
+ * In CHOLMOD, the syntax:
+ *
+ * cholmod_free (n, sizeof (int), p, Common) ;
+ *
+ * is used if p is a local pointer and the routine is returning shortly.
+ * Uses a pointer to the free routine (or its equivalent) defined in Common.
+ * Nothing is freed if the pointer is NULL.
+ */
+
+void *CHOLMOD(free) /* always returns NULL */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to free */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (p != NULL)
+ {
+ /* only free the object if the pointer is not NULL */
+ /* call free, or its equivalent */
+ (Common->free_memory) (p) ;
+ Common->malloc_count-- ;
+ Common->memory_inuse -= (n * size) ;
+ PRINTM (("cholmod_free %p %d cnt: %d inuse %d\n",
+ p, n*size, Common->malloc_count, Common->memory_inuse)) ;
+ /* This assertion will fail if the user calls cholmod_malloc and
+ * cholmod_free with mismatched memory sizes. It shouldn't fail
+ * otherwise. */
+ DEBUG (if (Common->malloc_count == 0 && Common->memory_inuse != 0)
+ PRINT0 (("inuse: %d\n", Common->memory_inuse))) ;
+ ASSERT (IMPLIES (Common->malloc_count == 0, Common->memory_inuse == 0));
+ }
+ /* return NULL, and the caller should assign this to p. This avoids
+ * freeing the same pointer twice. */
+ return (NULL) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_calloc ======================================================= */
+/* ========================================================================== */
+
+/* Wrapper around calloc routine.
+ *
+ * Uses a pointer to the calloc routine (or its equivalent) defined in Common.
+ * This routine is identical to malloc, except that it zeros the newly allocated
+ * block to zero.
+ */
+
+void *CHOLMOD(calloc) /* returns pointer to the newly calloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ void *p ;
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (size == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ;
+ p = NULL ;
+ }
+ else if (n >= (Size_max / size) || n >= Int_max)
+ {
+ /* object is too big to allocate without causing integer overflow */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ p = NULL ;
+ }
+ else
+ {
+ /* call calloc, or its equivalent */
+ p = (Common->calloc_memory) (MAX (1,n), size) ;
+ if (p == NULL)
+ {
+ /* failure: out of memory */
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ else
+ {
+ /* success: increment the count of objects allocated */
+ Common->malloc_count++ ;
+ Common->memory_inuse += (n * size) ;
+ Common->memory_usage =
+ MAX (Common->memory_usage, Common->memory_inuse) ;
+ PRINTM (("cholmod_calloc %p %d cnt: %d inuse %d\n",
+ p, n*size, Common->malloc_count, Common->memory_inuse)) ;
+ }
+ }
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_realloc ====================================================== */
+/* ========================================================================== */
+
+/* Wrapper around realloc routine. Given a pointer p to a block of size
+ * (*n)*size memory, it changes the size of the block pointed to by p to be
+ * MAX(1,nnew)*size in size. It may return a pointer different than p. This
+ * should be used as (for a pointer to int):
+ *
+ * p = cholmod_realloc (nnew, sizeof (int), p, *n, Common) ;
+ *
+ * If p is NULL, this is the same as p = cholmod_malloc (...).
+ * A size of nnew=0 is treated as nnew=1.
+ *
+ * If the realloc fails, p is returned unchanged and Common->status is set
+ * to CHOLMOD_OUT_OF_MEMORY. If successful, Common->status is not modified,
+ * and p is returned (possibly changed) and pointing to a large block of memory.
+ *
+ * Uses a pointer to the realloc routine (or its equivalent) defined in Common.
+ */
+
+void *CHOLMOD(realloc) /* returns pointer to reallocated block */
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated block */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to realloc */
+ size_t *n, /* current size on input, nnew on output if successful*/
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ size_t nold = (*n) ;
+ void *pnew ;
+ size_t s ;
+ int ok = TRUE ;
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (size == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ;
+ p = NULL ;
+ }
+ else if (p == NULL)
+ {
+ /* A fresh object is being allocated. */
+ PRINT1 (("realloc fresh: %d %d\n", nnew, size)) ;
+ p = CHOLMOD(malloc) (nnew, size, Common) ;
+ *n = (p == NULL) ? 0 : nnew ;
+ }
+ else if (nold == nnew)
+ {
+ /* Nothing to do. Do not change p or n. */
+ PRINT1 (("realloc nothing: %d %d\n", nnew, size)) ;
+ }
+ else if (nnew >= (Size_max / size) || nnew >= Int_max)
+ {
+ /* failure: nnew is too big. Do not change p or n. */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ }
+ else
+ {
+ /* The object exists, and is changing to some other nonzero size. */
+ /* call realloc, or its equivalent */
+ PRINT1 (("realloc : %d to %d, %d\n", nold, nnew, size)) ;
+ pnew = NULL ;
+
+ s = CHOLMOD(mult_size_t) (MAX (1,nnew), size, &ok) ;
+ pnew = ok ? ((Common->realloc_memory) (p, s)) : NULL ;
+
+ if (pnew == NULL)
+ {
+ /* Do not change p, since it still points to allocated memory */
+ if (nnew <= nold)
+ {
+ /* The attempt to reduce the size of the block from n to
+ * nnew has failed. The current block is not modified, so
+ * pretend to succeed, but do not change p. Do change
+ * CHOLMOD's notion of the size of the block, however. */
+ *n = nnew ;
+ PRINTM (("nnew <= nold failed, pretend to succeed\n")) ;
+ PRINTM (("cholmod_realloc_old: %p %d cnt: %d inuse %d\n"
+ "cholmod_realloc_new: %p %d cnt: %d inuse %d\n",
+ p, nold*size, Common->malloc_count-1,
+ Common->memory_inuse - nold*size,
+ p, nnew*size, Common->malloc_count,
+ Common->memory_inuse + (nnew-nold)*size)) ;
+ Common->memory_inuse += ((nnew-nold) * size) ;
+ }
+ else
+ {
+ /* Increasing the size of the block has failed.
+ * Do not change n. */
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ }
+ else
+ {
+ /* success: return revised p and change the size of the block */
+ PRINTM (("cholmod_realloc_old: %p %d cnt: %d inuse %d\n"
+ "cholmod_realloc_new: %p %d cnt: %d inuse %d\n",
+ p, nold*size, Common->malloc_count-1,
+ Common->memory_inuse - nold*size,
+ pnew, nnew*size, Common->malloc_count,
+ Common->memory_inuse + (nnew-nold)*size)) ;
+ p = pnew ;
+ *n = nnew ;
+ Common->memory_inuse += ((nnew-nold) * size) ;
+ }
+ Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse);
+ }
+
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_realloc_multiple ============================================= */
+/* ========================================================================== */
+
+/* reallocate multiple blocks of memory, all of the same size (up to two integer
+ * and two real blocks). Either reallocations all succeed, or all are returned
+ * in the original size (they are freed if the original size is zero). The nnew
+ * blocks are of size 1 or more.
+ */
+
+int CHOLMOD(realloc_multiple)
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated blocks */
+ int nint, /* number of int/UF_long blocks */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* ---- in/out --- */
+ void **I, /* int or UF_long block */
+ void **J, /* int or UF_long block */
+ void **X, /* complex or double block */
+ void **Z, /* zomplex case only: double block */
+ size_t *nold_p, /* current size of the I,J,X,Z blocks on input,
+ * nnew on output if successful */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *xx, *zz ;
+ size_t i, j, x, z, nold ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid xtype") ;
+ return (FALSE) ;
+ }
+
+ nold = *nold_p ;
+
+ if (nint < 1 && xtype == CHOLMOD_PATTERN)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ i = nold ;
+ j = nold ;
+ x = nold ;
+ z = nold ;
+
+ if (nint > 0)
+ {
+ *I = CHOLMOD(realloc) (nnew, sizeof (Int), *I, &i, Common) ;
+ }
+ if (nint > 1)
+ {
+ *J = CHOLMOD(realloc) (nnew, sizeof (Int), *J, &j, Common) ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ *X = CHOLMOD(realloc) (nnew, sizeof (double), *X, &x, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *X = CHOLMOD(realloc) (nnew, 2*sizeof (double), *X, &x, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *X = CHOLMOD(realloc) (nnew, sizeof (double), *X, &x, Common) ;
+ *Z = CHOLMOD(realloc) (nnew, sizeof (double), *Z, &z, Common) ;
+ break ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* one or more realloc's failed. Resize all back down to nold. */
+
+ if (nold == 0)
+ {
+
+ if (nint > 0)
+ {
+ *I = CHOLMOD(free) (i, sizeof (Int), *I, Common) ;
+ }
+ if (nint > 1)
+ {
+ *J = CHOLMOD(free) (j, sizeof (Int), *J, Common) ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ *X = CHOLMOD(free) (x, sizeof (double), *X, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *X = CHOLMOD(free) (x, 2*sizeof (double), *X, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *X = CHOLMOD(free) (x, sizeof (double), *X, Common) ;
+ *Z = CHOLMOD(free) (x, sizeof (double), *Z, Common) ;
+ break ;
+ }
+
+ }
+ else
+ {
+ if (nint > 0)
+ {
+ *I = CHOLMOD(realloc) (nold, sizeof (Int), *I, &i, Common) ;
+ }
+ if (nint > 1)
+ {
+ *J = CHOLMOD(realloc) (nold, sizeof (Int), *J, &j, Common) ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ *X = CHOLMOD(realloc) (nold, sizeof (double), *X, &x,
+ Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *X = CHOLMOD(realloc) (nold, 2*sizeof (double), *X, &x,
+ Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *X = CHOLMOD(realloc) (nold, sizeof (double), *X, &x,
+ Common) ;
+ *Z = CHOLMOD(realloc) (nold, sizeof (double), *Z, &z,
+ Common) ;
+ break ;
+ }
+
+ }
+
+ return (FALSE) ;
+ }
+
+ if (nold == 0)
+ {
+ /* New space was allocated. Clear the first entry so that valgrind
+ * doesn't complain about its access in change_complexity
+ * (Core/cholmod_complex.c). */
+ xx = *X ;
+ zz = *Z ;
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ xx [0] = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ xx [0] = 0 ;
+ xx [1] = 0 ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ xx [0] = 0 ;
+ zz [0] = 0 ;
+ break ;
+ }
+ }
+
+ /* all realloc's succeeded, change size to reflect realloc'ed size. */
+ *nold_p = nnew ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_sparse.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_sparse.c
new file mode 100644
index 0000000..059f855
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_sparse.c
@@ -0,0 +1,652 @@
+/* ========================================================================== */
+/* === Core/cholmod_sparse ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_sparse object:
+ *
+ * A sparse matrix is held in compressed column form. In the basic type
+ * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix
+ * with nz entries is held in three arrays: p of size n+1, i of size nz, and x
+ * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and
+ * in the same locations in x. There may be no duplicate entries in a column.
+ * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track).
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_allocate_sparse allocate a sparse matrix
+ * cholmod_free_sparse free a sparse matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_reallocate_sparse change the size (# entries) of sparse matrix
+ * cholmod_nnz number of nonzeros in a sparse matrix
+ * cholmod_speye sparse identity matrix
+ * cholmod_spzeros sparse zero matrix
+ * cholmod_copy_sparse create a copy of a sparse matrix
+ *
+ * All xtypes are supported (pattern, real, complex, and zomplex)
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_sparse ============================================== */
+/* ========================================================================== */
+
+/* Allocate space for a matrix. A->i and A->x are not initialized. A->p
+ * (and A->nz if A is not packed) are set to zero, so a matrix containing no
+ * entries (all zero) is returned. See also cholmod_spzeros.
+ *
+ * workspace: none
+ */
+
+cholmod_sparse *CHOLMOD(allocate_sparse)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */
+ int packed, /* TRUE if A will be packed, FALSE otherwise */
+ int stype, /* stype of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A ;
+ Int *Ap, *Anz ;
+ size_t nzmax0 ;
+ Int j ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (stype != 0 && nrow != ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ;
+ return (NULL) ;
+ }
+ if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (NULL) ;
+ }
+ /* ensure the dimensions do not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ;
+ if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate header */
+ /* ---------------------------------------------------------------------- */
+
+ A = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ PRINT1 (("cholmod_allocate_sparse %d-by-%d nzmax %d sorted %d packed %d"
+ " xtype %d\n", nrow, ncol, nzmax, sorted, packed, xtype)) ;
+
+ nzmax = MAX (1, nzmax) ;
+
+ A->nrow = nrow ;
+ A->ncol = ncol ;
+ A->nzmax = nzmax ;
+ A->packed = packed ; /* default is packed (A->nz not present) */
+ A->stype = stype ;
+ A->itype = ITYPE ;
+ A->xtype = xtype ;
+ A->dtype = DTYPE ;
+
+ A->nz = NULL ;
+ A->p = NULL ;
+ A->i = NULL ;
+ A->x = NULL ;
+ A->z = NULL ;
+
+ /* A 1-by-m matrix always has sorted columns */
+ A->sorted = (nrow <= 1) ? TRUE : sorted ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix itself */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocate O(ncol) space */
+ A->p = CHOLMOD(malloc) (((size_t) ncol)+1, sizeof (Int), Common) ;
+ if (!packed)
+ {
+ A->nz = CHOLMOD(malloc) (ncol, sizeof (Int), Common) ;
+ }
+
+ /* allocate O(nz) space */
+ nzmax0 = 0 ;
+ CHOLMOD(realloc_multiple) (nzmax, 1, xtype, &(A->i), NULL, &(A->x), &(A->z),
+ &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize A->p and A->nz so that A is an empty matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ for (j = 0 ; j <= (Int) ncol ; j++)
+ {
+ Ap [j] = 0 ;
+ }
+ if (!packed)
+ {
+ Anz = A->nz ;
+ for (j = 0 ; j < (Int) ncol ; j++)
+ {
+ Anz [j] = 0 ;
+ }
+ }
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_sparse ================================================== */
+/* ========================================================================== */
+
+/* free a sparse matrix
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_sparse)
+(
+ /* ---- in/out --- */
+ cholmod_sparse **AHandle, /* matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int n, nz ;
+ cholmod_sparse *A ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (AHandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ A = *AHandle ;
+ if (A == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ n = A->ncol ;
+ nz = A->nzmax ;
+ A->p = CHOLMOD(free) (n+1, sizeof (Int), A->p, Common) ;
+ A->i = CHOLMOD(free) (nz, sizeof (Int), A->i, Common) ;
+ A->nz = CHOLMOD(free) (n, sizeof (Int), A->nz, Common) ;
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ A->x = CHOLMOD(free) (nz, 2*sizeof (double), A->x, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ;
+ A->z = CHOLMOD(free) (nz, sizeof (double), A->z, Common) ;
+ break ;
+ }
+
+ *AHandle = CHOLMOD(free) (1, sizeof (cholmod_sparse), (*AHandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_sparse ============================================ */
+/* ========================================================================== */
+
+/* Change the size of A->i, A->x, and A->z, or allocate them if their current
+ * size is zero. A->x and A->z are not modified if A->xtype is CHOLMOD_PATTERN.
+ * A->z is not modified unless A->xtype is CHOLMOD_ZOMPLEX.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_sparse)
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in A */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to reallocate */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ PRINT1 (("realloc matrix %d to %d, xtype: %d\n",
+ A->nzmax, nznew, A->xtype)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* resize the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(realloc_multiple) (MAX (1,nznew), 1, A->xtype, &(A->i), NULL,
+ &(A->x), &(A->z), &(A->nzmax), Common) ;
+
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_speye ======================================================== */
+/* ========================================================================== */
+
+/* Return a sparse identity matrix. */
+
+cholmod_sparse *CHOLMOD(speye)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az ;
+ cholmod_sparse *A ;
+ Int *Ap, *Ai ;
+ Int j, n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ n = MIN (nrow, ncol) ;
+ A = CHOLMOD(allocate_sparse) (nrow, ncol, n, TRUE, TRUE, 0, xtype,
+ Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory or inputs invalid */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create the identity matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Ap [j] = j ;
+ }
+ for (j = n ; j <= ((Int) ncol) ; j++)
+ {
+ Ap [j] = n ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Ai [j] = j ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (j = 0 ; j < n ; j++)
+ {
+ Ax [j] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ Ax [2*j ] = 1 ;
+ Ax [2*j+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ Ax [j] = 1 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Az [j] = 0 ;
+ }
+ break ;
+ }
+
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_spzeros ====================================================== */
+/* ========================================================================== */
+
+/* Return a sparse zero matrix. */
+
+cholmod_sparse *CHOLMOD(spzeros)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, TRUE, TRUE, 0, xtype,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_nnz ========================================================== */
+/* ========================================================================== */
+
+/* Return the number of entries in a sparse matrix.
+ *
+ * workspace: none
+ * integer overflow cannot occur, since the matrix is already allocated.
+ */
+
+UF_long CHOLMOD(nnz)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Anz ;
+ size_t nz ;
+ Int j, ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return nnz (A) */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ;
+ if (A->packed)
+ {
+ Ap = A->p ;
+ RETURN_IF_NULL (Ap, EMPTY) ;
+ nz = Ap [ncol] ;
+ }
+ else
+ {
+ Anz = A->nz ;
+ RETURN_IF_NULL (Anz, EMPTY) ;
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ nz += MAX (0, Anz [j]) ;
+ }
+ }
+ return (nz) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_sparse ================================================== */
+/* ========================================================================== */
+
+/* C = A. Create an exact copy of a sparse matrix, with one exception.
+ * Entries in unused space are not copied (they might not be initialized,
+ * and copying them would cause program checkers such as purify and
+ * valgrind to complain). The xtype of the resulting matrix C is the same as
+ * the xtype of the input matrix A.
+ *
+ * See also Core/cholmod_copy, which copies a matrix with possible changes
+ * in stype, presence of diagonal entries, pattern vs. numerical values,
+ * real and/or imaginary parts, and so on.
+ */
+
+cholmod_sparse *CHOLMOD(copy_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Cx, *Az, *Cz ;
+ Int *Ap, *Ai, *Anz, *Cp, *Ci, *Cnz ;
+ cholmod_sparse *C ;
+ Int p, pend, j, ncol, packed, nzmax, nz, xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype != 0 && A->nrow != A->ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "A original", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ;
+ nzmax = A->nzmax ;
+ packed = A->packed ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ xtype = A->xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the copy */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (A->nrow, A->ncol, A->nzmax, A->sorted,
+ A->packed, A->stype, A->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+ Cz = C->z ;
+ Cnz = C->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j <= ncol ; j++)
+ {
+ Cp [j] = Ap [j] ;
+ }
+
+ if (packed)
+ {
+ nz = Ap [ncol] ;
+ for (p = 0 ; p < nz ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (p = 0 ; p < nz ; p++)
+ {
+ Cx [p] = Ax [p] ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (p = 0 ; p < 2*nz ; p++)
+ {
+ Cx [p] = Ax [p] ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (p = 0 ; p < nz ; p++)
+ {
+ Cx [p] = Ax [p] ;
+ Cz [p] = Az [p] ;
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cnz [j] = Anz [j] ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_PATTERN:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_REAL:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ Cx [p] = Ax [p] ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ Cx [2*p ] = Ax [2*p ] ;
+ Cx [2*p+1] = Ax [2*p+1] ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ Cx [p] = Ax [p] ;
+ Cz [p] = Az [p] ;
+ }
+ }
+ break ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C, "C copy", Common) >= 0) ;
+ return (C) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_transpose.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_transpose.c
new file mode 100644
index 0000000..7e94aa8
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_transpose.c
@@ -0,0 +1,1139 @@
+/* ========================================================================== */
+/* === Core/cholmod_transpose =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_sparse object to
+ * compute the transpose or permuted transpose of a matrix:
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_transpose transpose sparse matrix
+ * cholmod_ptranspose transpose and permute sparse matrix
+ * cholmod_sort sort row indices in each column of sparse matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_transpose_unsym transpose unsymmetric sparse matrix
+ * cholmod_transpose_sym transpose symmetric sparse matrix
+ *
+ * All xtypes (pattern, real, complex, and zomplex) are supported.
+ *
+ * ---------------------------------------
+ * Unsymmetric case: A->stype is zero.
+ * ---------------------------------------
+ *
+ * Computes F = A', F = A (:,f)' or F = A (p,f)', except that the indexing by
+ * f does not work the same as the MATLAB notation (see below). A->stype
+ * is zero, which denotes that both the upper and lower triangular parts of
+ * A are present (and used). A may in fact be symmetric in pattern and/or
+ * value; A->stype just denotes which part of A are stored. A may be
+ * rectangular.
+ *
+ * p is a permutation of 0:m-1, and f is a subset of 0:n-1, where A is m-by-n.
+ * There can be no duplicate entries in p or f.
+ *
+ * The set f is held in fset and fsize.
+ * fset = NULL means ":" in MATLAB. fsize is ignored.
+ * fset != NULL means f = fset [0..fsize-1].
+ * fset != NULL and fsize = 0 means f is the empty set.
+ *
+ * Columns not in the set f are considered to be zero. That is,
+ * if A is 5-by-10 then F = A (:,[3 4])' is not 2-by-5, but 10-by-5, and rows
+ * 3 and 4 of F are equal to columns 3 and 4 of A (the other rows of F are
+ * zero). More precisely, in MATLAB notation:
+ *
+ * [m n] = size (A) ;
+ * F = A ;
+ * notf = ones (1,n) ;
+ * notf (f) = 0 ;
+ * F (:, find (notf)) = 0
+ * F = F'
+ *
+ * If you want the MATLAB equivalent F=A(p,f) operation, use cholmod_submatrix
+ * instead (which does not compute the transpose).
+ *
+ * F->nzmax must be large enough to hold the matrix F. It is not modified.
+ * If F->nz is present then F->nz [j] = # of entries in column j of F.
+ *
+ * A can be sorted or unsorted, with packed or unpacked columns.
+ *
+ * If f is present and not sorted in ascending order, then F is unsorted
+ * (that is, it may contain columns whose row indices do not appear in
+ * ascending order). Otherwise, F is sorted (the row indices in each
+ * column of F appear in strictly ascending order).
+ *
+ * F is returned in packed or unpacked form, depending on F->packed on input.
+ * If F->packed is false, then F is returned in unpacked form (F->nz must be
+ * present). Each row i of F is large enough to hold all the entries in row i
+ * of A, even if f is provided. That is, F->i and
+ * F->x [F->p [i] .. F->p [i] + F->nz [i] - 1] contain all entries in A (i,f),
+ * but F->p [i+1] - F->p [i] is equal to the number of nonzeros in A (i,:),
+ * not just A (i,f).
+ *
+ * The cholmod_transpose_unsym routine is the only operation in CHOLMOD that
+ * can produce an unpacked matrix.
+ *
+ * ---------------------------------------
+ * Symmetric case: A->stype is nonzero.
+ * ---------------------------------------
+ *
+ * Computes F = A' or F = A(p,p)', the transpose or permuted transpose, where
+ * A->stype is nonzero.
+ *
+ * If A->stype > 0, then A is a symmetric matrix where just the upper part
+ * of the matrix is stored. Entries in the lower triangular part may be
+ * present, but are ignored. A must be square. If F=A', then F is returned
+ * sorted; otherwise F is unsorted for the F=A(p,p)' case.
+ *
+ * There can be no duplicate entries in p.
+ * The fset and fsize parameters are not used.
+ *
+ * Three kinds of transposes are available, depending on the "values" parameter:
+ * 0: do not transpose the numerical values; create a CHOLMOD_PATTERN matrix
+ * 1: array transpose
+ * 2: complex conjugate transpose (same as 2 if input is real or pattern)
+ *
+ * -----------------------------------------------------------------------------
+ *
+ * For cholmod_transpose_unsym and cholmod_transpose_sym, the output matrix
+ * F must already be pre-allocated by the caller, with the correct dimensions.
+ * If F is not valid or has the wrong dimensions, it is not modified.
+ * Otherwise, if F is too small, the transpose is not computed; the contents
+ * of F->p contain the column pointers of the resulting matrix, where
+ * F->p [F->ncol] > F->nzmax. In this case, the remaining contents of F are
+ * not modified. F can still be properly free'd with cholmod_free_sparse.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define PATTERN
+#include "t_cholmod_transpose.c"
+#define REAL
+#include "t_cholmod_transpose.c"
+#define COMPLEX
+#include "t_cholmod_transpose.c"
+#define COMPLEX
+#define NCONJUGATE
+#include "t_cholmod_transpose.c"
+#define ZOMPLEX
+#include "t_cholmod_transpose.c"
+#define ZOMPLEX
+#define NCONJUGATE
+#include "t_cholmod_transpose.c"
+
+
+/* ========================================================================== */
+/* === cholmod_transpose_unsym ============================================== */
+/* ========================================================================== */
+
+/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
+ * already allocated. See cholmod_transpose for a simpler routine.
+ *
+ * workspace:
+ * Iwork (MAX (nrow,ncol)) if fset is present
+ * Iwork (nrow) if fset is NULL
+ *
+ * The xtype of A and F must match, unless values is zero or F->xtype is
+ * CHOLMOD_PATTERN (in which case only the pattern of A is transpose into F).
+ */
+
+int CHOLMOD(transpose_unsym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values */
+ Int *Perm, /* size nrow, if present (can be NULL) */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Fp, *Fnz, *Ap, *Ai, *Anz, *Wi ;
+ Int nrow, ncol, permute, use_fset, Apacked, Fpacked, p, pend,
+ i, j, k, Fsorted, nf, jj, jlast ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->nrow != F->ncol || A->ncol != F->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nf = fsize ;
+ use_fset = (fset != NULL) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Anz = A->nz ;
+ Apacked = A->packed ;
+ ASSERT (IMPLIES (!Apacked, Anz != NULL)) ;
+
+ permute = (Perm != NULL) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ;
+
+ nf = (use_fset) ? nf : ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = nrow + ((fset != NULL) ? ncol : 0) */
+ s = CHOLMOD(add_size_t) (nrow, ((fset != NULL) ? ncol : 0), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ Wi = Common->Iwork ; /* size nrow (i/l/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* check Perm and fset */
+ /* ---------------------------------------------------------------------- */
+
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = 1 ;
+ }
+ for (k = 0 ; k < nrow ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i > nrow || Wi [i] == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid permutation") ;
+ return (FALSE) ;
+ }
+ Wi [i] = 0 ;
+ }
+ }
+
+ if (use_fset)
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wi [j] = 1 ;
+ }
+ for (k = 0 ; k < nf ; k++)
+ {
+ j = fset [k] ;
+ if (j < 0 || j > ncol || Wi [j] == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid fset") ;
+ return (FALSE) ;
+ }
+ Wi [j] = 0 ;
+ }
+ }
+
+ /* Perm and fset are now valid */
+ ASSERT (CHOLMOD(dump_perm) (Perm, nrow, nrow, "Perm", Common)) ;
+ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of A or A(:,f) */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = 0 ;
+ }
+
+ jlast = EMPTY ;
+ Fsorted = TRUE ;
+
+ if (use_fset)
+ {
+ /* count entries in each row of A(:,f) */
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = fset [jj] ;
+ if (j <= jlast)
+ {
+ Fsorted = FALSE ;
+ }
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Wi [Ai [p]]++ ;
+ }
+ jlast = j ;
+ }
+
+ /* save the nz counts if F is unpacked, and recount all of A */
+ if (!Fpacked)
+ {
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [Perm [i]] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [i] ;
+ }
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = 0 ;
+ }
+
+ /* count entries in each row of A */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Wi [Ai [p]]++ ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* count entries in each row of A */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Wi [Ai [p]]++ ;
+ }
+ }
+
+ /* save the nz counts if F is unpacked */
+ if (!Fpacked)
+ {
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [Perm [i]] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [i] ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fp [i] = p ;
+ p += Wi [Perm [i]] ;
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [Perm [i]] = Fp [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fp [i] = p ;
+ p += Wi [i] ;
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = Fp [i] ;
+ }
+ }
+ Fp [nrow] = p ;
+
+ if (p > (Int) (F->nzmax))
+ {
+ ERROR (CHOLMOD_INVALID, "F is too small") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ ok = FALSE ;
+ if (values == 0 || F->xtype == CHOLMOD_PATTERN)
+ {
+ ok = p_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_REAL)
+ {
+ ok = r_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_COMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ ok = ct_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ ok = c_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ }
+ else if (F->xtype == CHOLMOD_ZOMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ ok = zt_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ ok = z_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize result F */
+ /* ---------------------------------------------------------------------- */
+
+ if (ok)
+ {
+ F->sorted = Fsorted ;
+ }
+ ASSERT (CHOLMOD(dump_sparse) (F, "output F unsym", Common) >= 0) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_transpose_sym ================================================ */
+/* ========================================================================== */
+
+/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
+ * See cholmod_transpose for a simpler routine.
+ *
+ * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL.
+ */
+
+int CHOLMOD(transpose_sym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values */
+ Int *Perm, /* size nrow, if present (can be NULL) */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A' or A(p,p)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Anz, *Ai, *Fp, *Wi, *Pinv, *Iwork ;
+ Int p, pend, packed, upper, permute, jold, n, i, j, k, iold ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->nrow != A->ncol || A->stype == 0)
+ {
+ /* this routine handles square symmetric matrices only */
+ ERROR (CHOLMOD_INVALID, "matrix must be symmetric") ;
+ return (FALSE) ;
+ }
+ if (A->nrow != F->ncol || A->ncol != F->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ permute = (Perm != NULL) ;
+ n = A->nrow ;
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+ upper = (A->stype > 0) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = (Perm != NULL) ? 2*n : n */
+ s = CHOLMOD(add_size_t) (n, ((Perm != NULL) ? n : 0), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size n (i/l/l) */
+ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */
+
+ /* ---------------------------------------------------------------------- */
+ /* check Perm and construct inverse permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (permute)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Pinv [i] = EMPTY ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i > n || Pinv [i] != EMPTY)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid permutation") ;
+ return (FALSE) ;
+ }
+ Pinv [i] = k ;
+ }
+ }
+
+ /* Perm is now valid */
+ ASSERT (CHOLMOD(dump_perm) (Perm, n, n, "Perm", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of F */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = 0 ;
+ }
+
+ if (packed)
+ {
+ if (permute)
+ {
+ if (upper)
+ {
+ /* packed, permuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ pend = Ap [jold+1] ;
+ for (p = Ap [jold] ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold <= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MIN (i, j)]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* packed, permuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ pend = Ap [jold+1] ;
+ for (p = Ap [jold] ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold >= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MAX (i, j)]++ ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (upper)
+ {
+ /* packed, unpermuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* packed, unpermuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (permute)
+ {
+ if (upper)
+ {
+ /* unpacked, permuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold <= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MIN (i, j)]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* unpacked, permuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold >= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MAX (i, j)]++ ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (upper)
+ {
+ /* unpacked, unpermuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* unpacked, unpermuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Fp [i] = p ;
+ p += Wi [i] ;
+ }
+ Fp [n] = p ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = Fp [i] ;
+ }
+
+ if (p > (Int) (F->nzmax))
+ {
+ ERROR (CHOLMOD_INVALID, "F is too small") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ ok = FALSE ;
+ if (values == 0 || F->xtype == CHOLMOD_PATTERN)
+ {
+ PRINT2 (("\n:::: p_transpose_sym Perm %p\n", Perm)) ;
+ ok = p_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_REAL)
+ {
+ PRINT2 (("\n:::: r_transpose_sym Perm %p\n", Perm)) ;
+ ok = r_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_COMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ PRINT2 (("\n:::: ct_transpose_sym Perm %p\n", Perm)) ;
+ ok = ct_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ PRINT2 (("\n:::: c_transpose_sym Perm %p\n", Perm)) ;
+ ok = c_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ }
+ else if (F->xtype == CHOLMOD_ZOMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ PRINT2 (("\n:::: zt_transpose_sym Perm %p\n", Perm)) ;
+ ok = zt_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ PRINT2 (("\n:::: z_transpose_sym Perm %p\n", Perm)) ;
+ ok = z_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize result F */
+ /* ---------------------------------------------------------------------- */
+
+ /* F is sorted if there is no permutation vector */
+ if (ok)
+ {
+ F->sorted = !permute ;
+ F->packed = TRUE ;
+ F->stype = - SIGN (A->stype) ; /* flip the stype */
+ ASSERT (CHOLMOD(dump_sparse) (F, "output F sym", Common) >= 0) ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_transpose ==================================================== */
+/* ========================================================================== */
+
+/* Returns A'. See also cholmod_ptranspose below. */
+
+cholmod_sparse *CHOLMOD(transpose)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values
+ (returns its result as CHOLMOD_PATTERN) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_ptranspose =================================================== */
+/* ========================================================================== */
+
+/* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if
+ * A is unsymmetric.
+ *
+ * workspace:
+ * Iwork (MAX (nrow,ncol)) if unsymmetric and fset is non-NULL
+ * Iwork (nrow) if unsymmetric and fset is NULL
+ * Iwork (2*nrow) if symmetric and Perm is non-NULL.
+ * Iwork (nrow) if symmetric and Perm is NULL.
+ *
+ * A simple worst-case upper bound on the workspace is nrow+ncol.
+ */
+
+cholmod_sparse *CHOLMOD(ptranspose)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values */
+ Int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Anz ;
+ cholmod_sparse *F ;
+ Int nrow, ncol, use_fset, j, jj, fnz, packed, stype, nf, xtype ;
+ size_t ineed ;
+ int ok = TRUE ;
+
+ nf = fsize ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ stype = A->stype ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ if (stype != 0)
+ {
+ use_fset = FALSE ;
+ if (Perm != NULL)
+ {
+ ineed = CHOLMOD(mult_size_t) (A->nrow, 2, &ok) ;
+ }
+ else
+ {
+ ineed = A->nrow ;
+ }
+ }
+ else
+ {
+ use_fset = (fset != NULL) ;
+ if (use_fset)
+ {
+ ineed = MAX (A->nrow, A->ncol) ;
+ }
+ else
+ {
+ ineed = A->nrow ;
+ }
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ CHOLMOD(allocate_work) (0, ineed, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+ xtype = values ? A->xtype : CHOLMOD_PATTERN ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate F */
+ /* ---------------------------------------------------------------------- */
+
+ /* determine # of nonzeros in F */
+ if (stype != 0)
+ {
+ /* F=A' or F=A(p,p)', fset is ignored */
+ fnz = CHOLMOD(nnz) (A, Common) ;
+ }
+ else
+ {
+ nf = (use_fset) ? nf : ncol ;
+ if (use_fset)
+ {
+ fnz = 0 ;
+ /* F=A(:,f)' or F=A(p,f)' */
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ /* The fset is not yet checked; it will be thoroughly checked
+ * in cholmod_transpose_unsym. For now, just make sure we don't
+ * access Ap and Anz out of bounds. */
+ j = fset [jj] ;
+ if (j >= 0 && j < ncol)
+ {
+ fnz += packed ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ;
+ }
+ }
+ }
+ else
+ {
+ /* F=A' or F=A(p,:)' */
+ fnz = CHOLMOD(nnz) (A, Common) ;
+ }
+ }
+
+ /* F is ncol-by-nrow, fnz nonzeros, sorted unless f is present and unsorted,
+ * packed, of opposite stype as A, and with/without numerical values */
+ F = CHOLMOD(allocate_sparse) (ncol, nrow, fnz, TRUE, TRUE, -SIGN(stype),
+ xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose and optionally permute the matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype != 0)
+ {
+ /* F = A (p,p)', using upper or lower triangular part of A only */
+ ok = CHOLMOD(transpose_sym) (A, values, Perm, F, Common) ;
+ }
+ else
+ {
+ /* F = A (p,f)' */
+ ok = CHOLMOD(transpose_unsym) (A, values, Perm, fset, nf, F, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the matrix F, or NULL if an error occured */
+ /* ---------------------------------------------------------------------- */
+
+ if (!ok)
+ {
+ CHOLMOD(free_sparse) (&F, Common) ;
+ }
+ return (F) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sort ========================================================= */
+/* ========================================================================== */
+
+/* Sort the columns of A, in place. Returns A in packed form, even if it
+ * starts as unpacked. Removes entries in the ignored part of a symmetric
+ * matrix.
+ *
+ * workspace: Iwork (max (nrow,ncol)). Allocates additional workspace for a
+ * temporary copy of A'.
+ */
+
+int CHOLMOD(sort)
+(
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to sort */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap ;
+ cholmod_sparse *F ;
+ Int anz, ncol, nrow, stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ nrow = A->nrow ;
+ if (nrow <= 1)
+ {
+ /* a 1-by-n sparse matrix must be sorted */
+ A->sorted = TRUE ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ;
+ CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ anz = CHOLMOD(nnz) (A, Common) ;
+ stype = A->stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sort the columns of the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocate workspace for transpose: ncol-by-nrow, same # of nonzeros as A,
+ * sorted, packed, same stype as A, and of the same numeric type as A. */
+ F = CHOLMOD(allocate_sparse) (ncol, nrow, anz, TRUE, TRUE, stype,
+ A->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ if (stype != 0)
+ {
+ /* F = A', upper or lower triangular part only */
+ CHOLMOD(transpose_sym) (A, 1, NULL, F, Common) ;
+ A->packed = TRUE ;
+ /* A = F' */
+ CHOLMOD(transpose_sym) (F, 1, NULL, A, Common) ;
+ }
+ else
+ {
+ /* F = A' */
+ CHOLMOD(transpose_unsym) (A, 1, NULL, NULL, 0, F, Common) ;
+ A->packed = TRUE ;
+ /* A = F' */
+ CHOLMOD(transpose_unsym) (F, 1, NULL, NULL, 0, A, Common) ;
+ }
+
+ ASSERT (A->sorted && A->packed) ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "Asorted", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce A in size, if needed. This must succeed. */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ anz = Ap [ncol] ;
+ ASSERT ((size_t) anz <= A->nzmax) ;
+ CHOLMOD(reallocate_sparse) (anz, A, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&F, Common) ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/cholmod_triplet.c b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_triplet.c
new file mode 100644
index 0000000..5ce7ad8
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/cholmod_triplet.c
@@ -0,0 +1,773 @@
+/* ========================================================================== */
+/* === Core/cholmod_triplet ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_triplet object:
+ *
+ * A sparse matrix held in triplet form is the simplest one for a user to
+ * create. It consists of a list of nz entries in arbitrary order, held in
+ * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k],
+ * column j[k], with value x[k]. There may be duplicate values; if A(i,j)
+ * appears more than once, its value is the sum of the entries with those row
+ * and column indices.
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_allocate_triplet allocate a triplet matrix
+ * cholmod_free_triplet free a triplet matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_reallocate_triplet reallocate a triplet matrix
+ * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix
+ * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix
+ * cholmod_copy_triplet create a copy of a triplet matrix
+ *
+ * The relationship between an m-by-n cholmod_sparse matrix A and a
+ * cholmod_triplet matrix (i, j, and x) is identical to how they are used in
+ * the MATLAB "sparse" and "find" functions:
+ *
+ * [i j x] = find (A)
+ * [m n] = size (A)
+ * A = sparse (i,j,x,m,n)
+ *
+ * with the exception that the cholmod_sparse matrix may be "unpacked", may
+ * have either sorted or unsorted columns (depending on the option selected),
+ * and may be symmetric with just the upper or lower triangular part stored.
+ * Likewise, the cholmod_triplet matrix may contain just the entries in the
+ * upper or lower triangular part of a symmetric matrix.
+ *
+ * MATLAB sparse matrices are always "packed", always have sorted columns,
+ * and always store both parts of a symmetric matrix. In some cases, MATLAB
+ * behaves like CHOLMOD by ignoring entries in the upper or lower triangular
+ * part of a matrix that is otherwise assumed to be symmetric (such as the
+ * input to chol). In CHOLMOD, that option is a characteristic of the object.
+ * In MATLAB, that option is based on how a matrix is used as the input to
+ * a function.
+ *
+ * The triplet matrix is provided to give the user a simple way of constructing
+ * a sparse matrix. There are very few operations supported for triplet
+ * matrices. The assumption is that they will be converted to cholmod_sparse
+ * matrix form first.
+ *
+ * Adding two triplet matrices simply involves concatenating the contents of
+ * the three arrays (i, j, and x). To permute a triplet matrix, just replace
+ * the row and column indices with their permuted values. For example, if
+ * P is a permutation vector, then P [k] = j means row/column j is the kth
+ * row/column in C=P*A*P'. In MATLAB notation, C=A(p,p). If Pinv is an array
+ * of size n and T is the triplet form of A, then:
+ *
+ * Ti = T->i ;
+ * Tj = T->j ;
+ * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ;
+ * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ;
+ * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ;
+ *
+ * overwrites T with the triplet form of C=P*A*P'. The conversion
+ *
+ * C = cholmod_triplet_to_sparse (T, 0, &Common) ;
+ *
+ * will then return the matrix C = P*A*P'.
+ *
+ * Note that T->stype > 0 means that entries in the lower triangular part of
+ * T are transposed into the upper triangular part when T is converted to
+ * sparse matrix (cholmod_sparse) form with cholmod_triplet_to_sparse. The
+ * opposite is true for T->stype < 0.
+ *
+ * Since the triplet matrix T is so simple to generate, it's quite easy
+ * to remove entries that you do not want, prior to converting T to the
+ * cholmod_sparse form. So if you include these entries in T, CHOLMOD
+ * assumes that there must be a reason (such as the one above). Thus,
+ * no entry in a triplet matrix is ever ignored.
+ *
+ * Other operations, such as extacting a submatrix, horizontal and vertical
+ * concatenation, multiply a triplet matrix times a dense matrix, are also
+ * simple. Multiplying two triplet matrices is not trivial; the simplest
+ * method is to convert them to cholmod_sparse matrices first.
+ *
+ * Supports all xtypes (pattern, real, complex, and zomplex).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define PATTERN
+#include "t_cholmod_triplet.c"
+#define REAL
+#include "t_cholmod_triplet.c"
+#define COMPLEX
+#include "t_cholmod_triplet.c"
+#define ZOMPLEX
+#include "t_cholmod_triplet.c"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_triplet ============================================= */
+/* ========================================================================== */
+
+/* allocate space for a triplet matrix
+ *
+ * workspace: none
+ */
+
+cholmod_triplet *CHOLMOD(allocate_triplet)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of T */
+ size_t ncol, /* # of columns of T */
+ size_t nzmax, /* max # of nonzeros of T */
+ int stype, /* stype of T */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_triplet *T ;
+ size_t nzmax0 ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (NULL) ;
+ }
+ /* ensure the dimensions do not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ;
+ if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate header */
+ /* ---------------------------------------------------------------------- */
+
+ T = CHOLMOD(malloc) (sizeof (cholmod_triplet), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ PRINT1 (("cholmod_allocate_triplet %d-by-%d nzmax %d xtype %d\n",
+ nrow, ncol, nzmax, xtype)) ;
+
+ nzmax = MAX (1, nzmax) ;
+
+ T->nrow = nrow ;
+ T->ncol = ncol ;
+ T->nzmax = nzmax ;
+ T->nnz = 0 ;
+ T->stype = stype ;
+ T->itype = ITYPE ;
+ T->xtype = xtype ;
+ T->dtype = DTYPE ;
+
+ T->j = NULL ;
+ T->i = NULL ;
+ T->x = NULL ;
+ T->z = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix itself */
+ /* ---------------------------------------------------------------------- */
+
+ nzmax0 = 0 ;
+ CHOLMOD(realloc_multiple) (nzmax, 2, xtype, &(T->i), &(T->j),
+ &(T->x), &(T->z), &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_triplet) (&T, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_triplet ================================================= */
+/* ========================================================================== */
+
+/* free a triplet matrix
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_triplet)
+(
+ /* ---- in/out --- */
+ cholmod_triplet **THandle, /* matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int nz ;
+ cholmod_triplet *T ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (THandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ T = *THandle ;
+ if (T == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ nz = T->nzmax ;
+ T->j = CHOLMOD(free) (nz, sizeof (Int), T->j, Common) ;
+ T->i = CHOLMOD(free) (nz, sizeof (Int), T->i, Common) ;
+ if (T->xtype == CHOLMOD_REAL)
+ {
+ T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ;
+ }
+ else if (T->xtype == CHOLMOD_COMPLEX)
+ {
+ T->x = CHOLMOD(free) (nz, 2*sizeof (double), T->x, Common) ;
+ }
+ else if (T->xtype == CHOLMOD_ZOMPLEX)
+ {
+ T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ;
+ T->z = CHOLMOD(free) (nz, sizeof (double), T->z, Common) ;
+ }
+ *THandle = CHOLMOD(free) (1, sizeof (cholmod_triplet), (*THandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_triplet =========================================== */
+/* ========================================================================== */
+
+/* Change the size of T->i, T->j, and T->x, or allocate them if their current
+ * size is zero. T->x is not modified if T->xtype is CHOLMOD_PATTERN.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_triplet)
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in T */
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (T, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ PRINT1 (("realloc triplet %d to %d, xtype: %d\n",
+ T->nzmax, nznew, T->xtype)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* resize the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(realloc_multiple) (MAX (1,nznew), 2, T->xtype, &(T->i), &(T->j),
+ &(T->x), &(T->z), &(T->nzmax), Common) ;
+
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_triplet_to_sparse ============================================ */
+/* ========================================================================== */
+
+/* Convert a set of triplets into a cholmod_sparse matrix. In MATLAB notation,
+ * for unsymmetric matrices:
+ *
+ * A = sparse (Ti, Tj, Tx, nrow, ncol, nzmax) ;
+ *
+ * For the symmetric upper case:
+ *
+ * A = sparse (min(Ti,Tj), max(Ti,Tj), Tx, nrow, ncol, nzmax) ;
+ *
+ * For the symmetric lower case:
+ *
+ * A = sparse (max(Ti,Tj), min(Ti,Tj), Tx, nrow, ncol, nzmax) ;
+ *
+ * If Tx is NULL, then A->x is not allocated, and only the pattern of A is
+ * computed. A is returned in packed form, and can be of any stype
+ * (upper/lower/unsymmetric). It has enough space to hold the values in T,
+ * or nzmax, whichever is larger.
+ *
+ * workspace: Iwork (max (nrow,ncol))
+ * allocates a temporary copy of its output matrix.
+ *
+ * The resulting sparse matrix has the same xtype as the input triplet matrix.
+ */
+
+cholmod_sparse *CHOLMOD(triplet_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ size_t nzmax, /* allocate at least this much space in output matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *R, *A = NULL ;
+ Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ;
+ Int i, j, p, k, stype, nrow, ncol, nz, ok ;
+ size_t anz = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (T, NULL) ;
+ Ti = T->i ;
+ Tj = T->j ;
+ RETURN_IF_NULL (Ti, NULL) ;
+ RETURN_IF_NULL (Tj, NULL) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ stype = SIGN (T->stype) ;
+ if (stype && T->nrow != T->ncol)
+ {
+ /* inputs invalid */
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_triplet) (T, "T", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ nz = T->nnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate temporary matrix R */
+ /* ---------------------------------------------------------------------- */
+
+ R = CHOLMOD(allocate_sparse) (ncol, nrow, nz, FALSE, FALSE, -stype,
+ T->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ Rp = R->p ;
+ Ri = R->i ;
+ Rnz = R->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of A (also counting duplicates) */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Rnz [i] = 0 ;
+ }
+
+ if (stype > 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= nrow || j < 0 || j >= ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "index out of range") ;
+ break ;
+ }
+ /* A will be symmetric with just the upper triangular part stored.
+ * Create a matrix R that is lower triangular. Entries in the
+ * upper part of R are transposed to the lower part. */
+ Rnz [MIN (i,j)]++ ;
+ }
+ }
+ else if (stype < 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= nrow || j < 0 || j >= ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "index out of range") ;
+ break ;
+ }
+ /* A will be symmetric with just the lower triangular part stored.
+ * Create a matrix R that is upper triangular. Entries in the
+ * lower part of R are transposed to the upper part. */
+ Rnz [MAX (i,j)]++ ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= nrow || j < 0 || j >= ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "index out of range") ;
+ break ;
+ }
+ /* constructing an unsymmetric matrix */
+ Rnz [i]++ ;
+ }
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* triplet matrix is invalid */
+ CHOLMOD(free_sparse) (&R, Common) ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Rp [i] = p ;
+ p += Rnz [i] ;
+ }
+ Rp [nrow] = p ;
+
+ /* use Wj (i/l/l) as temporary row pointers */
+ Wj = Common->Iwork ; /* size MAX (nrow,ncol) FUTURE WORK: (i/l/l) */
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wj [i] = Rp [i] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct triplet matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (T->xtype)
+ {
+ case CHOLMOD_PATTERN:
+ anz = p_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+
+ case CHOLMOD_REAL:
+ anz = r_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ anz = c_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ anz = z_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* A = R' (array transpose, not complex conjugate transpose) */
+ /* ---------------------------------------------------------------------- */
+
+ /* workspace: Iwork (R->nrow), which is A->ncol */
+
+ ASSERT (CHOLMOD(dump_sparse) (R, "R", Common) >= 0) ;
+
+ A = CHOLMOD(allocate_sparse) (nrow, ncol, MAX (anz, nzmax), TRUE, TRUE,
+ stype, T->xtype, Common) ;
+
+ if (stype)
+ {
+ ok = CHOLMOD(transpose_sym) (R, 1, NULL, A, Common) ;
+ }
+ else
+ {
+ ok = CHOLMOD(transpose_unsym) (R, 1, NULL, NULL, 0, A, Common) ;
+ }
+
+ CHOLMOD(free_sparse) (&R, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A = triplet(T) result", Common) >= 0) ;
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sparse_to_triplet ============================================ */
+/* ========================================================================== */
+
+/* Converts a sparse column-oriented matrix to triplet form.
+ * The resulting triplet matrix has the same xtype as the sparse matrix.
+ *
+ * workspace: none
+ */
+
+cholmod_triplet *CHOLMOD(sparse_to_triplet)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az, *Tx, *Tz ;
+ Int *Ap, *Ai, *Ti, *Tj, *Anz ;
+ cholmod_triplet *T ;
+ Int i, xtype, p, pend, k, j, nrow, ncol, nz, stype, packed, up, lo,
+ both ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ stype = SIGN (A->stype) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ if (stype && nrow != ncol)
+ {
+ /* inputs invalid */
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Ax = A->x ;
+ Az = A->z ;
+ xtype = A->xtype ;
+ Common->status = CHOLMOD_OK ;
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ nz = CHOLMOD(nnz) (A, Common) ;
+ T = CHOLMOD(allocate_triplet) (nrow, ncol, nz, A->stype, A->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to a sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ T->stype = A->stype ;
+
+ both = (A->stype == 0) ;
+ up = (A->stype > 0) ;
+ lo = (A->stype < 0) ;
+
+ k = 0 ;
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (both || (up && i <= j) || (lo && i >= j))
+ {
+ Ti [k] = Ai [p] ;
+ Tj [k] = j ;
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ Tx [k] = Ax [p] ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Tx [2*k ] = Ax [2*p ] ;
+ Tx [2*k+1] = Ax [2*p+1] ;
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ Tx [k] = Ax [p] ;
+ Tz [k] = Az [p] ;
+ }
+
+ k++ ;
+ ASSERT (k <= nz) ;
+ }
+ }
+ }
+
+ T->nnz = k ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_triplet) (T, "T", Common)) ;
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_triplet ================================================= */
+/* ========================================================================== */
+
+/* Create an exact copy of a triplet matrix, except that entries in unused
+ * space are not copied (they might not be initialized, and copying them would
+ * cause program checkers such as purify and valgrind to complain).
+ * The output triplet matrix has the same xtype as the input triplet matrix.
+ */
+
+cholmod_triplet *CHOLMOD(copy_triplet)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Tx, *Tz, *Cx, *Cz ;
+ Int *Ci, *Cj, *Ti, *Tj ;
+ cholmod_triplet *C ;
+ Int xtype, k, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (T, NULL) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ nz = T->nnz ;
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ xtype = T->xtype ;
+ RETURN_IF_NULL (Ti, NULL) ;
+ RETURN_IF_NULL (Tj, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_triplet) (T, "T input", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate copy */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_triplet) (T->nrow, T->ncol, T->nzmax, T->stype,
+ xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ci = C->i ;
+ Cj = C->j ;
+ Cx = C->x ;
+ Cz = C->z ;
+ C->nnz = nz ;
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [k] = Ti [k] ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cj [k] = Tj [k] ;
+ }
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cx [k] = Tx [k] ;
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cx [2*k ] = Tx [2*k ] ;
+ Cx [2*k+1] = Tx [2*k+1] ;
+ }
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cx [k] = Tx [k] ;
+ Cz [k] = Tz [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_triplet) (C, "C triplet copy", Common)) ;
+ return (C) ;
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/lesser.txt b/src/C/SuiteSparse/CHOLMOD/Core/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/lesser.txt
@@ -0,0 +1,504 @@
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+ 13. The Free Software Foundation may publish revised and/or new
+versions of the Lesser General Public License from time to time.
+Such new versions will be similar in spirit to the present version,
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+license version number, you may choose any version ever published by
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+
+ 14. If you wish to incorporate parts of the Library into other free
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+Software Foundation; we sometimes make exceptions for this. Our
+decision will be guided by the two goals of preserving the free status
+of all derivatives of our free software and of promoting the sharing
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+ 15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO
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+DAMAGES.
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+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
+everyone can redistribute and change. You can do so by permitting
+redistribution under these terms (or, alternatively, under the terms of the
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+ To apply these terms, attach the following notices to the library. It is
+safest to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the library's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
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+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
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+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
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+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_change_factor.c b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_change_factor.c
new file mode 100644
index 0000000..548f883
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_change_factor.c
@@ -0,0 +1,661 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_change_factor ========================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_change_factor. All xtypes supported. */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_change_simplicial_numeric ========================================== */
+/* ========================================================================== */
+
+static void TEMPLATE (change_simplicial_numeric)
+(
+ cholmod_factor *L,
+ Int to_ll,
+ Int to_packed,
+ Int *newLi,
+ double *newLx,
+ double *newLz,
+ Int lnz,
+ Int grow,
+ double grow1,
+ Int grow2,
+ Int make_ll,
+ Int make_monotonic,
+ Int make_ldl,
+ cholmod_common *Common
+)
+{
+ double xlen, dj [1], ljj [1], lj2 [1] ;
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz ;
+ Int n, j, len, pnew, pold, k, p, pend ;
+
+ n = L->n ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+
+ if (make_ll)
+ {
+ L->minor = n ;
+ }
+
+ if (make_monotonic)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* reorder the columns to make them monotonic */
+ /* ------------------------------------------------------------------ */
+
+ pnew = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* copy and pack column j */
+ len = Lnz [j] ;
+ PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n",
+ j, Lnz [j], len, pnew)) ;
+ pold = Lp [j] ;
+ ASSERT (Li [pold] == j) ;
+
+ if (make_ll)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* copy and convert LDL' to LL' */
+ /* ---------------------------------------------------------- */
+
+ /* dj = Lx [pold] ; */
+ ASSIGN_REAL (dj,0, Lx,pold) ;
+
+ if (IS_LE_ZERO (dj [0]))
+ {
+ /* Conversion has failed; matrix is not positive definite.
+ * Do not modify the column so that the LDL' factorization
+ * can be restored if desired, by converting back to LDL'.
+ * Continue the conversion, but flag the error. */
+ if (L->minor == (size_t) n)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ;
+ L->minor = j ;
+ }
+ for (k = 0 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ ljj [0] = sqrt (dj [0]) ;
+ newLi [pnew] = j ;
+ /* newLx [pnew] = ljj ; */
+ ASSIGN_REAL (newLx, pnew, ljj, 0) ;
+ CLEAR_IMAG (newLx, newLz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] * ljj ; */
+ MULT_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0);
+ }
+ }
+
+ }
+ else if (make_ldl)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* copy and convert LL' to LDL' */
+ /* ---------------------------------------------------------- */
+
+ /* ljj = Lx [pold] ; */
+ ASSIGN_REAL (ljj, 0, Lx, pold) ;
+
+ if (ljj [0] <= 0)
+ {
+ /* matrix is not positive-definite; copy column as-is */
+ for (k = 0 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ newLi [pnew] = j ;
+ /* newLx [pnew] = ljj*ljj ; */
+ lj2 [0] = ljj [0] * ljj [0] ;
+ ASSIGN_REAL (newLx, pnew, lj2, 0) ;
+ CLEAR_IMAG (newLx, newLz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] / ljj ; */
+ DIV_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0) ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* copy and leave LL' or LDL' as-is */
+ /* ---------------------------------------------------------- */
+
+ for (k = 0 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+
+ Lp [j] = pnew ;
+
+ /* compute len in double to avoid integer overflow */
+ if (grow)
+ {
+ xlen = (double) len ;
+ xlen = grow1 * xlen + grow2 ;
+ xlen = MIN (xlen, n-j) ;
+ len = (Int) xlen ;
+ }
+ ASSERT (len >= Lnz [j] && len <= n-j) ;
+ pnew += len ;
+ ASSERT (pnew > 0) ; /* integer overflow case already covered */
+ }
+ Lp [n] = pnew ;
+ PRINT1 (("final pnew = "ID", lnz "ID" lnzmax %g\n",
+ pnew, lnz, (double) L->nzmax)) ;
+ ASSERT (pnew <= lnz) ;
+
+ /* free the old L->i and L->x and replace with the new ones */
+ CHOLMOD(free) (L->nzmax, sizeof (Int), L->i, Common) ;
+
+#ifdef REAL
+ CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ;
+#elif defined (COMPLEX)
+ CHOLMOD(free) (L->nzmax, 2*sizeof (double), L->x, Common) ;
+#else
+ CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ;
+ CHOLMOD(free) (L->nzmax, sizeof (double), L->z, Common) ;
+#endif
+
+ L->i = newLi ;
+ L->x = newLx ;
+ L->z = newLz ;
+ L->nzmax = lnz ;
+
+ /* reconstruct the link list */
+ natural_list (L) ;
+
+ }
+ else if (to_packed)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* already monotonic, just pack the columns of L */
+ /* ------------------------------------------------------------------ */
+
+ pnew = 0 ;
+
+ if (make_ll)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pack and convert LDL' to LL' */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+ ASSERT (len > 0) ;
+ ASSERT (Li [pold] == j) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+
+ /* dj = Lx [pold] ; */
+ ASSIGN_REAL (dj,0, Lx,pold) ;
+
+ if (IS_LE_ZERO (dj [0]))
+ {
+ /* Conversion has failed; matrix is not positive definite.
+ * Do not modify the column so that the LDL' factorization
+ * can be restored if desired, by converting back to LDL'.
+ * Continue the conversion, but flag the error. */
+ if (L->minor == (size_t) n)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ;
+ L->minor = j ;
+ }
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ ljj [0] = sqrt (dj [0]) ;
+ Li [pnew] = j ;
+
+ /* Lx [pnew] = ljj ; */
+ ASSIGN_REAL (Lx, pnew, ljj, 0) ;
+ CLEAR_IMAG (Lx, Lz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] * ljj ; */
+ MULT_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ;
+ }
+ }
+ Lp [j] = pnew ;
+ pnew += len ;
+ }
+
+ }
+ else if (make_ldl)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pack and convert LL' to LDL' */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+
+ /* ljj = Lx [pold] ; */
+ ASSIGN_REAL (ljj, 0, Lx, pold) ;
+
+ ASSERT (len > 0) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+ if (ljj [0] <= 0)
+ {
+ /* matrix is not positive-definite; pack column as-is */
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ Li [pnew] = Li [pold] ;
+
+ /* Lx [pnew] = ljj*ljj ; */
+ lj2 [0] = ljj [0] * ljj [0] ;
+ ASSIGN_REAL (Lx, pnew, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] / ljj ; */
+ DIV_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ;
+ }
+ }
+ Lp [j] = pnew ;
+ pnew += len ;
+ }
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* pack and leave LL' or LDL' as-is */
+ /* ---------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+ ASSERT (len > 0) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+ if (pnew < pold)
+ {
+ PRINT2 ((" pack this column\n")) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ Lp [j] = pnew ;
+ }
+ pnew += len ;
+ }
+ }
+
+ Lp [n] = pnew ;
+ PRINT2 (("Lp [n] = "ID"\n", pnew)) ;
+
+ }
+ else if (make_ll)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert LDL' to LL', but do so in-place */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+
+ /* dj = Lx [p] ; */
+ ASSIGN_REAL (dj,0, Lx,p) ;
+
+ if (IS_LE_ZERO (dj [0]))
+ {
+ /* Conversion has failed; matrix is not positive definite.
+ * Do not modify the column so that the LDL' factorization
+ * can be restored if desired, by converting back to LDL'.
+ * Continue the conversion, but flag the error. */
+ if (L->minor == (size_t) n)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ;
+ L->minor = j ;
+ }
+ }
+ else
+ {
+ ljj [0] = sqrt (dj [0]) ;
+ /* Lx [p] = ljj ; */
+ ASSIGN_REAL (Lx,p, ljj,0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* Lx [p] *= ljj ; */
+ MULT_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ;
+ }
+ }
+ }
+
+ }
+ else if (make_ldl)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert LL' to LDL', but do so in-place */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+
+ /* ljj = Lx [p] ; */
+ ASSIGN_REAL (ljj, 0, Lx, p) ;
+
+ if (ljj [0] > 0)
+ {
+ /* Lx [p] = ljj*ljj ; */
+ lj2 [0] = ljj [0] * ljj [0] ;
+ ASSIGN_REAL (Lx, p, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* Lx [p] /= ljj ; */
+ DIV_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ;
+ }
+ }
+ }
+ }
+
+ L->is_ll = to_ll ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "done change simplicial numeric", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === t_ll_super_to_simplicial_numeric ===================================== */
+/* ========================================================================== */
+
+/* A supernodal L can only be real or complex, not zomplex */
+
+#ifndef ZOMPLEX
+
+static void TEMPLATE (ll_super_to_simplicial_numeric)
+(
+ cholmod_factor *L,
+ Int to_packed,
+ Int to_ll,
+ cholmod_common *Common
+)
+{
+ double ljj [1], lj2 [1] ;
+ double *Lx ;
+ Int *Ls, *Lpi, *Lpx, *Super, *Lp, *Li, *Lnz ;
+ Int n, lnz, s, nsuper, p, psi, psx, psend, nsrow, nscol, ii, jj, j, k1, k2,
+ q ;
+
+ L->is_ll = to_ll ;
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lnz = L->nz ;
+ lnz = L->nzmax ;
+
+ n = L->n ;
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+
+ p = 0 ;
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ /* column j of L starts here */
+ j = jj + k1 ;
+
+ if (to_ll)
+ {
+ if (to_packed)
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LL' packed */
+ /* ------------------------------------------------------ */
+
+ Lp [j] = p ;
+ PRINT2 (("Col j "ID" p "ID"\n", j, p)) ;
+ for (ii = jj ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ;
+ Li [p] = Ls [psi + ii] ;
+ /* Lx [p] = Lx [psx + ii + jj*nsrow] ; */
+ q = psx + ii + jj*nsrow ;
+ ASSIGN (Lx,-,p, Lx,-,q) ;
+ PRINT2 ((" i "ID" ", Li [p])) ;
+ XPRINT2 (Lx,-,q) ;
+ PRINT2 (("\n")) ;
+ p++ ;
+ }
+ Lnz [j] = p - Lp [j] ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LL' unpacked */
+ /* ------------------------------------------------------ */
+
+ p = psx + jj + jj*nsrow ;
+ Lp [j] = p ;
+ Li [p] = j ;
+ Lnz [j] = nsrow - jj ;
+ p++ ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ;
+ }
+
+ }
+ }
+ else
+ {
+ if (to_packed)
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LDL' packed */
+ /* ------------------------------------------------------ */
+
+ Lp [j] = p ;
+ PRINT2 (("Col j "ID" p "ID"\n", Lp [j], p)) ;
+ /* ljj = Lx [psx + jj + jj*nsrow] ; */
+ ASSIGN_REAL (ljj, 0, Lx, psx + jj + jj*nsrow) ;
+
+ if (ljj [0] <= 0)
+ {
+ /* the matrix is not positive definite; do not divide */
+ /* Lx [p] = ljj ; */
+ ASSIGN_REAL (Lx, p, ljj, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ ljj [0] = 1 ;
+ }
+ else
+ {
+ lj2 [0] = ljj [0] * ljj [0] ;
+ /* Lx [p] = ljj*ljj ; */
+ ASSIGN_REAL (Lx, p, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ }
+ Li [p] = j ;
+ p++ ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ;
+ Li [p] = Ls [psi + ii] ;
+
+ /* Lx [p] = Lx [psx + ii + jj*nsrow] / ljj ; */
+ q = psx + ii + jj*nsrow ;
+ DIV_REAL (Lx, Lz, p, Lx, Lz, q, ljj,0) ;
+
+ PRINT2 ((" i "ID" %g\n", Li [p], Lx [p])) ;
+ p++ ;
+ }
+ Lnz [j] = p - Lp [j] ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LDL' unpacked */
+ /* ------------------------------------------------------ */
+
+ p = psx + jj + jj*nsrow ;
+ Lp [j] = p ;
+
+ /* ljj = Lx [p] ; */
+ ASSIGN_REAL (ljj,0, Lx,p) ;
+
+ if (ljj [0] <= 0)
+ {
+ /* the matrix is not positive definite; do not divide */
+ /* Lx [p] = ljj ; */
+ ASSIGN_REAL (Lx, p, ljj, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ ljj [0] = 1 ;
+ }
+ else
+ {
+ lj2 [0] = ljj [0] * ljj [0] ;
+ /* Lx [p] = ljj*ljj ; */
+ ASSIGN_REAL (Lx, p, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ }
+ Li [p] = j ;
+ Lnz [j] = nsrow - jj ;
+ p++ ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ;
+
+ /* Lx [psx + ii + jj*nsrow] /= ljj ; */
+ q = psx + ii + jj*nsrow ;
+ DIV_REAL (Lx, Lz, q, Lx, Lz, q, ljj,0) ;
+ }
+ }
+ }
+ }
+ }
+
+ if (to_packed)
+ {
+ Lp [n] = p ;
+ PRINT1 (("Final Lp "ID" n "ID" lnz "ID"\n", p, n, lnz)) ;
+ ASSERT (Lp [n] == lnz) ;
+ ASSERT (lnz <= (Int) (L->xsize)) ;
+ /* reduce size of L->x to match L->i. This cannot fail. */
+ L->x = CHOLMOD(realloc) (lnz,
+#ifdef COMPLEX
+ 2 *
+#endif
+ sizeof (double), L->x, &(L->xsize), Common) ;
+ ASSERT (lnz == (Int) (L->xsize)) ;
+ Common->status = CHOLMOD_OK ;
+ }
+ else
+ {
+ Lp [n] = Lpx [nsuper] ;
+ ASSERT (MAX (1,Lp [n]) == (Int) (L->xsize)) ;
+ ASSERT (MAX (1,Lp [n]) == (Int) (L->nzmax)) ;
+ }
+}
+
+#endif
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_dense.c b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_dense.c
new file mode 100644
index 0000000..6be9e6d
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_dense.c
@@ -0,0 +1,266 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_dense ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_dense. All xtypes supported, except that there
+ * are no dense matrices with an xtype of pattern. */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_cholmod_sparse_to_dense ============================================ */
+/* ========================================================================== */
+
+static cholmod_dense *TEMPLATE (cholmod_sparse_to_dense)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Xx, *Az, *Xz ;
+ Int *Ap, *Ai, *Anz ;
+ cholmod_dense *X ;
+ Int i, j, p, pend, nrow, ncol, packed ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ packed = A->packed ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate result */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(zeros) (nrow, ncol, XTYPE2, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ Xx = X->x ;
+ Xz = X->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy into dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype < 0)
+ {
+ /* A is symmetric with lower stored, but both parts of X are present */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ;
+ ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ else if (A->stype > 0)
+ {
+ /* A is symmetric with upper stored, but both parts of X are present */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ;
+ ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* both parts of A and X are present */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ;
+ }
+ }
+ }
+
+ return (X) ;
+}
+
+
+#ifndef PATTERN
+
+/* There are no dense matrices of xtype CHOLMOD_PATTERN */
+
+/* ========================================================================== */
+/* === t_cholmod_dense_to_sparse ============================================ */
+/* ========================================================================== */
+
+static cholmod_sparse *TEMPLATE (cholmod_dense_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ int values, /* TRUE if values to be copied, FALSE otherwise */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Xx, *Cx, *Xz, *Cz ;
+ Int *Ci, *Cp ;
+ cholmod_sparse *C ;
+ Int i, j, p, d, nrow, ncol, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the number of nonzeros in the result */
+ /* ---------------------------------------------------------------------- */
+
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d))
+ {
+ nz++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the result C */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, TRUE, TRUE, 0,
+ values ? XTYPE : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+ Cz = C->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the dense matrix X into the sparse matrix C */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cp [j] = p ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d))
+ {
+ Ci [p] = i ;
+ if (values)
+ {
+ ASSIGN (Cx, Cz, p, Xx, Xz, i+j*d) ;
+ }
+ p++ ;
+ }
+ }
+ }
+ ASSERT (p == nz) ;
+ Cp [ncol] = nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C, "C", Common) >= 0) ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === t_cholmod_copy_dense2 ================================================ */
+/* ========================================================================== */
+
+/* Y = X, where X and Y are both already allocated. */
+
+static int TEMPLATE (cholmod_copy_dense2)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* ---- output --- */
+ cholmod_dense *Y /* copy of matrix X */
+)
+{
+ double *Xx, *Xz, *Yx, *Yz ;
+ Int i, j, nrow, ncol, dy, dx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ dx = X->d ;
+ dy = Y->d ;
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy */
+ /* ---------------------------------------------------------------------- */
+
+ CLEAR (Yx, Yz, 0) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ ASSIGN (Yx, Yz, i+j*dy, Xx, Xz, i+j*dx) ;
+ }
+ }
+ return (TRUE) ;
+}
+
+#endif
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_transpose.c b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_transpose.c
new file mode 100644
index 0000000..f36a20b
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_transpose.c
@@ -0,0 +1,318 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_transpose ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_transpose. All xtypes are supported. For
+ * complex matrices, either the array tranpose or complex conjugate transpose
+ * can be computed. */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_cholmod_transpose_unsym ============================================ */
+/* ========================================================================== */
+
+/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
+ * already allocated. The complex case performs either the array transpose
+ * or complex conjugate transpose.
+ *
+ * workspace:
+ * Iwork (MAX (nrow,ncol)) if fset is present
+ * Iwork (nrow) if fset is NULL
+ */
+
+static int TEMPLATE (cholmod_transpose_unsym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ Int *Perm, /* size nrow, if present (can be NULL) */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ Int nf, /* size of fset */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az, *Fx, *Fz ;
+ Int *Ap, *Anz, *Ai, *Fp, *Fnz, *Fj, *Wi, *Iwork ;
+ Int j, p, pend, nrow, ncol, Apacked, use_fset, fp, Fpacked, jj, permute ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* ensure the xtype of A and F match (ignored if this is pattern version) */
+ if (!XTYPE_OK (A->xtype))
+ {
+ ERROR (CHOLMOD_INVALID, "real/complex mismatch") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ use_fset = (fset != NULL) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Ax = A->x ; /* size nz, real values of A */
+ Az = A->z ; /* size nz, imag values of A */
+ Anz = A->nz ;
+ Apacked = A->packed ;
+ ASSERT (IMPLIES (!Apacked, Anz != NULL)) ;
+
+ permute = (Perm != NULL) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+ Fj = F->i ; /* size nz, column indices of F */
+ Fx = F->x ; /* size nz, real values of F */
+ Fz = F->z ; /* size nz, imag values of F */
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ;
+
+ nf = (use_fset) ? nf : ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size nrow (i/l/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the transpose */
+ /* ---------------------------------------------------------------------- */
+
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = (use_fset) ? (fset [jj]) : jj ;
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ fp = Wi [Ai [p]]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === t_cholmod_transpose_sym ============================================== */
+/* ========================================================================== */
+
+/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
+ * The complex case performs either the array transpose or complex conjugate
+ * transpose.
+ *
+ * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL.
+ */
+
+static int TEMPLATE (cholmod_transpose_sym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ Int *Perm, /* size n, if present (can be NULL) */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A' or A(p,p)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az, *Fx, *Fz ;
+ Int *Ap, *Anz, *Ai, *Fp, *Fj, *Wi, *Pinv, *Iwork ;
+ Int p, pend, packed, fp, upper, permute, jold, n, i, j, iold ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* ensure the xtype of A and F match (ignored if this is pattern version) */
+ if (!XTYPE_OK (A->xtype))
+ {
+ ERROR (CHOLMOD_INVALID, "real/complex mismatch") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ permute = (Perm != NULL) ;
+ n = A->nrow ;
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Ax = A->x ; /* size nz, real values of A */
+ Az = A->z ; /* size nz, imag values of A */
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+ upper = (A->stype > 0) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+ Fj = F->i ; /* size nz, column indices of F */
+ Fx = F->x ; /* size nz, real values of F */
+ Fz = F->z ; /* size nz, imag values of F */
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size n (i/l/l) */
+ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the transpose */
+ /* ---------------------------------------------------------------------- */
+
+ if (permute)
+ {
+ if (upper)
+ {
+ /* permuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = (packed) ? Ap [jold+1] : p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold <= jold)
+ {
+ i = Pinv [iold] ;
+ if (i < j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ else
+ {
+ fp = Wi [j]++ ;
+ Fj [fp] = i ;
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ /* permuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = (packed) ? Ap [jold+1] : p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold >= jold)
+ {
+ i = Pinv [iold] ;
+ if (i > j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ else
+ {
+ fp = Wi [j]++ ;
+ Fj [fp] = i ;
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (upper)
+ {
+ /* unpermuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ }
+ }
+ }
+ else
+ {
+ /* unpermuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ }
+ }
+ }
+ }
+
+ return (TRUE) ;
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
+#undef NCONJUGATE
diff --git a/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_triplet.c b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_triplet.c
new file mode 100644
index 0000000..d917175
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Core/t_cholmod_triplet.c
@@ -0,0 +1,176 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_triplet =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_triplet. All xtypes supported */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_cholmod_triplet_to_sparse ========================================== */
+/* ========================================================================== */
+
+static size_t TEMPLATE (cholmod_triplet_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ /* ---- in/out --- */
+ cholmod_sparse *R, /* output matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Rx, *Rz, *Tx, *Tz ;
+ Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ;
+ Int i, j, p, p1, p2, pdest, pj, k, stype, nrow, ncol, nz ;
+ size_t anz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* Wj contains a copy of Rp on input [ */
+ Wj = Common->Iwork ; /* size MAX (nrow,ncol). (i/l/l) */
+
+ Rp = R->p ;
+ Ri = R->i ;
+ Rnz = R->nz ;
+ Rx = R->x ;
+ Rz = R->z ;
+
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ nz = T->nnz ;
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ stype = SIGN (T->stype) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row form */
+ /* ---------------------------------------------------------------------- */
+
+ /* if Ti is jumbled, this part dominates the run time */
+
+ if (stype > 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < j)
+ {
+ /* place triplet (j,i,x) in column i of R */
+ p = Wj [i]++ ;
+ Ri [p] = j ;
+ }
+ else
+ {
+ /* place triplet (i,j,x) in column j of R */
+ p = Wj [j]++ ;
+ Ri [p] = i ;
+ }
+ ASSIGN (Rx, Rz, p, Tx, Tz, k) ;
+ }
+ }
+ else if (stype < 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i > j)
+ {
+ /* place triplet (j,i,x) in column i of R */
+ p = Wj [i]++ ;
+ Ri [p] = j ;
+ }
+ else
+ {
+ /* place triplet (i,j,x) in column j of R */
+ p = Wj [j]++ ;
+ Ri [p] = i ;
+ }
+ ASSIGN (Rx, Rz, p, Tx, Tz, k) ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* place triplet (i,j,x) in column i of R */
+ p = Wj [Ti [k]]++ ;
+ Ri [p] = Tj [k] ;
+ ASSIGN (Rx, Rz, p, Tx, Tz, k) ;
+ }
+ }
+
+ /* done using Wj (i/l/l) as temporary row pointers ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* sum up duplicates */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Wj (i/l/l) of size ncol to keep track of duplicates in each row [ */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wj [j] = EMPTY ;
+ }
+
+ anz = 0 ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ p1 = Rp [i] ;
+ p2 = Rp [i+1] ;
+ pdest = p1 ;
+ /* at this point Wj [j] < p1 holds true for all columns j, because
+ * Ri/Rx is stored in row oriented manner */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ j = Ri [p] ;
+ pj = Wj [j] ;
+ if (pj >= p1)
+ {
+ /* this column index j is already in row i at position pj;
+ * sum up the duplicate entry */
+ /* Rx [pj] += Rx [p] ; */
+ ASSEMBLE (Rx, Rz, pj, Rx, Rz, p) ;
+ }
+ else
+ {
+ /* keep the entry and keep track in Wj [j] for case above */
+ Wj [j] = pdest ;
+ if (pdest != p)
+ {
+ Ri [pdest] = j ;
+ ASSIGN (Rx, Rz, pdest, Rx, Rz, p) ;
+ }
+ pdest++ ;
+ }
+ }
+ Rnz [i] = pdest - p1 ;
+ anz += (pdest - p1) ;
+ }
+ /* done using Wj to keep track of duplicate entries in each row ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* return number of entries after summing up duplicates */
+ /* ---------------------------------------------------------------------- */
+
+ return (anz) ;
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/ChangeLog b/src/C/SuiteSparse/CHOLMOD/Doc/ChangeLog
new file mode 100644
index 0000000..f16584d
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/ChangeLog
@@ -0,0 +1,146 @@
+Dec 12, 2006, version 1.4.0
+
+ * added support for large files (larger than 2GB)
+
+ * minor MATLAB cleanup
+
+ * renamed MATLAB function from cholmod to cholmod2, to avoid filename clash
+ with itself (the built-in version of cholmod).
+
+Dec 2, 2006, version 1.3.0
+
+ * Major modification to cholmod_read.c; now fully supports all forms of the
+ Matrix Market format. Added cholmod_read_dense and cholmod_read_matrix
+ functions to cholmod_read.c. Major changes to mread MATLAB function.
+ Added Common->prefer_binary option for cholmod_read.
+
+ * Added cholmod_write.c (cholmod_write_sparse and cholmod_write_dense
+ functions). Added mwrite MATLAB function.
+
+ * Added 2nd output argument to sparse2 (Z, binary pattern of explicit
+ zero entries).
+
+ * Added the function cholmod_symmetry to the MatrixOps module.
+ Added spsym MATLAB function.
+
+ * 2nd argument to cholmod_triplet_to_sparse changed from int to size_t.
+
+ * minor correction to cholmod_analyze_ordering, cholmod_dense.c
+
+ * minor change to cholmod_rowfac.c, cholmod_solve.c, ...
+ to allow for easier testing.
+
+Sept 28, 2006, version 1.2.1
+
+ * bug fix to cholmod_matlab.c, when working with sparse INT64 matrices
+ in the "sparse2" function
+
+Aug 31, 2006, version 1.2
+
+ * Common->default_nesdis parameter and Common->called_nd statistic added.
+ Otherwise, no change to user interface. v1.2 is fully upward
+ compatible with v1.1 (even binary compatible).
+
+ * non-supernodal Lx=b and L'x=b solves simplified, slight increase in
+ performance.
+
+ * update/downdate performance improved.
+
+ * ordering options and output statistics added to MATLAB/cholmod
+ mexFunction.
+
+July 27, 2006, version 1.1.1
+
+ * bug fix for cholmod_rowfac_mask, for the complex case. Has no
+ effect on MATLAB.
+
+June 27, 2006:
+
+ * trivial changes to nested dissection code, and cholmod_read.c (for
+ debugging, and to add explicit typecasts so compilers don't complain).
+
+May, 2006:
+
+ * Added new routines for LPDASA: cholmod_rowfac_mask, cholmod_updown_mask.
+ Added cholmod_collapse_septree. Added nd_oksep, nd_components
+ parameters to Common.
+
+Apr 30, 2006: version 1.1
+
+ * added interface to CAMD. cholmod_nested_dissection can now call
+ CCOLAMD, CSYMAMD, and CAMD. Common->nd_camd usage extended.
+ New argument added to nesdis mexFunction. New cholmod_camd function
+ added. No other changes to CHOLMOD user interface.
+
+ * more careful integer overflow checks. Added non-user-callable functions
+ to add and multiply size_t integers, with overflow checks.
+
+ * added Common->no_workspace_reallocate
+
+ * flop count is now correct for A*A' case (Common->rowfacfl).
+
+Jan 18, 2006: version 1.0.2
+
+ * bug fix: MATLAB interface incorrect for full logical matrices.
+
+ * Tcov tests modified to generate fewer intentional nan's, to make it
+ easier to look for errors in BLAS libraries that incorrectly
+ generate nan's.
+
+Dec 16, 2005: version 1.0.1
+
+ * bug fix: cholmod_amd allocated too small of a workspace when ordering A*A'
+
+Dec 8, 2005: version 1.0
+
+ * no real changes. Version 1.0 is the same as version 0.8. Version 1.0 is
+ simply the formal stable release.
+
+ * known issue: the floating point operation count, Common->rowfacfl, is
+ statistic is incorrect when factorizing A*A'. This will be fixed in
+ version 1.1.
+
+Nov 15, 2005: version 0.8
+
+ * bug fix in t_cholmod_super_numeric, for [R,p]=chol(A) usage.
+
+ * Common->quick_return_if_not_posdef added.
+
+ * Added cholmod_row_lsubtree (required for LPDASA)
+
+ * bug fix: cholmod_rcond returned sqrt(1/cond) for an LL' factorization;
+ 1/cond is required.
+
+ * new statistics added: flop counts for cholmod_rowfac, # of factor column
+ reallocations, # of factor reallocations due to column reallocations,
+ and # of times the (non-default) bounds on diag(L) are hit.
+
+ * factor column reallocation skipped if space already big enough.
+
+ * bug fix: cholmod_copy_factor did not copy L->is_monotonic.
+
+ * bug fix: cholmod_change_factor (diagonal entry was wrong in one case)
+
+ * rcond added to cholmod mexFunction ([x,rcond] = cholmod(A,b)).
+
+ * cholmod_rowadd, cholmod_rowdel modified. rowdel no longer removes
+ entries from the matrix; it sets them to zero instead.
+
+Oct 10, 2005: version 0.7
+
+ * minor changes: minor change to Check/cholmod_check.c (coerce
+ sizeof(...) to (int) when printing. Less strict check on A->p for
+ unpacked matrices) , removed a few unused variables in
+ Check/cholmod_read.c and Demo/cholmod*demo.c, changed "exit(0)" to
+ "return(0)" in Demo/cholmod_simple.c. Changed Makefile so that "." is
+ not assumed to be on the $path. Added Cygwin to architecture detection
+ in Include/cholmod_blas.h. Added cparent and cmember to nesdis.m.
+ Space for future expansion added to cholmod_common.
+
+ * removed "rowmark" from the Modify module, which affects how partial
+ updates to Lx=b solves are done during update/downdate. Should only
+ affect LPDASA.
+
+ * added CHOLMOD_SUBSUB_VERSION
+
+Aug 31, 2005: version 0.6 released.
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/Makefile b/src/C/SuiteSparse/CHOLMOD/Doc/Makefile
new file mode 100644
index 0000000..e661e91
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/Makefile
@@ -0,0 +1,227 @@
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+all: UserGuide.pdf
+
+I = \
+ ../Include/cholmod.h \
+ ../Include/cholmod_blas.h \
+ ../Include/cholmod_check.h \
+ ../Include/cholmod_cholesky.h \
+ ../Include/cholmod_complexity.h \
+ ../Include/cholmod_config.h \
+ ../Include/cholmod_core.h \
+ ../Include/cholmod_internal.h \
+ ../Include/cholmod_matrixops.h \
+ ../Include/cholmod_modify.h \
+ ../Include/cholmod_partition.h \
+ ../Include/cholmod_supernodal.h \
+ ../Include/cholmod_template.h
+
+C = ../Demo/cholmod_simple.c
+
+M = \
+ ../MATLAB/analyze.m \
+ ../MATLAB/bisect.m \
+ ../MATLAB/chol2.m \
+ ../MATLAB/cholmod2.m \
+ ../MATLAB/cholmod_demo.m \
+ ../MATLAB/cholmod_make.m \
+ ../MATLAB/etree2.m \
+ ../MATLAB/graph_demo.m \
+ ../MATLAB/lchol.m \
+ ../MATLAB/ldlchol.m \
+ ../MATLAB/ldl_normest.m \
+ ../MATLAB/ldlsolve.m \
+ ../MATLAB/ldlsplit.m \
+ ../MATLAB/ldlupdate.m \
+ ../MATLAB/lu_normest.m \
+ ../MATLAB/metis.m \
+ ../MATLAB/nesdis.m \
+ ../MATLAB/resymbol.m \
+ ../MATLAB/sdmult.m \
+ ../MATLAB/sparse2.m \
+ ../MATLAB/spsym.m \
+ ../MATLAB/mread.m \
+ ../MATLAB/mwrite.m \
+ ../MATLAB/symbfact2.m
+
+UserGuide.pdf: UserGuide.tex UserGuide.bib $(I) $(C) $(M) Makefile getproto rule.awk header.tex footer.tex getmproto mfooter.tex mheader.tex mfile.awk
+ ./getmproto ../MATLAB/analyze.m > _analyze_m.tex
+ ./getmproto ../MATLAB/bisect.m > _bisect_m.tex
+ ./getmproto ../MATLAB/chol2.m > _chol2_m.tex
+ ./getmproto ../MATLAB/cholmod2.m > _cholmod2_m.tex
+ ./getmproto ../MATLAB/cholmod_demo.m > _cholmod_demo_m.tex
+ ./getmproto ../MATLAB/cholmod_make.m > _cholmod_make_m.tex
+ ./getmproto ../MATLAB/etree2.m > _etree2_m.tex
+ ./getmproto ../MATLAB/graph_demo.m > _graph_demo_m.tex
+ ./getmproto ../MATLAB/lchol.m > _lchol_m.tex
+ ./getmproto ../MATLAB/ldlchol.m > _ldlchol_m.tex
+ ./getmproto ../MATLAB/ldl_normest.m > _ldl_normest_m.tex
+ ./getmproto ../MATLAB/ldlsolve.m > _ldlsolve_m.tex
+ ./getmproto ../MATLAB/ldlsplit.m > _ldlsplit_m.tex
+ ./getmproto ../MATLAB/ldlupdate.m > _ldlupdate_m.tex
+ ./getmproto ../MATLAB/lu_normest.m > _lu_normest_m.tex
+ ./getmproto ../MATLAB/metis.m > _metis_m.tex
+ ./getmproto ../MATLAB/mread.m > _mread_m.tex
+ ./getmproto ../MATLAB/spsym.m > _spsym_m.tex
+ ./getmproto ../MATLAB/mwrite.m > _mwrite_m.tex
+ ./getmproto ../MATLAB/nesdis.m > _nesdis_m.tex
+ ./getmproto ../MATLAB/resymbol.m > _resymbol_m.tex
+ ./getmproto ../MATLAB/sdmult.m > _sdmult_m.tex
+ ./getmproto ../MATLAB/sparse2.m > _sparse2_m.tex
+ ./getmproto ../MATLAB/symbfact2.m > _symbfact2_m.tex
+ ./getproto '/include/, /^}/' ../Demo/cholmod_simple.c > _simple.tex
+ ./getproto '/typedef struct cholmod_common/, /^}/' ../Include/cholmod_core.h > _common.tex
+ ./getproto '/int cholmod_start/, /\*\) ;/' ../Include/cholmod_core.h > _start.tex
+ ./getproto '/int cholmod_finish/, /\*\) ;/' ../Include/cholmod_core.h > _finish.tex
+ ./getproto '/int cholmod_defaults/, /\*\) ;/' ../Include/cholmod_core.h > _defaults.tex
+ ./getproto '/size_t cholmod_maxrank/, /\*\) ;/' ../Include/cholmod_core.h > _maxrank.tex
+ ./getproto '/int cholmod_allocate_work/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_work.tex
+ ./getproto '/int cholmod_free_work/, /\*\) ;/' ../Include/cholmod_core.h > _free_work.tex
+ ./getproto '/long cholmod_clear_flag/, /\*\) ;/' ../Include/cholmod_core.h > _clear_flag.tex
+ ./getproto '/int cholmod_error/, /\*\) ;/' ../Include/cholmod_core.h > _error.tex
+ ./getproto '/double cholmod_dbound/, /\*\) ;/' ../Include/cholmod_core.h > _dbound.tex
+ ./getproto '/double cholmod_hypot/, /double\) ;/' ../Include/cholmod_core.h > _hypot.tex
+ ./getproto '/int cholmod_divcomplex/, /\*\) ;/' ../Include/cholmod_core.h > _divcomplex.tex
+ ./getproto '/typedef struct cholmod_sparse/, /^}/' ../Include/cholmod_core.h > _sparse.tex
+ ./getproto '/cholmod_sparse \*cholmod_allocate_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_sparse.tex
+ ./getproto '/int cholmod_free_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _free_sparse.tex
+ ./getproto '/int cholmod_reallocate_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_sparse.tex
+ ./getproto '/long cholmod_nnz/, /\*\) ;/' ../Include/cholmod_core.h > _nnz.tex
+ ./getproto '/cholmod_sparse \*cholmod_speye/, /\*\) ;/' ../Include/cholmod_core.h > _speye.tex
+ ./getproto '/cholmod_sparse \*cholmod_spzeros/, /\*\) ;/' ../Include/cholmod_core.h > _spzeros.tex
+ ./getproto '/cholmod_sparse \*cholmod_transpose/, /\*\) ;/' ../Include/cholmod_core.h > _transpose.tex
+ ./getproto '/int cholmod_transpose_unsym/, /\*\) ;/' ../Include/cholmod_core.h > _transpose_unsym.tex
+ ./getproto '/int cholmod_transpose_sym/, /\*\) ;/' ../Include/cholmod_core.h > _transpose_sym.tex
+ ./getproto '/cholmod_sparse \*cholmod_ptranspose/, /\*\) ;/' ../Include/cholmod_core.h > _ptranspose.tex
+ ./getproto '/int cholmod_sort/, /\*\) ;/' ../Include/cholmod_core.h > _sort.tex
+ ./getproto '/cholmod_sparse \*cholmod_band/, /\*\) ;/' ../Include/cholmod_core.h > _band.tex
+ ./getproto '/int cholmod_band_inplace/, /\*\) ;/' ../Include/cholmod_core.h > _band_inplace.tex
+ ./getproto '/cholmod_sparse \*cholmod_aat/, /\*\) ;/' ../Include/cholmod_core.h > _aat.tex
+ ./getproto '/cholmod_sparse \*cholmod_copy_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _copy_sparse.tex
+ ./getproto '/cholmod_sparse \*cholmod_copy /, /\*\) ;/' ../Include/cholmod_core.h > _copy.tex
+ ./getproto '/cholmod_sparse \*cholmod_add/, /\*\) ;/' ../Include/cholmod_core.h > _add.tex
+ ./getproto '/int cholmod_sparse_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_xtype.tex
+ ./getproto '/typedef struct cholmod_factor/, /^}/' ../Include/cholmod_core.h > _factor.tex
+ ./getproto '/cholmod_factor \*cholmod_allocate_factor/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_factor.tex
+ ./getproto '/int cholmod_free_factor/, /\*\) ;/' ../Include/cholmod_core.h > _free_factor.tex
+ ./getproto '/int cholmod_reallocate_factor/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_factor.tex
+ ./getproto '/int cholmod_change_factor/, /\*\) ;/' ../Include/cholmod_core.h > _change_factor.tex
+ ./getproto '/int cholmod_pack_factor/, /\*\) ;/' ../Include/cholmod_core.h > _pack_factor.tex
+ ./getproto '/int cholmod_reallocate_column/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_column.tex
+ ./getproto '/cholmod_sparse \*cholmod_factor_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _factor_to_sparse.tex
+ ./getproto '/cholmod_factor \*cholmod_copy_factor/, /\*\) ;/' ../Include/cholmod_core.h > _copy_factor.tex
+ ./getproto '/int cholmod_factor_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _factor_xtype.tex
+ ./getproto '/typedef struct cholmod_dense/, /^}/' ../Include/cholmod_core.h > _dense.tex
+ ./getproto '/cholmod_dense \*cholmod_allocate_dense/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_dense.tex
+ ./getproto '/cholmod_dense \*cholmod_zeros/, /\*\) ;/' ../Include/cholmod_core.h > _zeros.tex
+ ./getproto '/cholmod_dense \*cholmod_ones/, /\*\) ;/' ../Include/cholmod_core.h > _ones.tex
+ ./getproto '/cholmod_dense \*cholmod_eye/, /\*\) ;/' ../Include/cholmod_core.h > _eye.tex
+ ./getproto '/int cholmod_free_dense/, /\*\) ;/' ../Include/cholmod_core.h > _free_dense.tex
+ ./getproto '/cholmod_dense \*cholmod_sparse_to_dense/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_to_dense.tex
+ ./getproto '/cholmod_sparse \*cholmod_dense_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _dense_to_sparse.tex
+ ./getproto '/cholmod_dense \*cholmod_copy_dense/, /\*\) ;/' ../Include/cholmod_core.h > _copy_dense.tex
+ ./getproto '/int cholmod_copy_dense2/, /\*\) ;/' ../Include/cholmod_core.h > _copy_dense2.tex
+ ./getproto '/int cholmod_dense_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _dense_xtype.tex
+ ./getproto '/typedef struct cholmod_triplet/, /^}/' ../Include/cholmod_core.h > _triplet.tex
+ ./getproto '/cholmod_triplet \*cholmod_allocate_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_triplet.tex
+ ./getproto '/int cholmod_free_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _free_triplet.tex
+ ./getproto '/int cholmod_reallocate_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_triplet.tex
+ ./getproto '/cholmod_triplet \*cholmod_sparse_to_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_to_triplet.tex
+ ./getproto '/cholmod_sparse \*cholmod_triplet_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _triplet_to_sparse.tex
+ ./getproto '/cholmod_triplet \*cholmod_copy_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _copy_triplet.tex
+ ./getproto '/int cholmod_triplet_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _triplet_xtype.tex
+ ./getproto '/void \*cholmod_malloc/, /\*\) ;/' ../Include/cholmod_core.h > _malloc.tex
+ ./getproto '/void \*cholmod_calloc/, /\*\) ;/' ../Include/cholmod_core.h > _calloc.tex
+ ./getproto '/void \*cholmod_free/, /\*\) ;/' ../Include/cholmod_core.h > _free.tex
+ ./getproto '/void \*cholmod_realloc/, /\*\) ;/' ../Include/cholmod_core.h > _realloc.tex
+ ./getproto '/int cholmod_realloc_multiple/, /\*\) ;/' ../Include/cholmod_core.h > _realloc_multiple.tex
+ ./getproto '/itype defines the/, /define CHOLMOD_SUPERNODAL/' ../Include/cholmod_core.h > _defn.tex
+ ./getproto '/int cholmod_check_common/, /\*\) ;/' ../Include/cholmod_check.h > _check_common.tex
+ ./getproto '/int cholmod_print_common/, /\*\) ;/' ../Include/cholmod_check.h > _print_common.tex
+ ./getproto '/int cholmod_check_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _check_sparse.tex
+ ./getproto '/int cholmod_print_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _print_sparse.tex
+ ./getproto '/int cholmod_check_dense/, /\*\) ;/' ../Include/cholmod_check.h > _check_dense.tex
+ ./getproto '/int cholmod_print_dense/, /\*\) ;/' ../Include/cholmod_check.h > _print_dense.tex
+ ./getproto '/int cholmod_check_factor/, /\*\) ;/' ../Include/cholmod_check.h > _check_factor.tex
+ ./getproto '/int cholmod_print_factor/, /\*\) ;/' ../Include/cholmod_check.h > _print_factor.tex
+ ./getproto '/int cholmod_check_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _check_triplet.tex
+ ./getproto '/int cholmod_print_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _print_triplet.tex
+ ./getproto '/int cholmod_check_subset/, /\*\) ;/' ../Include/cholmod_check.h > _check_subset.tex
+ ./getproto '/int cholmod_print_subset/, /\*\) ;/' ../Include/cholmod_check.h > _print_subset.tex
+ ./getproto '/int cholmod_check_perm/, /\*\) ;/' ../Include/cholmod_check.h > _check_perm.tex
+ ./getproto '/int cholmod_print_perm/, /\*\) ;/' ../Include/cholmod_check.h > _print_perm.tex
+ ./getproto '/int cholmod_check_parent/, /\*\) ;/' ../Include/cholmod_check.h > _check_parent.tex
+ ./getproto '/int cholmod_print_parent/, /\*\) ;/' ../Include/cholmod_check.h > _print_parent.tex
+ ./getproto '/cholmod_triplet \*cholmod_read_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _read_triplet.tex
+ ./getproto '/cholmod_sparse \*cholmod_read_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _read_sparse.tex
+ ./getproto '/cholmod_dense \*cholmod_read_dense/, /\*\) ;/' ../Include/cholmod_check.h > _read_dense.tex
+ ./getproto '/void \*cholmod_read_matrix/, /\*\) ;/' ../Include/cholmod_check.h > _read_matrix.tex
+ ./getproto '/int cholmod_write_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _write_sparse.tex
+ ./getproto '/int cholmod_write_dense/, /\*\) ;/' ../Include/cholmod_check.h > _write_dense.tex
+ ./getproto '/cholmod_factor \*cholmod_analyze /, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze.tex
+ ./getproto '/cholmod_factor \*cholmod_analyze_p/, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze_p.tex
+ ./getproto '/int cholmod_factorize /, /\*\) ;/' ../Include/cholmod_cholesky.h > _factorize.tex
+ ./getproto '/int cholmod_factorize_p/, /\*\) ;/' ../Include/cholmod_cholesky.h > _factorize_p.tex
+ ./getproto '/cholmod_dense \*cholmod_solve/, /\*\) ;/' ../Include/cholmod_cholesky.h > _solve.tex
+ ./getproto '/cholmod_sparse \*cholmod_spsolve/, /\*\) ;/' ../Include/cholmod_cholesky.h > _spsolve.tex
+ ./getproto '/int cholmod_etree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _etree.tex
+ ./getproto '/int cholmod_rowcolcounts/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowcolcounts.tex
+ ./getproto '/int cholmod_analyze_ordering/, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze_ordering.tex
+ ./getproto '/int cholmod_amd/, /\*\) ;/' ../Include/cholmod_cholesky.h > _amd.tex
+ ./getproto '/int cholmod_colamd/, /\*\) ;/' ../Include/cholmod_cholesky.h > _colamd.tex
+ ./getproto '/int cholmod_rowfac/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowfac.tex
+ ./getproto '/int cholmod_rowfac_mask/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowfac_mask.tex
+ ./getproto '/int cholmod_row_subtree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _row_subtree.tex
+ ./getproto '/int cholmod_row_lsubtree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _row_lsubtree.tex
+ ./getproto '/int cholmod_resymbol /, /\*\) ;/' ../Include/cholmod_cholesky.h > _resymbol.tex
+ ./getproto '/int cholmod_resymbol_noperm/, /\*\) ;/' ../Include/cholmod_cholesky.h > _resymbol_noperm.tex
+ ./getproto '/double cholmod_rcond/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rcond.tex
+ ./getproto '/long cholmod_postorder/, /\*\) ;/' ../Include/cholmod_cholesky.h > _postorder.tex
+ ./getproto '/int cholmod_updown /, /\*\) ;/' ../Include/cholmod_modify.h > _updown.tex
+ ./getproto '/int cholmod_updown_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_solve.tex
+ ./getproto '/int cholmod_updown_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_mark.tex
+ ./getproto '/int cholmod_updown_mask/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_mask.tex
+ ./getproto '/int cholmod_rowadd /, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd.tex
+ ./getproto '/int cholmod_rowadd_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd_solve.tex
+ ./getproto '/int cholmod_rowadd_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd_mark.tex
+ ./getproto '/int cholmod_rowdel /, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel.tex
+ ./getproto '/int cholmod_rowdel_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel_solve.tex
+ ./getproto '/int cholmod_rowdel_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel_mark.tex
+ ./getproto '/int cholmod_drop/, /\*\) ;/' ../Include/cholmod_matrixops.h > _drop.tex
+ ./getproto '/double cholmod_norm_dense/, /\*\) ;/' ../Include/cholmod_matrixops.h > _norm_dense.tex
+ ./getproto '/double cholmod_norm_sparse/, /\*\) ;/' ../Include/cholmod_matrixops.h > _norm_sparse.tex
+ ./getproto '/cholmod_sparse \*cholmod_horzcat/, /\*\) ;/' ../Include/cholmod_matrixops.h > _horzcat.tex
+ ./getproto '/define CHOLMOD_SCALAR/, /\*\) ;/' ../Include/cholmod_matrixops.h > _scale.tex
+ ./getproto '/int cholmod_sdmult/, /\*\) ;/' ../Include/cholmod_matrixops.h > _sdmult.tex
+ ./getproto '/cholmod_sparse \*cholmod_ssmult/, /\*\) ;/' ../Include/cholmod_matrixops.h > _ssmult.tex
+ ./getproto '/cholmod_sparse \*cholmod_submatrix/, /\*\) ;/' ../Include/cholmod_matrixops.h > _submatrix.tex
+ ./getproto '/cholmod_sparse \*cholmod_vertcat/, /\*\) ;/' ../Include/cholmod_matrixops.h > _vertcat.tex
+ ./getproto '/int cholmod_symmetry/, /\*\) ;/' ../Include/cholmod_matrixops.h > _symmetry.tex
+ ./getproto '/int cholmod_super_symbolic/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_symbolic.tex
+ ./getproto '/int cholmod_super_numeric/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_numeric.tex
+ ./getproto '/int cholmod_super_lsolve/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_lsolve.tex
+ ./getproto '/int cholmod_super_ltsolve/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_ltsolve.tex
+ ./getproto '/long cholmod_nested_dissection/, /\*\) ;/' ../Include/cholmod_partition.h > _nested_dissection.tex
+ ./getproto '/int cholmod_metis/, /\*\) ;/' ../Include/cholmod_partition.h > _metis.tex
+ ./getproto '/int cholmod_ccolamd/, /\*\) ;/' ../Include/cholmod_partition.h > _ccolamd.tex
+ ./getproto '/int cholmod_camd/, /\*\) ;/' ../Include/cholmod_partition.h > _camd.tex
+ ./getproto '/int cholmod_csymamd/, /\*\) ;/' ../Include/cholmod_partition.h > _csymamd.tex
+ ./getproto '/int cholmod_csymamd/, /\*\) ;/' ../Include/cholmod_partition.h > _csymamd.tex
+ ./getproto '/long cholmod_bisect/, /\*\) ;/' ../Include/cholmod_partition.h > _bisect.tex
+ ./getproto '/long cholmod_metis_bisector/, /\*\) ;/' ../Include/cholmod_partition.h > _metis_bisector.tex
+ ./getproto '/long cholmod_collapse_septree/, /\*\) ;/' ../Include/cholmod_partition.h > _collapse_septree.tex
+ pdflatex UserGuide
+ bibtex UserGuide
+ pdflatex UserGuide
+ pdflatex UserGuide
+
+distclean: purge
+
+purge: clean
+ - $(RM) _temp.awk _*.tex *.dvi *.aux *.log *.lof *.lot *.toc *.bak *.bbl *.blg
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.bib b/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.bib
new file mode 100644
index 0000000..c804ad2
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.bib
@@ -0,0 +1,196 @@
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Applic."}
+ at string{TOMS = "{ACM} Trans. Math. Softw."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+
+ at article{DavisHager06,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Dynamic supernodes in sparse {Cholesky} update/downdate and triangular
+ solves},
+ journal=TOMS,
+ year={submitted in 2006}
+ }
+
+ at article{ChenDavisHagerRajamanickam06,
+ author={Chen, Y. and Davis, T. A. and Hager, W. W. and Rajamanickam, S.},
+ title={Algorithm 8xx: {CHOLMOD}, supernodal sparse {Cholesky} factorization and
+ update/downdate},
+ journal=TOMS,
+ year={submitted in 2006}
+ }
+
+ at article{DavisHager99,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Modifying a sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1999}
+ ,volume={20}
+ ,number={3}
+ ,pages={606--627}
+ }
+
+ at article{DavisHager01,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Multiple-Rank Modifications of a Sparse {C}holesky Factorization},
+ journal=SIMAX,
+ year={2001}
+ ,volume={22}
+ ,number={4}
+ ,pages={997--1013}
+ }
+
+ at article{DavisHager05,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Row modifications of a sparse {Cholesky} factorization},
+ journal=SIMAX,
+ year={2005}
+ ,volume={26}
+ ,number={3}
+ ,pages={621--639}
+ }
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886--905}
+ }
+
+ at article{Davis05,
+ author={Davis, T. A.},
+ title={Algorithm 849: A concise sparse {Cholesky} algorithm},
+ journal=TOMS,
+ year={2005},volume={31},number={4},pages={587--591}}
+
+ at article{DavisGilbertLarimoreNg00,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={353--376}}
+
+ at article{DavisGilbertLarimoreNg00_algo,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={377--380}}
+
+ at article{NgPeyton91b,
+ author={Ng, E. and Peyton, B.},
+ title={Block sparse {C}holesky algorithms on advanced uniprocessor computers},
+ journal=SIAMJSC,
+ year={1993}
+ ,volume={14}
+ ,pages={1034--1056}
+ }
+
+ at article{Liu86c,
+ author={Liu, J. W. H.},
+ title={A Compact Row Storage Scheme for {C}holesky Factors Using Elimination Trees},
+ journal=TOMS,
+ year={1986},
+ volume={12},
+ number={2},
+ pages={127--148},
+ }
+
+ at article{Liu90a,
+ author={Liu, J. W. H.},
+ title={The Role of Elimination Trees in Sparse Factorization},
+ journal=SIMAX,
+ year={1990}
+ ,volume={11}
+ ,number={1}
+ ,pages={134--172}
+ }
+
+ at article{GilbertNgPeyton94,
+ author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.},
+ title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1994}
+ ,volume={15}
+ ,number={4}
+ ,pages={1075--1091}
+ }
+
+ at article{GilbertLiNgPeyton01,
+ author={Gilbert, J. R. and Li, X. S. and Ng, E. G. and Peyton, B. W.},
+ title={Computing row and column counts for sparse {QR} and {LU} factorization},
+ journal={{BIT}},
+ year={2001}
+ ,volume={41}
+ ,number={4}
+ ,pages={693--710}
+ }
+
+ at book{LAPACK,
+ author={Anderson, E. and Bai, Z. and Bischof, C. and Blackford, S. and Demmel, J. and Dongarra, J. and {Du Croz}, J. and Greenbaum, A. and Hammarling, S. and McKenny, A. and Sorensen, D.},
+ title={{LAPACK} Users' Guide, 3rd ed.},
+ publisher={{SIAM}},
+ year={1999}
+ }
+
+ at article{ACM679a,
+ author={Dongarra, J. J. and {Du Croz}, J. and Duff, I. S. and Hammarling, S.},
+ title={A set of level-3 basic linear algebra subprograms},
+ journal=TOMS,
+ year={1990}
+ ,volume={16}
+ ,number={1}
+ ,pages={1--17}
+ }
+
+
+ at article{KarypisKumar98,
+ author={Karypis, G. and Kumar, V.},
+ title={A fast and high quality multilevel scheme for partitioning irregular graphs},
+ journal=SIAMJSC,
+ year=1998
+ ,volume={20}
+ ,number={1}
+ ,pages={359--392}
+ }
+
+ at article{GilbertMolerSchreiber,
+ author={Gilbert, J. R. and Moler, C. and Schreiber, R.},
+ title={Sparse matrices in {MATLAB}: design and implementation},
+ journal=SIMAX,
+ year={1992}
+ ,volume={13}
+ ,number={1}
+ ,pages={333--356}
+ }
+
+ at article{AmestoyDavisDuff03,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}}
+
+
+ at article{GouldHuScott05,
+ author={Gould, N. I. M. and Hu, Y. and Scott, J. A.},
+ title={A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations},
+ journal=TOMS,
+ year={to appear}
+ }
+
+ at techreport{GouldHuScott05b,
+ author={Gould, N. I. M. and Hu, Y. and Scott, J. A.},
+ title={Complete results from a numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations},
+ institution={CCLRC, Rutherford Appleton Laboratory},
+ number={Internal report 2005-1 (revision 1)},
+ year={2005},
+ howpublished={www.numerical.rl.ac.uk/reports/reports.shtml}
+ }
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.pdf b/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.pdf
new file mode 100644
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Binary files /dev/null and b/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.pdf differ
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.tex b/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.tex
new file mode 100644
index 0000000..c3fa5a9
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/UserGuide.tex
@@ -0,0 +1,3366 @@
+%-------------------------------------------------------------------------------
+% The CHOLMOD/Doc/UserGuide.tex file.
+%-------------------------------------------------------------------------------
+
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+\newcommand{\new}[1]{\overline{#1}}
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+\begin{document}
+
+\author{Timothy A. Davis \\
+Dept. of Computer and Information Science and Engineering \\
+Univ. of Florida, Gainesville, FL}
+\title{User Guide for CHOLMOD: a sparse Cholesky factorization and
+modification package}
+\date{Version 1.4, Dec 12, 2006}
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+ CHOLMOD\footnote{CHOLMOD is short for CHOLesky MODification,
+ since a key feature of the package is its ability to update/downdate
+ a sparse Cholesky factorization}
+ is a set of routines for factorizing sparse symmetric positive
+ definite matrices of the form $\m{A}$ or $\m{AA}\tr$, updating/downdating
+ a sparse Cholesky factorization, solving linear systems, updating/downdating
+ the solution to the triangular system $\m{Lx}=\m{b}$, and many other sparse
+ matrix functions for both symmetric and unsymmetric matrices.
+ Its supernodal Cholesky factorization
+ relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction
+ of the peak performance of the BLAS. Both real and complex matrices
+ are supported. CHOLMOD is written in ANSI/ISO C, with both
+ C and MATLAB interfaces. This code works on Microsoft Windows and many versions
+ of Unix and Linux.
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+CHOLMOD Copyright\copyright 2005-2006 by Timothy A. Davis. Portions are also
+copyrighted by William W. Hager (the {\tt Modify} Module),
+and the University of Florida (the {\tt Partition} and {\tt Core} Modules).
+All Rights Reserved. Some of CHOLMOD's Modules are distributed under the GNU
+General Public License, and others under the GNU Lesser General Public License.
+Refer to each Module for details.
+CHOLMOD is also available under other licenses that permit its use in
+proprietary applications; contact the authors for details.
+See http://www.cise.ufl.edu/research/sparse for the code and all documentation,
+including this User Guide.
+
+\newpage
+\tableofcontents
+
+%-------------------------------------------------------------------------------
+\newpage \section{Overview}
+%-------------------------------------------------------------------------------
+
+CHOLMOD is a set of ANSI C routines for solving systems of linear
+equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and symmetric positive definite,
+and $\m{x}$ and $\m{b}$ can be either sparse or dense.\footnote{Some support
+is provided for symmetric indefinite matrices.}
+Complex matrices are supported, in two different formats.
+CHOLMOD includes high-performance left-looking supernodal factorization
+and solve methods \cite{NgPeyton91b},
+based on LAPACK \cite{LAPACK} and the BLAS \cite{ACM679a}.
+After a matrix is factorized, its factors can be updated or downdated using
+the techniques described by Davis and Hager
+in \cite{DavisHager99,DavisHager01,DavisHager05}.
+Many additional sparse matrix operations are provided, for both
+symmetric and unsymmetric matrices (square or rectangular), including
+sparse matrix multiply, add, transpose, permutation, scaling,
+norm, concatenation, sub-matrix access, and converting to alternate data structures.
+Interfaces to many ordering methods are provided, including minimum degree
+(AMD \cite{AmestoyDavisDuff96,AmestoyDavisDuff03},
+COLAMD \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}),
+constrained minimum degree (CSYMAMD, CCOLAMD, CAMD), and
+graph-partitioning-based nested dissection (METIS \cite{KarypisKumar98}).
+Most of its operations are available within MATLAB via mexFunction interfaces.
+
+A pair of articles on CHOLMOD has been submitted to the ACM Transactions
+on Mathematical Softare:
+\cite{ChenDavisHagerRajamanickam06,DavisHager06}.
+
+CHOLMOD 1.0 replaces {\tt chol} (the sparse case), {\tt symbfact}, and {\tt etree}
+in MATLAB 7.2 (R2006a), and is used for {\tt x=A}$\backslash${\tt b}
+when {\tt A} is symmetric positive definite \cite{GilbertMolerSchreiber}.
+It will replace {\tt sparse} in a future version of MATLAB.
+
+The C-callable CHOLMOD library consists of 133 user-callable routines and one
+include file. Each routine comes in two versions, one for {\tt int} integers
+and another for {\tt long}. Many of the routines can support either real or
+complex matrices, simply by passing a matrix of the appropriate type.
+
+Nick Gould, Yifan Hu, and Jennifer Scott have independently tested CHOLMOD's
+performance, comparing it with nearly a dozen or so other solvers
+\cite{GouldHuScott05,GouldHuScott05b}. Its performance was quite competitive.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Primary routines and data structures}
+%-------------------------------------------------------------------------------
+
+Five primary CHOLMOD routines are required to factorize $\m{A}$ or $\m{AA}\tr$
+and solve the related system $\m{Ax}=\m{b}$ or $\m{AA}\tr\m{x}=\m{b}$,
+for either the real or complex cases:
+\begin{enumerate}
+\item {\tt cholmod\_start}:
+ This must be the first call to CHOLMOD.
+
+\item {\tt cholmod\_analyze}:
+ Finds a fill-reducing ordering, and performs the symbolic factorization,
+ either simplicial (non-supernodal) or supernodal.
+
+\item {\tt cholmod\_factorize}:
+ Numerical factorization, either simplicial or supernodal, $\m{LL}\tr$ or $\m{LDL}\tr$
+ using either the symbolic factorization from {\tt cholmod\_analyze} or the numerical
+ factorization from a prior call to {\tt cholmod\_factorize}.
+
+\item {\tt cholmod\_solve}:
+ Solves $\m{Ax}=\m{b}$, or many other related systems, where $\m{x}$ and
+ $\m{b}$ are dense matrices. The {\tt cholmod\_spsolve} routine handles
+ the sparse case. Any mixture of real and complex $\m{A}$ and $\m{b}$ are
+ allowed.
+
+\item {\tt cholmod\_finish}:
+ This must be the last call to CHOLMOD.
+\end{enumerate}
+
+Additional routines are also required to create and destroy
+the matrices $\m{A}$, $\m{x}$, $\m{b}$, and the $\m{LL}\tr$ or $\m{LDL}\tr$ factorization.
+CHOLMOD has five kinds of data structures, referred to as objects and implemented
+as pointers to {\tt struct}'s:
+
+\begin{enumerate}
+\item {\tt cholmod\_common}: parameter settings, statistics, and workspace
+ used internally by CHOLMOD.
+ See Section~\ref{cholmod_common} for details.
+
+\item {\tt cholmod\_sparse}: a sparse matrix in compressed-column form,
+ either pattern-only, real, complex, or ``zomplex.'' In its basic form,
+ the matrix {\tt A} contains:
+ \begin{itemize}
+ \item {\tt A->p}, an integer array of size {\tt A->ncol+1}.
+ \item {\tt A->i}, an integer array of size {\tt A->nzmax}.
+ \item {\tt A->x}, a {\tt double} array of size {\tt A->nzmax} or twice that for the complex case.
+ This is compatible with the Fortran and ANSI C99 complex data type.
+ \item {\tt A->z}, a {\tt double} array of size {\tt A->nzmax} if {\tt A} is zomplex.
+ A zomplex matrix has a {\tt z} array, thus the name.
+ This is compatible with the MATLAB representation of complex matrices.
+ \end{itemize}
+ For all four types of matrices, the row indices of entries of column {\tt j}
+ are located in {\tt A->i [A->p [j] ... A->p [j+1]-1]}.
+ For a real matrix, the corresponding numerical values are in {\tt A->x} at the same location.
+ For a complex matrix, the entry whose row index is {\tt A->i [p]} is contained in
+ {\tt A->x [2*p]} (the real part) and {\tt A->x [2*p+1]} (the imaginary part).
+ For a zomplex matrix, the real part is in {\tt A->x [p]} and imaginary part is in {\tt A->z [p]}.
+ See Section~\ref{cholmod_sparse} for more details.
+
+\item {\tt cholmod\_factor}:
+ A symbolic or numeric factorization, either real, complex, or zomplex.
+ It can be either an $\m{LL}\tr$ or $\m{LDL}\tr$ factorization, and either
+ simplicial or supernodal. You will normally not need to examine its contents.
+ See Section~\ref{cholmod_factor} for more details.
+
+\item {\tt cholmod\_dense}:
+ A dense matrix, either real, complex or zomplex, in column-major order.
+ This differs from the row-major convention used in C. A dense matrix {\tt X} contains
+ \begin{itemize}
+ \item {\tt X->x}, a double array of size {\tt X->nzmax} or twice that for the complex case.
+ \item {\tt X->z}, a double array of size {\tt X->nzmax} if {\tt X} is zomplex.
+ \end{itemize}
+ For a real dense matrix $x_{ij}$ is {\tt X->x [i+j*d]} where {\tt d = X->d} is the leading dimension of {\tt X}.
+ For a complex dense matrix, the real part of $x_{ij}$ is {\tt X->x [2*(i+j*d)]} and the imaginary part is {\tt X->x [2*(i+j*d)+1]}.
+ For a zomplex dense matrix, the real part of $x_{ij}$ is {\tt X->x [i+j*d]} and the imaginary part is {\tt X->z [i+j*d]}.
+ Real and complex dense matrices can be passed to LAPACK and the BLAS.
+ See Section~\ref{cholmod_dense} for more details.
+
+\item {\tt cholmod\_triplet}:
+ CHOLMOD's sparse matrix ({\tt cholmod\_sparse}) is the primary input for nearly all CHOLMOD
+ routines, but it can be difficult for the user to construct.
+ A simpler method of creating a sparse matrix is to first create a {\tt cholmod\_triplet} matrix,
+ and then convert it to a {\tt cholmod\_sparse} matrix via
+ the {\tt cholmod\_triplet\_to\_sparse} routine.
+ In its basic form, the triplet matrix {\tt T} contains
+ \begin{itemize}
+ \item {\tt T->i} and {\tt T->j}, integer arrays of size {\tt T->nzmax}.
+ \item {\tt T->x}, a double array of size {\tt T->nzmax} or twice that for the complex case.
+ \item {\tt T->z}, a double array of size {\tt T->nzmax} if {\tt T} is zomplex.
+ \end{itemize}
+ The {\tt k}th entry in the data structure has row index
+ {\tt T->i [k]} and column index {\tt T->j [k]}.
+ For a real triplet matrix, its numerical value is {\tt T->x [k]}.
+ For a complex triplet matrix, its real part is {\tt T->x [2*k]} and its imaginary part is {\tt T->x [2*k+1]}.
+ For a zomplex matrix, the real part is {\tt T->x [k]} and imaginary part is {\tt T->z [k]}.
+ The entries can be in any order, and duplicates are permitted.
+ See Section~\ref{cholmod_triplet} for more details.
+
+\end{enumerate}
+
+Each of the five objects has a routine in CHOLMOD to create and destroy it.
+CHOLMOD provides many other operations on these objects as well.
+A few of the most important ones are illustrated in the sample program in the
+next section.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Simple example program}
+%-------------------------------------------------------------------------------
+
+\input{_simple.tex}
+The {\tt Demo/cholmod\_simple.c} program illustrates the
+basic usage of CHOLMOD. It reads a triplet matrix from a file
+(in Matrix Market format), converts it into a sparse matrix,
+creates a linear system, solves it, and prints the norm of the residual.
+
+See the {\tt CHOLMOD/Demo/cholmod\_demo.c} program for a more elaborate
+example, and \newline
+{\tt CHOLMOD/Demo/cholmod\_l\_demo.c} for its {\tt long} integer version.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Installation of the C-callable library}
+\label{Install}
+%-------------------------------------------------------------------------------
+
+CHOLMOD requires a suite of external packages, many of which are distributed
+along with CHOLMOD, but three of which are not. Those included with CHOLMOD are:
+\begin{itemize}
+\item AMD: an approximate minimum degree ordering algorithm,
+ by Tim Davis, Patrick Amestoy, and Iain Duff
+ \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}.
+\item COLAMD: an approximate column minimum degree ordering algorithm,
+ by Tim Davis, Stefan Larimore, John Gilbert, and Esmond Ng
+ \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}.
+\item CCOLAMD: a constrained approximate column minimum degree ordering
+ algorithm,
+ by Tim Davis and Siva Rajamanickam, based directly on COLAMD.
+ This package is not required if CHOLMOD is compiled with the
+ {\tt -DNPARTITION} flag.
+\item CAMD: a constrained approximate minimum degree ordering
+ algorithm,
+ by Tim Davis and Yanqing Chen, based directly on AMD.
+ This package is not required if CHOLMOD is compiled with the
+ {\tt -DNPARTITION} flag.
+\item {\tt UFconfig}: a single place where all sparse matrix packages authored
+ or co-authored by Davis are configured. Also includes a version of the
+ {\tt xerbla} routine for the BLAS.
+\end{itemize}
+
+Three other packages are required for optimal performance:
+\begin{itemize}
+\item {\tt METIS 4.0.1}: a graph partitioning package by George Karypis,
+ Univ. of Minnesota. Not needed if {\tt -DNPARTITION} is used.
+ See http://www-users.cs.umn.edu/$\sim$karypis/metis.
+\item BLAS: the Basic Linear Algebra Subprograms.
+ Not needed if {\tt -DNSUPERNODAL} is used.
+ See http://www.netlib.org for the reference BLAS (not meant for production
+ use). For Kazushige Goto's optimized BLAS (highly recommended for CHOLMOD)
+ see \newline
+ http://www.tacc.utexas.edu/$\sim$kgoto/ or
+ http://www.cs.utexas.edu/users/flame/goto/.
+ I recommend that you avoid the Intel MKL BLAS; one recent
+ version returns NaN's, where both the Goto BLAS and the standard
+ Fortran reference BLAS return the correct answer.
+ See {\tt CHOLMOD/README} for more information.
+\item LAPACK: the Basic Linear Algebra Subprograms.
+ Not needed if {\tt -DNSUPERNODAL} is used.
+ See http://www.netlib.org.
+\end{itemize}
+
+You must first obtain and install METIS, LAPACK, and the BLAS.
+Next edit the system-dependent configurations in the
+{\tt UFconfig/UFconfig.mk} file. Sample configurations are provided
+for Linux, Macintosh, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+The most important configuration is the location of the BLAS, LAPACK, and METIS
+packages, since in its default configuration CHOLMOD cannot be compiled without them.
+
+\noindent
+Here are the various parameters that you can control in your {\tt UFconfig/UFconfig.mk} file:
+\begin{itemize}
+\item {\tt CC = } your C compiler, such as {\tt cc}.
+\item {\tt CFLAGS = } optimization flags, such as {\tt -O}.
+\item {\tt RANLIB = } your system's {\tt ranlib} program, if needed.
+\item {\tt AR =} the command to create a library (such as {\tt ar}).
+\item {\tt RM =} the command to delete a file.
+\item {\tt MV =} the command to rename a file.
+\item {\tt F77 =} the command to compile a Fortran program (optional).
+\item {\tt F77FLAGS =} the Fortran compiler flags (optional).
+\item {\tt F77LIB =} the Fortran libraries (optional).
+\item {\tt LIB = } basic libraries, such as {\tt -lm}.
+\item {\tt MEX =} the command to compile a MATLAB mexFunction.
+\item {\tt BLAS =} your BLAS library.
+\item {\tt LAPACK =} your LAPACK library.
+\item {\tt XERBLA =} a library containing the BLAS {\tt xerbla} routine, if required.
+\item {\tt METIS\_PATH =} the path to your copy of the METIS 4.0.1 source code.
+\item {\tt METIS =} your METIS library.
+\item {\tt CHOLMOD\_CONFIG = } configuration settings specific to CHOLMOD.
+\end{itemize}
+
+\noindent
+CHOLMOD's specific settings are given by the {\tt CHOLMOD\_CONFIG} string:
+\begin{itemize}
+\item {\tt -DNCHECK}: do not include the Check module. License: GNU LGPL.
+\item {\tt -DNCHOLESKY}: do not include the Cholesky module. License: GNU LGPL.
+\item {\tt -DNPARTITION}: do not include the Partition module. License: GNU LGPL.
+\item {\tt -DNGPL}: do not include any GNU GPL Modules in the CHOLMOD library.
+\item {\tt -DNMATRIXOPS}: do not include the MatrixOps module. License: GNU GPL.
+\item {\tt -DNMODIFY}: do not include the Modify module. License: GNU GPL.
+\item {\tt -DNSUPERNODAL}: do not include the Supernodal module. License: GNU GPL.
+\item {\tt -DNPRINT}: do not print anything.
+\item {\tt -D'LONGBLAS=long'} or {\tt -DLONGBLAS='long long'}
+ defines the integers used by LAPACK and the BLAS (defaults to {\tt int}).
+\item {\tt -DNSUNPERF}: for Solaris only. If defined, do not use the Sun Performance Library.
+\item {\tt -DNLARGEFILE}: CHOLMOD now assumes support for large files (2GB or
+larger). If this causes problems, you can compile CHOLMOD with -DNLARGEFILE.
+To use large files, you should {\tt \#include "cholmod.h"} (or at least
+{\tt \#include "cholmod\_io64.h"}) before any other {\tt \#include} statements,
+in your application that uses CHOLMOD. You may need to use {\tt fopen64}
+to create a file pointer to pass to CHOLMOD, if you are using a non-gcc
+compiler.
+\end{itemize}
+
+Type {\tt make} in the {\tt CHOLMOD} directory. The AMD,
+COLAMD, CAMD, CCOLAMD, and {\tt CHOLMOD} libraries will be compiled,
+as will the C version of the null-output {\tt xerbla} routine in case you need it.
+No Fortran compiler is required in this case. A short demo program will
+be compiled and tested on a few matrices. The residuals should all be small.
+Compare your output with the {\tt CHOLMOD/Demo/make.out} file.
+
+CHOLMOD is now ready for use in your own applications. You must link
+your programs with the
+{\tt CHOLMOD/Lib/libcholmod.a},
+{\tt AMD/Lib/libamd.a},
+{\tt COLAMD/libcolamd.a},
+{\tt CAMD/libcamd.a}, \newline
+{\tt CCOLAMD/libccolamd.a},
+{\tt metis-4.0/libmetis.a},
+LAPACK,
+and
+BLAS libraries,
+as well as the {\tt xerbla} library if you need it
+({\tt UFconfig/xerlib/libcerbla.a} for the C version or
+\newline
+ {\tt UFconfig/xerlib/libxerbla.a} for the Fortran version).
+Your compiler needs to know the location of the CHOLMOD {\tt Include} directory,
+so that it can find the {\tt cholmod.h} include file, by
+adding the {\tt -ICHOLMOD/Include} to your C compiler options
+(modified appropriately to reflect the location of your copy of CHOLMOD).
+
+%-------------------------------------------------------------------------------
+\newpage \section{Using CHOLMOD in MATLAB}
+%-------------------------------------------------------------------------------
+
+CHOLMOD includes a set of m-files and mexFunctions in the CHOLMOD/MATLAB
+directory. The following functions are provided:
+
+\vspace{0.1in}
+\begin{tabular}{ll}
+\hline
+{\tt analyze} & order and analyze a matrix \\
+{\tt bisect} & find a node separator \\
+{\tt chol2} & same as {\tt chol} \\
+{\tt cholmod2} & same as {\tt x=A}$\backslash${\tt b} if {\tt A} is symmetric positive definite \\
+{\tt cholmod\_demo} & a short demo program \\
+{\tt cholmod\_make} & compiles CHOLMOD for use in MATLAB \\
+{\tt etree2} & same as {\tt etree} \\
+{\tt graph\_demo} & graph partitioning demo \\
+{\tt lchol} & {\tt L*L'} factorization \\
+{\tt ldlchol} & {\tt L*D*L'} factorization \\
+{\tt ldl\_normest} & estimate {\tt norm(A-L*D*L')} \\
+{\tt ldlsolve} & {\tt x = L'}$\backslash${\tt (D}$\backslash${\tt (L}$\backslash${\tt b))} \\
+{\tt ldlsplit} & split the output of {\tt ldlchol} into {\tt L} and {\tt D} \\
+{\tt ldlupdate} & update/downdate an {\tt L*D*L'} factorization \\
+{\tt lu\_normest} & estimate {\tt norm(A-L*U')} \\
+{\tt metis} & interface to {\tt METIS\_NodeND} ordering \\
+{\tt mread} & read a sparse or dense Matrix Market file \\
+{\tt mwrite} & write a sparse or dense Matrix Market file \\
+{\tt nesdis} & CHOLMOD's nested dissection ordering \\
+{\tt resymbol} & recomputes the symbolic factorization \\
+{\tt sdmult} & {\tt S*F} where {\tt S} is sparse and {\tt F} is dense \\
+{\tt spsym} & determine symmetry \\
+{\tt sparse2} & same as {\tt sparse} \\
+{\tt symbfact2} & same as {\tt symbfact} \\
+\hline
+\end{tabular}
+
+\vspace{0.1in}\noindent
+Each function is described in the next sections.
+
+\newpage
+\subsection{{\tt analyze}: order and analyze} \input{_analyze_m.tex}
+\subsection{{\tt bisect}: find a node separator} \input{_bisect_m.tex}
+\subsection{{\tt chol2}: same as {\tt chol}} \input{_chol2_m.tex}
+\newpage
+\subsection{{\tt cholmod2}: supernodal backslash} \input{_cholmod2_m.tex}
+\newpage
+\subsection{{\tt cholmod\_demo}: a short demo program} \input{_cholmod_demo_m.tex}
+\subsection{{\tt cholmod\_make}: compile CHOLMOD in MATLAB} \input{_cholmod_make_m.tex}
+\newpage
+\subsection{{\tt etree2}: same as {\tt etree}} \input{_etree2_m.tex}
+\subsection{{\tt graph\_demo}: graph partitioning demo} \input{_graph_demo_m.tex}
+\newpage
+\subsection{{\tt lchol}: $\m{LL}\tr$ factorization} \input{_lchol_m.tex}
+\subsection{{\tt ldlchol}: $\m{LDL}\tr$ factorization} \input{_ldlchol_m.tex}
+\newpage
+\subsection{{\tt ldl\_normest}: estimate $||\m{A}-\m{LDL}\tr||$} \input{_ldl_normest_m.tex}
+\subsection{{\tt ldlsolve}: solve using an $\m{LDL}\tr$ factorization} \input{_ldlsolve_m.tex}
+\subsection{{\tt ldlsplit}: split an $\m{LDL}\tr$ factorization} \input{_ldlsplit_m.tex}
+\newpage
+\subsection{{\tt ldlupdate}: update/downdate an $\m{LDL}\tr$ factorization} \input{_ldlupdate_m.tex}
+\newpage
+\subsection{{\tt lu\_normest}: estimate $||\m{A}-\m{LU}||$} \input{_lu_normest_m.tex}
+\newpage
+\subsection{{\tt mread}: read a sparse or dense matrix from a Matrix Market file}\input{_mread_m.tex}
+\subsection{{\tt mwrite}: write a sparse or densematrix to a Matrix Market file} \input{_mwrite_m.tex}
+\newpage
+\subsection{{\tt metis}: order with METIS} \input{_metis_m.tex}
+\newpage
+\subsection{{\tt nesdis}: order with CHOLMOD nested dissection} \input{_nesdis_m.tex}
+\newpage
+\subsection{{\tt resymbol}: re-do symbolic factorization} \input{_resymbol_m.tex}
+\subsection{{\tt sdmult}: sparse matrix times dense matrix} \input{_sdmult_m.tex}
+\newpage
+\subsection{{\tt spsym}: determine symmetry} \input{_spsym_m.tex}
+\newpage
+\subsection{{\tt sparse2}: same as {\tt sparse}} \input{_sparse2_m.tex}
+\newpage
+\subsection{{\tt symbfact2}: same as {\tt symbfact}} \input{_symbfact2_m.tex}
+
+%-------------------------------------------------------------------------------
+\newpage \section{Installation for use in MATLAB}
+%-------------------------------------------------------------------------------
+
+If you wish to use METIS within CHOLMOD, you should first obtain a copy of METIS 4.0.1.
+See http://www-users.cs.umn.edu/$\sim$karypis/metis. Place your copy
+of the {\tt metis-4.0} directory (folder, for Windows users) in the same directory
+that contains your copy of the {\tt CHOLMOD} directory. If you do not have
+METIS, however, you can still use CHOLMOD. Some of the CHOLMOD functions will not
+be available ({\tt metis}, {\tt bisect}, and {\tt nesdis}),
+and you may experience higher fill-in for large matrices
+(particularly those arising in 3D finite-element problems) when using
+{\tt analyze}, {\tt chol2}, {\tt cholmod2}, {\tt lchol}, and {\tt ldlchol}.
+There are two methods for compiling CHOLMOD for use in MATLAB; both
+are described below.
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt cholmod\_make}: compiling CHOLMOD in MATLAB}
+%-------------------------------------------------------------------------------
+
+This is the preferred method, since it allows METIS to be reconfigured to
+use the MATLAB memory-management functions instead of {\tt malloc} and {\tt free};
+this avoids the issue of METIS terminating MATLAB if it runs out of memory.
+It is also simpler for Windows users, who do not have the {\tt make}
+command (unless you obtain a copy of {\tt Cygwin}).
+
+Start MATLAB, {\tt cd} to the {\tt CHOLMOD/MATLAB} directory, and
+type {\tt cholmod\_make} in the MATLAB command window. This will compile
+the MATLAB interfaces for AMD, COLAMD, CAMD, CCOLAMD, METIS, and CHOLMOD.
+If you do not have METIS, type {\tt cholmod\_make('')}.
+If your copy of METIS is in another location, type
+{\tt cholmod\_make ('path')} where {\tt path} is the pathname
+of your copy of the {\tt metis-4.0} directory.
+
+When METIS is compiled {\tt malloc}, {\tt free}, {\tt calloc}, and {\tt realloc}
+are redefined to the MATLAB-equivalents ({\tt mxMalloc}, ...).
+These memory-management functions safely terminate a mexFunction if they
+fail, and will free all memory allocated by the mexFunction.
+Thus, METIS will safely abort without terminating MATLAB, if it runs out
+of memory.
+The {\tt cholmod\_make} handles this redefinition without making any
+changes to your METIS source code.
+
+%-------------------------------------------------------------------------------
+\subsection{Unix {\tt make} for compiling CHOLMOD}
+%-------------------------------------------------------------------------------
+
+You can also compile the CHOLMOD mexFunctions using the Unix/Linux {\tt make}
+command. When using the {\tt gcc} compiler, I strongly recommend editing the
+{\tt metis-4.0/Makefile.in} file and changing {\tt COPTIONS} to
+\begin{verbatim}
+ COPTIONS = -fexceptions
+\end{verbatim}
+Also ensure {\tt -fexceptions} is in the {\tt CFLAGS} option in the
+{\tt UFconfig/UFconfig.mk} file that comes with CHOLMOD.
+If you do not make these modifications, the CHOLMOD mexFunctions
+will terminate MATLAB if they encounter an error.
+
+Next, compile your METIS 4.0.1 library by typing {\tt make} in the
+{\tt metis-4.0} directory. Then type {\tt make} in the {\tt CHOLMOD/MATLAB}
+directory. This will compile the C-callable libraries for
+AMD, COLAMD, CAMD, CCOLAMD, METIS, and CHOLMOD, and then compile the
+mexFunction interfaces to those libraries.
+If METIS tries {\tt malloc} and encounters an out-of-memory condition,
+it calls {\tt abort}, which will terminate MATLAB. This problem does not
+occur using the method described in the previous section.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Integer and floating-point types, and notation used}
+%-------------------------------------------------------------------------------
+
+CHOLMOD supports both {\tt int} and {\tt long} integers. CHOLMOD
+routines with the prefix {\tt cholmod\_} use {\tt int} integers,
+{\tt cholmod\_l\_} routines use {\tt long}. All floating-point
+values are {\tt double}.
+
+The {\tt long} integer is redefinable, via {\tt UFconfig.h}.
+That file defines a C preprocessor token {\tt UF\_long} which is
+{\tt long} on all systems except for Windows-64, in which case it is
+defined as {\tt \_\_int64}. The intent is that with suitable compile-time
+switches, {\tt int} is a 32-bit integer and {\tt UF\_long} is a 64-bit
+integer. The term {\tt long} is used to describe the latter
+integer throughout this document (except in the prototypes).
+
+Two kinds of complex matrices are supported: complex and zomplex.
+A complex matrix is held in a manner that is compatible with the
+Fortran and ANSI C99 complex data type. A complex array of size {\tt n}
+is a {\tt double} array {\tt x} of size {\tt 2*n}, with the real and imaginary
+parts interleaved (the real part comes first, as a {\tt double}, followed the
+imaginary part, also as a {\tt double}. Thus, the real part of the {\tt k}th
+entry is {\tt x[2*k]} and the imaginary part is {\tt x[2*k+1]}.
+
+A zomplex matrix of size {\tt n} stores its real part in one
+{\tt double} array of size {\tt n} called {\tt x} and its imaginary part
+in another {\tt double} array of size {\tt n} called {\tt z} (thus the
+name ``zomplex''). This also how MATLAB stores its complex matrices.
+The real part of the {\tt k}th entry is {\tt x[k]} and the imaginary part is
+{\tt z[k]}.
+
+Unlike {\tt UMFPACK}, the same routine name in CHOLMOD is used for pattern-only,
+real, complex, and zomplex matrices. For example, the statement
+\begin{verbatim}
+ C = cholmod_copy_sparse (A, &Common) ;
+\end{verbatim}
+creates a copy of a pattern, real, complex, or zomplex sparse matrix {\tt A}.
+The xtype (pattern, real, complex, or zomplex) of the resulting sparse matrix {\tt C}
+is the same as {\tt A} (a pattern-only sparse matrix contains no floating-point
+values). In the above case, {\tt C} and {\tt A} use {\tt int} integers.
+For {\tt long} integers, the statement would become:
+\begin{verbatim}
+ C = cholmod_l_copy_sparse (A, &Common) ;
+\end{verbatim}
+The last parameter of all CHOLMOD routines is always {\tt \&Common},
+a pointer to the
+{\tt cholmod\_common} object, which contains parameters, statistics,
+and workspace used throughout CHOLMOD.
+
+The {\tt xtype} of a CHOLMOD object (sparse matrix, triplet matrix, dense
+matrix, or factorization) determines whether it is pattern-only,
+real, complex, or zomplex.
+
+The names of the {\tt int} versions are primarily used in this document.
+To obtain the name of the {\tt long} version of the same routine, simply
+replace {\tt cholmod\_} with {\tt cholmod\_l\_}.
+
+MATLAB matrix notation is used throughout this document and in
+the comments in the CHOLMOD code itself. If you are not familiar with
+MATLAB, here is a short introduction to the notation, and a few
+minor variations used in CHOLMOD:
+
+\begin{itemize}
+ \item {\tt C=A+B} and {\tt C=A*B}, respectively are a matrix add and multiply if both
+ {\tt A} and {\tt B} are matrices of appropriate size. If {\tt A} is
+ a scalar, then it is added to or multiplied with every entry in {\tt B}.
+ \item {\tt a:b} where {\tt a} and {\tt b} are integers refers to the
+ sequence {\tt a}, {\tt a+1}, ... {\tt b}.
+ \item {\tt [A B]} and {\tt [A,B]} are the horizontal concatenation of {\tt A} and {\tt B}.
+ \item {\tt [A;B]} is the vertical concatenation of {\tt A} and {\tt B}.
+ \item {\tt A(i,j)} can refer either to a scalar or a submatrix.
+ For example: \newline
+ \vspace{0.05in}
+ \begin{tabular}{ll}
+ \hline
+ {\tt A(1,1)} & a scalar. \\
+ {\tt A(:,j)} & column {\tt j} of {\tt A}. \\
+ {\tt A(i,:)} & row {\tt i} of {\tt A}. \\
+ {\tt A([1 2], [1 2])} & a 2-by-2 matrix containing the 2-by-2 leading minor of {\tt A}. \\
+ \hline
+ \end{tabular} \newline
+ \vspace{0.1in}
+ If {\tt p} is a permutation of {\tt 1:n}, and {\tt A} is {\tt n}-by-{\tt n},
+ then {\tt A(p,p)} corresponds to the permuted matrix $\m{PAP}\tr$.
+ \item {\tt tril(A)} is the lower triangular part of {\tt A}, including the diagonal.
+ \item {\tt tril(A,k)} is the lower triangular part of {\tt A}, including entries
+ on and below the $k$th diagonal.
+ \item {\tt triu(A)} is the upper triangular part of {\tt A}, including the diagonal.
+ \item {\tt triu(A,k)} is the upper triangular part of {\tt A}, including entries
+ on and above the $k$th diagonal.
+ \item {\tt size(A)} returns the dimensions of {\tt A}.
+ \item {\tt find(x)} if {\tt x} is a vector returns a list of indices {\tt i}
+ for which {\tt x(i)} is nonzero.
+ \item {\tt A'} is the transpose of {\tt A} if {\tt A} is real, or
+ the complex conjugate transpose if {\tt A} is complex.
+ \item {\tt A.'} is the array transpose of {\tt A}.
+ \item {\tt diag(A)} is the diagonal of {\tt A} if {\tt A} is a matrix.
+ \item {\tt C=diag(s)} is a diagonal matrix if {\tt s} is a vector,
+ with the values of {\tt s} on the diagonal of {\tt C}.
+ \item {\tt S=spones(A)} returns a binary matrix {\tt S} with the
+ same nonzero pattern of {\tt A}.
+ \item {\tt nnz(A)} is the number of nonzero entries in {\tt A}.
+\end{itemize}
+
+\noindent Variations to MATLAB notation used in this document:
+\begin{itemize}
+ \item CHOLMOD uses 0-based notation (the first entry in the matrix is
+ {\tt A(0,0)}). MATLAB is 1-based. The context is usually clear.
+ \item {\tt I} is the identity matrix.
+ \item {\tt A(:,f)}, where {\tt f} is a set of columns, is interpreted
+ differently in CHOLMOD, but just for the set named {\tt f}.
+ See {\tt cholmod\_transpose\_unsym} for details.
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \section{The CHOLMOD Modules, objects, and functions}
+\label{Modules}
+%-------------------------------------------------------------------------------
+
+CHOLMOD contains a total of 133 {\tt int}-based routines (and the same number
+of {\tt long} routines), divided into a set of inter-related
+Modules. Each Module contains a set of related functions. The functions
+are divided into two types: Primary and Secondary, to reflect how a user will
+typically use CHOLMOD. Most users will find the Primary routines to be
+sufficient to use CHOLMOD in their programs. Each Module exists as a
+sub-directory (a folder for Windows users) within the CHOLMOD directory
+(or folder).
+
+\vspace{0.1in}
+\noindent There are seven Modules that provide user-callable routines for CHOLMOD.
+ \begin{enumerate}
+ \item {\tt Core}: basic data structures and definitions
+ \item {\tt Check}: prints/checks each of CHOLMOD's objects
+ \item {\tt Cholesky}: sparse Cholesky factorization
+ \item {\tt Modify}: sparse Cholesky update/downdate and row-add/row-delete
+ \item {\tt MatrixOps}: sparse matrix operators (add, multiply, norm, scale)
+ \item {\tt Supernodal}: supernodal sparse Cholesky factorization
+ \item {\tt Partition}: graph-partitioning-based orderings
+ \end{enumerate}
+
+\noindent Two additional Modules are required to compile the CHOLMOD library:
+ \begin{enumerate}
+ \item {\tt Include}: include files for CHOLMOD and programs that use CHOLMOD
+ \item {\tt Lib}: where the CHOLMOD library is built
+ \end{enumerate}
+
+\noindent Five additional Modules provide support functions and documentation:
+ \begin{enumerate}
+ \item {\tt Demo}: simple programs that illustrate the use of CHOLMOD
+ \item {\tt Doc}: documentation (including this document)
+ \item {\tt MATLAB}: CHOLMOD's interface to MATLAB
+ \item {\tt Tcov}: an exhaustive test coverage (requires Linux or Solaris)
+ \item {\tt Valgrind}: runs the {\tt Tcov} test under {\tt valgrind} (requires Linux)
+ \end{enumerate}
+
+The following Modules are licensed under the GNU Lesser General Public
+License: {\tt Check}, {\tt Cholesky}, {\tt Core}, and {\tt Partition}.
+The following Modules are licensed under the GNU General Public
+License: {\tt Demo}, {\tt Modify}, {\tt MatrixOps}, {\tt Supernodal},
+the {\tt MATLAB} Module (not MATLAB itself!), {\tt Tcov}, and {\tt Valgrind}.
+The files in the {\tt Include} Module are licensed according to
+their respective Modules. The {\tt Lib} and {\tt Doc} Modules need
+no license; the compiled binaries are licensed the same as their source code.
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Core} Module: basic data structures and definitions}
+%-------------------------------------------------------------------------------
+
+CHOLMOD includes five basic objects, defined in the {\tt Core} Module.
+The {\tt Core Module} provides basic operations for these objects
+and is required by all six other CHOLMOD library Modules:
+
+\subsubsection{{\tt cholmod\_common}: parameters, statistics, and workspace}
+ You must call {\tt cholmod\_start} before calling any other
+ CHOLMOD routine, and you must call {\tt cholmod\_finish} as your
+ last call to CHOLMOD (with the exception of
+ {\tt cholmod\_print\_common} and {\tt cholmod\_check\_common}
+ in the {\tt Check} Module).
+ Once the {\tt cholmod\_common} object is initialized,
+ the user may modify CHOLMOD's parameters held in this object,
+ and obtain statistics on CHOLMOD's activity.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_common} object:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_start}: the first call to CHOLMOD.
+ \item {\tt cholmod\_finish}: the last call to CHOLMOD (frees workspace in the {\tt cholmod\_common} object).
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_common} object:
+% 9
+ \begin{itemize}
+ \item {\tt cholmod\_defaults}: restores default parameters
+ \item {\tt cholmod\_maxrank}: determine maximum rank for update/downdate.
+ \item {\tt cholmod\_allocate\_work}: allocate workspace.
+ \item {\tt cholmod\_free\_work}: free workspace.
+ \item {\tt cholmod\_clear\_flag}: clear {\tt Flag} array.
+ \item {\tt cholmod\_error}: called when CHOLMOD encounters and error.
+ \item {\tt cholmod\_dbound}: bounds the diagonal of $\m{L}$ or $\m{D}$.
+ \item {\tt cholmod\_hypot}: compute {\tt sqrt(x*x+y*y)} accurately.
+ \item {\tt cholmod\_divcomplex}: complex divide.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsubsection{{\tt cholmod\_sparse}: a sparse matrix in compressed column form}
+%-------------------------------------------------------------------------------
+ A sparse matrix {\tt A} is held in compressed column form. In the basic
+ type (``packed,'' which corresponds to how MATLAB stores its sparse
+ matrices), and {\tt nrow}-by-{\tt ncol} matrix with {\tt nzmax} entries
+ is held in three arrays: {\tt p} of size {\tt ncol+1},
+ {\tt i} of size {\tt nzmax}, and {\tt x} of size {\tt nzmax}.
+ Row indices of nonzero entries in column {\tt j} are held in
+ {\tt i [p[j] ... p[j+1]-1]}, and their corresponding numerical values
+ are held in {\tt x [p[j] ... p[j+1]-1]}. The first column starts at
+ location zero ({\tt p[0]=0}).
+ There may be no duplicate entries. Row indices in each column may
+ be sorted or unsorted (the {\tt A->sorted} flag must be false if
+ the columns are unsorted). The {\tt A->stype} determines the
+ storage mode: 0 if the matrix is unsymmetric, 1 if the matrix is
+ symmetric with just the upper triangular part stored, and -1 if
+ the matrix is symmetric with just the lower triangular part stored.
+
+ In ``unpacked'' form, an additional array {\tt nz} of size {\tt ncol}
+ is used. The end of column {\tt j} in {\tt i} and {\tt x}
+ is given by {\tt p[j]+nz[j]}. Columns not need be in any particular
+ order ({\tt p[0]} need not be zero), and there may be gaps between
+ the columns.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_sparse} object:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_sparse}: allocate a sparse matrix
+ \item {\tt cholmod\_free\_sparse}: free a sparse matrix
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_sparse} object:
+% 16
+ \begin{itemize}
+ \item {\tt cholmod\_reallocate\_sparse}: change the size (number of entries) of a sparse matrix.
+ \item {\tt cholmod\_nnz}: number of nonzeros in a sparse matrix.
+ \item {\tt cholmod\_speye}: sparse identity matrix.
+ \item {\tt cholmod\_spzeros}: sparse zero matrix.
+ \item {\tt cholmod\_transpose}: transpose a sparse matrix.
+ \item {\tt cholmod\_ptranspose}: transpose/permute a sparse matrix.
+ \item {\tt cholmod\_transpose\_unsym}: transpose/permute an unsymmetric sparse matrix.
+ \item {\tt cholmod\_transpose\_sym}: transpose/permute a symmetric sparse matrix.
+ \item {\tt cholmod\_sort}: sort row indices in each column of a sparse matrix.
+ \item {\tt cholmod\_band}: extract a band of a sparse matrix.
+ \item {\tt cholmod\_band\_inplace}: remove entries not with a band.
+ \item {\tt cholmod\_aat}: {\tt C = A*A'}.
+ \item {\tt cholmod\_copy\_sparse}: {\tt C = A}, create an exact copy of a sparse matrix.
+ \item {\tt cholmod\_copy}: {\tt C = A}, with possible change of {\tt stype}.
+ \item {\tt cholmod\_add}: {\tt C = alpha*A + beta*B}.
+ \item {\tt cholmod\_sparse\_xtype}: change the {\tt xtype} of a sparse matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsubsection{{\tt cholmod\_factor}: a symbolic or numeric factorization}
+%-------------------------------------------------------------------------------
+
+ A factor can be in $\m{LL}\tr$ or $\m{LDL}\tr$ form, and either supernodal
+ or simplicial form. In simplicial form, this is very much like a
+ packed or unpacked {\tt cholmod\_sparse} matrix. In supernodal
+ form, adjacent columns with similar nonzero pattern are stored as
+ a single block (a supernode).
+
+\vspace{0.1in}
+\noindent Primary routine for the {\tt cholmod\_factor} object:
+% 1
+ \begin{itemize}
+ \item {\tt cholmod\_free\_factor}: free a factor
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_factor} object:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_factor}: allocate a factor. You will normally use {\tt cholmod\_analyze} to create a factor.
+ \item {\tt cholmod\_reallocate\_factor}: change the number of entries in a factor.
+ \item {\tt cholmod\_change\_factor}: change the type of a factor ($\m{LDL}\tr$ to $\m{LL}\tr$, supernodal to simplicial, etc.).
+ \item {\tt cholmod\_pack\_factor}: pack the columns of a factor.
+ \item {\tt cholmod\_reallocate\_column}: resize a single column of a factor.
+ \item {\tt cholmod\_factor\_to\_sparse}: create a sparse matrix copy of a factor.
+ \item {\tt cholmod\_copy\_factor}: create a copy of a factor.
+ \item {\tt cholmod\_factor\_xtype}: change the xtype of a factor.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsubsection{{\tt cholmod\_dense}: a dense matrix}
+%-------------------------------------------------------------------------------
+ This consists of a dense array of numerical values and its dimensions.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_dense} object:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_dense}: allocate a dense matrix.
+ \item {\tt cholmod\_free\_dense}: free a dense matrix.
+ \end{itemize}
+
+\vspace{0.1in}
+\noindent Secondary routines for the {\tt cholmod\_dense} object:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_zeros}: allocate a dense matrix of all zeros.
+ \item {\tt cholmod\_ones}: allocate a dense matrix of all ones.
+ \item {\tt cholmod\_eye}: allocate a dense identity matrix .
+ \item {\tt cholmod\_sparse\_to\_dense}: create a dense matrix copy of a sparse matrix.
+ \item {\tt cholmod\_dense\_to\_sparse}: create a sparse matrix copy of a dense matrix.
+ \item {\tt cholmod\_copy\_dense}: create a copy of a dense matrix.
+ \item {\tt cholmod\_copy\_dense2}: copy a dense matrix (pre-allocated).
+ \item {\tt cholmod\_dense\_xtype}: change the {\tt xtype} of a dense matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsubsection{{\tt cholmod\_triplet}: a sparse matrix in ``triplet'' form}
+%-------------------------------------------------------------------------------
+ The {\tt cholmod\_sparse} matrix is the basic sparse matrix used in
+ CHOLMOD, but it can be difficult for the user to construct. It also
+ does not easily support the inclusion of new entries in the matrix.
+ The {\tt cholmod\_triplet} matrix is provided to address these issues.
+ A sparse matrix in triplet form consists of three arrays of size
+ {\tt nzmax}: {\tt i}, {\tt j}, and {\tt x}, and a {\tt z} array
+ for the zomplex case.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_triplet} object:
+% 3
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_triplet}: allocate a triplet matrix.
+ \item {\tt cholmod\_free\_triplet}: free a triplet matrix.
+ \item {\tt cholmod\_triplet\_to\_sparse}: create a sparse matrix copy of a triplet matrix.
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_triplet} object:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_reallocate\_triplet}: change the number of entries in a triplet matrix.
+ \item {\tt cholmod\_sparse\_to\_triplet}: create a triplet matrix copy of a sparse matrix.
+ \item {\tt cholmod\_copy\_triplet}: create a copy of a triplet matrix.
+ \item {\tt cholmod\_triplet\_xtype}: change the {\tt xtype} of a triplet matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsubsection{Memory management routines}
+%-------------------------------------------------------------------------------
+ By default, CHOLMOD uses the ANSI C {\tt malloc}, {\tt free},
+ {\tt calloc}, and {\tt realloc} routines. You may use different
+ routines by modifying function pointers in the {\tt cholmod\_common} object.
+
+\vspace{0.1in}
+\noindent Primary routines:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_malloc}: {\tt malloc} wrapper.
+ \item {\tt cholmod\_free}: {\tt free} wrapper.
+ \end{itemize}
+
+\noindent Secondary routines:
+% 3
+ \begin{itemize}
+ \item {\tt cholmod\_calloc}: {\tt calloc} wrapper.
+ \item {\tt cholmod\_realloc}: {\tt realloc} wrapper.
+ \item {\tt cholmod\_realloc\_multiple}: {\tt realloc} wrapper for multiple objects.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Check} Module: print/check the CHOLMOD objects}
+%-------------------------------------------------------------------------------
+ The {\tt Check} Module contains routines that check and print the five
+ basic objects in CHOLMOD, and three kinds of integer vectors (a set,
+ a permutation, and a tree). It also provides a routine to read a sparse
+ matrix from a file in Matrix Market format (http://www.nist.gov/MatrixMarket).
+ Requires the {\tt Core} Module.
+
+\vspace{0.1in}
+\noindent Primary routines:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_print\_common}: print the {\tt cholmod\_common} object,
+ including statistics on CHOLMOD's behavior (fill-in, flop count,
+ ordering methods used, and so on).
+ \item {\tt cholmod\_write\_sparse}: write a sparse matrix to a file
+ in Matrix Market format.
+ \item {\tt cholmod\_write\_dense}: write a sparse matrix to a file
+ in Matrix Market format.
+ \item {\tt cholmod\_read\_matrix}: read a sparse or dense matrix from a file
+ in Matrix Market format.
+ \end{itemize}
+
+\vspace{0.1in}
+\noindent Secondary routines:
+% 18
+ \begin{itemize}
+ \item {\tt cholmod\_check\_common}: check the {\tt cholmod\_common} object
+ \item {\tt cholmod\_check\_sparse}: check a sparse matrix
+ \item {\tt cholmod\_print\_sparse}: print a sparse matrix
+ \item {\tt cholmod\_check\_dense}: check a dense matrix
+ \item {\tt cholmod\_print\_dense}: print a dense matrix
+ \item {\tt cholmod\_check\_factor}: check a Cholesky factorization
+ \item {\tt cholmod\_print\_factor}: print a Cholesky factorization
+ \item {\tt cholmod\_check\_triplet}: check a triplet matrix
+ \item {\tt cholmod\_print\_triplet}: print a triplet matrix
+ \item {\tt cholmod\_check\_subset}: check a subset (integer vector in given range)
+ \item {\tt cholmod\_print\_subset}: print a subset (integer vector in given range)
+ \item {\tt cholmod\_check\_perm}: check a permutation (an integer vector)
+ \item {\tt cholmod\_print\_perm}: print a permutation (an integer vector)
+ \item {\tt cholmod\_check\_parent}: check an elimination tree (an integer vector)
+ \item {\tt cholmod\_print\_parent}: print an elimination tree (an integer vector)
+ \item {\tt cholmod\_read\_triplet}: read a triplet matrix from a file
+ \item {\tt cholmod\_read\_sparse}: read a sparse matrix from a file
+ \item {\tt cholmod\_read\_dense}: read a dense matrix from a file
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Cholesky} Module: sparse Cholesky factorization}
+%-------------------------------------------------------------------------------
+
+The primary routines are all that a user requires to order, analyze, and
+factorize a sparse symmetric positive definite matrix $\m{A}$ (or $\m{AA}\tr$), and
+to solve $\m{Ax}=\m{b}$ (or $\m{AA}\tr\m{x}=\m{b}$). The primary routines rely on the secondary
+routines, the {\tt Core} Module, and the AMD and COLAMD packages. They
+make optional use of the {\tt Supernodal} and {\tt Partition} Modules, the
+METIS package, the CAMD package, and
+the CCOLAMD package. The {\tt Cholesky} Module is
+required by the {\tt Partition} Module.
+
+\vspace{0.1in}
+\noindent Primary routines:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_analyze}: order and analyze (simplicial or supernodal).
+ \item {\tt cholmod\_factorize}: simplicial or supernodal Cholesky factorization.
+ \item {\tt cholmod\_solve}: solve a linear system (simplicial or supernodal, dense $\m{x}$ and $\m{b}$).
+ \item {\tt cholmod\_spsolve}: solve a linear system (simplicial or supernodal, sparse $\m{x}$ and $\m{b}$ ).
+ \end{itemize}
+
+\noindent Secondary routines:
+% 15
+ \begin{itemize}
+ \item {\tt cholmod\_analyze\_p}: analyze, with user-provided permutation or $\m{f}$ set.
+ \item {\tt cholmod\_factorize\_p}: factorize, with user-provided permutation or $\m{f}$.
+ \item {\tt cholmod\_analyze\_ordering}: analyze a permutation
+ \item {\tt cholmod\_etree}: find the elimination tree.
+ \item {\tt cholmod\_rowcolcounts}: compute the row/column counts of $\m{L}$.
+ \item {\tt cholmod\_amd}: order using AMD.
+ \item {\tt cholmod\_colamd}: order using COLAMD.
+ \item {\tt cholmod\_rowfac}: incremental simplicial factorization.
+ \item {\tt cholmod\_row\_subtree}: find the nonzero pattern of a row of $\m{L}$.
+ \item {\tt cholmod\_row\_lsubtree}: find the nonzero pattern of a row of $\m{L}$.
+ \item {\tt cholmod\_resymbol}: recompute the symbolic pattern of $\m{L}$.
+ \item {\tt cholmod\_resymbol\_noperm}: recompute the symbolic pattern of $\m{L}$, no permutation.
+ \item {\tt cholmod\_postorder}: postorder a tree.
+ \item {\tt cholmod\_rcond}: compute the reciprocal condition number estimate.
+ \item {\tt cholmod\_rowfac\_mask}: for use in LPDASA only.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Modify} Module: update/downdate a sparse Cholesky factorization}
+%-------------------------------------------------------------------------------
+
+The {\tt Modify} Module contains sparse Cholesky modification routines:
+update, downdate, row-add, and row-delete.
+It can also modify a corresponding solution to $\m{Lx}=\m{b}$ when L is modified.
+This module is most useful when applied on a Cholesky factorization computed by
+the {\tt Cholesky} module, but it does not actually require the {\tt Cholesky} module.
+The {\tt Core} module can create an identity Cholesky factorization ($\m{LDL}\tr$ where
+$\m{L}=\m{D}=\m{I}$) that can then be modified by these routines.
+Requires the {\tt Core} module. Not required by any other CHOLMOD Module.
+
+\vspace{0.1in}
+\noindent Primary routine:
+% 1
+ \begin{itemize}
+ \item {\tt cholmod\_updown}: multiple rank update/downdate
+ \end{itemize}
+
+\noindent Secondary routines:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_updown\_solve}: update/downdate, and modify solution to $\m{Lx=b}$
+ \item {\tt cholmod\_updown\_mark}: update/downdate, and modify solution to partial $\m{Lx=b}$
+ \item {\tt cholmod\_updown\_mask}: for use in LPDASA only.
+ \item {\tt cholmod\_rowadd}: add a row to an $\m{LDL}\tr$ factorization
+ \item {\tt cholmod\_rowadd\_solve}: add a row, and update solution to $\m{Lx=b}$
+ \item {\tt cholmod\_rowadd\_mark}: add a row, and update solution to partial $\m{Lx=b}$
+ \item {\tt cholmod\_rowdel}: delete a row from an $\m{LDL}\tr$ factorization
+ \item {\tt cholmod\_rowdel\_solve}: delete a row, and downdate $\m{Lx=b}$
+ \item {\tt cholmod\_rowdel\_mark}: delete a row, and downdate solution to partial $\m{Lx=b}$
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt MatrixOps} Module: basic sparse matrix operations}
+%-------------------------------------------------------------------------------
+
+The {\tt MatrixOps} Module provides
+basic operations on sparse and dense matrices.
+Requires the {\tt Core} module. Not required by any other CHOLMOD module.
+In the descriptions below,
+{\tt A}, {\tt B}, and {\tt C:} are sparse matrices ({\tt cholmod\_sparse}),
+{\tt X} and {\tt Y} are dense matrices ({\tt cholmod\_dense}),
+{\tt s} is a scalar or vector, and
+{\tt alpha} {\tt beta} are scalars.
+
+% 10
+ \begin{itemize}
+ \item {\tt cholmod\_drop}: drop entries from A with absolute value $\ge$ a given tolerance.
+ \item {\tt cholmod\_norm\_dense}: {\tt s = norm (X)}, 1-norm, infinity-norm, or 2-norm
+ \item {\tt cholmod\_norm\_sparse}: {\tt s = norm (A)}, 1-norm or infinity-norm
+ \item {\tt cholmod\_horzcat}: {\tt C = [A,B]}
+ \item {\tt cholmod\_scale}: {\tt A = diag(s)*A}, {\tt A*diag(s)}, {\tt s*A} or {\tt diag(s)*A*diag(s)}.
+ \item {\tt cholmod\_sdmult}: {\tt Y = alpha*(A*X) + beta*Y} or {\tt alpha*(A'*X) + beta*Y}.
+ \item {\tt cholmod\_ssmult}: {\tt C = A*B}
+ \item {\tt cholmod\_submatrix}: {\tt C = A (i,j)}, where {\tt i} and {\tt j} are arbitrary integer vectors.
+ \item {\tt cholmod\_vertcat}: {\tt C = [A ; B]}.
+ \item {\tt cholmod\_symmetry}: determine symmetry of a matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Supernodal} Module: supernodal sparse Cholesky factorization}
+%-------------------------------------------------------------------------------
+
+The {\tt Supernodal} Module performs
+supernodal analysis, factorization, and solve. The simplest way to use
+these routines is via the {\tt Cholesky} Module. This Module does not provide any
+fill-reducing orderings. It normally operates on matrices ordered by the
+{\tt Cholesky} Module.
+It does not require the {\tt Cholesky} Module itself, however.
+Requires the {\tt Core} Module, and two external packages: LAPACK and the BLAS.
+Optionally used by the {\tt Cholesky} Module. All are secondary routines
+since these functions are more easily used via the {\tt Cholesky} Module.
+
+\vspace{0.1in}
+\noindent Secondary routines:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_super\_symbolic}: supernodal symbolic analysis
+ \item {\tt cholmod\_super\_numeric}: supernodal numeric factorization
+ \item {\tt cholmod\_super\_lsolve}: supernodal $\m{Lx}=\m{b}$ solve
+ \item {\tt cholmod\_super\_ltsolve}: supernodal $\m{L}\tr\m{x}=\m{b}$ solve
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt Partition} Module: graph-partitioning-based orderings}
+%-------------------------------------------------------------------------------
+
+The {\tt Partition} Module provides
+graph partitioning and graph-partition-based orderings. It includes an
+interface to CAMD, CCOLAMD, and CSYMAMD, constrained minimum degree ordering
+methods which order a matrix following constraints determined via nested
+dissection.
+Requires the {\tt Core} and {\tt Cholesky} Modules, and two packages: {\tt METIS 4.0.1}, CAMD, and CCOLAMD.
+Optionally used by the {\tt Cholesky} Module. All are secondary routines since
+these are more easily used by the {\tt Cholesky} Module.
+
+Note that METIS does not have a version that uses {\tt long} integers. If you try to use
+these routines (except the CAMD, CCOLAMD, and CSYMAMD interfaces)
+on a matrix that is too large, an error code will be returned.
+
+\vspace{0.1in}
+\noindent Secondary routines:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_nested\_dissection}: CHOLMOD nested dissection ordering
+ \item {\tt cholmod\_metis}: METIS nested dissection ordering ({\tt METIS\_NodeND})
+ \item {\tt cholmod\_camd}: interface to CAMD ordering
+ \item {\tt cholmod\_ccolamd}: interface to CCOLAMD ordering
+ \item {\tt cholmod\_csymamd}: interface to CSYMAMD ordering
+ \item {\tt cholmod\_bisect}: graph partitioner (currently based on METIS)
+ \item {\tt cholmod\_metis\_bisector}: direct interface to {\tt METIS\_NodeComputeSeparator}.
+ \item {\tt cholmod\_collapse\_septree}: pruned a separator tree from
+ {\tt cholmod\_nested\_dissection}.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \section{CHOLMOD naming convention, parameters, and return values}
+%-------------------------------------------------------------------------------
+
+All routine names, data types, and CHOLMOD library files use the
+{\tt cholmod\_} prefix. All macros and other {\tt \#define} statements
+visible to the user program use the {\tt CHOLMOD} prefix.
+The {\tt cholmod.h} file must be included in user programs that use CHOLMOD:
+
+{\footnotesize
+\begin{verbatim}
+ #include "cholmod.h"
+\end{verbatim}
+}
+
+\noindent
+All CHOLMOD routines (in all modules) use the following protocol for return values:
+\begin{itemize}
+\item {\tt int}: {\tt TRUE} (1) if successful, or {\tt FALSE} (0) otherwise. (exception: {\tt cholmod\_divcomplex}).
+\item {\tt long}: a value $\ge 0$ if successful, or -1 otherwise.
+\item {\tt double}: a value $\ge 0$ if successful, or -1 otherwise.
+\item {\tt size\_t}: a value $>$ 0 if successful, or 0 otherwise.
+\item {\tt void *}: a non-{\tt NULL} pointer to newly allocated memory if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_sparse *}: a non-{\tt NULL} pointer to a newly allocated sparse matrix if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_factor *}: a non-{\tt NULL} pointer to a newly allocated factor if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_triplet *}: a non-{\tt NULL} pointer to a newly allocated triplet matrix if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_dense *}: a non-{\tt NULL} pointer to a newly allocated dense matrix if successful, or {\tt NULL} otherwise.
+\end{itemize}
+
+{\tt TRUE} and {\tt FALSE} are not defined in {\tt cholmod.h},
+since they may conflict with the user program. A routine that described
+here returning {\tt TRUE} or {\tt FALSE} returns 1 or 0, respectively.
+Any {\tt TRUE}/{\tt FALSE} parameter is true if nonzero, false if zero.
+
+\noindent
+Input, output, and input/output parameters:
+\begin{itemize}
+\item Input parameters appear first in the parameter lists of all CHOLMOD routines.
+They are not modified by CHOLMOD.
+\item Input/output parameters (except for {\tt Common}) appear next.
+They must be defined on input, and are modified on output.
+\item Output parameters are listed next. If they are pointers, they must
+point to allocated space on input, but their contents are not defined on input.
+\item Workspace parameters appear next. They are used in only two routines in the Supernodal module.
+\item The {\tt cholmod\_common *Common} parameter always appears as the last parameter
+(with two exceptions: {\tt cholmod\_hypot} and {\tt cholmod\_divcomplex}).
+It is always an input/output parameter.
+\end{itemize}
+
+A floating-point scalar is passed to CHOLMOD as a pointer to a {\tt double}
+array of size two. The first entry in this array is the real part of the
+scalar, and the second entry is the imaginary part. The imaginary part is
+only accessed if the other inputs are complex or zomplex. In some cases
+the imaginary part is always ignored ({\tt cholmod\_factor\_p}, for example).
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_common} object}
+\label{cholmod_common}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{Constant definitions}
+%---------------------------------------
+
+\input{_defn.tex}
+These definitions are used within the {\tt cholmod\_common} object,
+called {\tt Common} both here and throughout the code.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_common}: parameters, statistics, and workspace}
+%---------------------------------------
+
+\input{_common.tex}
+The {\tt cholmod\_common Common} object contains parameters, statistics, and
+workspace used within CHOLMOD. The first call to CHOLMOD must be
+{\tt cholmod\_start}, which initializes this object.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_start}: start CHOLMOD}
+%---------------------------------------
+
+\input{_start.tex}
+Sets the default parameters, clears the statistics, and initializes all
+workspace pointers to {\tt NULL}. The {\tt int}/{\tt long} type
+is set in {\tt Common->itype}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_finish}: finish CHOLMOD}
+%---------------------------------------
+
+\input{_finish.tex}
+This must be the last call to CHOLMOD.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_defaults}: set default parameters}
+%---------------------------------------
+
+\input{_defaults.tex}
+Sets the default parameters.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_maxrank}: maximum update/downdate rank}
+%---------------------------------------
+
+\input{_maxrank.tex}
+Returns the maximum rank for an update/downdate.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_work}: allocate workspace}
+%---------------------------------------
+
+\input{_allocate_work.tex}
+Allocates workspace in {\tt Common}. The workspace consists
+of the integer {\tt Head}, {\tt Flag}, and {\tt Iwork} arrays,
+of size {\tt nrow+1}, {\tt nrow}, and {\tt iworksize},
+respectively, and a {\tt double} array {\tt Xwork} of size
+{\tt xworksize}. The {\tt Head} array is normally equal to -1
+when it is cleared. If the {\tt Flag} array is cleared,
+all entries are less than {\tt Common->mark}. The {\tt Iwork} array is
+not kept in any particular state.
+The integer type is {\tt int} or {\tt long}, depending
+on whether the {\tt cholmod\_} or {\tt cholmod\_l\_} routines
+are used.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_work}: free workspace}
+%---------------------------------------
+
+\input{_free_work.tex}
+Frees the workspace in {\tt Common}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_clear\_flag}: clear Flag array}
+%---------------------------------------
+
+\input{_clear_flag.tex}
+Increments {\tt Common->mark} so that the {\tt Flag} array is now cleared.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_error}: report error}
+%---------------------------------------
+
+\input{_error.tex}
+This routine is called when CHOLMOD encounters an error.
+It prints a message (if printing is enabled), sets
+{\tt Common->status}. It then calls the
+user error handler routine {\tt Common->error\_handler},
+if it is not {\tt NULL}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dbound}: bound diagonal of $\m{L}$}
+%---------------------------------------
+
+\input{_dbound.tex}
+Ensures that entries on the diagonal of $\m{L}$ for an $\m{LL}\tr$
+factorization are greater than or equal to {\tt Common->dbound}.
+For an $\m{LDL}\tr$ factorization, it ensures that the magnitude
+of the entries of $\m{D}$ are greater than or equal to {\tt Common->dbound}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_hypot}: {\tt sqrt(x*x+y*y)}}
+%---------------------------------------
+
+\input{_hypot.tex}
+Computes the magnitude of a complex number.
+This routine is the default value for the {\tt Common->hypotenuse} function pointer.
+See also {\tt hypot}, in the standard {\tt math.h} header. If you have
+the ANSI C99 {\tt hypot}, you can use {\tt Common->hypotenuse = hypot}.
+The {\tt cholmod\_hypot} routine is provided in case you are using the
+ANSI C89 standard, which does not have {\tt hypot}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_divcomplex}: complex divide}
+%---------------------------------------
+
+\input{_divcomplex.tex}
+Divides two complex numbers. It returns 1 if a divide-by-zero occurred, or 0 otherwise.
+This routine is the default value for the {\tt Common->complex\_divide} function pointer.
+This return value is the single exception to the CHOLMOD rule that states all {\tt int} return
+values are {\tt TRUE} if successful or {\tt FALSE} otherwise.
+The exception is made to match the return value of a different complex divide routine
+that is not a part of CHOLMOD, but can be used via the function pointer.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_sparse} object}
+\label{cholmod_sparse}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sparse}: compressed-column sparse matrix}
+%---------------------------------------
+
+\input{_sparse.tex}
+Stores a sparse matrix in compressed-column form.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_allocate\_sparse}: allocate sparse matrix}
+%---------------------------------------
+
+\input{_allocate_sparse.tex}
+Allocates a sparse matrix. {\tt A->i}, {\tt A->x}, and {\tt A->z} are not initialized.
+The matrix returned is all zero, but it contains space enough for {\tt nzmax} entries.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_sparse}: free sparse matrix}
+%---------------------------------------
+
+\input{_free_sparse.tex}
+Frees a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_reallocate\_sparse}: reallocate sparse matrix}
+%---------------------------------------
+
+\input{_reallocate_sparse.tex}
+Reallocates a sparse matrix, so that it can contain {\tt nznew} entries.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_nnz}: number of entries in sparse matrix}
+%---------------------------------------
+
+\input{_nnz.tex}
+Returns the number of entries in a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_speye}: sparse identity matrix}
+%---------------------------------------
+
+\input{_speye.tex}
+Returns the sparse identity matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_spzeros}: sparse zero matrix}
+%---------------------------------------
+
+\input{_spzeros.tex}
+Returns the sparse zero matrix. This is another name
+for {\tt cholmod\_allocate\_sparse}, but with fewer parameters
+(the matrix is packed, sorted, and unsymmetric).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_transpose}: transpose sparse matrix}
+%---------------------------------------
+
+\input{_transpose.tex}
+Returns the transpose or complex conjugate transpose of a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_ptranspose}: transpose/permute sparse matrix}
+%---------------------------------------
+
+\input{_ptranspose.tex}
+Returns {\tt A'} or {\tt A(p,p)'} if {\tt A} is symmetric.
+Returns {\tt A'}, {\tt A(:,f)'}, or {\tt A(p,f)'} if {\tt A} is unsymmetric.
+See {\tt cholmod\_transpose\_unsym} for a discussion of how {\tt f} is used;
+this usage deviates from the MATLAB notation.
+Can also return the array transpose.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sort}: sort columns of a sparse matrix}
+%---------------------------------------
+
+\input{_sort.tex}
+Sorts the columns of the matrix {\tt A}. Returns {\tt A} in packed form, even if it
+starts as unpacked. Removes entries in the ignored part of a symmetric matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_transpose\_unsym}: transpose/permute unsymmetric sparse matrix}
+%---------------------------------------
+
+\input{_transpose_unsym.tex}
+Transposes and optionally permutes an unsymmetric sparse matrix.
+The output matrix must be preallocated before calling this routine.
+
+Computes {\tt F=A'}, {\tt F=A(:,f)'} or {\tt F=A(p,f)'}, except that the
+indexing by {\tt f} does not work the same as the MATLAB notation (see below).
+{\tt A->stype} is zero, which denotes that both the upper and lower triangular
+parts of A are present (and used). The matrix {\tt A} may in fact be symmetric in pattern
+and/or value; {\tt A->stype} just denotes which part of {\tt A} are stored. {\tt A} may be
+rectangular.
+
+The integer vector
+{\tt p} is a permutation of {\tt 0:m-1}, and {\tt f} is a subset of {\tt 0:n-1},
+where A is {\tt m}-by-{\tt n}.
+There can be no duplicate entries in {\tt p} or {\tt f}.
+
+\noindent
+Three kinds of transposes are available, depending on the {\tt values} parameter:
+\begin{itemize}
+\item 0: do not transpose the numerical values; create a {\tt CHOLMOD\_PATTERN} matrix
+\item 1: array transpose
+\item 2: complex conjugate transpose (same as 2 if input is real or pattern)
+\end{itemize}
+
+\noindent
+The set {\tt f} is held in fset and fsize:
+\begin{itemize}
+\item {\tt fset = NULL} means ``{\tt :}'' in MATLAB. {\tt fset} is ignored.
+\item {\tt fset != NULL} means {\tt f = fset [0..fsize-1]}.
+\item {\tt fset != NULL} and {\tt fsize = 0} means {\tt f} is the empty set.
+\end{itemize}
+
+Columns not in the set {\tt f} are considered to be zero. That is,
+if {\tt A} is 5-by-10 then {\tt F=A(:,[3 4])'} is not 2-by-5, but 10-by-5,
+and rows 3 and 4 of {\tt F} are equal to columns 3 and 4 of {\tt A} (the other
+rows of {\tt F} are zero). More precisely, in MATLAB notation:
+
+\begin{verbatim}
+ [m n] = size (A)
+ F = A
+ notf = ones (1,n)
+ notf (f) = 0
+ F (:, find (notf)) = 0
+ F = F'
+\end{verbatim}
+
+If you want the MATLAB equivalent {\tt F=A(p,f)} operation, use
+{\tt cholmod\_submatrix} instead (which does not compute the transpose).
+{\tt F->nzmax} must be large enough to hold the matrix {\tt F}.
+If {\tt F->nz} is present then {\tt F->nz [j]} is equal to the number of entries in column {\tt j} of {\tt F}.
+{\tt A} can be sorted or unsorted, with packed or unpacked columns.
+If {\tt f} is present and not sorted in ascending order, then {\tt F} is unsorted
+(that is, it may contain columns whose row indices do not appear in
+ascending order). Otherwise, {\tt F} is sorted (the row indices in each
+column of {\tt F} appear in strictly ascending order).
+
+{\tt F} is returned in packed or unpacked form, depending on {\tt F->packed} on input.
+If {\tt F->packed} is {\tt FALSE}, then {\tt F} is returned in unpacked form ({\tt F->nz} must be
+present). Each row {\tt i} of {\tt F} is large enough to hold all the entries in row {\tt i}
+of {\tt A}, even if {\tt f} is provided. That is, {\tt F->i} and
+{\tt F->x [F->p [i] .. F->p [i] + F->nz [i] - 1]} contain all entries in {\tt A(i,f)},
+but {\tt F->p [i+1] - F->p [i]} is equal to the number of nonzeros in {\tt A (i,:)},
+not just {\tt A (i,f)}.
+The {\tt cholmod\_transpose\_unsym} routine is the only operation in CHOLMOD that
+can produce an unpacked matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_transpose\_sym}: transpose/permute symmetric sparse matrix}
+%---------------------------------------
+
+\input{_transpose_sym.tex}
+Computes {\tt F = A'} or {\tt F = A(p,p)'}, the transpose or permuted transpose, where
+{\tt A->stype} is nonzero. {\tt A} must be square and symmetric.
+If {\tt A->stype} $> 0$, then {\tt A} is a symmetric matrix where just the upper part
+of the matrix is stored. Entries in the lower triangular part may be
+present, but are ignored.
+If {\tt A->stype} $< 0$, then {\tt A} is a symmetric matrix where just the lower part
+of the matrix is stored. Entries in the upper triangular part may be present, but are ignored.
+If {\tt F=A'}, then {\tt F} is returned
+sorted; otherwise {\tt F} is unsorted for the {\tt F=A(p,p)'} case.
+There can be no duplicate entries in {\tt p}.
+
+Three kinds of transposes are available, depending on the {\tt values} parameter:
+\begin{itemize}
+\item 0: do not transpose the numerical values; create a {\tt CHOLMOD\_PATTERN} matrix
+\item 1: array transpose
+\item 2: complex conjugate transpose (same as 2 if input is real or pattern)
+\end{itemize}
+
+For {\tt cholmod\_transpose\_unsym} and {\tt cholmod\_transpose\_sym}, the output matrix
+{\tt F} must already be pre-allocated by the caller, with the correct dimensions.
+If {\tt F} is not valid or has the wrong dimensions, it is not modified.
+Otherwise, if {\tt F} is too small, the transpose is not computed; the contents
+of {\tt F->p} contain the column pointers of the resulting matrix, where
+{\tt F->p [F->ncol] > F->nzmax}. In this case, the remaining contents of {\tt F} are
+not modified. {\tt F} can still be properly freed with {\tt cholmod\_free\_sparse}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_band}: extract band of a sparse matrix}
+%---------------------------------------
+
+\input{_band.tex}
+Returns {\tt C = tril (triu (A,k1), k2)}.
+{\tt C} is a matrix consisting of the diagonals of A from {\tt k1} to {\tt k2}.
+{\tt k=0} is the main diagonal of {\tt A}, {\tt k=1} is the superdiagonal, {\tt k=-1} is the
+subdiagonal, and so on. If {\tt A} is {\tt m}-by-{\tt n}, then:
+\begin{itemize}
+\item {\tt k1=-m} means {\tt C = tril (A,k2)}
+\item {\tt k2=n} means {\tt C = triu (A,k1)}
+\item {\tt k1=0} and {\tt k2=0} means {\tt C = diag(A)}, except {\tt C} is a matrix, not a vector
+\end{itemize}
+Values of {\tt k1} and {\tt k2} less than {\tt -m} are treated as {\tt -m}, and values greater
+than {\tt n} are treated as {\tt n}.
+
+{\tt A} can be of any symmetry (upper, lower, or unsymmetric); {\tt C} is returned in
+the same form, and packed. If {\tt A->stype} $> 0$, entries in the lower
+triangular part of {\tt A} are ignored, and the opposite is true if
+{\tt A->stype} $< 0$. If {\tt A} has sorted columns, then so does {\tt C}.
+{\tt C} has the same size as {\tt A}.
+
+{\tt C} can be returned as a numerical valued matrix (if {\tt A} has numerical values
+and {\tt mode} $> 0$), as a pattern-only ({\tt mode} $=0$), or as a pattern-only but with
+the diagonal entries removed ({\tt mode} $< 0$).
+
+The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only
+if {\tt mode} is $\le 0$ (in which case the numerical values are ignored).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_band\_inplace}: extract band, in place}
+%---------------------------------------
+
+\input{_band_inplace.tex}
+Same as {\tt cholmod\_band}, except that it always operates in place.
+Only packed matrices can be converted in place.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_aat}: compute $\m{AA}\tr$}
+%---------------------------------------
+
+\input{_aat.tex}
+Computes {\tt C = A*A'} or {\tt C = A(:,f)*A(:,f)'}.
+{\tt A} can be packed or unpacked, sorted or unsorted, but must be stored with
+both upper and lower parts ({\tt A->stype} of zero). {\tt C} is returned as packed,
+{\tt C->stype} of zero (both upper and lower parts present), and unsorted. See
+{\tt cholmod\_ssmult} in the {\tt MatrixOps} Module for a more general matrix-matrix
+multiply.
+The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only
+if {\tt mode} is $\le 0$ (in which case the numerical values are ignored).
+You can trivially convert {\tt C} to a symmetric upper/lower matrix
+by changing {\tt C->stype} to 1 or -1, respectively, after calling this routine.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_copy\_sparse}: copy sparse matrix}
+%---------------------------------------
+
+\input{_copy_sparse.tex}
+Returns an exact copy of the input sparse matrix {\tt A}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_copy}: copy (and change) sparse matrix}
+%---------------------------------------
+
+\input{_copy.tex}
+{\tt C = A}, which allocates {\tt C} and copies {\tt A} into {\tt C}, with possible change of
+{\tt stype}. The diagonal can optionally be removed. The numerical entries
+can optionally be copied. This routine differs from {\tt cholmod\_copy\_sparse},
+which makes an exact copy of a sparse matrix.
+
+{\tt A} can be of any type (packed/unpacked, upper/lower/unsymmetric). {\tt C} is
+packed and can be of any stype (upper/lower/unsymmetric), except that if
+{\tt A} is rectangular {\tt C} can only be unsymmetric. If the stype of A and C
+differ, then the appropriate conversion is made.
+
+\noindent
+There are three cases for {\tt A->stype}:
+\begin{itemize}
+\item $<0$, lower: assume {\tt A} is symmetric with just {\tt tril(A)} stored; the rest of {\tt A} is ignored
+\item $ 0$, unsymmetric: assume {\tt A} is unsymmetric; consider all entries in A
+\item $>0$, upper: assume {\tt A} is symmetric with just {\tt triu(A)} stored; the rest of {\tt A} is ignored
+\end{itemize}
+
+\noindent
+There are three cases for the requested symmetry of {\tt C} ({\tt stype} parameter):
+\begin{itemize}
+\item $<0$, lower: return just {\tt tril(C)}
+\item $0$, unsymmetric: return all of {\tt C}
+\item $>0$, upper: return just {\tt triu(C)}
+\end{itemize}
+
+\noindent
+This gives a total of nine combinations: \newline
+\begin{tabular}{ll}
+\hline
+Equivalent MATLAB statements & Using {\tt cholmod\_copy} \\
+\hline
+{\tt C = A ; }& {\tt A} unsymmetric, {\tt C} unsymmetric \\
+{\tt C = tril (A) ; }& {\tt A} unsymmetric, {\tt C} lower \\
+{\tt C = triu (A) ; }& {\tt A} unsymmetric, {\tt C} upper \\
+{\tt U = triu (A) ; L = tril (U',-1) ; C = L+U ; }& {\tt A} upper, {\tt C} unsymmetric \\
+{\tt C = triu (A)' ; }& {\tt A} upper, {\tt C} lower \\
+{\tt C = triu (A) ; }& {\tt A} upper, {\tt C} upper \\
+{\tt L = tril (A) ; U = triu (L',1) ; C = L+U ; }& {\tt A} lower, {\tt C} unsymmetric \\
+{\tt C = tril (A) ; }& {\tt A} lower, {\tt C} lower \\
+{\tt C = tril (A)' ; }& {\tt A} lower, {\tt C} upper \\
+\hline
+\end{tabular}
+
+\vspace{0.1in}
+The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only
+if {\tt values} is {\tt FALSE} (in which case the numerical values are ignored).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_add}: add sparse matrices}
+%---------------------------------------
+
+\input{_add.tex}
+Returns {\tt C = alpha*A + beta*B}.
+If the {\tt stype} of {\tt A} and {\tt B} match, then {\tt C} has
+the same {\tt stype}. Otherwise, {\tt C->stype} is zero ({\tt C} is
+unsymmetric).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sparse\_xtype}: change sparse xtype}
+%---------------------------------------
+
+\input{_sparse_xtype.tex}
+Changes the {\tt xtype} of a sparse matrix, to pattern, real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_factor} object}
+\label{cholmod_factor}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_factor} object: a sparse Cholesky factorization}
+%---------------------------------------
+
+\input{_factor.tex}
+An $\m{LL}\tr$ or $\m{LDL}\tr$ factorization in simplicial or supernodal form.
+A simplicial factor is very similar to a {\tt cholmod\_sparse} matrix.
+For an $\m{LDL}\tr$ factorization, the diagonal matrix $\m{D}$ is stored
+as the diagonal of $\m{L}$; the unit-diagonal of $\m{L}$ is not stored.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_free\_factor}: free factor}
+%---------------------------------------
+
+\input{_free_factor.tex}
+Frees a factor.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_factor}: allocate factor}
+%---------------------------------------
+
+\input{_allocate_factor.tex}
+Allocates a factor and sets it to identity.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_reallocate\_factor}: reallocate factor}
+%---------------------------------------
+
+\input{_reallocate_factor.tex}
+Reallocates a simplicial factor so that it can contain {\tt nznew} entries.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_change\_factor}: change factor}
+%---------------------------------------
+
+\input{_change_factor.tex}
+Change the numeric or symbolic, $\m{LL}\tr$ or $\m{LDL}\tr$, simplicial or super, packed or unpacked, and
+monotonic or non-monotonic status of a {\tt cholmod\_factor} object.
+
+There are four basic classes of factor types:
+\begin{enumerate}
+\item simplicial symbolic: Consists of two size-{\tt n} arrays: the fill-reducing
+permutation ({\tt L->Perm}) and the nonzero count for each column of L
+({\tt L->ColCount}). All other factor types also include this information.
+{\tt L->ColCount} may be exact (obtained from the analysis routines), or
+it may be a guess. During factorization, and certainly after update/downdate,
+the columns of {\tt L} can have a different number of nonzeros.
+{\tt L->ColCount} is used to allocate space. {\tt L->ColCount} is exact for the
+supernodal factorizations. The nonzero pattern of {\tt L} is not kept.
+
+\item simplicial numeric: These represent {\tt L} in a compressed column form. The
+variants of this type are:
+
+\begin{itemize}
+\item $\m{LDL}\tr$: {\tt L} is unit diagonal. Row indices in column {\tt j} are located in
+ {\tt L->i [L->p [j] ... L->p [j] + L->nz [j]]}, and corresponding numeric
+ values are in the same locations in {\tt L->x}. The total number of
+ entries is the sum of {\tt L->nz [j]}. The unit diagonal is not stored;
+ {\tt D} is stored on the diagonal of {\tt L} instead. {\tt L->p} may or may not be
+ monotonic. The order of storage of the columns in {\tt L->i} and {\tt L->x} is
+ given by a doubly-linked list ({\tt L->prev} and {\tt L->next}). {\tt L->p} is of
+ size {\tt n+1}, but only the first {\tt n} entries are used.
+
+ For the complex case, {\tt L->x} is stored interleaved with real and imaginary
+ parts, and is of size {\tt 2*lnz*sizeof(double)}. For the zomplex case,
+ {\tt L->x} is of size {\tt lnz*sizeof(double)} and holds the real part; {\tt L->z}
+ is the same size and holds the imaginary part.
+
+\item $\m{LL}\tr$: This is identical to the $\m{LDL}\tr$ form, except that the non-unit
+ diagonal of {\tt L} is stored as the first entry in each column of {\tt L}.
+\end{itemize}
+
+\item supernodal symbolic: A representation of the nonzero pattern of the
+supernodes for a supernodal factorization. There are {\tt L->nsuper}
+supernodes. Columns {\tt L->super [k]} to {\tt L->super [k+1]-1} are in the {\tt k}th
+supernode. The row indices for the {\tt k}th supernode are in
+{\tt L->s [L->pi [k] ... L->pi [k+1]-1]}. The numerical values are not
+allocated ({\tt L->x}), but when they are they will be located in
+{\tt L->x [L->px [k] ... L->px [k+1]-1]}, and the {\tt L->px} array is defined
+in this factor type.
+
+For the complex case, {\tt L->x} is stored interleaved with real/imaginary parts,
+and is of size \newline
+{\tt 2*L->xsize*sizeof(double)}. The zomplex supernodal case
+is not supported, since it is not compatible with LAPACK and the BLAS.
+
+\item supernodal numeric: Always an $\m{LL}\tr$ factorization. {\tt L} has a non-unit
+ diagonal. {\tt L->x} contains the numerical values of the supernodes, as
+ described above for the supernodal symbolic factor.
+ For the complex case, {\tt L->x} is stored interleaved, and is of size
+ {\tt 2*L->xsize*sizeof(double)}. The zomplex supernodal case is not
+ supported, since it is not compatible with LAPACK and the BLAS.
+\end{enumerate}
+
+
+In all cases, the row indices in each column ({\tt L->i} for simplicial {\tt L} and
+{\tt L->s} for supernodal {\tt L}) are kept sorted from low indices to high indices.
+This means the diagonal of {\tt L} (or {\tt D} for a $\m{LDL}\tr$ factorization) is always kept as the
+first entry in each column. The elimination tree is not kept. The parent
+of node {\tt j} can be found as the second row index in the {\tt j}th column.
+If column {\tt j} has no off-diagonal entries then node {\tt j} is a root
+of the elimination tree.
+
+The {\tt cholmod\_change\_factor} routine can do almost all possible conversions.
+It cannot do the following conversions:
+
+\begin{itemize}
+\item Simplicial numeric types cannot be converted to a supernodal
+ symbolic type. This would simultaneously deallocate the
+ simplicial pattern and numeric values and reallocate uninitialized
+ space for the supernodal pattern. This isn't useful for the user,
+ and not needed by CHOLMOD's own routines either.
+\item Only a symbolic factor (simplicial to supernodal) can be converted
+ to a supernodal numeric factor.
+\end{itemize}
+
+Some conversions are meant only to be used internally by other CHOLMOD
+routines, and should not be performed by the end user. They allocate space
+whose contents are undefined:
+
+\begin{itemize}
+\item converting from simplicial symbolic to supernodal symbolic.
+\item converting any factor to supernodal numeric.
+\end{itemize}
+
+Supports all xtypes, except that there is no supernodal zomplex L.
+
+The {\tt to\_xtype} parameter is used only when converting from symbolic to numeric
+or numeric to symbolic. It cannot be used to convert a numeric xtype (real,
+complex, or zomplex) to a different numeric xtype. For that conversion,
+use {\tt cholmod\_factor\_xtype} instead.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_pack\_factor}: pack the columns of a factor}
+%---------------------------------------
+
+\input{_pack_factor.tex}
+Pack the columns of a simplicial $\m{LDL}\tr$ or $\m{LL}\tr$ factorization. This can be followed
+by a call to {\tt cholmod\_reallocate\_factor} to reduce the size of {\tt L} to the exact
+size required by the factor, if desired. Alternatively, you can leave the
+size of {\tt L->i} and {\tt L->x} the same, to allow space for future updates/rowadds.
+Each column is reduced in size so that it has at most {\tt Common->grow2} free
+space at the end of the column.
+Does nothing and returns silently if given any other type of factor.
+Does not force the columns of {\tt L} to be monotonic. It thus differs from
+\begin{verbatim}
+ cholmod_change_factor (xtype, L->is_ll, FALSE, TRUE, TRUE, L, Common)
+\end{verbatim}
+which packs the columns and ensures that they appear in monotonic order.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_reallocate\_column}: reallocate one column of a factor}
+%---------------------------------------
+
+\input{_reallocate_column.tex}
+Reallocates the space allotted to a single column of $\m{L}$.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_factor\_to\_sparse}: sparse matrix copy of a factor}
+%---------------------------------------
+
+\input{_factor_to_sparse.tex}
+Returns a column-oriented sparse matrix containing the pattern and values
+of a simplicial or supernodal numerical factor, and then converts the factor
+into a simplicial symbolic factor. If {\tt L} is already packed, monotonic,
+and simplicial (which is the case when {\tt cholmod\_factorize} uses the simplicial
+Cholesky factorization algorithm) then this routine requires only a small
+amount of time and memory, independent of {\tt n}.
+It only operates on numeric factors (real, complex, or zomplex). It does not
+change {\tt L->xtype} (the resulting sparse matrix has the same {\tt xtype}
+as {\tt L}). If this routine fails, {\tt L} is left unmodified.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_copy\_factor}: copy factor}
+%---------------------------------------
+
+\input{_copy_factor.tex}
+Returns an exact copy of a factor.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_factor\_xtype}: change factor xtype}
+%---------------------------------------
+
+\input{_factor_xtype.tex}
+Changes the {\tt xtype} of a factor, to pattern, real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+You cannot change a supernodal factor to the zomplex xtype.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_dense} object}
+\label{cholmod_dense}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dense} object: a dense matrix}
+%---------------------------------------
+
+\input{_dense.tex}
+Contains a dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_dense}: allocate dense matrix}
+%---------------------------------------
+
+\input{_allocate_dense.tex}
+Allocates a dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_dense}: free dense matrix}
+%---------------------------------------
+
+\input{_free_dense.tex}
+Frees a dense matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_zeros}: dense zero matrix}
+%---------------------------------------
+
+\input{_zeros.tex}
+Returns an all-zero dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_ones}: dense matrix, all ones}
+%---------------------------------------
+
+\input{_ones.tex}
+Returns a dense matrix with each entry equal to one.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_eye}: dense identity matrix}
+%---------------------------------------
+
+\input{_eye.tex}
+Returns a dense identity matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_sparse\_to\_dense}: dense matrix copy of a sparse matrix}
+%---------------------------------------
+
+\input{_sparse_to_dense.tex}
+Returns a dense copy of a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dense\_to\_sparse}: sparse matrix copy of a dense matrix}
+%---------------------------------------
+
+\input{_dense_to_sparse.tex}
+Returns a sparse copy of a dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_copy\_dense}: copy dense matrix}
+%---------------------------------------
+
+\input{_copy_dense.tex}
+Returns a copy of a dense matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_copy\_dense2}: copy dense matrix (preallocated)}
+%---------------------------------------
+
+\input{_copy_dense2.tex}
+Returns a copy of a dense matrix, placing the result in a preallocated matrix {\tt Y}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dense\_xtype}: change dense matrix xtype}
+%---------------------------------------
+
+\input{_dense_xtype.tex}
+Changes the {\tt xtype} of a dense matrix, to real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_triplet} object}
+\label{cholmod_triplet}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_triplet} object: sparse matrix in triplet form}
+%---------------------------------------
+
+\input{_triplet.tex}
+Contains a sparse matrix in triplet form.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_triplet}: allocate triplet matrix}
+%---------------------------------------
+
+\input{_allocate_triplet.tex}
+Allocates a triplet matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_triplet}: free triplet matrix}
+%---------------------------------------
+
+\input{_free_triplet.tex}
+Frees a triplet matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_reallocate\_triplet}: reallocate triplet matrix}
+%---------------------------------------
+
+\input{_reallocate_triplet.tex}
+Reallocates a triplet matrix so that it can hold {\tt nznew} entries.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sparse\_to\_triplet}: triplet matrix copy of a sparse matrix}
+%---------------------------------------
+
+\input{_sparse_to_triplet.tex}
+Returns a triplet matrix copy of a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_triplet\_to\_sparse}: sparse matrix copy of a triplet matrix}
+%---------------------------------------
+
+\input{_triplet_to_sparse.tex}
+Returns a sparse matrix copy of a triplet matrix.
+If the triplet matrix is symmetric with just the lower part present ({\tt T->stype} $< 0$),
+then entries in the upper part are transposed and placed in the lower part when
+converting to a sparse matrix. Similarly,
+if the triplet matrix is symmetric with just the upper part present ({\tt T->stype} $> 0$),
+then entries in the lower part are transposed and placed in the upper part when
+converting to a sparse matrix.
+Any duplicate entries are summed.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_copy\_triplet}: copy triplet matrix}
+%---------------------------------------
+
+\input{_copy_triplet.tex}
+Returns an exact copy of a triplet matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_triplet\_xtype}: change triplet xtype}
+%---------------------------------------
+
+\input{_triplet_xtype.tex}
+Changes the {\tt xtype} of a dense matrix, to real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: memory management}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_malloc}: allocate memory}
+%---------------------------------------
+
+\input{_malloc.tex}
+Allocates a block of memory of size {\tt n*size},
+using the {\tt Common->malloc\_memory}
+function pointer (default is to use the ANSI C {\tt malloc} routine).
+A value of {\tt n=0} is treated as {\tt n=1}.
+If not successful, {\tt NULL} is returned and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_calloc}: allocate and clear memory}
+%---------------------------------------
+
+\input{_calloc.tex}
+Allocates a block of memory of size {\tt n*size},
+using the {\tt Common->calloc\_memory}
+function pointer (default is to use the ANSI C {\tt calloc} routine).
+A value of {\tt n=0} is treated as {\tt n=1}.
+If not successful, {\tt NULL} is returned and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_free}: free memory}
+%---------------------------------------
+
+\input{_free.tex}
+Frees a block of memory of size {\tt n*size},
+using the {\tt Common->free\_memory}
+function pointer (default is to use the ANSI C {\tt free} routine).
+The size of the block ({\tt n} and {\tt size}) is only required so that CHOLMOD
+can keep track of its current and peak memory usage. This is a useful statistic,
+and it can also help in tracking down memory leaks. After the call to
+{\tt cholmod\_finish}, the count of allocated blocks ({\tt Common->malloc\_count})
+should be zero, and the count of bytes in use ({\tt Common->memory\_inuse}) also
+should be zero. If you allocate a block with one size and free it with another,
+the {\tt Common->memory\_inuse} count will be wrong, but CHOLMOD will not
+have a memory leak.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_realloc}: reallocate memory}
+%---------------------------------------
+
+\input{_realloc.tex}
+Reallocates a block of memory whose current size {\tt n*size},
+and whose new size will be {\tt nnew*size} if successful,
+using the {\tt Common->calloc\_memory}
+function pointer (default is to use the ANSI C {\tt realloc} routine).
+If the reallocation is not successful, {\tt p} is returned unchanged
+and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}.
+The value of {\tt n} is set to {\tt nnew} if successful, or left
+unchanged otherwise.
+A value of {\tt nnew=0} is treated as {\tt nnew=1}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_realloc\_multiple}: reallocate memory}
+%---------------------------------------
+
+\input{_realloc_multiple.tex}
+Reallocates multiple blocks of memory, all with the same number of items
+(but with different item sizes). Either all reallocations succeed,
+or all are returned to their original size.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Check} Module routines}
+%-------------------------------------------------------------------------------
+
+No CHOLMOD routines print anything, except for the {\tt cholmod\_print\_*}
+routines in the {\tt Check} Module, and the {\tt cholmod\_error} routine. The
+{\tt Common->print\_function} is a pointer to {\tt printf} by default;
+you can redirect the output of CHOLMOD by redefining this pointer.
+If {\tt Common->print\_function} is {\tt NULL}, CHOLMOD does not print anything.
+
+The {\tt Common->print} parameter determines how much detail is printed.
+Each value of {\tt Common->print} listed below also prints the items listed
+for smaller values of {\tt Common->print}:
+\begin{itemize}
+\item 0: print nothing; check the data structures and return {\tt TRUE} or {\tt FALSE}.
+\item 1: print error messages.
+\item 2: print warning messages.
+\item 3: print a one-line summary of the object.
+\item 4: print a short summary of the object (first and last few entries).
+\item 5: print the entire contents of the object.
+\end{itemize}
+Values less than zero are treated as zero, and values greater than five are
+treated as five.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_check\_common}: check Common object}
+%---------------------------------------
+
+\input{_check_common.tex}
+Check if the {\tt Common} object is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_common}: print Common object}
+%---------------------------------------
+
+\input{_print_common.tex}
+Print the {\tt Common} object and check if it is valid.
+This prints the CHOLMOD parameters and statistics.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_sparse}: check sparse matrix}
+%---------------------------------------
+
+\input{_check_sparse.tex}
+Check if a sparse matrix is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_sparse}: print sparse matrix}
+%---------------------------------------
+
+\input{_print_sparse.tex}
+Print a sparse matrix and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_dense}: check dense matrix}
+%---------------------------------------
+
+\input{_check_dense.tex}
+Check if a dense matrix is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_dense}: print dense matrix}
+%---------------------------------------
+
+\input{_print_dense.tex}
+Print a dense matrix and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_factor}: check factor}
+%---------------------------------------
+
+\input{_check_factor.tex}
+Check if a factor is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_factor}: print factor}
+%---------------------------------------
+
+\input{_print_factor.tex}
+Print a factor and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_triplet}: check triplet matrix}
+%---------------------------------------
+
+\input{_check_triplet.tex}
+Check if a triplet matrix is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_triplet}: print triplet matrix}
+%---------------------------------------
+
+\input{_print_triplet.tex}
+Print a triplet matrix and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_subset}: check subset}
+%---------------------------------------
+
+\input{_check_subset.tex}
+Check if a subset is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_subset}: print subset}
+%---------------------------------------
+
+\input{_print_subset.tex}
+Print a subset and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_perm}: check permutation}
+%---------------------------------------
+
+\input{_check_perm.tex}
+Check if a permutation is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_perm}: print permutation}
+%---------------------------------------
+
+\input{_print_perm.tex}
+Print a permutation and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_parent}: check elimination tree}
+%---------------------------------------
+
+\input{_check_parent.tex}
+Check if an elimination tree is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_parent}: print elimination tree}
+%---------------------------------------
+
+\input{_print_parent.tex}
+Print an elimination tree and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_read\_triplet}: read triplet matrix from file}
+%---------------------------------------
+
+\input{_read_triplet.tex}
+Read a sparse matrix in triplet form, using the the {\tt coord}
+Matrix Market format (http://www.nist.gov/MatrixMarket).
+Skew-symmetric and complex symmetric matrices are returned with
+both upper and lower triangular parts present (an stype of zero).
+Real symmetric and complex Hermitian matrices are returned with just
+their upper or lower triangular part, depending on their stype.
+The Matrix Market {\tt array} data type for dense matrices is not supported
+(use {\tt cholmod\_read\_dense} for that case).
+
+If the first line of the file starts with {\tt \%\%MatrixMarket}, then it is
+interpreted as a file in Matrix Market format. The header line is optional.
+If present, this line must have the following format:
+\vspace{0.1in}
+
+ {\tt \%\%MatrixMarket matrix coord} {\em type storage}
+
+\vspace{0.1in}
+\noindent
+where {\em type} is one of: {\tt real}, {\tt complex}, {\tt pattern},
+or {\tt integer}, and {\em storage} is one of: {\tt general}, {\tt hermitian},
+{\tt symmetric}, or {\tt skew-symmetric}.
+In CHOLMOD, these roughly correspond to the {\tt xtype}
+(pattern, real, complex, or zomplex) and {\tt stype}
+(unsymmetric, symmetric/upper, and symmetric/lower).
+The strings are case-insensitive. Only the first character (or the
+first two for skew-symmetric) is significant.
+The {\tt coord} token can be replaced with {\tt array} in the Matrix Market format, but
+this format not supported by {\tt cholmod\_read\_triplet}.
+The {\tt integer} type is converted to real.
+The {\em type} is ignored; the actual type (real, complex, or pattern) is
+inferred from the number of tokens in each line of the file (2: pattern,
+3: real, 4: complex). This is compatible with the Matrix Market format.
+
+A storage of {\tt general} implies an stype of zero
+(see below). A storage of {\tt symmetric} and {\tt hermitian} imply an stype of -1.
+Skew-symmetric and complex symmetric matrices are returned with an stype of 0.
+Blank lines, any other lines starting with ``{\tt \%}'' are treated as comments, and are ignored.
+
+The first non-comment line contains 3 or 4 integers:
+\vspace{0.1in}
+
+ {\em nrow ncol nnz stype}
+
+\vspace{0.1in}
+\noindent
+where {\em stype} is optional (stype does not appear in the Matrix Market format).
+The matrix is {\em nrow}-by-{\em ncol}. The following {\em nnz} lines (excluding comments)
+each contain a single entry. Duplicates are permitted, and are summed in
+the output matrix.
+
+If stype is present, it denotes the storage format for the matrix.
+\begin{itemize}
+\item stype = 0 denotes an unsymmetric matrix (same as Matrix Market {\tt general}).
+\item stype = -1 denotes a symmetric or Hermitian matrix whose lower triangular
+ entries are stored. Entries may be present in the upper triangular
+ part, but these are ignored (same as Matrix Market {\tt symmetric}
+ for the real case, {\tt hermitian} for the complex case).
+\item stype = 1 denotes a symmetric or Hermitian matrix whose upper triangular
+ entries are stored. Entries may be present in the lower triangular
+ part, but these are ignored. This format is not available in the Matrix
+ Market format.
+\end{itemize}
+
+If neither the stype nor the Matrix Market header are present, then
+the stype is inferred from the rest of the data. If the matrix is
+rectangular, or has
+entries in both the upper and lower triangular parts, then it is assumed to
+be unsymmetric (stype=0). If only entries in the lower triangular part are
+present, the matrix is assumed to have stype = -1. If only entries in the
+upper triangular part are present, the matrix is assumed to have stype = 1.
+
+Each nonzero consists of one line with 2, 3, or 4 entries. All lines must
+have the same number of entries. The first two entries are the row and
+column indices of the nonzero. If 3 entries are present, the 3rd entry is
+the numerical value, and the matrix is real. If 4 entries are present,
+the 3rd and 4th entries in the line are the real and imaginary parts of
+a complex value.
+
+The matrix can be either 0-based or 1-based. It is first assumed to be
+one-based (compatible with Matrix Market), with row indices in the range
+1 to ncol and column indices in the range 1 to nrow. If a row or column
+index of zero is found, the matrix is assumed to be zero-based (with row
+indices in the range 0 to ncol-1 and column indices in the range 0 to
+nrow-1). This test correctly determines that all Matrix Market
+matrices are in 1-based form.
+
+For symmetric pattern-only matrices, the kth diagonal (if present) is set to
+one plus the degree of the row k or column k (whichever is larger), and the
+off-diagonals are set to -1. A symmetric pattern-only matrix with a
+zero-free diagonal is thus converted into a symmetric positive definite
+matrix. All entries are set to one for an unsymmetric pattern-only matrix.
+This differs from the MatrixMarket format ({\tt A = mmread ('file')} returns
+a binary pattern for A for symmetric pattern-only matrices).
+To return a binary format for all pattern-only matrices, use
+{\tt A = mread('file',1)}.
+
+Example matrices that follow this format can be found in the
+{\tt CHOLMOD/Demo/Matrix} and \newline
+{\tt CHOLMOD/Tcov/Matrix} directories.
+You can also try any of the matrices in the Matrix Market collection
+at http://www.nist.gov/MatrixMarket.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_read\_sparse}: read sparse matrix from file}
+%---------------------------------------
+
+\input{_read_sparse.tex}
+Read a sparse matrix in triplet form from a file (using {\tt cholmod\_read\_triplet})
+and convert to a CHOLMOD sparse matrix.
+The Matrix Market format is used.
+If {\tt Common->prefer\_upper} is {\tt TRUE} (the default case), a symmetric matrix is
+returned stored in upper-triangular form ({\tt A->stype} is 1).
+Otherwise, it is left in its original form, either upper or lower.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_read\_dense}: read dense matrix from file}
+%---------------------------------------
+
+\input{_read_dense.tex}
+Read a dense matrix from a file, using the the {\tt array}
+Matrix Market format
+\newline (http://www.nist.gov/MatrixMarket).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_read\_matrix}: read a matrix from file}
+%---------------------------------------
+
+\input{_read_matrix.tex}
+Read a sparse or dense matrix from a file, in Matrix Market format.
+Returns a {\tt void} pointer to either a
+{\tt cholmod\_triplet},
+{\tt cholmod\_sparse}, or
+{\tt cholmod\_dense} object.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_write\_sparse}: write a sparse matrix to a file}
+%---------------------------------------
+
+\input{_write_sparse.tex}
+Write a sparse matrix to a file in Matrix Market format. Optionally include
+comments, and print explicit zero entries given by the pattern of the {\tt Z}
+matrix. If not NULL, the {\tt Z} matrix must have the same dimensions and stype
+as {\tt A}.
+
+Returns the symmetry in which the matrix was printed
+(1 to 7) or -1 on failure. See the {\tt cholmod\_symmetry} function for
+a description of the return codes.
+
+If {\tt A} and {\tt Z} are sorted on input, and either unsymmetric (stype = 0) or
+symmetric-lower (stype < 0), and if {\tt A} and {\tt Z} do not overlap,
+then the triplets
+are sorted, first by column and then by row index within each column, with
+no duplicate entries. If all the above holds except stype > 0, then the
+triplets are sorted by row first and then column.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_write\_dense}: write a dense matrix to a file}
+%---------------------------------------
+
+\input{_write_dense.tex}
+Write a dense matrix to a file in Matrix Market format. Optionally include
+comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if
+square).
+A dense matrix is written in "general" format; symmetric formats in the
+Matrix Market standard are not exploited.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Cholesky} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_analyze}: symbolic factorization}
+%---------------------------------------
+
+\input{_analyze.tex}
+Orders and analyzes a matrix (either simplicial or supernodal), in preparation
+for numerical factorization via {\tt cholmod\_factorize} or via the ``expert''
+routines {\tt cholmod\_rowfac} and {\tt cholmod\_super\_numeric}.
+
+In the symmetric case, {\tt A} or {\tt A(p,p)} is analyzed,
+where {\tt p} is the fill-reducing ordering.
+In the unsymmetric case, {\tt A*A'} or {\tt A(p,:)*A(p,:)'} is analyzed.
+The {\tt cholmod\_analyze\_p} routine can be given a user-provided permutation {\tt p}
+(see below).
+
+The default ordering strategy is to first try AMD.
+The ordering quality is analyzed, and if AMD obtains an ordering where
+{\tt nnz(L)} is greater than or equal to {\tt 5*nnz(tril(A))}
+(or {\tt 5*nnz(tril(A*A'))} if {\tt A} is unsymmetric) and
+the floating-point operation count for the subsequent factorization is
+greater than or equal to {\tt 500*nnz(L)}, then METIS is tried (if installed).
+For {\tt cholmod\_analyze\_p}, the user-provided ordering is also tried.
+This default behavior is obtained when {\tt Common->nmethods} is zero.
+In this case, methods 0, 1, and 2 in {\tt Common->method[...]} are reset
+to user-provided, AMD, and METIS, respectively.
+The ordering with the smallest {\tt nnz(L)} is kept.
+
+If {\tt Common->default\_nesdis} is true (nonzero), then CHOLMOD's
+nested dissection (NESDIS) is used for the default strategy described
+above, in place of METIS.
+
+Other ordering options can be requested. These include:
+\begin{enumerate}
+\item natural: A is not permuted to reduce fill-in.
+\item user-provided: a permutation can be provided to {\tt cholmod\_analyze\_p}.
+\item AMD: approximate minimum degree (AMD for the symmetric case, COLAMD for the {\tt A*A'} case).
+\item METIS: nested dissection with {\tt METIS\_NodeND}
+\item {\tt NESDIS}: CHOLMOD's nested dissection using
+ {\tt METIS\_NodeComputeSeparator},
+ followed by a constrained minimum degree
+ (CAMD or CSYMAMD for the symmetric case, CCOLAMD for the {\tt A*A'} case).
+ This is typically slower than METIS, but typically provides better orderings.
+\end{enumerate}
+
+Multiple ordering options can be tried (up to 9 of them), and the best one
+is selected (the one that gives the smallest number of nonzeros in the
+simplicial factor L). If one method fails, {\tt cholmod\_analyze} keeps going, and
+picks the best among the methods that succeeded. This routine fails (and
+returns {\tt NULL}) if either the initial memory allocation fails, all ordering methods
+fail, or the supernodal analysis (if requested) fails. Change {\tt Common->nmethods} to the
+number of methods you wish to try. By default, the 9 methods available are:
+
+\begin{enumerate}
+\item user-provided permutation (only for {\tt cholmod\_analyze\_p}).
+\item AMD with default parameters.
+\item METIS with default parameters.
+\item {\tt NESDIS} with default parameters: stopping the partitioning when
+ the graph is of size {\tt nd\_small} = 200 or less, remove nodes with
+ more than {\tt max (16, prune\_dense * sqrt (n))} nodes where
+ {\tt prune\_dense} = 10, and follow partitioning with
+ constrained minimum degree ordering
+ (CAMD for the symmetric case,
+ CCOLAMD for the unsymmetric case).
+\item natural ordering (with weighted postorder).
+\item NESDIS, {\tt nd\_small} = 20000, {\tt prune\_dense} = 10.
+\item NESDIS, {\tt nd\_small} = 4, {\tt prune\_dense} = 10,
+ no constrained minimum degree.
+\item NESDIS, {\tt nd\_small} = 200, {\tt prune\_dense} = 0.
+\item COLAMD for {\tt A*A'} or AMD for {\tt A}
+\end{enumerate}
+
+You can modify these 9 methods and the number of methods tried by changing
+parameters in the {\tt Common} argument. If you know the best ordering for your
+matrix, set {\tt Common->nmethods} to 1 and set {\tt Common->method[0].ordering} to the
+requested ordering method. Parameters for each method can also be modified
+(refer to the description of {\tt cholmod\_common} for details).
+
+Note that it is possible for METIS to terminate your program if it runs out
+of memory. This is not the case for any CHOLMOD or minimum degree ordering
+routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD).
+Since {\tt NESDIS} relies on METIS, it too can terminate your program.
+
+The selected ordering is followed by a weighted postorder of the elimination
+tree by default (see {\tt cholmod\_postorder} for details),
+unless {\tt Common->postorder} is set to {\tt FALSE}.
+The postorder does not change the number of nonzeros in $\m{L}$ or
+the floating-point operation count. It does improve performance,
+particularly for the supernodal factorization.
+If you truly want the natural ordering with no postordering,
+you must set {\tt Common->postorder} to {\tt FALSE}.
+
+The factor {\tt L} is returned as simplicial symbolic if
+{\tt Common->supernodal} is {\tt CHOLMOD\_SIMPLICIAL} (zero) or as supernodal symbolic if
+{\tt Common->supernodal} is {\tt CHOLMOD\_SUPERNODAL} (two). If \newline
+{\tt Common->supernodal} is {\tt CHOLMOD\_AUTO} (one),
+then {\tt L} is simplicial if the flop count per nonzero in {\tt L} is less than
+{\tt Common->supernodal\_switch} (default: 40), and
+supernodal otherwise. In both cases, {\tt L->xtype} is {\tt CHOLMOD\_PATTERN}.
+A subsequent call to {\tt cholmod\_factorize} will perform a
+simplicial or supernodal factorization, depending on the type of {\tt L}.
+
+For the simplicial case, {\tt L} contains the fill-reducing permutation ({\tt L->Perm})
+and the counts of nonzeros in each column of {\tt L} ({\tt L->ColCount}). For the
+supernodal case, {\tt L} also contains the nonzero pattern of each supernode.
+
+If a simplicial factorization is selected, it will be $\m{LDL}\tr$ by default, since
+this is the kind required by the {\tt Modify} Module. CHOLMOD does not include a
+supernodal $\m{LDL}\tr$ factorization, so if a supernodal factorization is selected,
+it will be in the form $\m{LL}\tr$. The $\m{LDL}\tr$ method can be used to
+factorize positive definite matrices and indefinite matrices whose leading minors
+are well-conditioned (2-by-2 pivoting is not supported). The $\m{LL}\tr$ method
+is restricted to positive definite matrices. To factorize a large indefinite matrix,
+set {\tt Common->supernodal} to {\tt CHOLMOD\_SIMPLICIAL}, and the simplicial
+$\m{LDL}\tr$ method will always be used. This will be significantly slower than
+a supernodal $\m{LL}\tr$ factorization, however.
+
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_factorize}: numeric factorization}
+%---------------------------------------
+
+\input{_factorize.tex}
+Computes the numerical factorization of a symmetric matrix. The % primary
+inputs to this routine are a sparse matrix {\tt A} and the symbolic factor {\tt L} from
+{\tt cholmod\_analyze} or a prior numerical factor {\tt L}. If {\tt A} is symmetric, this
+routine factorizes {\tt A(p,p)}. %+beta*I (beta can be zero),
+where p is the fill-reducing permutation ({\tt L->Perm}). If {\tt A} is unsymmetric,
+% either
+{\tt A(p,:)*A(p,:)'} % +beta*I or A(p,f)*A(p,f)'+beta*I
+is factorized. % The set f and
+The nonzero pattern of the matrix {\tt A} must be the same as the matrix passed to
+{\tt cholmod\_analyze} for the supernodal case. For the simplicial case, it can
+be different, but it should be the same for best performance. % beta is real.
+
+A simplicial factorization or supernodal factorization is chosen, based on
+the type of the factor {\tt L}. If {\tt L->is\_super} is {\tt TRUE}, a supernodal $\m{LL}\tr$
+factorization is computed. Otherwise, a simplicial numeric factorization
+is computed, either $\m{LL}\tr$ or $\m{LDL}\tr$, depending on {\tt Common->final\_ll}
+(the default for the simplicial case is to compute an $\m{LDL}\tr$ factorization).
+
+Once the factorization is complete, it can be left as is or optionally
+converted into any simplicial numeric type, depending on the
+{\tt Common->final\_*} parameters. If converted from a supernodal to simplicial
+type, and {\tt Common->final\_resymbol} is {\tt TRUE}, then numerically
+zero entries in {\tt L} due to relaxed supernodal amalgamation are removed from
+the simplicial factor (they are always left in the supernodal form of {\tt L}).
+Entries that are numerically zero but present in the simplicial symbolic
+pattern of {\tt L} are left in place (the graph of {\tt L} remains chordal).
+This is required for the update/downdate/rowadd/rowdel routines to work
+properly.
+
+If the matrix is not positive definite the routine returns {\tt TRUE}, but
+{\tt Common->status} is set to {\tt CHOLMOD\_NOT\_POSDEF} and {\tt L->minor} is set to the
+column at which the failure occurred. Columns {\tt L->minor} to {\tt L->n-1}
+are set to zero.
+
+Supports any xtype (pattern, real, complex, or zomplex), except that the
+input matrix {\tt A} cannot be pattern-only. If {\tt L} is simplicial, its numeric
+xtype matches {\tt A} on output. If {\tt L} is supernodal, its xtype is real if {\tt A} is
+real, or complex if {\tt A} is complex or zomplex. CHOLMOD does not provide
+a supernodal zomplex factor, since it is incompatible with how complex numbers are
+stored in LAPACK and the BLAS.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_analyze\_p}: symbolic factorization, given permutation}
+%---------------------------------------
+
+\input{_analyze_p.tex}
+Identical to {\tt cholmod\_analyze}, except that a user-provided
+permutation {\tt p} can be provided, and the set {\tt f} for the unsymmetric case
+can be provided. The matrices {\tt A(:,f)*A(:,f)'} or {\tt A(p,f)*A(p,f)'}
+can be analyzed in the the unsymmetric case.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_factorize\_p}: numeric factorization, given permutation}
+%---------------------------------------
+
+\input{_factorize_p.tex}
+Identical to {\tt cholmod\_factorize}, but with additional options.
+The set {\tt f} can be provided for the unsymmetric case;
+{\tt A(p,f)*A(p,f)'} is factorized. The term {\tt beta*I} can be added to
+the matrix before it is factorized, where {\tt beta} is real.
+Only the real part, {\tt beta[0]}, is used.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_solve}: solve a linear system}
+%---------------------------------------
+
+\input{_solve.tex}
+Returns a solution {\tt X} that solves one of the following systems:
+
+\begin{tabular}{ll|ll}
+ \hline
+ system & {\tt sys} parameter & system & {\tt sys} parameter \\
+ $\m{Ax}=\m{b}$ & 0: {\tt CHOLMOD\_A} & & \\
+ $\m{LDL}\tr\m{x}=\m{b}$ & 1: {\tt CHOLMOD\_LDLt} & $\m{L}\tr\m{x}=\m{b}$ & 5: {\tt CHOLMOD\_Lt} \\
+ $\m{LDx}=\m{b}$ & 2: {\tt CHOLMOD\_LD} & $\m{Dx}=\m{b}$ & 6: {\tt CHOLMOD\_D} \\
+ $\m{DL}\tr\m{x}=\m{b}$ & 3: {\tt CHOLMOD\_DLt} & $\m{x}=\m{Pb}$ & 7: {\tt CHOLMOD\_P} \\
+ $\m{Lx}=\m{b}$ & 4: {\tt CHOLMOD\_L} & $\m{x}=\m{P}\tr\m{b}$ & 8: {\tt CHOLMOD\_Pt} \\
+ \hline
+\end{tabular}
+
+The factorization can be simplicial $\m{LDL}\tr$, simplicial $\m{LL}\tr$, or supernodal $\m{LL}\tr$.
+For an $\m{LL}\tr$ factorization, $\m{D}$ is the identity matrix. Thus {\tt CHOLMOD\_LD} and
+{\tt CHOLMOD\_L} solve the same system if an $\m{LL}\tr$ factorization was performed,
+for example.
+This is one of the few routines in CHOLMOD for which the xtype of the input
+arguments need not match.
+If both {\tt L} and {\tt B} are real, then {\tt X} is returned real. If either is complex
+or zomplex, {\tt X} is returned as either complex or zomplex, depending on the
+{\tt Common->prefer\_zomplex} parameter (default is complex).
+
+This routine does not check to see if the diagonal of $\m{L}$ or $\m{D}$ is zero,
+because sometimes a partial solve can be done with an indefinite or singular
+matrix. If you wish to check in your own code, test {\tt L->minor}. If
+{\tt L->minor == L->n}, then the matrix has no zero diagonal entries.
+If {\tt k = L->minor < L->n}, then {\tt L(k,k)} is zero for an $\m{LL}\tr$ factorization, or
+{\tt D(k,k)} is zero for an $\m{LDL}\tr$ factorization.
+
+Iterative refinement is not performed, but this can be easily done with
+the {\tt MatrixOps} Module. See {\tt Demo/cholmod\_demo.c} for an example.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_spsolve}: solve a linear system}
+%---------------------------------------
+
+\input{_spsolve.tex}
+Identical to {\tt cholmod\_spsolve}, except that {\tt B} and {\tt X} are sparse.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_etree}: find elimination tree}
+%---------------------------------------
+
+\input{_etree.tex}
+Computes the elimination tree of {\tt A} or {\tt A'*A}.
+In the symmetric case, the upper triangular part of {\tt A} is used. Entries not
+in this part of the matrix are ignored. Computing the etree of a symmetric
+matrix from just its lower triangular entries is not supported.
+In the unsymmetric case, all of {\tt A} is used, and the etree of {\tt A'*A} is computed.
+Refer to \cite{Liu90a} for a discussion of the elimination tree
+and its use in sparse Cholesky factorization.
+% J. Liu, "The role of elimination trees in sparse factorization", SIAM J.
+% Matrix Analysis \& Applic., vol 11, 1990, pp. 134-172.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowcolcounts}: nonzeros counts of a factor}
+%---------------------------------------
+
+\input{_rowcolcounts.tex}
+Compute the row and column counts of the Cholesky factor {\tt L} of the matrix
+{\tt A} or {\tt A*A'}. The etree and its postordering must already be computed (see
+{\tt cholmod\_etree} and {\tt cholmod\_postorder}) and given as inputs to this routine.
+For the symmetric case ($\m{LL}\tr=\m{A}$), {\tt A} must be stored in
+symmetric/lower form ({\tt A->stype = -1}).
+In the unsymmetric case, {\tt A*A'} or {\tt A(:,f)*A(:,f)'} can be analyzed.
+The fundamental floating-point operation count is returned in {\tt Common->fl}
+(this excludes extra flops due to relaxed supernodal amalgamation).
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+The algorithm is described in \cite{GilbertLiNgPeyton01,GilbertNgPeyton94}.
+
+% J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and
+% column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis \&
+% Applic., vol 15, 1994, pp. 1075-1091.
+%
+% J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for
+% sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_analyze\_ordering}: analyze a permutation}
+%---------------------------------------
+
+\input{_analyze_ordering.tex}
+Given a matrix {\tt A} and its fill-reducing permutation, compute the elimination
+tree, its (non-weighted) postordering, and the number of nonzeros in each
+column of {\tt L}. Also computes the flop count, the total nonzeros in {\tt L}, and
+the nonzeros in {\tt tril(A)} ({\tt Common->fl}, {\tt Common->lnz}, and {\tt Common->anz}).
+In the unsymmetric case, {\tt A(p,f)*A(p,f)'} is analyzed, and {\tt Common->anz}
+is the number of nonzero entries in the lower triangular part of the product,
+not in {\tt A} itself.
+
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+The column counts of {\tt L}, flop count, and other statistics from
+{\tt cholmod\_rowcolcounts} are not computed if {\tt ColCount} is {\tt NULL}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_amd}: interface to AMD}
+%---------------------------------------
+
+\input{_amd.tex}
+CHOLMOD interface to the AMD ordering package. Orders {\tt A} if the matrix is
+symmetric. On output, {\tt Perm [k] = i} if row/column {\tt i} of {\tt A} is the {\tt k}th
+row/column of {\tt P*A*P'}. This corresponds to {\tt A(p,p)} in MATLAB notation.
+If A is unsymmetric, {\tt cholmod\_amd} orders {\tt A*A'} or {\tt A(:,f)*A(:,f)'}.
+On output, {\tt Perm [k] = i} if
+row/column {\tt i} of {\tt A*A'} is the {\tt k}th row/column of {\tt P*A*A'*P'}.
+This corresponds to {\tt A(p,:)*A(p,:)'} in MATLAB notation.
+If {\tt f} is present, {\tt A(p,f)*A(p,f)'} is the permuted matrix.
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+Computes the flop count for a subsequent $\m{LL}\tr$ factorization, the number
+of nonzeros in {\tt L}, and the number of nonzeros in the matrix ordered
+({\tt A}, {\tt A*A'} or {\tt A(:,f)*A(:,f)'}).
+These statistics are returned in
+{\tt Common->fl}, {\tt Common->lnz}, and {\tt Common->anz}, respectively.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_colamd}: interface to COLAMD}
+%---------------------------------------
+
+\input{_colamd.tex}
+CHOLMOD interface to the COLAMD ordering package.
+Finds a permutation {\tt p} such that the Cholesky factorization of {\tt P*A*A'*P'} is
+sparser than {\tt A*A'}, using COLAMD. If the {\tt postorder} input parameter is {\tt TRUE},
+the column elimination tree is found and postordered, and the COLAMD ordering is then
+combined with its postordering (COLAMD itself does not perform this postordering).
+{\tt A} must be unsymmetric ({\tt A->stype = 0}).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowfac}: row-oriented Cholesky factorization}
+%---------------------------------------
+
+\input{_rowfac.tex}
+Full or incremental numerical $\m{LDL}\tr$ or $\m{LL}\tr$ factorization (simplicial, not
+supernodal). {\tt cholmod\_factorize} is the ``easy'' wrapper for this code, but it
+does not provide access to incremental factorization.
+The algorithm is the row-oriented, up-looking method described in \cite{Davis05}.
+See also \cite{Liu86c}. No 2-by-2 pivoting (or any other pivoting) is performed.
+
+{\tt cholmod\_rowfac} computes the full or incremental $\m{LDL}\tr$ or $\m{LL}\tr$ factorization of
+{\tt A+beta*I} (where {\tt A} is symmetric) or {\tt A*F+beta*I}
+(where {\tt A} and {\tt F} are unsymmetric
+and only the upper triangular part of {\tt A*F+beta*I} is used). It computes
+{\tt L} (and {\tt D}, for $\m{LDL}\tr$) one row at a time.
+The input scalar {\tt beta} is real; only the real part ({\tt beta[0]}) is used.
+
+{\tt L} can be a simplicial symbolic or numeric ({\tt L->is\_super} must be {\tt FALSE}).
+A symbolic factor is converted immediately into a numeric factor containing
+the identity matrix.
+
+For a full factorization, use {\tt kstart = 0} and {\tt kend = nrow}. The existing nonzero
+entries (numerical values in {\tt L->x} and {\tt L->z} for the zomplex case, and indices
+in {\tt L->i}) are overwritten.
+
+To compute an incremental factorization, select {\tt kstart} and {\tt kend} as the range
+of rows of {\tt L} you wish to compute. Rows {\tt kstart} to {\tt kend-1} of {\tt L}
+will be computed. A correct factorization will be computed
+only if all descendants of all nodes {\tt kstart} to {\tt kend-1} in the elimination tree have
+been factorized by a prior call to this routine, and if rows {\tt kstart} to {\tt kend-1}
+have not been factorized. This condition is {\bf not} checked on input.
+
+In the symmetric case, {\tt A} must be stored in upper form ({\tt A->stype} is greater than zero).
+The matrix {\tt F} is not accessed and may be {\tt NULL}. Only
+columns {\tt kstart} to {\tt kend-1} of {\tt A} are accessed.
+
+In the unsymmetric case,
+ the typical case is {\tt F=A'}. Alternatively, if {\tt F=A(:,f)'}, then this
+ routine factorizes the matrix {\tt S = beta*I + A(:,f)*A(:,f)'}.
+ The product {\tt A*F} is assumed to be symmetric;
+ only the upper triangular part of {\tt A*F} is used.
+ {\tt F} must be of size {\tt A->ncol} by {\tt A->nrow}.
+
+% J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans.
+% Math. Software, vol 12, 1986, pp. 127-148.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowfac\_mask}: row-oriented Cholesky factorization}
+%---------------------------------------
+
+\input{_rowfac_mask.tex}
+For use in LPDASA only.
+
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_row\_subtree}: pattern of row of a factor}
+%---------------------------------------
+
+\input{_row_subtree.tex}
+Compute the nonzero pattern of the solution to the lower triangular system
+\begin{verbatim}
+ L(0:k-1,0:k-1) * x = A (0:k-1,k)
+\end{verbatim}
+if {\tt A} is symmetric, or
+\begin{verbatim}
+ L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)'
+\end{verbatim}
+if {\tt A} is unsymmetric.
+This gives the nonzero pattern of row {\tt k} of {\tt L} (excluding the diagonal).
+The pattern is returned postordered, according to the subtree of the elimination
+tree rooted at node {\tt k}.
+
+The symmetric case requires {\tt A} to be in symmetric-upper form.
+
+The result is returned in {\tt R}, a pre-allocated sparse matrix of size {\tt nrow}-by-1,
+with {\tt R->nzmax >= nrow}. {\tt R} is assumed to be packed ({\tt Rnz [0]} is not updated);
+the number of entries in {\tt R} is given by {\tt Rp [0]}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_row\_lsubtree}: pattern of row of a factor}
+%---------------------------------------
+
+\input{_row_lsubtree.tex}
+Identical to {\tt cholmod\_row\_subtree}, except the elimination tree is
+found from {\tt L} itself, not {\tt Parent}. Also, {\tt F=A'} is not provided;
+the nonzero pattern of the {\tt k}th column of {\tt F} is given by
+{\tt Fi} and {\tt fnz} instead.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_resymbol}: re-do symbolic factorization}
+%---------------------------------------
+
+\input{_resymbol.tex}
+Recompute the symbolic pattern of {\tt L}. Entries not in the symbolic pattern
+of the factorization of {\tt A(p,p)} or {\tt F*F'}, where
+{\tt F=A(p,f)} or {\tt F=A(:,f)}, are dropped, where
+{\tt p = L->Perm} is used to permute the input matrix {\tt A}.
+
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+If an entry in {\tt L} is kept, its numerical value does not change.
+
+This routine is used after a supernodal factorization is converted into
+a simplicial one, to remove zero entries that were added due to relaxed
+supernode amalgamation. It can also be used after a series of downdates
+to remove entries that would no longer be present if the matrix were
+factorized from scratch. A downdate ({\tt cholmod\_updown}) does not remove any
+entries from {\tt L}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_resymbol\_noperm}: re-do symbolic factorization}
+%---------------------------------------
+
+\input{_resymbol_noperm.tex}
+Identical to {\tt cholmod\_resymbol}, except that the fill-reducing
+ordering {\tt L->Perm} is not used.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_postorder}: tree postorder}
+%---------------------------------------
+
+\input{_postorder.tex}
+Postorder a tree. The tree is either an elimination tree (the output from
+{\tt cholmod\_etree}) or a component tree (from {\tt cholmod\_nested\_dissection}).
+
+An elimination tree is a complete tree of {\tt n} nodes with {\tt Parent [j] > j} or
+{\tt Parent [j] = -1} if j is a root. On output {\tt Post [0..n-1]} is a complete
+permutation vector;
+{\tt Post [k] = j} if node {\tt j} is the {\tt k}th node in the
+postordered elimination tree, where {\tt k} is in the range 0 to {\tt n-1}.
+
+A component tree is a subset of {\tt 0:n-1}. {\tt Parent [j] = -2} if node {\tt j} is not
+in the component tree. {\tt Parent [j] = -1} if {\tt j} is a root of the component
+tree, and {\tt Parent [j]} is in the range 0 to {\tt n-1} if {\tt j} is in the component
+tree but not a root. On output, {\tt Post [k]} is defined only for nodes in
+the component tree. {\tt Post [k] = j} if node {\tt j} is the {\tt k}th node in the
+postordered component tree, where {\tt k} is in the range 0 to the number of
+components minus 1.
+Node {\tt j} is ignored and not included in the postorder if {\tt Parent [j] < -1}.
+As a result, {\tt cholmod\_check\_parent (Parent, ...)} and {\tt cholmod\_check\_perm (Post, ...)}
+fail if used for a component tree and its postordering.
+
+An optional node weight can be given. When starting a postorder at node {\tt j},
+the children of {\tt j} are ordered in decreasing order of their weight.
+If no weights are given ({\tt Weight} is {\tt NULL}) then children are ordered in
+decreasing order of their node number. The weight of a node must be in the
+range 0 to {\tt n-1}. Weights outside that range are silently converted to that
+range (weights $<$ 0 are treated as zero, and weights $\ge$ {\tt n} are treated as {\tt n-1}).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rcond}: reciprocal condition number}
+%---------------------------------------
+
+\input{_rcond.tex}
+Returns a rough estimate of the reciprocal of the condition number:
+the minimum entry on the diagonal of {\tt L} (or absolute entry of {\tt D} for an $\m{LDL}\tr$
+factorization) divided by the maximum entry. {\tt L} can be real, complex, or
+zomplex. Returns -1 on error, 0 if the matrix is singular or has a zero or NaN
+entry on the diagonal of {\tt L}, 1 if the matrix is 0-by-0, or
+{\tt min(diag(L))/max(diag(L))} otherwise. Never returns NaN; if {\tt L} has a NaN on
+the diagonal it returns zero instead.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Modify} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_updown}: update/downdate}
+%---------------------------------------
+
+\input{_updown.tex}
+Updates/downdates the $\m{LDL}\tr$ factorization (symbolic, then numeric), by
+computing a new factorization of
+\[
+\new{\m{L}}\new{\m{D}}\new{\m{L}}\tr = \m{LDL}\tr \pm \m{CC}\tr
+\]
+where $\new{\m{L}}$ denotes the new factor.
+{\tt C} must be sorted. It can be either packed or unpacked. As in all CHOLMOD
+routines, the columns of {\tt L} are sorted on input, and also on output.
+If {\tt L} does not contain a simplicial numeric $\m{LDL}\tr$ factorization, it
+is converted into one. Thus, a supernodal $\m{LL}\tr$ factorization
+can be passed to {\tt cholmod\_updown}.
+A symbolic {\tt L} is converted into a numeric identity matrix.
+If the initial conversion fails, the factor is returned unchanged.
+
+If memory runs out during the update, the factor is returned as a simplicial
+symbolic factor. That is, everything is freed except for the fill-reducing
+ordering and its corresponding column counts (typically computed by
+{\tt cholmod\_analyze}).
+
+Note that the fill-reducing permutation {\tt L->Perm} is not used. The row
+indices of {\tt C} refer to the rows of {\tt L}, not {\tt A}. If your original system is
+$\m{LDL}\tr = \m{PAP}\tr$ (where $\m{P} =$ {\tt L->Perm}), and you want to compute the $\m{LDL}\tr$
+factorization of $\m{A}+\m{CC}\tr$, then you must permute $\m{C}$ first. That is,
+if
+\[
+ \m{PAP}\tr = \m{LDL}\tr
+\]
+is the initial factorization, then
+\[
+\m{P}(\m{A}+\m{CC}\tr)\m{P}\tr
+ = \m{PAP}\tr+\m{PCC}\tr\m{P}\tr
+ = \m{LDL}\tr + (\m{PC})(\m{PC})\tr
+ = \m{LDL}\tr + \new{\m{C}}\new{\m{C}}\tr
+\]
+where $\new{\m{C}} = \m{PC}$.
+
+You can use the {\tt cholmod\_submatrix} routine in the {\tt MatrixOps} Module
+to permute {\tt C}, with:
+\begin{verbatim}
+ Cnew = cholmod_submatrix (C, L->Perm, L->n, NULL, -1, TRUE, TRUE, Common) ;
+\end{verbatim}
+
+Note that the {\tt sorted} input parameter to {\tt cholmod\_submatrix} must be {\tt TRUE},
+because {\tt cholmod\_updown} requires {\tt C} with sorted columns.
+Only real matrices are supported.
+The algorithms are described in \cite{DavisHager99,DavisHager01}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_updown\_solve}: update/downdate}
+%---------------------------------------
+
+\input{_updown_solve.tex}
+Identical to {\tt cholmod\_updown}, except
+the system $\m{Lx}=\m{b}$ is also updated/downdated.
+The new system is $\new{\m{L}}\new{\m{x}}=\m{b} + \Delta \m{b}$. The old solution $\m{x}$ is overwritten
+with $\new{\m{x}}$. Note that as in the update/downdate of $\m{L}$ itself, the fill-
+reducing permutation {\tt L->Perm} is not used. The vectors $\m{x}$ and $\m{b}$ are in the permuted
+ordering, not your original ordering. This routine does not handle multiple right-hand-sides.
+
+%---------------------------------------
+\newpage
+\subsection{{\tt cholmod\_updown\_mark}: update/downdate}
+%---------------------------------------
+
+\input{_updown_mark.tex}
+Identical to {\tt cholmod\_updown\_solve}, except that only part of $\m{L}$
+is used in the update of the solution to $\m{Lx}=\m{b}$. For more details,
+see the source code file {\tt CHOLMOD/Modify/cholmod\_updown.c}.
+This routine is meant for use in the {\tt LPDASA} linear program solver only,
+by Hager and Davis.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_updown\_mask}: update/downdate}
+%---------------------------------------
+
+\input{_updown_mask.tex}
+For use in LPDASA only.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowadd}: add row to factor}
+%---------------------------------------
+
+\input{_rowadd.tex}
+Adds a row and column to an $\m{LDL}\tr$ factorization. The {\tt k}th
+row and column of {\tt L} must be equal to the {\tt k}th row and
+column of the identity matrix on input.
+Only real matrices are supported.
+The algorithm is described in \cite{DavisHager05}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowadd\_solve}: add row to factor}
+%---------------------------------------
+
+\input{_rowadd_solve.tex}
+Identical to {\tt cholmod\_rowadd}, except the system $\m{Lx}=\m{b}$ is also updated/downdated, just like {\tt cholmod\_updown\_solve}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowdel}: delete row from factor}
+%---------------------------------------
+
+\input{_rowdel.tex}
+Deletes a row and column from an $\m{LDL}\tr$ factorization. The {\tt k}th
+row and column of {\tt L} is equal to the {\tt k}th row and
+column of the identity matrix on output.
+Only real matrices are supported.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowdel\_solve}: delete row from factor}
+%---------------------------------------
+
+\input{_rowdel_solve.tex}
+Identical to {\tt cholmod\_rowdel}, except the system $\m{Lx}=\m{b}$ is also updated/downdated, just like {\tt cholmod\_updown\_solve}.
+When row/column $k$ of $\m{A}$ is deleted from the system $\m{Ay}=\m{b}$, this can induce
+a change to $\m{x}$, in addition to changes arising when $\m{L}$ and $\m{b}$ are modified.
+If this is the case, the kth entry of $\m{y}$ is required as input ({\tt yk}).
+The algorithm is described in \cite{DavisHager05}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowadd\_mark}: add row to factor}
+%---------------------------------------
+
+\input{_rowadd_mark.tex}
+Identical to {\tt cholmod\_rowadd\_solve}, except that only part of $\m{L}$
+is used in the update of the solution to $\m{Lx}=\m{b}$. For more details,
+see the source code file {\tt CHOLMOD/Modify/cholmod\_rowadd.c}.
+This routine is meant for use in the {\tt LPDASA} linear program solver only.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowdel\_mark}: delete row from factor}
+%---------------------------------------
+
+\input{_rowdel_mark.tex}
+Identical to {\tt cholmod\_rowadd\_solve}, except that only part of $\m{L}$
+is used in the update of the solution to $\m{Lx}=\m{b}$. For more details,
+see the source code file {\tt CHOLMOD/Modify/cholmod\_rowdel.c}.
+This routine is meant for use in the {\tt LPDASA} linear program solver only.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt MatrixOps} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_drop}: drop small entries}
+%---------------------------------------
+
+\input{_drop.tex}
+Drop small entries from {\tt A}, and entries in the ignored part of {\tt A} if {\tt A}
+is symmetric. No CHOLMOD routine drops small numerical entries
+from a matrix, except for this one. NaN's and Inf's are kept.
+
+Supports pattern and real matrices; complex and zomplex matrices are not supported.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_norm\_dense}: dense matrix norm}
+%---------------------------------------
+
+\input{_norm_dense.tex}
+Returns the infinity-norm, 1-norm, or 2-norm of a dense matrix.
+Can compute the 2-norm only for a dense column vector.
+All xtypes are supported.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_norm\_sparse}: sparse matrix norm}
+%---------------------------------------
+
+\input{_norm_sparse.tex}
+Returns the infinity-norm or 1-norm of a sparse matrix.
+All xtypes are supported.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_scale}: scale sparse matrix}
+%---------------------------------------
+
+\input{_scale.tex}
+Scales a matrix: {\tt A = diag(s)*A}, {\tt A*diag(s)}, {\tt s*A}, or {\tt diag(s)*A*diag(s)}.
+
+{\tt A} can be of any type (packed/unpacked, upper/lower/unsymmetric).
+The symmetry of {\tt A} is ignored; all entries in the matrix are modified.
+
+If {\tt A} is {\tt m}-by-{\tt n} unsymmetric but scaled symmetrically, the result is
+\begin{verbatim}
+ A = diag (s (1:m)) * A * diag (s (1:n))
+\end{verbatim}
+
+Row or column scaling of a symmetric matrix still results in a symmetric
+matrix, since entries are still ignored by other routines.
+For example, when row-scaling a symmetric matrix where just the upper
+triangular part is stored (and lower triangular entries ignored)
+{\tt A = diag(s)*triu(A)} is performed, where the result {\tt A} is also
+symmetric-upper. This has the effect of modifying the implicit lower
+triangular part. In MATLAB notation:
+\begin{verbatim}
+ U = diag(s)*triu(A) ;
+ L = tril (U',-1)
+ A = L + U ;
+\end{verbatim}
+
+The scale parameter determines the kind of scaling to perform and the size of {\tt S}:
+
+\begin{tabular}{lll}
+\hline
+{\tt scale} & operation & size of {\tt S} \\
+\hline
+{\tt CHOLMOD\_SCALAR} & {\tt s[0]*A} & 1 \\
+{\tt CHOLMOD\_ROW} & {\tt diag(s)*A} & {\tt nrow}-by-1 or 1-by-{\tt nrow} \\
+{\tt CHOLMOD\_COL} & {\tt A*diag(s)} & {\tt ncol}-by-1 or 1-by-{\tt ncol} \\
+{\tt CHOLMOD\_SYM} & {\tt diag(s)*A*diag(s)} & {\tt max(nrow,ncol)}-by-1, or 1-by-{\tt max(nrow,ncol)} \\
+\hline
+\end{tabular}
+
+Only real matrices are supported.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_sdmult}: sparse-times-dense matrix}
+%---------------------------------------
+
+\input{_sdmult.tex}
+Sparse matrix times dense matrix:
+{\tt Y = alpha*(A*X) + beta*Y} or {\tt Y = alpha*(A'*X) + beta*Y},
+where {\tt A} is sparse and {\tt X} and {\tt Y} are dense.
+When using {\tt A}, {\tt X} has {\tt A->ncol} columns and {\tt Y} has {\tt A->nrow} rows.
+When using {\tt A'}, {\tt X} has {\tt A->nrow} columns and {\tt Y} has {\tt A->ncol} rows.
+If {\tt transpose = 0}, then {\tt A} is used;
+otherwise, {\tt A'} is used (the complex conjugate transpose).
+The {\tt transpose} parameter is ignored if the matrix is symmetric or Hermitian.
+(the array transpose {\tt A.'} is not supported).
+Supports real, complex, and zomplex matrices, but the xtypes of {\tt A}, {\tt X}, and {\tt Y} must all match.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_ssmult}: sparse-times-sparse matrix}
+%---------------------------------------
+
+\input{_ssmult.tex}
+Computes {\tt C = A*B}; multiplying two sparse matrices.
+{\tt C} is returned as packed, and either unsorted or sorted, depending on the
+{\tt sorted} input parameter. If {\tt C} is returned sorted, then either {\tt C = (B'*A')'}
+or {\tt C = (A*B)''} is computed, depending on the number of nonzeros in {\tt A}, {\tt B}, and {\tt C}.
+The stype of {\tt C} is determined by the {\tt stype} parameter.
+Only pattern and real matrices are supported. Complex and zomplex matrices
+are supported only when the numerical values are not computed ({\tt values}
+is {\tt FALSE}).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_submatrix}: sparse submatrix}
+%---------------------------------------
+
+\input{_submatrix.tex}
+Returns {\tt C = A (rset,cset)}, where {\tt C} becomes {\tt length(rset)}-by-{\tt length(cset)} in dimension.
+{\tt rset} and {\tt cset} can have duplicate entries. {\tt A} must be unsymmetric. {\tt C} unsymmetric and
+is packed. If {\tt sorted} is {\tt TRUE} on input, or {\tt rset} is sorted and {\tt A} is
+sorted, then {\tt C} is sorted; otherwise {\tt C} is unsorted.
+
+If {\tt rset} is {\tt NULL}, it means ``{\tt [ ]}'' in MATLAB notation, the empty set.
+The number of rows in the result {\tt C} will be zero if {\tt rset} is {\tt NULL}.
+Likewise if {\tt cset} means the empty set; the number of columns in the result {\tt C} will be zero if {\tt cset} is {\tt NULL}.
+If {\tt rsize} or {\tt csize} is negative, it denotes ``{\tt :}'' in MATLAB notation.
+Thus, if both {\tt rsize} and {\tt csize} are negative {\tt C = A(:,:) = A} is returned.
+
+For permuting a matrix, this routine is an alternative to {\tt cholmod\_ptranspose}
+(which permutes and transposes a matrix and can work on symmetric matrices).
+
+The time taken by this routine is O({\tt A->nrow}) if the {\tt Common} workspace needs
+to be initialized, plus O({\tt C->nrow + C->ncol + nnz (A (:,cset))}). Thus, if {\tt C}
+is small and the workspace is not initialized, the time can be dominated by
+the call to {\tt cholmod\_allocate\_work}. However, once the workspace is
+allocated, subsequent calls take less time.
+
+Only pattern and real matrices are supported. Complex and zomplex matrices
+are supported only when {\tt values} is {\tt FALSE}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_horzcat}: horizontal concatenation}
+%---------------------------------------
+
+\input{_horzcat.tex}
+Horizontal concatenation, returns {\tt C = [A,B]} in MATLAB notation.
+{\tt A} and {\tt B} can have any stype. {\tt C} is returned unsymmetric and packed.
+{\tt A} and {\tt B} must have the same number of rows.
+{\tt C} is sorted if both {\tt A} and {\tt B} are sorted.
+{\tt A} and {\tt B} must have the same numeric xtype, unless {\tt values} is {\tt FALSE}.
+{\tt A} and {\tt B} cannot be complex or zomplex, unless {\tt values} is {\tt FALSE}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_vertcat}: vertical concatenation}
+%---------------------------------------
+
+\input{_vertcat.tex}
+Vertical concatenation, returns {\tt C = [A;B]} in MATLAB notation.
+{\tt A} and {\tt B} can have any stype. {\tt C} is returned unsymmetric and packed.
+{\tt A} and {\tt B} must have the same number of columns.
+{\tt C} is sorted if both {\tt A} and {\tt B} are sorted.
+{\tt A} and {\tt B} must have the same numeric xtype, unless {\tt values} is {\tt FALSE}.
+{\tt A} and {\tt B} cannot be complex or zomplex, unless {\tt values} is {\tt FALSE}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_symmetry}: compute the symmetry of a matrix}
+%---------------------------------------
+
+\input{_symmetry.tex}
+
+Determines if a sparse matrix is rectangular, unsymmetric, symmetric,
+skew-symmetric, or Hermitian. It does so by looking at its numerical values
+of both upper and lower triangular parts of a CHOLMOD "unsymmetric"
+matrix, where A->stype == 0. The transpose of A is NOT constructed.
+
+If not unsymmetric, it also determines if the matrix has a diagonal whose
+entries are all real and positive (and thus a candidate for sparse Cholesky
+if A->stype is changed to a nonzero value).
+
+Note that a Matrix Market "general" matrix is either rectangular or
+unsymmetric.
+
+The row indices in the column of each matrix MUST be sorted for this function
+to work properly (A->sorted must be TRUE). This routine returns EMPTY if
+A->stype is not zero, or if A->sorted is FALSE. The exception to this rule
+is if A is rectangular.
+
+If option == 0, then this routine returns immediately when it finds a
+non-positive diagonal entry (or one with nonzero imaginary part). If the
+matrix is not a candidate for sparse Cholesky, it returns the value
+{\tt CHOLMOD\_MM\_UNSYMMETRIC}, even if the matrix might in fact be symmetric or
+Hermitian.
+
+This routine is useful inside the MATLAB backslash, which must look at an
+arbitrary matrix (A->stype == 0) and determine if it is a candidate for
+sparse Cholesky. In that case, option should be 0.
+
+This routine is also useful when writing a MATLAB matrix to a file in
+Rutherford/Boeing or Matrix Market format. Those formats require a
+determination as to the symmetry of the matrix, and thus this routine should
+not return upon encountering the first non-positive diagonal. In this case,
+option should be 1.
+
+If option is 2, this function can be used to compute the numerical and
+pattern symmetry, where 0 is a completely unsymmetric matrix, and 1 is a
+perfectly symmetric matrix. This option is used when computing the following
+statistics for the matrices in the UF Sparse Matrix Collection.
+
+ numerical symmetry: number of matched offdiagonal nonzeros over
+ the total number of offdiagonal entries. A real entry $a_{ij}$, $i \ne j$,
+ is matched if $a_{ji} = a_{ij}$, but this is only counted if both
+ $a_{ji}$ and $a_{ij}$ are nonzero. This does not depend on {\tt Z}.
+ (If A is complex, then the above test is modified; $a_{ij}$ is matched
+ if $\mbox{conj}(a_{ji}) = a_{ij}$.
+
+ Then numeric symmetry = xmatched / nzoffdiag, or 1 if nzoffdiag = 0.
+
+ pattern symmetry: number of matched offdiagonal entries over the
+ total number of offdiagonal entries. An entry $a_{ij}$, $i \ne j$, is
+ matched if $a_{ji}$ is also an entry.
+
+ Then pattern symmetry = pmatched / nzoffdiag, or 1 if nzoffdiag = 0.
+
+The symmetry of a matrix with no offdiagonal entries is equal to 1.
+
+A workspace of size ncol integers is allocated; EMPTY is returned if this
+allocation fails.
+
+Summary of return values:
+
+\begin{tabular}{ll}
+{\tt EMPTY (-1)} & out of memory, stype not zero, A not sorted \\
+{\tt CHOLMOD\_MM\_RECTANGULAR 1} & A is rectangular \\
+{\tt CHOLMOD\_MM\_UNSYMMETRIC 2} & A is unsymmetric \\
+{\tt CHOLMOD\_MM\_SYMMETRIC 3} & A is symmetric, but with non-pos. diagonal \\
+{\tt CHOLMOD\_MM\_HERMITIAN 4} & A is Hermitian, but with non-pos. diagonal \\
+{\tt CHOLMOD\_MM\_SKEW\_SYMMETRIC 5} & A is skew symmetric \\
+{\tt CHOLMOD\_MM\_SYMMETRIC\_POSDIAG 6} & A is symmetric with positive diagonal \\
+{\tt CHOLMOD\_MM\_HERMITIAN\_POSDIAG 7} & A is Hermitian with positive diagonal \\
+\end{tabular}
+
+See also the {\tt spsym} mexFunction, which is a MATLAB interface for this code.
+
+If the matrix is a candidate for sparse Cholesky, it will return a result
+\newline
+{\tt CHOLMOD\_MM\_SYMMETRIC\_POSDIAG} if real, or {\tt CHOLMOD\_MM\_HERMITIAN\_POSDIAG} if
+complex. Otherwise, it will return a value less than this. This is true
+regardless of the value of the option parameter.
+
+
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Supernodal} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_super\_symbolic}: supernodal symbolic factorization}
+%---------------------------------------
+
+\input{_super_symbolic.tex}
+Supernodal symbolic analysis of the $\m{LL}\tr$ factorization of {\tt A}, {\tt A*A'}, or {\tt A(:,f)*A(:,f)'}.
+This routine must be preceded by a simplicial symbolic analysis
+({\tt cholmod\_rowcolcounts}). See {\tt Cholesky/cholmod\_analyze.c} for an example of how to use
+this routine.
+The user need not call this directly; {\tt cholmod\_analyze} is a ``simple'' wrapper for this routine.
+{\tt A} can be symmetric (upper), or unsymmetric. The symmetric/lower form is not supported.
+In the unsymmetric case {\tt F} is the normally transpose of {\tt A}.
+Alternatively, if {\tt F=A(:,f)'} then {\tt F*F'} is analyzed.
+Requires {\tt Parent} and {\tt L->ColCount} to be defined on input; these are the
+simplicial {\tt Parent} and {\tt ColCount} arrays as computed by {\tt cholmod\_rowcolcounts}.
+Does not use {\tt L->Perm}; the input matrices {\tt A} and {\tt F} must already be properly
+permuted. Allocates and computes the supernodal pattern of {\tt L}
+({\tt L->super}, {\tt L->pi}, {\tt L->px}, and {\tt L->s}).
+Does not allocate the real part ({\tt L->x}).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_super\_numeric}: supernodal numeric factorization}
+%---------------------------------------
+
+\input{_super_numeric.tex}
+Computes the numerical Cholesky factorization of {\tt A+beta*I} or {\tt A*F+beta*I}. Only the
+lower triangular part of {\tt A+beta*I} or {\tt A*F+beta*I} is accessed. The
+matrices {\tt A} and {\tt F} must already be permuted according to the fill-reduction
+permutation {\tt L->Perm}. {\tt cholmod\_factorize} is an "easy" wrapper for this code
+which applies that permutation.
+The input scalar {\tt beta} is real; only the real part ({\tt beta[0]} is used.
+
+Symmetric case: {\tt A} is a symmetric (lower) matrix. {\tt F} is not accessed and may be {\tt NULL}.
+With a fill-reducing permutation, {\tt A(p,p)} should be passed for {\tt A}, where is
+{\tt p} is {\tt L->Perm}.
+
+Unsymmetric case: {\tt A} is unsymmetric, and {\tt F} must be present. Normally, {\tt F=A'}.
+With a fill-reducing permutation, {\tt A(p,f)} and {\tt A(p,f)'} should be passed as the
+parameters {\tt A} and {\tt F}, respectively, where {\tt f} is a list of the subset of the columns of {\tt A}.
+
+The input factorization {\tt L} must be supernodal ({\tt L->is\_super} is {\tt TRUE}). It can
+either be symbolic or numeric. In the first case, {\tt L} has been analyzed by
+{\tt cholmod\_analyze} or {\tt cholmod\_super\_symbolic}, but the matrix has not yet been
+numerically factorized. The numerical values are allocated here and the
+factorization is computed. In the second case, a prior matrix has been
+analyzed and numerically factorized, and a new matrix is being factorized.
+The numerical values of {\tt L} are replaced with the new numerical factorization.
+
+{\tt L->is\_ll} is ignored on input, and set to {\tt TRUE} on output. This routine always computes an $\m{LL}\tr$
+factorization. Supernodal $\m{LDL}\tr$ factorization is not supported.
+
+If the matrix is not positive definite the routine returns {\tt TRUE}, but sets
+{\tt Common->status} to {\tt CHOLMOD\_NOT\_POSDEF} and {\tt L->minor} is set to the column at
+which the failure occurred. Columns {\tt L->minor} to {\tt L->n-1} are set to zero.
+
+If {\tt L} is supernodal symbolic on input, it is converted to a supernodal numeric
+factor on output, with an xtype of real if {\tt A} is real, or complex if {\tt A} is
+complex or zomplex. If {\tt L} is supernodal numeric on input, its xtype must
+match {\tt A} (except that {\tt L} can be complex and {\tt A} zomplex). The xtype of {\tt A} and {\tt F}
+must match.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_super\_lsolve}: supernodal forward solve}
+%---------------------------------------
+
+\input{_super_lsolve.tex}
+Solve $\m{Lx}=\m{b}$ for a supernodal factorization. This routine does not
+apply the permutation {\tt L->Perm}. See {\tt cholmod\_solve} for a more general
+interface that performs that operation.
+Only real and complex xtypes are supported.
+{\tt L}, {\tt X}, and {\tt E} must have the same xtype.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_super\_ltsolve}: supernodal backsolve}
+%---------------------------------------
+
+\input{_super_ltsolve.tex}
+Solve $\m{L}\tr\m{x}=\m{b}$ for a supernodal factorization. This routine does not
+apply the permutation {\tt L->Perm}. See {\tt cholmod\_solve} for a more general
+interface that performs that operation.
+Only real and complex xtypes are supported.
+{\tt L}, {\tt X}, and {\tt E} must have the same xtype.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Partition} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_nested\_dissection}: nested dissection ordering}
+%---------------------------------------
+
+\input{_nested_dissection.tex}
+CHOLMOD's nested dissection algorithm:
+ using its own compression and connected-components
+ algorithms, an external graph partitioner (METIS), and a constrained
+ minimum degree ordering algorithm (CAMD, CCOLAMD, or CSYMAMD). Typically
+ gives better orderings than {\tt METIS\_NodeND} (about 5\% to 10\% fewer
+ nonzeros in {\tt L}).
+
+This method uses a node bisector, applied recursively (but using a
+non-recursive implementation). Once the graph is partitioned, it calls a
+constrained minimum degree code (CAMD or CSYMAMD for {\tt A+A'},
+and CCOLAMD for {\tt A*A'}) to
+order all the nodes in the graph - but obeying the constraints determined
+by the separators. This routine is similar to {\tt METIS\_NodeND}, except for
+how
+it treats the leaf nodes. {\tt METIS\_NodeND} orders the leaves of the separator
+tree with {\tt MMD}, ignoring the rest of the matrix when ordering a single leaf.
+This routine orders the whole matrix with CAMD, CSYMAMD, or CCOLAMD, all at once,
+when the graph partitioning is done.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_metis}: interface to METIS nested dissection}
+%---------------------------------------
+
+\input{_metis.tex}
+CHOLMOD wrapper for the {\tt METIS\_NodeND} ordering routine. Creates {\tt A+A'},
+{\tt A*A'} or {\tt A(:,f)*A(:,f)'} and then calls {\tt METIS\_NodeND} on the resulting graph.
+This routine is comparable to {\tt cholmod\_nested\_dissection}, except that it
+calls {\tt METIS\_NodeND} directly, and it does not return the separator tree.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_camd}: interface to CAMD}
+%---------------------------------------
+
+\input{_camd.tex}
+CHOLMOD interface to the CAMD ordering routine. Finds a permutation
+{\tt p} such that the Cholesky factorization of {\tt A(p,p)}
+is sparser than {\tt A}. If {\tt A} is unsymmetric,
+{\tt A*A'} is ordered.
+If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}.
+All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_ccolamd}: interface to CCOLAMD}
+%---------------------------------------
+
+\input{_ccolamd.tex}
+CHOLMOD interface to the CCOLAMD ordering routine. Finds a permutation
+{\tt p} such that the Cholesky factorization of {\tt A(p,:)*A(p,:)'} is sparser than {\tt A*A'}.
+The column elimination is found and postordered, and the CCOLAMD ordering is then
+combined with its postordering. {\tt A} must be unsymmetric.
+If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}.
+All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_csymamd}: interface to CSYMAMD}
+%---------------------------------------
+
+\input{_csymamd.tex}
+CHOLMOD interface to the CSYMAMD ordering routine. Finds a permutation
+{\tt p} such that the Cholesky factorization of {\tt A(p,p)} is sparser than {\tt A}.
+The elimination tree is found and postordered, and the CSYMAMD
+ordering is then combined with its postordering. If {\tt A} is unsymmetric,
+{\tt A+A'} is ordered ({\tt A} must be square).
+If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}.
+All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on.
+
+%---------------------------------------
+\newpage
+\subsection{{\tt cholmod\_bisect}: graph bisector}
+%---------------------------------------
+
+\input{_bisect.tex}
+Finds a node bisector of {\tt A}, {\tt A*A'}, {\tt A(:,f)*A(:,f)'}:
+a set of nodes that partitions the graph into two parts.
+Compresses the graph first, and then calls METIS.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_metis\_bisector}: interface to METIS node bisector}
+%---------------------------------------
+
+\input{_metis_bisector.tex}
+Finds a set of nodes that bisects the graph of {\tt A} or {\tt A*A'} (a direct interface to \newline
+{\tt METIS\_NodeComputeSeparator}).
+
+The input matrix {\tt A} must be square, symmetric (with both upper and lower
+parts present) and with no diagonal entries. These conditions are not
+checked.
+
+%---------------------------------------
+\newpage
+\subsection{{\tt cholmod\_collapse\_septree}: prune a separator tree}
+%---------------------------------------
+
+\input{_collapse_septree.tex}
+Prunes a separator tree obtained from {\tt cholmod\_nested\_dissection}.
+
+\newpage
+\bibliographystyle{plain}
+\bibliography{UserGuide}
+\end{document}
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/footer.tex b/src/C/SuiteSparse/CHOLMOD/Doc/footer.tex
new file mode 100644
index 0000000..112a2d1
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/footer.tex
@@ -0,0 +1,6 @@
+\end{verbatim}
+}
+\noindent\hspace{0.85in}\rule[0.25in]{5.2in}{1pt}
+\vspace{-0.15in}
+
+\noindent {\bf Purpose:}
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/getmproto b/src/C/SuiteSparse/CHOLMOD/Doc/getmproto
new file mode 100755
index 0000000..644a48c
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/getmproto
@@ -0,0 +1,4 @@
+#!/bin/sh
+cat mheader.tex
+expand -8 $1 | awk -f mfile.awk
+cat mfooter.tex
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/getproto b/src/C/SuiteSparse/CHOLMOD/Doc/getproto
new file mode 100755
index 0000000..b3b30a6
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/getproto
@@ -0,0 +1,6 @@
+#!/bin/sh
+echo -n $1 > _temp.awk
+cat rule.awk >> _temp.awk
+cat header.tex
+expand -8 $2 | awk -f _temp.awk
+cat footer.tex
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/header.tex b/src/C/SuiteSparse/CHOLMOD/Doc/header.tex
new file mode 100644
index 0000000..4f28f1b
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/header.tex
@@ -0,0 +1,4 @@
+\noindent\hspace{0.85in}\rule[0.05in]{5.2in}{1pt}
+\vspace{-0.15in}
+{\footnotesize
+\begin{verbatim}
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/mfile.awk b/src/C/SuiteSparse/CHOLMOD/Doc/mfile.awk
new file mode 100644
index 0000000..5106442
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/mfile.awk
@@ -0,0 +1 @@
+/^%/ { print " ", substr ($0,2) }
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/mfooter.tex b/src/C/SuiteSparse/CHOLMOD/Doc/mfooter.tex
new file mode 100644
index 0000000..4bce503
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/mfooter.tex
@@ -0,0 +1,4 @@
+\end{verbatim}
+}
+\noindent\hspace{0.85in}\rule[0.25in]{5.2in}{1pt}
+\vspace{-0.15in}
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/mheader.tex b/src/C/SuiteSparse/CHOLMOD/Doc/mheader.tex
new file mode 100644
index 0000000..90d3203
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/mheader.tex
@@ -0,0 +1,5 @@
+
+\noindent\hspace{0.85in}\rule[0.05in]{5.2in}{1pt}
+\vspace{-0.15in}
+{\footnotesize
+\begin{verbatim}
diff --git a/src/C/SuiteSparse/CHOLMOD/Doc/rule.awk b/src/C/SuiteSparse/CHOLMOD/Doc/rule.awk
new file mode 100644
index 0000000..16e6ac1
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Doc/rule.awk
@@ -0,0 +1 @@
+{ print " ", $0 }
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/License.txt b/src/C/SuiteSparse/CHOLMOD/Include/License.txt
new file mode 100644
index 0000000..cfca615
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/License.txt
@@ -0,0 +1,9 @@
+CHOLMOD/Include/* files.
+Copyright (C) 2005-2006, either Univ. of Florida or T. Davis,
+depending on the file.
+http://www.cise.ufl.edu/research/sparse
+
+Refer to each include file in this directory; each file is licensed
+separately, according to the Module for which it contains definitions
+and prototypes.
+
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/README.txt b/src/C/SuiteSparse/CHOLMOD/Include/README.txt
new file mode 100644
index 0000000..387eb6e
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/README.txt
@@ -0,0 +1,25 @@
+CHOLMOD: a sparse Cholesky factorization package.
+
+The Include/*.h files in this directory provide a basic documentation of all
+user-callable routines and user-visible data structures in the CHOLMOD
+package. Start with cholmod.h, which describes the general structure of
+the parameter lists of CHOLMOD routines. cholmod_core.h describes the
+data structures and basic operations on them (creating and deleting them).
+
+cholmod.h single include file for all user programs
+cholmod_config.h CHOLMOD compile-time configuration
+
+cholmod_core.h Core module: data structures and basic support routines
+cholmod_check.h Check module: check/print CHOLMOD data structures
+cholmod_cholesky.h Cholesky module: LL' and LDL' factorization
+cholmod_matrixops.h MatrixOps module: sparse matrix operators (add, mult,..)
+cholmod_modify.h Modify module: update/downdate/...
+cholmod_partition.h Partition module: nested dissection ordering
+cholmod_supernodal.h Supernodal module: supernodal Cholesky
+
+These include files are not used in user programs, but in CHOLMOD only:
+
+cholmod_blas.h BLAS definitions
+cholmod_complexity.h complex arithmetic
+cholmod_template.h complex arithmetic for template routines
+cholmod_internal.h internal definitions, not visible to user program
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod.h
new file mode 100644
index 0000000..1332516
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod.h
@@ -0,0 +1,122 @@
+/* ========================================================================== */
+/* === Include/cholmod.h ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ *
+ * Portions of CHOLMOD (the Core and Partition Modules) are copyrighted by the
+ * University of Florida. The Modify Module is co-authored by William W.
+ * Hager, Univ. of Florida.
+ *
+ * Acknowledgements: this work was supported in part by the National Science
+ * Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia
+ * National Laboratories (Dept. of Energy) which supported the development of
+ * CHOLMOD's Partition Module.
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD include file, for inclusion user programs.
+ *
+ * The include files listed below include a short description of each user-
+ * callable routine. Each routine in CHOLMOD has a consistent interface.
+ * More details about the CHOLMOD data types is in the cholmod_core.h file.
+ *
+ * Naming convention:
+ * ------------------
+ *
+ * All routine names, data types, and CHOLMOD library files use the
+ * cholmod_ prefix. All macros and other #define's use the CHOLMOD
+ * prefix.
+ *
+ * Return value:
+ * -------------
+ *
+ * Most CHOLMOD routines return an int (TRUE (1) if successful, or FALSE
+ * (0) otherwise. A UF_long or double return value is >= 0 if successful,
+ * or -1 otherwise. A size_t return value is > 0 if successful, or 0
+ * otherwise.
+ *
+ * If a routine returns a pointer, it is a pointer to a newly allocated
+ * object or NULL if a failure occured, with one exception. cholmod_free
+ * always returns NULL.
+ *
+ * "Common" parameter:
+ * ------------------
+ *
+ * The last parameter in all CHOLMOD routines is a pointer to the CHOLMOD
+ * "Common" object. This contains control parameters, statistics, and
+ * workspace used between calls to CHOLMOD. It is always an input/output
+ * parameter.
+ *
+ * Input, Output, and Input/Output parameters:
+ * -------------------------------------------
+ *
+ * Input parameters are listed first. They are not modified by CHOLMOD.
+ *
+ * Input/output are listed next. They must be defined on input, and
+ * are modified on output.
+ *
+ * Output parameters are listed next. If they are pointers, they must
+ * point to allocated space on input, but their contents are not defined
+ * on input.
+ *
+ * Workspace parameters appear next. They are used in only two routines
+ * in the Supernodal module.
+ *
+ * The cholmod_common *Common parameter always appears as the last
+ * parameter. It is always an input/output parameter.
+ */
+
+#ifndef CHOLMOD_H
+#define CHOLMOD_H
+
+/* make it easy for C++ programs to include CHOLMOD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* assume large file support. If problems occur, compile with -DNLARGEFILE */
+#include "cholmod_io64.h"
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#include "cholmod_config.h"
+
+/* CHOLMOD always includes the Core module. */
+#include "cholmod_core.h"
+
+#ifndef NCHECK
+#include "cholmod_check.h"
+#endif
+
+#ifndef NCHOLESKY
+#include "cholmod_cholesky.h"
+#endif
+
+#ifndef NMATRIXOPS
+#include "cholmod_matrixops.h"
+#endif
+
+#ifndef NMODIFY
+#include "cholmod_modify.h"
+#endif
+
+#ifndef NPARTITION
+#include "cholmod_partition.h"
+#endif
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_blas.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_blas.h
new file mode 100644
index 0000000..7d2b051
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_blas.h
@@ -0,0 +1,451 @@
+/* ========================================================================== */
+/* === Include/cholmod_blas.h =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_blas.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* This does not need to be included in the user's program. */
+
+#ifndef CHOLMOD_BLAS_H
+#define CHOLMOD_BLAS_H
+
+/* ========================================================================== */
+/* === Architecture ========================================================= */
+/* ========================================================================== */
+
+#if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2)
+#define CHOLMOD_SOL2
+#define CHOLMOD_ARCHITECTURE "Sun Solaris"
+
+#elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI)
+#define CHOLMOD_SGI
+#define CHOLMOD_ARCHITECTURE "SGI Irix"
+
+#elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86)
+#define CHOLMOD_LINUX
+#define CHOLMOD_ARCHITECTURE "Linux"
+
+#elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS)
+#define CHOLMOD_AIX
+#define CHOLMOD_ARCHITECTURE "IBM AIX"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA)
+#define CHOLMOD_ALPHA
+#define CHOLMOD_ARCHITECTURE "Compaq Alpha"
+
+#elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64)
+#if defined (__MINGW32__) || defined (__MINGW32__)
+#define CHOLMOD_MINGW
+#elif defined (__CYGWIN32__) || defined (__CYGWIN32__)
+#define CHOLMOD_CYGWIN
+#else
+#define CHOLMOD_WINDOWS
+#define BLAS_NO_UNDERSCORE
+#endif
+#define CHOLMOD_ARCHITECTURE "Microsoft Windows"
+
+#elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP Unix"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP 700 Unix"
+#define BLAS_NO_UNDERSCORE
+
+#else
+/* If the architecture is unknown, and you call the BLAS, you may need to */
+/* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */
+#define CHOLMOD_ARCHITECTURE "unknown"
+#endif
+
+
+/* ========================================================================== */
+/* === BLAS and LAPACK names ================================================ */
+/* ========================================================================== */
+
+/* Prototypes for the various versions of the BLAS. */
+
+/* Determine if the 64-bit Sun Performance BLAS is to be used */
+#if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(LONG) && defined(LONGBLAS)
+#define SUN64
+#endif
+
+#ifdef SUN64
+
+#define BLAS_DTRSV dtrsv_64_
+#define BLAS_DGEMV dgemv_64_
+#define BLAS_DTRSM dtrsm_64_
+#define BLAS_DGEMM dgemm_64_
+#define BLAS_DSYRK dsyrk_64_
+#define BLAS_DGER dger_64_
+#define BLAS_DSCAL dscal_64_
+#define LAPACK_DPOTRF dpotrf_64_
+
+#define BLAS_ZTRSV ztrsv_64_
+#define BLAS_ZGEMV zgemv_64_
+#define BLAS_ZTRSM ztrsm_64_
+#define BLAS_ZGEMM zgemm_64_
+#define BLAS_ZHERK zherk_64_
+#define BLAS_ZGER zgeru_64_
+#define BLAS_ZSCAL zscal_64_
+#define LAPACK_ZPOTRF zpotrf_64_
+
+#elif defined (BLAS_NO_UNDERSCORE)
+
+#define BLAS_DTRSV dtrsv
+#define BLAS_DGEMV dgemv
+#define BLAS_DTRSM dtrsm
+#define BLAS_DGEMM dgemm
+#define BLAS_DSYRK dsyrk
+#define BLAS_DGER dger
+#define BLAS_DSCAL dscal
+#define LAPACK_DPOTRF dpotrf
+
+#define BLAS_ZTRSV ztrsv
+#define BLAS_ZGEMV zgemv
+#define BLAS_ZTRSM ztrsm
+#define BLAS_ZGEMM zgemm
+#define BLAS_ZHERK zherk
+#define BLAS_ZGER zgeru
+#define BLAS_ZSCAL zscal
+#define LAPACK_ZPOTRF zpotrf
+
+#else
+
+#define BLAS_DTRSV dtrsv_
+#define BLAS_DGEMV dgemv_
+#define BLAS_DTRSM dtrsm_
+#define BLAS_DGEMM dgemm_
+#define BLAS_DSYRK dsyrk_
+#define BLAS_DGER dger_
+#define BLAS_DSCAL dscal_
+#define LAPACK_DPOTRF dpotrf_
+
+#define BLAS_ZTRSV ztrsv_
+#define BLAS_ZGEMV zgemv_
+#define BLAS_ZTRSM ztrsm_
+#define BLAS_ZGEMM zgemm_
+#define BLAS_ZHERK zherk_
+#define BLAS_ZGER zgeru_
+#define BLAS_ZSCAL zscal_
+#define LAPACK_ZPOTRF zpotrf_
+
+#endif
+
+/* ========================================================================== */
+/* === BLAS and LAPACK integer arguments ==================================== */
+/* ========================================================================== */
+
+/* CHOLMOD can be compiled with -D'LONGBLAS=long' for the Sun Performance
+ * Library, or -D'LONGBLAS=long long' for SGI's SCSL BLAS. This defines the
+ * integer used in the BLAS for the cholmod_l_* routines.
+ *
+ * The "int" version of CHOLMOD always uses the "int" version of the BLAS.
+ */
+
+#if defined (LONGBLAS) && defined (LONG)
+#define BLAS_INT LONGBLAS
+#else
+#define BLAS_INT int
+#endif
+
+/* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need
+ * to check for integer overflow when converting from one to the other. If
+ * any integer overflows, the externally-defined blas_ok variable is set to
+ * FALSE. blas_ok should be set to TRUE before calling any BLAS_* macro.
+ */
+
+#define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int))
+#define EQ(K,k) (((BLAS_INT) K) == ((Int) k))
+
+/* ========================================================================== */
+/* === BLAS and LAPACK prototypes and macros ================================ */
+/* ========================================================================== */
+
+void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_dpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_zpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+/* ========================================================================== */
+
+void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+void BLAS_ZGERU (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_check.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_check.h
new file mode 100644
index 0000000..58e4ad0
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_check.h
@@ -0,0 +1,417 @@
+/* ========================================================================== */
+/* === Include/cholmod_check.h ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_check.h. Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_check.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Check module.
+ *
+ * Routines that check and print the 5 basic data types in CHOLMOD, and 3 kinds
+ * of integer vectors (subset, perm, and parent), and read in matrices from a
+ * file:
+ *
+ * cholmod_check_common check/print the Common object
+ * cholmod_print_common
+ *
+ * cholmod_check_sparse check/print a sparse matrix in column-oriented form
+ * cholmod_print_sparse
+ *
+ * cholmod_check_dense check/print a dense matrix
+ * cholmod_print_dense
+ *
+ * cholmod_check_factor check/print a Cholesky factorization
+ * cholmod_print_factor
+ *
+ * cholmod_check_triplet check/print a sparse matrix in triplet form
+ * cholmod_print_triplet
+ *
+ * cholmod_check_subset check/print a subset (integer vector in given range)
+ * cholmod_print_subset
+ *
+ * cholmod_check_perm check/print a permutation (an integer vector)
+ * cholmod_print_perm
+ *
+ * cholmod_check_parent check/print an elimination tree (an integer vector)
+ * cholmod_print_parent
+ *
+ * cholmod_read_triplet read a matrix in triplet form (any Matrix Market
+ * "coordinate" format, or a generic triplet format).
+ *
+ * cholmod_read_sparse read a matrix in sparse form (same file format as
+ * cholmod_read_triplet).
+ *
+ * cholmod_read_dense read a dense matrix (any Matrix Market "array"
+ * format, or a generic dense format).
+ *
+ * cholmod_write_sparse write a sparse matrix to a Matrix Market file.
+ *
+ * cholmod_write_dense write a dense matrix to a Matrix Market file.
+ *
+ * cholmod_print_common and cholmod_check_common are the only two routines that
+ * you may call after calling cholmod_finish.
+ *
+ * Requires the Core module. Not required by any CHOLMOD module, except when
+ * debugging is enabled (in which case all modules require the Check module).
+ *
+ * See cholmod_read.c for a description of the file formats supported by the
+ * cholmod_read_* routines.
+ */
+
+#ifndef CHOLMOD_CHECK_H
+#define CHOLMOD_CHECK_H
+
+#include "cholmod_core.h"
+#include <stdio.h>
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_common: check the Common object */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_common
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_common (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_common: print the Common object */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_common
+(
+ /* ---- input ---- */
+ char *name, /* printed name of Common object */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_common (char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_sparse: check a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_sparse (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_sparse */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to print */
+ char *name, /* printed name of sparse matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_sparse (cholmod_sparse *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_dense: check a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_dense (cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_dense: print a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to print */
+ char *name, /* printed name of dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_dense (cholmod_dense *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_factor: check a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_factor
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_factor (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_factor: print a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_factor
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to print */
+ char *name, /* printed name of factor */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_factor (cholmod_factor *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_triplet: check a sparse matrix in triplet form */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_triplet
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_triplet (cholmod_triplet *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_triplet: print a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_triplet
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to print */
+ char *name, /* printed name of triplet matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_triplet (cholmod_triplet *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_subset: check a subset */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_subset
+(
+ /* ---- input ---- */
+ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_subset (UF_long *, UF_long, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_subset: print a subset */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_subset
+(
+ /* ---- input ---- */
+ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Set */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_subset (UF_long *, UF_long, size_t, char *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_perm: check a permutation */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_perm
+(
+ /* ---- input ---- */
+ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_perm (UF_long *, size_t, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_perm: print a permutation vector */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_perm
+(
+ /* ---- input ---- */
+ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Perm */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_perm (UF_long *, size_t, size_t, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_parent: check an elimination tree */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_parent
+(
+ /* ---- input ---- */
+ int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_parent (UF_long *, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_parent */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_parent
+(
+ /* ---- input ---- */
+ int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ char *name, /* printed name of Parent */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_parent (UF_long *, size_t, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_sparse: read a sparse matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_read_sparse
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_read_sparse (FILE *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_triplet: read a triplet matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_read_triplet
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_read_triplet (FILE *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_dense: read a dense matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_read_dense
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_read_dense (FILE *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_matrix: read a sparse or dense matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+void *cholmod_read_matrix
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ int prefer, /* If 0, a sparse matrix is always return as a
+ * cholmod_triplet form. It can have any stype
+ * (symmetric-lower, unsymmetric, or
+ * symmetric-upper).
+ * If 1, a sparse matrix is returned as an unsymmetric
+ * cholmod_sparse form (A->stype == 0), with both
+ * upper and lower triangular parts present.
+ * This is what the MATLAB mread mexFunction does,
+ * since MATLAB does not have an stype.
+ * If 2, a sparse matrix is returned with an stype of 0
+ * or 1 (unsymmetric, or symmetric with upper part
+ * stored).
+ * This argument has no effect for dense matrices.
+ */
+ /* ---- output---- */
+ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_read_matrix (FILE *, int, int *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_write_sparse: write a sparse matrix to a file */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_write_sparse
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_sparse *A, /* matrix to print */
+ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_write_sparse (FILE *, cholmod_sparse *, cholmod_sparse *,
+ char *c, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_write_dense: write a dense matrix to a file */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_write_dense
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_dense *X, /* matrix to print */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_write_dense (FILE *, cholmod_dense *, char *, cholmod_common *) ;
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_cholesky.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_cholesky.h
new file mode 100644
index 0000000..7388afb
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_cholesky.h
@@ -0,0 +1,498 @@
+/* ========================================================================== */
+/* === Include/cholmod_cholesky.h =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_cholesky.h. Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_cholesky.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Cholesky module.
+ *
+ * Sparse Cholesky routines: analysis, factorization, and solve.
+ *
+ * The primary routines are all that a user requires to order, analyze, and
+ * factorize a sparse symmetric positive definite matrix A (or A*A'), and
+ * to solve Ax=b (or A*A'x=b). The primary routines rely on the secondary
+ * routines, the CHOLMOD Core module, and the AMD and COLAMD packages. They
+ * make optional use of the CHOLMOD Supernodal and Partition modules, the
+ * METIS package, and the CCOLAMD package.
+ *
+ * Primary routines:
+ * -----------------
+ *
+ * cholmod_analyze order and analyze (simplicial or supernodal)
+ * cholmod_factorize simplicial or supernodal Cholesky factorization
+ * cholmod_solve solve a linear system (simplicial or supernodal)
+ * cholmod_spsolve solve a linear system (sparse x and b)
+ *
+ * Secondary routines:
+ * ------------------
+ *
+ * cholmod_analyze_p analyze, with user-provided permutation or f set
+ * cholmod_factorize_p factorize, with user-provided permutation or f
+ * cholmod_analyze_ordering analyze a fill-reducing ordering
+ * cholmod_etree find the elimination tree
+ * cholmod_rowcolcounts compute the row/column counts of L
+ * cholmod_amd order using AMD
+ * cholmod_colamd order using COLAMD
+ * cholmod_rowfac incremental simplicial factorization
+ * cholmod_rowfac_mask rowfac, specific to LPDASA
+ * cholmod_row_subtree find the nonzero pattern of a row of L
+ * cholmod_resymbol recompute the symbolic pattern of L
+ * cholmod_resymbol_noperm recompute the symbolic pattern of L, no L->Perm
+ * cholmod_postorder postorder a tree
+ *
+ * Requires the Core module, and two packages: AMD and COLAMD.
+ * Optionally uses the Supernodal and Partition modules.
+ * Required by the Partition module.
+ */
+
+#ifndef CHOLMOD_CHOLESKY_H
+#define CHOLMOD_CHOLESKY_H
+
+#include "cholmod_config.h"
+#include "cholmod_core.h"
+
+#ifndef NPARTITION
+#include "cholmod_partition.h"
+#endif
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_analyze: order and analyze (simplicial or supernodal) */
+/* -------------------------------------------------------------------------- */
+
+/* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor
+ * that can later be passed to cholmod_factorize. */
+
+cholmod_factor *cholmod_analyze
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_analyze (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_analyze_p: analyze, with user-provided permutation or f set */
+/* -------------------------------------------------------------------------- */
+
+/* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a
+ * symbolic factor that can later be passed to cholmod_factorize, where
+ * F = A(:,fset) if fset is not NULL and A->stype is zero.
+ * UserPerm is tried if non-NULL. */
+
+cholmod_factor *cholmod_analyze_p
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ int *UserPerm, /* user-provided permutation, size A->nrow */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_analyze_p (cholmod_sparse *, UF_long *, UF_long *,
+ size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factorize: simplicial or supernodal Cholesky factorization */
+/* -------------------------------------------------------------------------- */
+
+/* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained
+ * from cholmod_analyze. The analysis can be re-used simply by calling this
+ * routine a second time with another matrix. A must have the same nonzero
+ * pattern as that passed to cholmod_analyze. */
+
+int cholmod_factorize
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_factorize (cholmod_sparse *, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factorize_p: factorize, with user-provided permutation or fset */
+/* -------------------------------------------------------------------------- */
+
+/* Same as cholmod_factorize, but with more options. */
+
+int cholmod_factorize_p
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_factorize_p (cholmod_sparse *, double *, UF_long *, size_t,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_solve: solve a linear system (simplicial or supernodal) */
+/* -------------------------------------------------------------------------- */
+
+/* Solves one of many linear systems with a dense right-hand-side, using the
+ * factorization from cholmod_factorize (or as modified by any other CHOLMOD
+ * routine). D is identity for LL' factorizations. */
+
+#define CHOLMOD_A 0 /* solve Ax=b */
+#define CHOLMOD_LDLt 1 /* solve LDL'x=b */
+#define CHOLMOD_LD 2 /* solve LDx=b */
+#define CHOLMOD_DLt 3 /* solve DL'x=b */
+#define CHOLMOD_L 4 /* solve Lx=b */
+#define CHOLMOD_Lt 5 /* solve L'x=b */
+#define CHOLMOD_D 6 /* solve Dx=b */
+#define CHOLMOD_P 7 /* permute x=Px */
+#define CHOLMOD_Pt 8 /* permute x=P'x */
+
+cholmod_dense *cholmod_solve /* returns the solution X */
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_dense *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_solve (int, cholmod_factor *, cholmod_dense *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_spsolve: solve a linear system with a sparse right-hand-side */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_spsolve
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_sparse *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_spsolve (int, cholmod_factor *, cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_etree: find the elimination tree of A or A'*A */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_etree
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* ---- output --- */
+ int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_etree (cholmod_sparse *, UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowcolcounts: compute the row/column counts of L */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_rowcolcounts
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */
+ int *Post, /* size nrow. Post [k] = i if i is the kth node in
+ * the postordered etree. */
+ /* ---- output --- */
+ int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of
+ * L, including the diagonal. */
+ int *ColCount, /* size nrow. ColCount [i] = # entries in the ith
+ * column of L, including the diagonal. */
+ int *First, /* size nrow. First [i] = k is the least postordering
+ * of any descendant of i. */
+ int *Level, /* size nrow. Level [i] is the length of the path from
+ * i to the root, with Level [root] = 0. */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowcolcounts (cholmod_sparse *, UF_long *, size_t, UF_long *,
+ UF_long *, UF_long *, UF_long *, UF_long *, UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_analyze_ordering: analyze a fill-reducing ordering */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_analyze_ordering
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int ordering, /* ordering method used */
+ int *Perm, /* size n, fill-reducing permutation to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Parent, /* size n, elimination tree */
+ int *Post, /* size n, postordering of elimination tree */
+ int *ColCount, /* size n, nnz in each column of L */
+ /* ---- workspace */
+ int *First, /* size nworkspace for cholmod_postorder */
+ int *Level, /* size n workspace for cholmod_postorder */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_analyze_ordering (cholmod_sparse *, int, UF_long *, UF_long *,
+ size_t, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_amd: order using AMD */
+/* -------------------------------------------------------------------------- */
+
+/* Finds a permutation P to reduce fill-in in the factorization of P*A*P'
+ * or P*A*A'P' */
+
+int cholmod_amd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_amd (cholmod_sparse *, UF_long *, size_t, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_colamd: order using COLAMD */
+/* -------------------------------------------------------------------------- */
+
+/* Finds a permutation P to reduce fill-in in the factorization of P*A*A'*P'.
+ * Orders F*F' where F = A (:,fset) if fset is not NULL */
+
+int cholmod_colamd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with a coletree postorder */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_colamd (cholmod_sparse *, UF_long *, size_t, int, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowfac: incremental simplicial factorization */
+/* -------------------------------------------------------------------------- */
+
+/* Partial or complete simplicial factorization. Rows and columns kstart:kend-1
+ * of L and D must be initially equal to rows/columns kstart:kend-1 of the
+ * identity matrix. Row k can only be factorized if all descendants of node
+ * k in the elimination tree have been factorized. */
+
+int cholmod_rowfac
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowfac (cholmod_sparse *, cholmod_sparse *, double *, size_t,
+ size_t, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowfac_mask: incremental simplicial factorization */
+/* -------------------------------------------------------------------------- */
+
+/* cholmod_rowfac_mask is a version of cholmod_rowfac that is specific to
+ * LPDASA. It is unlikely to be needed by any other application. */
+
+int cholmod_rowfac_mask
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ int *mask, /* if mask[i] >= 0, then set row i to zero */
+ int *RLinkUp, /* link list of rows to compute */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowfac_mask (cholmod_sparse *, cholmod_sparse *, double *, size_t,
+ size_t, UF_long *, UF_long *, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_row_subtree: find the nonzero pattern of a row of L */
+/* -------------------------------------------------------------------------- */
+
+/* Find the nonzero pattern of x for the system Lx=b where L = (0:k-1,0:k-1)
+ * and b = kth column of A or A*A' (rows 0 to k-1 only) */
+
+int cholmod_row_subtree
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */
+ size_t k, /* row k of L */
+ int *Parent, /* elimination tree */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_row_subtree (cholmod_sparse *, cholmod_sparse *, size_t,
+ UF_long *, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_row_lsubtree: find the nonzero pattern of a row of L */
+/* -------------------------------------------------------------------------- */
+
+/* Identical to cholmod_row_subtree, except that it finds the elimination tree
+ * from L itself. */
+
+int cholmod_row_lsubtree
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required
+ * for the symmetric case. Need not be sorted. */
+ size_t k, /* row k of L */
+ cholmod_factor *L, /* the factor L from which parent(i) is derived */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_row_lsubtree (cholmod_sparse *, UF_long *, size_t,
+ size_t, cholmod_factor *, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_resymbol: recompute the symbolic pattern of L */
+/* -------------------------------------------------------------------------- */
+
+/* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P',
+ * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not).
+ *
+ * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it
+ * first permutes A according to L->Perm. A can be upper/lower/unsymmetric,
+ * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */
+
+int cholmod_resymbol
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_resymbol (cholmod_sparse *, UF_long *, size_t, int,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_resymbol_noperm: recompute the symbolic pattern of L, no L->Perm */
+/* -------------------------------------------------------------------------- */
+
+/* Remove entries from L that are not in the factorization of A, A*A',
+ * or F*F' (depending on A->stype and whether fset is NULL or not). */
+
+int cholmod_resymbol_noperm
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_resymbol_noperm (cholmod_sparse *, UF_long *, size_t, int,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rcond: compute rough estimate of reciprocal of condition number */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_rcond /* return min(diag(L)) / max(diag(L)) */
+(
+ /* ---- input ---- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_rcond (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_postorder: Compute the postorder of a tree */
+/* -------------------------------------------------------------------------- */
+
+UF_long cholmod_postorder /* return # of nodes postordered */
+(
+ /* ---- input ---- */
+ int *Parent, /* size n. Parent [j] = p if p is the parent of j */
+ size_t n,
+ int *Weight_p, /* size n, optional. Weight [j] is weight of node j */
+ /* ---- output --- */
+ int *Post, /* size n. Post [k] = j is kth in postordered tree */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_postorder (UF_long *, size_t, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_complexity.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_complexity.h
new file mode 100644
index 0000000..a84583a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_complexity.h
@@ -0,0 +1,264 @@
+/* ========================================================================== */
+/* === Include/cholmod_complexity.h ========================================= */
+/* ========================================================================== */
+
+/* Define operations on pattern, real, complex, and zomplex objects.
+ *
+ * The xtype of an object defines it numerical type. A qttern object has no
+ * numerical values (A->x and A->z are NULL). A real object has no imaginary
+ * qrt (A->x is used, A->z is NULL). A complex object has an imaginary qrt
+ * that is stored interleaved with its real qrt (A->x is of size 2*nz, A->z
+ * is NULL). A zomplex object has both real and imaginary qrts, which are
+ * stored seqrately, as in MATLAB (A->x and A->z are both used).
+ *
+ * XTYPE is CHOLMOD_PATTERN, _REAL, _COMPLEX or _ZOMPLEX, and is the xtype of
+ * the template routine under construction. XTYPE2 is equal to XTYPE, except
+ * if XTYPE is CHOLMOD_PATTERN, in which case XTYPE is CHOLMOD_REAL.
+ * XTYPE and XTYPE2 are defined in cholmod_template.h.
+ */
+
+/* -------------------------------------------------------------------------- */
+/* pattern */
+/* -------------------------------------------------------------------------- */
+
+#define P_TEMPLATE(name) p_ ## name
+#define P_ASSIGN2(x,z,p,ax,az,q) x [p] = 1
+#define P_PRINT(k,x,z,p) PRK(k, ("1"))
+
+/* -------------------------------------------------------------------------- */
+/* real */
+/* -------------------------------------------------------------------------- */
+
+#define R_TEMPLATE(name) r_ ## name
+#define R_ASSEMBLE(x,z,p,ax,az,q) x [p] += ax [q]
+#define R_ASSIGN(x,z,p,ax,az,q) x [p] = ax [q]
+#define R_ASSIGN_CONJ(x,z,p,ax,az,q) x [p] = ax [q]
+#define R_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q]
+#define R_XTYPE_OK(type) ((type) == CHOLMOD_REAL)
+#define R_IS_NONZERO(ax,az,q) IS_NONZERO (ax [q])
+#define R_IS_ZERO(ax,az,q) IS_ZERO (ax [q])
+#define R_IS_ONE(ax,az,q) (ax [q] == 1)
+#define R_MULT(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] * bx [r]
+#define R_MULTADD(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r]
+#define R_MULTSUB(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r]
+#define R_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r]
+#define R_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r]
+#define R_ADD(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] + bx [r]
+#define R_ADD_REAL(x,p, ax,q, bx,r) x [p] = ax [q] + bx [r]
+#define R_CLEAR(x,z,p) x [p] = 0
+#define R_CLEAR_IMAG(x,z,p)
+#define R_DIV(x,z,p,ax,az,q) x [p] /= ax [q]
+#define R_LLDOT(x,p, ax,az,q) x [p] -= ax [q] * ax [q]
+#define R_PRINT(k,x,z,p) PRK(k, ("%24.16e", x [p]))
+
+#define R_DIV_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] / bx [r]
+#define R_MULT_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] * bx [r]
+
+#define R_LDLDOT(x,p, ax,az,q, bx,r) x [p] -=(ax[q] * ax[q])/ bx[r]
+
+/* -------------------------------------------------------------------------- */
+/* complex */
+/* -------------------------------------------------------------------------- */
+
+#define C_TEMPLATE(name) c_ ## name
+#define CT_TEMPLATE(name) ct_ ## name
+
+#define C_ASSEMBLE(x,z,p,ax,az,q) \
+ x [2*(p) ] += ax [2*(q) ] ; \
+ x [2*(p)+1] += ax [2*(q)+1]
+
+#define C_ASSIGN(x,z,p,ax,az,q) \
+ x [2*(p) ] = ax [2*(q) ] ; \
+ x [2*(p)+1] = ax [2*(q)+1]
+
+#define C_ASSIGN_REAL(x,p,ax,q) x [2*(p)] = ax [2*(q)]
+
+#define C_ASSIGN_CONJ(x,z,p,ax,az,q) \
+ x [2*(p) ] = ax [2*(q) ] ; \
+ x [2*(p)+1] = -ax [2*(q)+1]
+
+#define C_XTYPE_OK(type) ((type) == CHOLMOD_COMPLEX)
+
+#define C_IS_NONZERO(ax,az,q) \
+ (IS_NONZERO (ax [2*(q)]) || IS_NONZERO (ax [2*(q)+1]))
+
+#define C_IS_ZERO(ax,az,q) \
+ (IS_ZERO (ax [2*(q)]) && IS_ZERO (ax [2*(q)+1]))
+
+#define C_IS_ONE(ax,az,q) \
+ ((ax [2*(q)] == 1) && IS_ZERO (ax [2*(q)+1]))
+
+#define C_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (ax [2*(q)+1]))
+
+#define C_MULT(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+#define C_MULTADD(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] += ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+#define C_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] -= ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+/* s += conj(a)*b */
+#define C_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] += (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+/* s -= conj(a)*b */
+#define C_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] -= (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+#define C_ADD(x,z,p, ax,az,q, bx,bz,r) \
+ x [2*(p) ] = ax [2*(q) ] + bx [2*(r) ] ; \
+ x [2*(p)+1] = ax [2*(q)+1] + bx [2*(r)+1]
+
+#define C_ADD_REAL(x,p, ax,q, bx,r) \
+ x [2*(p)] = ax [2*(q)] + bx [2*(r)]
+
+#define C_CLEAR(x,z,p) \
+ x [2*(p) ] = 0 ; \
+ x [2*(p)+1] = 0
+
+#define C_CLEAR_IMAG(x,z,p) \
+ x [2*(p)+1] = 0
+
+/* s = s / a */
+#define C_DIV(x,z,p,ax,az,q) \
+ Common->complex_divide ( \
+ x [2*(p)], x [2*(p)+1], \
+ ax [2*(q)], ax [2*(q)+1], \
+ &x [2*(p)], &x [2*(p)+1])
+
+/* s -= conj(a)*a ; note that the result of conj(a)*a is real */
+#define C_LLDOT(x,p, ax,az,q) \
+ x [2*(p)] -= ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1]
+
+#define C_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [2*(p)], x [2*(p)+1]))
+
+#define C_DIV_REAL(x,z,p, ax,az,q, bx,r) \
+ x [2*(p) ] = ax [2*(q) ] / bx [2*(r)] ; \
+ x [2*(p)+1] = ax [2*(q)+1] / bx [2*(r)]
+
+#define C_MULT_REAL(x,z,p, ax,az,q, bx,r) \
+ x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] ; \
+ x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)]
+
+/* s -= conj(a)*a/t */
+#define C_LDLDOT(x,p, ax,az,q, bx,r) \
+ x [2*(p)] -= (ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1]) / bx[r]
+
+/* -------------------------------------------------------------------------- */
+/* zomplex */
+/* -------------------------------------------------------------------------- */
+
+#define Z_TEMPLATE(name) z_ ## name
+#define ZT_TEMPLATE(name) zt_ ## name
+
+#define Z_ASSEMBLE(x,z,p,ax,az,q) \
+ x [p] += ax [q] ; \
+ z [p] += az [q]
+
+#define Z_ASSIGN(x,z,p,ax,az,q) \
+ x [p] = ax [q] ; \
+ z [p] = az [q]
+
+#define Z_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q]
+
+#define Z_ASSIGN_CONJ(x,z,p,ax,az,q) \
+ x [p] = ax [q] ; \
+ z [p] = -az [q]
+
+#define Z_XTYPE_OK(type) ((type) == CHOLMOD_ZOMPLEX)
+
+#define Z_IS_NONZERO(ax,az,q) \
+ (IS_NONZERO (ax [q]) || IS_NONZERO (az [q]))
+
+#define Z_IS_ZERO(ax,az,q) \
+ (IS_ZERO (ax [q]) && IS_ZERO (az [q]))
+
+#define Z_IS_ONE(ax,az,q) \
+ ((ax [q] == 1) && IS_ZERO (az [q]))
+
+#define Z_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (az [q]))
+
+#define Z_MULT(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] = ax [q] * bx [r] - az [q] * bz [r] ; \
+ z [p] = az [q] * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTADD(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] += ax [q] * bx [r] - az [q] * bz [r] ; \
+ z [p] += az [q] * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] -= ax [q] * bx [r] - az [q] * bz [r] ; \
+ z [p] -= az [q] * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] += ax [q] * bx [r] + az [q] * bz [r] ; \
+ z [p] += (-az [q]) * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] -= ax [q] * bx [r] + az [q] * bz [r] ; \
+ z [p] -= (-az [q]) * bx [r] + ax [q] * bz [r]
+
+#define Z_ADD(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] = ax [q] + bx [r] ; \
+ z [p] = az [q] + bz [r]
+
+#define Z_ADD_REAL(x,p, ax,q, bx,r) \
+ x [p] = ax [q] + bx [r]
+
+#define Z_CLEAR(x,z,p) \
+ x [p] = 0 ; \
+ z [p] = 0
+
+#define Z_CLEAR_IMAG(x,z,p) \
+ z [p] = 0
+
+/* s = s/a */
+#define Z_DIV(x,z,p,ax,az,q) \
+ Common->complex_divide (x [p], z [p], ax [q], az [q], &x [p], &z [p])
+
+/* s -= conj(a)*a ; note that the result of conj(a)*a is real */
+#define Z_LLDOT(x,p, ax,az,q) \
+ x [p] -= ax [q] * ax [q] + az [q] * az [q]
+
+#define Z_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [p], z [p]))
+
+#define Z_DIV_REAL(x,z,p, ax,az,q, bx,r) \
+ x [p] = ax [q] / bx [r] ; \
+ z [p] = az [q] / bx [r]
+
+#define Z_MULT_REAL(x,z,p, ax,az,q, bx,r) \
+ x [p] = ax [q] * bx [r] ; \
+ z [p] = az [q] * bx [r]
+
+/* s -= conj(a)*a/t */
+#define Z_LDLDOT(x,p, ax,az,q, bx,r) \
+ x [p] -= (ax [q] * ax [q] + az [q] * az [q]) / bx[r]
+
+/* -------------------------------------------------------------------------- */
+/* all classes */
+/* -------------------------------------------------------------------------- */
+
+/* Check if A->xtype and the two arrays A->x and A->z are valid. Set status to
+ * invalid, unless status is already "out of memory". A can be a sparse matrix,
+ * dense matrix, factor, or triplet. */
+
+#define RETURN_IF_XTYPE_INVALID(A,xtype1,xtype2,result) \
+{ \
+ if ((A)->xtype < (xtype1) || (A)->xtype > (xtype2) || \
+ ((A)->xtype != CHOLMOD_PATTERN && ((A)->x) == NULL) || \
+ ((A)->xtype == CHOLMOD_ZOMPLEX && ((A)->z) == NULL)) \
+ { \
+ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \
+ { \
+ ERROR (CHOLMOD_INVALID, "invalid xtype") ; \
+ } \
+ return (result) ; \
+ } \
+}
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_config.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_config.h
new file mode 100644
index 0000000..b9de51b
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_config.h
@@ -0,0 +1,83 @@
+/* ========================================================================== */
+/* === Include/cholmod_config.h ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_config.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_config.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD configuration file, for inclusion in user programs.
+ *
+ * You do not have to edit any CHOLMOD files to compile and install CHOLMOD.
+ * However, if you do not use all of CHOLMOD's modules, you need to compile
+ * with the appropriate flag, or edit this file to add the appropriate #define.
+ *
+ * If you wish to use CHOLMOD under the GNU LGPL license only, then you must
+ * compile CHOLMOD with -DNMATRIXOPS -DNSUPERNODAL and -DNMODIFY. This can
+ * be done using just -DNGPL.
+ *
+ * Compiler flags for CHOLMOD:
+ *
+ * -DNCHECK do not include the Check module. License: GNU LGPL
+ * -DNCHOLESKY do not include the Cholesky module. License: GNU LGPL
+ * -DNPARTITION do not include the Partition module. License: GNU LGPL
+ *
+ * -DNGPL do not include any GNU GPL Modules in the CHOLMOD library.
+ * -DNMATRIXOPS do not include the MatrixOps module. License: GNU GPL
+ * -DNMODIFY do not include the Modify module. License: GNU GPL
+ * -DNSUPERNODAL do not include the Supernodal module. License: GNU GPL
+ *
+ * -DNPRINT do not print anything
+ *
+ * -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by
+ * LAPACK and the BLAS. Use LONGBLAS=long on Solaris to use
+ * the 64-bit Sun Performance BLAS in cholmod_l_* routines.
+ * You may need to use -D'LONGBLAS=long long' on the SGI
+ * (this is not tested).
+ *
+ * -DNSUNPERF for Solaris only. If defined, do not use the Sun
+ * Performance Library. The default is to use SunPerf.
+ * You must compile CHOLMOD with -xlic_lib=sunperf.
+ *
+ * The Core Module (License GNU LGPL) is always included in the CHOLMOD library.
+ */
+
+#ifndef CHOLMOD_CONFIG_H
+#define CHOLMOD_CONFIG_H
+
+/* Use the compiler flag, or uncomment the definition(s), if you want to use
+ * one or more non-default installation options: */
+
+/*
+#define NCHECK
+#define NCHOLESKY
+#define NPARTITION
+
+#define NGPL
+#define NMATRIXOPS
+#define NMODIFY
+#define NSUPERNODAL
+
+#define NPRINT
+
+#define LONGBLAS long
+#define LONGBLAS long long
+#define NSUNPERF
+*/
+
+/* -------------------------------------------------------------------------- */
+/* if NGPL is defined, disable all GNU GPL Modules */
+/* -------------------------------------------------------------------------- */
+
+#ifdef NGPL
+#define NMATRIXOPS
+#define NMODIFY
+#define NSUPERNODAL
+#endif
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_core.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_core.h
new file mode 100644
index 0000000..65cf0c0
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_core.h
@@ -0,0 +1,2257 @@
+/* ========================================================================== */
+/* === Include/cholmod_core.h =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_core.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_core.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Core module: basic CHOLMOD objects and routines.
+ * Required by all CHOLMOD modules. Requires no other module or package.
+ *
+ * The CHOLMOD modules are:
+ *
+ * Core basic data structures and definitions
+ * Check check/print the 5 CHOLMOD objects, & 3 types of integer vectors
+ * Cholesky sparse Cholesky factorization
+ * Modify sparse Cholesky update/downdate/row-add/row-delete
+ * MatrixOps sparse matrix functions (add, multiply, norm, ...)
+ * Supernodal supernodal sparse Cholesky factorization
+ * Partition graph-partitioning based orderings
+ *
+ * The CHOLMOD objects:
+ * --------------------
+ *
+ * cholmod_common parameters, statistics, and workspace
+ * cholmod_sparse a sparse matrix in compressed column form
+ * cholmod_factor an LL' or LDL' factorization
+ * cholmod_dense a dense matrix
+ * cholmod_triplet a sparse matrix in "triplet" form
+ *
+ * The Core module described here defines the CHOLMOD data structures, and
+ * basic operations on them. To create and solve a sparse linear system Ax=b,
+ * the user must create A and b, populate them with values, and then pass them
+ * to the routines in the CHOLMOD Cholesky module. There are two primary
+ * methods for creating A: (1) allocate space for a column-oriented sparse
+ * matrix and fill it with pattern and values, or (2) create a triplet form
+ * matrix and convert it to a sparse matrix. The latter option is simpler.
+ *
+ * The matrices b and x are typically dense matrices, but can also be sparse.
+ * You can allocate and free them as dense matrices with the
+ * cholmod_allocate_dense and cholmod_free_dense routines.
+ *
+ * The cholmod_factor object contains the symbolic and numeric LL' or LDL'
+ * factorization of sparse symmetric matrix. The matrix must be positive
+ * definite for an LL' factorization. It need only be symmetric and have well-
+ * conditioned leading submatrices for it to have an LDL' factorization
+ * (CHOLMOD does not pivot for numerical stability). It is typically created
+ * with the cholmod_factorize routine in the Cholesky module, but can also
+ * be initialized to L=D=I in the Core module and then modified by the Modify
+ * module. It must be freed with cholmod_free_factor, defined below.
+ *
+ * The Core routines for each object are described below. Each list is split
+ * into two parts: the primary routines and secondary routines.
+ *
+ * ============================================================================
+ * === cholmod_common =========================================================
+ * ============================================================================
+ *
+ * The Common object contains control parameters, statistics, and
+ * You must call cholmod_start before calling any other CHOLMOD routine, and
+ * must call cholmod_finish as your last call to CHOLMOD, with two exceptions:
+ * you may call cholmod_print_common and cholmod_check_common in the Check
+ * module after calling cholmod_finish.
+ *
+ * cholmod_start first call to CHOLMOD
+ * cholmod_finish last call to CHOLMOD
+ * -----------------------------
+ * cholmod_defaults restore default parameters
+ * cholmod_maxrank maximum rank for update/downdate
+ * cholmod_allocate_work allocate workspace in Common
+ * cholmod_free_work free workspace in Common
+ * cholmod_clear_flag clear Flag workspace in Common
+ * cholmod_error called when CHOLMOD encounters an error
+ * cholmod_dbound for internal use in CHOLMOD only
+ * cholmod_hypot compute sqrt (x*x + y*y) accurately
+ * cholmod_divcomplex complex division, c = a/b
+ *
+ * ============================================================================
+ * === cholmod_sparse =========================================================
+ * ============================================================================
+ *
+ * A sparse matrix is held in compressed column form. In the basic type
+ * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix
+ * with nz entries is held in three arrays: p of size n+1, i of size nz, and x
+ * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and
+ * in the same locations in x. There may be no duplicate entries in a column.
+ * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track).
+ * A->stype determines the storage mode: 0 if both upper/lower parts are stored,
+ * -1 if A is symmetric and just tril(A) is stored, +1 if symmetric and triu(A)
+ * is stored.
+ *
+ * cholmod_allocate_sparse allocate a sparse matrix
+ * cholmod_free_sparse free a sparse matrix
+ * -----------------------------
+ * cholmod_reallocate_sparse change the size (# entries) of sparse matrix
+ * cholmod_nnz number of nonzeros in a sparse matrix
+ * cholmod_speye sparse identity matrix
+ * cholmod_spzeros sparse zero matrix
+ * cholmod_transpose transpose a sparse matrix
+ * cholmod_ptranspose transpose/permute a sparse matrix
+ * cholmod_transpose_unsym transpose/permute an unsymmetric sparse matrix
+ * cholmod_transpose_sym transpose/permute a symmetric sparse matrix
+ * cholmod_sort sort row indices in each column of sparse matrix
+ * cholmod_band C = tril (triu (A,k1), k2)
+ * cholmod_band_inplace A = tril (triu (A,k1), k2)
+ * cholmod_aat C = A*A'
+ * cholmod_copy_sparse C = A, create an exact copy of a sparse matrix
+ * cholmod_copy C = A, with possible change of stype
+ * cholmod_add C = alpha*A + beta*B
+ * cholmod_sparse_xtype change the xtype of a sparse matrix
+ *
+ * ============================================================================
+ * === cholmod_factor =========================================================
+ * ============================================================================
+ *
+ * The data structure for an LL' or LDL' factorization is too complex to
+ * describe in one sentence. This object can hold the symbolic analysis alone,
+ * or in combination with a "simplicial" (similar to a sparse matrix) or
+ * "supernodal" form of the numerical factorization. Only the routine to free
+ * a factor is primary, since a factor object is created by the factorization
+ * routine (cholmod_factorize). It must be freed with cholmod_free_factor.
+ *
+ * cholmod_free_factor free a factor
+ * -----------------------------
+ * cholmod_allocate_factor allocate a factor (LL' or LDL')
+ * cholmod_reallocate_factor change the # entries in a factor
+ * cholmod_change_factor change the type of factor (e.g., LDL' to LL')
+ * cholmod_pack_factor pack the columns of a factor
+ * cholmod_reallocate_column resize a single column of a factor
+ * cholmod_factor_to_sparse create a sparse matrix copy of a factor
+ * cholmod_copy_factor create a copy of a factor
+ * cholmod_factor_xtype change the xtype of a factor
+ *
+ * Note that there is no cholmod_sparse_to_factor routine to create a factor
+ * as a copy of a sparse matrix. It could be done, after a fashion, but a
+ * lower triangular sparse matrix would not necessarily have a chordal graph,
+ * which would break the many CHOLMOD routines that rely on this property.
+ *
+ * ============================================================================
+ * === cholmod_dense ==========================================================
+ * ============================================================================
+ *
+ * The solve routines and some of the MatrixOps and Modify routines use dense
+ * matrices as inputs. These are held in column-major order. With a leading
+ * dimension of d, the entry in row i and column j is held in x [i+j*d].
+ *
+ * cholmod_allocate_dense allocate a dense matrix
+ * cholmod_free_dense free a dense matrix
+ * -----------------------------
+ * cholmod_zeros allocate a dense matrix of all zeros
+ * cholmod_ones allocate a dense matrix of all ones
+ * cholmod_eye allocate a dense identity matrix
+ * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix
+ * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix
+ * cholmod_copy_dense create a copy of a dense matrix
+ * cholmod_copy_dense2 copy a dense matrix (pre-allocated)
+ * cholmod_dense_xtype change the xtype of a dense matrix
+ *
+ * ============================================================================
+ * === cholmod_triplet ========================================================
+ * ============================================================================
+ *
+ * A sparse matrix held in triplet form is the simplest one for a user to
+ * create. It consists of a list of nz entries in arbitrary order, held in
+ * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k],
+ * column j[k], with value x[k]. There may be duplicate values; if A(i,j)
+ * appears more than once, its value is the sum of the entries with those row
+ * and column indices.
+ *
+ * cholmod_allocate_triplet allocate a triplet matrix
+ * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix
+ * cholmod_free_triplet free a triplet matrix
+ * -----------------------------
+ * cholmod_reallocate_triplet change the # of entries in a triplet matrix
+ * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix
+ * cholmod_copy_triplet create a copy of a triplet matrix
+ * cholmod_triplet_xtype change the xtype of a triplet matrix
+ *
+ * ============================================================================
+ * === memory management ======================================================
+ * ============================================================================
+ *
+ * cholmod_malloc malloc wrapper
+ * cholmod_calloc calloc wrapper
+ * cholmod_free free wrapper
+ * cholmod_realloc realloc wrapper
+ * cholmod_realloc_multiple realloc wrapper for multiple objects
+ *
+ * ============================================================================
+ * === Core CHOLMOD prototypes ================================================
+ * ============================================================================
+ *
+ * All CHOLMOD routines (in all modules) use the following protocol for return
+ * values, with one exception:
+ *
+ * int TRUE (1) if successful, or FALSE (0) otherwise.
+ * (exception: cholmod_divcomplex)
+ * UF_long a value >= 0 if successful, or -1 otherwise.
+ * double a value >= 0 if successful, or -1 otherwise.
+ * size_t a value > 0 if successful, or 0 otherwise.
+ * void * a non-NULL pointer to newly allocated memory if
+ * successful, or NULL otherwise.
+ * cholmod_sparse * a non-NULL pointer to a newly allocated matrix
+ * if successful, or NULL otherwise.
+ * cholmod_factor * a non-NULL pointer to a newly allocated factor
+ * if successful, or NULL otherwise.
+ * cholmod_triplet * a non-NULL pointer to a newly allocated triplet
+ * matrix if successful, or NULL otherwise.
+ * cholmod_dense * a non-NULL pointer to a newly allocated triplet
+ * matrix if successful, or NULL otherwise.
+ *
+ * The last parameter to all routines is always a pointer to the CHOLMOD
+ * Common object.
+ *
+ * TRUE and FALSE are not defined here, since they may conflict with the user
+ * program. A routine that described here returning TRUE or FALSE returns 1
+ * or 0, respectively. Any TRUE/FALSE parameter is true if nonzero, false if
+ * zero.
+ */
+
+#ifndef CHOLMOD_CORE_H
+#define CHOLMOD_CORE_H
+
+/* ========================================================================== */
+/* === CHOLMOD version ====================================================== */
+/* ========================================================================== */
+
+/* All versions of CHOLMOD will include the following definitions.
+ * As an example, to test if the version you are using is 1.3 or later:
+ *
+ * if (CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)
+ * printf ("This is version 1.3 or later\n") ;
+ * #else
+ * printf ("This is version is earlier than 1.3\n") ;
+ * #endif
+ */
+
+#define CHOLMOD_DATE "Dec 12, 2006"
+#define CHOLMOD_VER_CODE(main,sub) ((main) * 1000 + (sub))
+#define CHOLMOD_MAIN_VERSION 1
+#define CHOLMOD_SUB_VERSION 4
+#define CHOLMOD_SUBSUB_VERSION 0
+#define CHOLMOD_VERSION \
+ CHOLMOD_VER_CODE(CHOLMOD_MAIN_VERSION,CHOLMOD_SUB_VERSION)
+
+
+/* ========================================================================== */
+/* === non-CHOLMOD include files ============================================ */
+/* ========================================================================== */
+
+/* This is the only non-CHOLMOD include file imposed on the user program.
+ * It required for size_t definition used here. CHOLMOD itself includes other
+ * ANSI C89 standard #include files, but does not expose them to the user.
+ *
+ * CHOLMOD assumes that your C compiler is ANSI C89 compliant. It does not make
+ * use of ANSI C99 features.
+ */
+
+#include <stddef.h>
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === CHOLMOD objects ====================================================== */
+/* ========================================================================== */
+
+/* Each CHOLMOD object has its own type code. */
+
+#define CHOLMOD_COMMON 0
+#define CHOLMOD_SPARSE 1
+#define CHOLMOD_FACTOR 2
+#define CHOLMOD_DENSE 3
+#define CHOLMOD_TRIPLET 4
+
+/* ========================================================================== */
+/* === CHOLMOD Common ======================================================= */
+/* ========================================================================== */
+
+/* itype defines the types of integer used: */
+#define CHOLMOD_INT 0 /* all integer arrays are int */
+#define CHOLMOD_INTLONG 1 /* most are int, some are UF_long */
+#define CHOLMOD_LONG 2 /* all integer arrays are UF_long */
+
+/* The itype of all parameters for all CHOLMOD routines must match.
+ * FUTURE WORK: CHOLMOD_INTLONG is not yet supported.
+ */
+
+/* dtype defines what the numerical type is (double or float): */
+#define CHOLMOD_DOUBLE 0 /* all numerical values are double */
+#define CHOLMOD_SINGLE 1 /* all numerical values are float */
+
+/* The dtype of all parameters for all CHOLMOD routines must match.
+ *
+ * Scalar floating-point values are always passed as double arrays of size 2
+ * (for the real and imaginary parts). They are typecast to float as needed.
+ * FUTURE WORK: the float case is not supported yet.
+ */
+
+/* xtype defines the kind of numerical values used: */
+#define CHOLMOD_PATTERN 0 /* pattern only, no numerical values */
+#define CHOLMOD_REAL 1 /* a real matrix */
+#define CHOLMOD_COMPLEX 2 /* a complex matrix (ANSI C99 compatible) */
+#define CHOLMOD_ZOMPLEX 3 /* a complex matrix (MATLAB compatible) */
+
+/* The xtype of all parameters for all CHOLMOD routines must match.
+ *
+ * CHOLMOD_PATTERN: x and z are ignored.
+ * CHOLMOD_DOUBLE: x is non-null of size nzmax, z is ignored.
+ * CHOLMOD_COMPLEX: x is non-null of size 2*nzmax doubles, z is ignored.
+ * CHOLMOD_ZOMPLEX: x and z are non-null of size nzmax
+ *
+ * In the real case, z is ignored. The kth entry in the matrix is x [k].
+ * There are two methods for the complex case. In the ANSI C99-compatible
+ * CHOLMOD_COMPLEX case, the real and imaginary parts of the kth entry
+ * are in x [2*k] and x [2*k+1], respectively. z is ignored. In the
+ * MATLAB-compatible CHOLMOD_ZOMPLEX case, the real and imaginary
+ * parts of the kth entry are in x [k] and z [k].
+ *
+ * Scalar floating-point values are always passed as double arrays of size 2
+ * (real and imaginary parts). The imaginary part of a scalar is ignored if
+ * the routine operates on a real matrix.
+ *
+ * These Modules support complex and zomplex matrices, with a few exceptions:
+ *
+ * Check all routines
+ * Cholesky all routines
+ * Core all except cholmod_aat, add, band, copy
+ * Demo all routines
+ * Partition all routines
+ * Supernodal all routines support any real, complex, or zomplex input.
+ * There will never be a supernodal zomplex L; a complex
+ * supernodal L is created if A is zomplex.
+ * Tcov all routines
+ * Valgrind all routines
+ *
+ * These Modules provide partial support for complex and zomplex matrices:
+ *
+ * MATLAB all routines support real and zomplex only, not complex,
+ * with the exception of ldlupdate, which supports
+ * real matrices only. This is a minor constraint since
+ * MATLAB's matrices are all real or zomplex.
+ * MatrixOps only norm_dense, norm_sparse, and sdmult support complex
+ * and zomplex
+ *
+ * These Modules do not support complex and zomplex matrices at all:
+ *
+ * Modify all routines support real matrices only
+ */
+
+/* Definitions for cholmod_common: */
+#define CHOLMOD_MAXMETHODS 9 /* maximum number of different methods that
+ * cholmod_analyze can try. Must be >= 9. */
+
+/* Common->status values. zero means success, negative means a fatal error,
+ * positive is a warning. */
+#define CHOLMOD_OK 0 /* success */
+#define CHOLMOD_NOT_INSTALLED (-1) /* failure: method not installed */
+#define CHOLMOD_OUT_OF_MEMORY (-2) /* failure: out of memory */
+#define CHOLMOD_TOO_LARGE (-3) /* failure: integer overflow occured */
+#define CHOLMOD_INVALID (-4) /* failure: invalid input */
+#define CHOLMOD_NOT_POSDEF (1) /* warning: matrix not pos. def. */
+#define CHOLMOD_DSMALL (2) /* warning: D for LDL' or diag(L) or
+ * LL' has tiny absolute value */
+
+/* ordering method (also used for L->ordering) */
+#define CHOLMOD_NATURAL 0 /* use natural ordering */
+#define CHOLMOD_GIVEN 1 /* use given permutation */
+#define CHOLMOD_AMD 2 /* use minimum degree (AMD) */
+#define CHOLMOD_METIS 3 /* use METIS' nested dissection */
+#define CHOLMOD_NESDIS 4 /* use CHOLMOD's version of nested dissection:
+ * node bisector applied recursively, followed
+ * by constrained minimum degree (CSYMAMD or
+ * CCOLAMD) */
+#define CHOLMOD_COLAMD 5 /* use AMD for A, COLAMD for A*A' */
+
+/* POSTORDERED is not a method, but a result of natural ordering followed by a
+ * weighted postorder. It is used for L->ordering, not method [ ].ordering. */
+#define CHOLMOD_POSTORDERED 6 /* natural ordering, postordered. */
+
+/* supernodal strategy (for Common->supernodal) */
+#define CHOLMOD_SIMPLICIAL 0 /* always do simplicial */
+#define CHOLMOD_AUTO 1 /* select simpl/super depending on matrix */
+#define CHOLMOD_SUPERNODAL 2 /* always do supernodal */
+
+typedef struct cholmod_common_struct
+{
+ /* ---------------------------------------------------------------------- */
+ /* parameters for symbolic/numeric factorization and update/downdate */
+ /* ---------------------------------------------------------------------- */
+
+ double dbound ; /* Smallest absolute value of diagonal entries of D
+ * for LDL' factorization and update/downdate/rowadd/
+ * rowdel, or the diagonal of L for an LL' factorization.
+ * Entries in the range 0 to dbound are replaced with dbound.
+ * Entries in the range -dbound to 0 are replaced with -dbound. No
+ * changes are made to the diagonal if dbound <= 0. Default: zero */
+
+ double grow0 ; /* For a simplicial factorization, L->i and L->x can
+ * grow if necessary. grow0 is the factor by which
+ * it grows. For the initial space, L is of size MAX (1,grow0) times
+ * the required space. If L runs out of space, the new size of L is
+ * MAX(1.2,grow0) times the new required space. If you do not plan on
+ * modifying the LDL' factorization in the Modify module, set grow0 to
+ * zero (or set grow2 to 0, see below). Default: 1.2 */
+
+ double grow1 ;
+
+ size_t grow2 ; /* For a simplicial factorization, each column j of L
+ * is initialized with space equal to
+ * grow1*L->ColCount[j] + grow2. If grow0 < 1, grow1 < 1, or grow2 == 0,
+ * then the space allocated is exactly equal to L->ColCount[j]. If the
+ * column j runs out of space, it increases to grow1*need + grow2 in
+ * size, where need is the total # of nonzeros in that column. If you do
+ * not plan on modifying the factorization in the Modify module, set
+ * grow2 to zero. Default: grow1 = 1.2, grow2 = 5. */
+
+ size_t maxrank ; /* rank of maximum update/downdate. Valid values:
+ * 2, 4, or 8. A value < 2 is set to 2, and a
+ * value > 8 is set to 8. It is then rounded up to the next highest
+ * power of 2, if not already a power of 2. Workspace (Xwork, below) of
+ * size nrow-by-maxrank double's is allocated for the update/downdate.
+ * If an update/downdate of rank-k is requested, with k > maxrank,
+ * it is done in steps of maxrank. Default: 8, which is fastest.
+ * Memory usage can be reduced by setting maxrank to 2 or 4.
+ */
+
+ double supernodal_switch ; /* supernodal vs simplicial factorization */
+ int supernodal ; /* If Common->supernodal <= CHOLMOD_SIMPLICIAL
+ * (0) then cholmod_analyze performs a
+ * simplicial analysis. If >= CHOLMOD_SUPERNODAL (2), then a supernodal
+ * analysis is performed. If == CHOLMOD_AUTO (1) and
+ * flop/nnz(L) < Common->supernodal_switch, then a simplicial analysis
+ * is done. A supernodal analysis done otherwise.
+ * Default: CHOLMOD_AUTO. Default supernodal_switch = 40 */
+
+ int final_asis ; /* If TRUE, then ignore the other final_* parameters
+ * (except for final_pack).
+ * The factor is left as-is when done. Default: TRUE.*/
+
+ int final_super ; /* If TRUE, leave a factor in supernodal form when
+ * supernodal factorization is finished. If FALSE,
+ * then convert to a simplicial factor when done.
+ * Default: TRUE */
+
+ int final_ll ; /* If TRUE, leave factor in LL' form when done.
+ * Otherwise, leave in LDL' form. Default: FALSE */
+
+ int final_pack ; /* If TRUE, pack the columns when done. If TRUE, and
+ * cholmod_factorize is called with a symbolic L, L is
+ * allocated with exactly the space required, using L->ColCount. If you
+ * plan on modifying the factorization, set Common->final_pack to FALSE,
+ * and each column will be given a little extra slack space for future
+ * growth in fill-in due to updates. Default: TRUE */
+
+ int final_monotonic ; /* If TRUE, ensure columns are monotonic when done.
+ * Default: TRUE */
+
+ int final_resymbol ;/* if cholmod_factorize performed a supernodal
+ * factorization, final_resymbol is true, and
+ * final_super is FALSE (convert a simplicial numeric factorization),
+ * then numerically zero entries that resulted from relaxed supernodal
+ * amalgamation are removed. This does not remove entries that are zero
+ * due to exact numeric cancellation, since doing so would break the
+ * update/downdate rowadd/rowdel routines. Default: FALSE. */
+
+ /* supernodal relaxed amalgamation parameters: */
+ double zrelax [3] ;
+ size_t nrelax [3] ;
+
+ /* Let ns be the total number of columns in two adjacent supernodes.
+ * Let z be the fraction of zero entries in the two supernodes if they
+ * are merged (z includes zero entries from prior amalgamations). The
+ * two supernodes are merged if:
+ * (ns <= nrelax [0]) || (no new zero entries added) ||
+ * (ns <= nrelax [1] && z < zrelax [0]) ||
+ * (ns <= nrelax [2] && z < zrelax [1]) || (z < zrelax [2])
+ *
+ * Default parameters result in the following rule:
+ * (ns <= 4) || (no new zero entries added) ||
+ * (ns <= 16 && z < 0.8) || (ns <= 48 && z < 0.1) || (z < 0.05)
+ */
+
+ int prefer_zomplex ; /* X = cholmod_solve (sys, L, B, Common) computes
+ * x=A\b or solves a related system. If L and B are
+ * both real, then X is real. Otherwise, X is returned as
+ * CHOLMOD_COMPLEX if Common->prefer_zomplex is FALSE, or
+ * CHOLMOD_ZOMPLEX if Common->prefer_zomplex is TRUE. This parameter
+ * is needed because there is no supernodal zomplex L. Suppose the
+ * caller wants all complex matrices to be stored in zomplex form
+ * (MATLAB, for example). A supernodal L is returned in complex form
+ * if A is zomplex. B can be real, and thus X = cholmod_solve (L,B)
+ * should return X as zomplex. This cannot be inferred from the input
+ * arguments L and B. Default: FALSE, since all data types are
+ * supported in CHOLMOD_COMPLEX form and since this is the native type
+ * of LAPACK and the BLAS. Note that the MATLAB/cholmod.c mexFunction
+ * sets this parameter to TRUE, since MATLAB matrices are in
+ * CHOLMOD_ZOMPLEX form.
+ */
+
+ int prefer_upper ; /* cholmod_analyze and cholmod_factorize work
+ * fastest when a symmetric matrix is stored in
+ * upper triangular form when a fill-reducing ordering is used. In
+ * MATLAB, this corresponds to how x=A\b works. When the matrix is
+ * ordered as-is, they work fastest when a symmetric matrix is in lower
+ * triangular form. In MATLAB, R=chol(A) does the opposite. This
+ * parameter affects only how cholmod_read returns a symmetric matrix.
+ * If TRUE (the default case), a symmetric matrix is always returned in
+ * upper-triangular form (A->stype = 1). */
+
+ int quick_return_if_not_posdef ; /* if TRUE, the supernodal numeric
+ * factorization will return quickly if
+ * the matrix is not positive definite. Default: FALSE. */
+
+ /* ---------------------------------------------------------------------- */
+ /* printing and error handling options */
+ /* ---------------------------------------------------------------------- */
+
+ int print ; /* print level. Default: 3 */
+ int precise ; /* if TRUE, print 16 digits. Otherwise print 5 */
+ int (*print_function) (const char *, ...) ; /* pointer to printf */
+
+ int try_catch ; /* if TRUE, then ignore errors; CHOLMOD is in the middle
+ * of a try/catch block. No error message is printed
+ * and the Common->error_handler function is not called. */
+
+ void (*error_handler) (int status, char *file, int line, char *message) ;
+
+ /* Common->error_handler is the user's error handling routine. If not
+ * NULL, this routine is called if an error occurs in CHOLMOD. status
+ * can be CHOLMOD_OK (0), negative for a fatal error, and positive for
+ * a warning. file is a string containing the name of the source code
+ * file where the error occured, and line is the line number in that
+ * file. message is a string describing the error in more detail. */
+
+ /* ---------------------------------------------------------------------- */
+ /* ordering options */
+ /* ---------------------------------------------------------------------- */
+
+ /* The cholmod_analyze routine can try many different orderings and select
+ * the best one. It can also try one ordering method multiple times, with
+ * different parameter settings. The default is to use three orderings,
+ * the user's permutation (if provided), AMD which is the fastest ordering
+ * and generally gives good fill-in, and METIS. CHOLMOD's nested dissection
+ * (METIS with a constrained AMD) usually gives a better ordering than METIS
+ * alone (by about 5% to 10%) but it takes more time.
+ *
+ * If you know the method that is best for your matrix, set Common->nmethods
+ * to 1 and set Common->method [0] to the set of parameters for that method.
+ * If you set it to 1 and do not provide a permutation, then only AMD will
+ * be called.
+ *
+ * If METIS is not available, the default # of methods tried is 2 (the user
+ * permutation, if any, and AMD).
+ *
+ * To try other methods, set Common->nmethods to the number of methods you
+ * want to try. The suite of default methods and their parameters is
+ * described in the cholmod_defaults routine, and summarized here:
+ *
+ * Common->method [i]:
+ * i = 0: user-provided ordering (cholmod_analyze_p only)
+ * i = 1: AMD (for both A and A*A')
+ * i = 2: METIS
+ * i = 3: CHOLMOD's nested dissection (NESDIS), default parameters
+ * i = 4: natural
+ * i = 5: NESDIS with nd_small = 20000
+ * i = 6: NESDIS with nd_small = 4, no constrained minimum degree
+ * i = 7: NESDIS with no dense node removal
+ * i = 8: AMD for A, COLAMD for A*A'
+ *
+ * You can modify the suite of methods you wish to try by modifying
+ * Common.method [...] after calling cholmod_start or cholmod_defaults.
+ *
+ * For example, to use AMD, followed by a weighted postordering:
+ *
+ * Common->nmethods = 1 ;
+ * Common->method [0].ordering = CHOLMOD_AMD ;
+ * Common->postorder = TRUE ;
+ *
+ * To use the natural ordering (with no postordering):
+ *
+ * Common->nmethods = 1 ;
+ * Common->method [0].ordering = CHOLMOD_NATURAL ;
+ * Common->postorder = FALSE ;
+ *
+ * If you are going to factorize hundreds or more matrices with the same
+ * nonzero pattern, you may wish to spend a great deal of time finding a
+ * good permutation. In this case, try setting Common->nmethods to 9.
+ * The time spent in cholmod_analysis will be very high, but you need to
+ * call it only once.
+ *
+ * cholmod_analyze sets Common->current to a value between 0 and nmethods-1.
+ * Each ordering method uses the set of options defined by this parameter.
+ */
+
+ int nmethods ; /* The number of ordering methods to try. Default: 0.
+ * nmethods = 0 is a special case. cholmod_analyze
+ * will try the user-provided ordering (if given) and AMD. Let fl and
+ * lnz be the flop count and nonzeros in L from AMD's ordering. Let
+ * anz be the number of nonzeros in the upper or lower triangular part
+ * of the symmetric matrix A. If fl/lnz < 500 or lnz/anz < 5, then this
+ * is a good ordering, and METIS is not attempted. Otherwise, METIS is
+ * tried. The best ordering found is used. If nmethods > 0, the
+ * methods used are given in the method[ ] array, below. The first
+ * three methods in the default suite of orderings is (1) use the given
+ * permutation (if provided), (2) use AMD, and (3) use METIS. Maximum
+ * allowed value is CHOLMOD_MAXMETHODS. */
+
+ int current ; /* The current method being tried. Default: 0. Valid
+ * range is 0 to nmethods-1. */
+
+ int selected ; /* The best method found. */
+
+ /* The suite of ordering methods and parameters: */
+
+ struct cholmod_method_struct
+ {
+ /* statistics for this method */
+ double lnz ; /* nnz(L) excl. zeros from supernodal amalgamation,
+ * for a "pure" L */
+
+ double fl ; /* flop count for a "pure", real simplicial LL'
+ * factorization, with no extra work due to
+ * amalgamation. Subtract n to get the LDL' flop count. Multiply
+ * by about 4 if the matrix is complex or zomplex. */
+
+ /* ordering method parameters */
+ double prune_dense ;/* dense row/col control for AMD, SYMAMD, CSYMAMD,
+ * and NESDIS (cholmod_nested_dissection). For a
+ * symmetric n-by-n matrix, rows/columns with more than
+ * MAX (16, prune_dense * sqrt (n)) entries are removed prior to
+ * ordering. They appear at the end of the re-ordered matrix.
+ *
+ * If prune_dense < 0, only completely dense rows/cols are removed.
+ *
+ * This paramater is also the dense column control for COLAMD and
+ * CCOLAMD. For an m-by-n matrix, columns with more than
+ * MAX (16, prune_dense * sqrt (MIN (m,n))) entries are removed prior
+ * to ordering. They appear at the end of the re-ordered matrix.
+ * CHOLMOD factorizes A*A', so it calls COLAMD and CCOLAMD with A',
+ * not A. Thus, this parameter affects the dense *row* control for
+ * CHOLMOD's matrix, and the dense *column* control for COLAMD and
+ * CCOLAMD.
+ *
+ * Removing dense rows and columns improves the run-time of the
+ * ordering methods. It has some impact on ordering quality
+ * (usually minimal, sometimes good, sometimes bad).
+ *
+ * Default: 10. */
+
+ double prune_dense2 ;/* dense row control for COLAMD and CCOLAMD.
+ * Rows with more than MAX (16, dense2 * sqrt (n))
+ * for an m-by-n matrix are removed prior to ordering. CHOLMOD's
+ * matrix is transposed before ordering it with COLAMD or CCOLAMD,
+ * so this controls the dense *columns* of CHOLMOD's matrix, and
+ * the dense *rows* of COLAMD's or CCOLAMD's matrix.
+ *
+ * If prune_dense2 < 0, only completely dense rows/cols are removed.
+ *
+ * Default: -1. Note that this is not the default for COLAMD and
+ * CCOLAMD. -1 is best for Cholesky. 10 is best for LU. */
+
+ double nd_oksep ; /* in NESDIS, when a node separator is computed, it
+ * discarded if nsep >= nd_oksep*n, where nsep is
+ * the number of nodes in the separator, and n is the size of the
+ * graph being cut. Valid range is 0 to 1. If 1 or greater, the
+ * separator is discarded if it consists of the entire graph.
+ * Default: 1 */
+
+ double other1 [4] ; /* future expansion */
+
+ size_t nd_small ; /* do not partition graphs with fewer nodes than
+ * nd_small, in NESDIS. Default: 200 (same as
+ * METIS) */
+
+ size_t other2 [4] ; /* future expansion */
+
+ int aggressive ; /* Aggresive absorption in AMD, COLAMD, SYMAMD,
+ * CCOLAMD, and CSYMAMD. Default: TRUE */
+
+ int order_for_lu ; /* CCOLAMD can be optimized to produce an ordering
+ * for LU or Cholesky factorization. CHOLMOD only
+ * performs a Cholesky factorization. However, you may wish to use
+ * CHOLMOD as an interface for CCOLAMD but use it for your own LU
+ * factorization. In this case, order_for_lu should be set to FALSE.
+ * When factorizing in CHOLMOD itself, you should *** NEVER *** set
+ * this parameter FALSE. Default: TRUE. */
+
+ int nd_compress ; /* If TRUE, compress the graph and subgraphs before
+ * partitioning them in NESDIS. Default: TRUE */
+
+ int nd_camd ; /* If 1, follow the nested dissection ordering
+ * with a constrained minimum degree ordering that
+ * respects the partitioning just found (using CAMD). If 2, use
+ * CSYMAMD instead. If you set nd_small very small, you may not need
+ * this ordering, and can save time by setting it to zero (no
+ * constrained minimum degree ordering). Default: 1. */
+
+ int nd_components ; /* The nested dissection ordering finds a node
+ * separator that splits the graph into two parts,
+ * which may be unconnected. If nd_components is TRUE, each of
+ * these connected components is split independently. If FALSE,
+ * each part is split as a whole, even if it consists of more than
+ * one connected component. Default: FALSE */
+
+ /* fill-reducing ordering to use */
+ int ordering ;
+
+ size_t other3 [4] ; /* future expansion */
+
+ } method [CHOLMOD_MAXMETHODS + 1] ;
+
+ int postorder ; /* If TRUE, cholmod_analyze follows the ordering with a
+ * weighted postorder of the elimination tree. Improves
+ * supernode amalgamation. Does not affect fundamental nnz(L) and
+ * flop count. Default: TRUE. */
+
+ /* ---------------------------------------------------------------------- */
+ /* memory management routines */
+ /* ---------------------------------------------------------------------- */
+
+ void *(*malloc_memory) (size_t) ; /* pointer to malloc */
+ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */
+ void (*free_memory) (void *) ; /* pointer to free */
+ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */
+
+ /* ---------------------------------------------------------------------- */
+ /* routines for complex arithmetic */
+ /* ---------------------------------------------------------------------- */
+
+ int (*complex_divide) (double ax, double az, double bx, double bz,
+ double *cx, double *cz) ;
+
+ /* flag = complex_divide (ax, az, bx, bz, &cx, &cz) computes the complex
+ * division c = a/b, where ax and az hold the real and imaginary part
+ * of a, and b and c are stored similarly. flag is returned as 1 if
+ * a divide-by-zero occurs, or 0 otherwise. By default, the function
+ * pointer Common->complex_divide is set equal to cholmod_divcomplex.
+ */
+
+ double (*hypotenuse) (double x, double y) ;
+
+ /* s = hypotenuse (x,y) computes s = sqrt (x*x + y*y), but does so more
+ * accurately. By default, the function pointer Common->hypotenuse is
+ * set equal to cholmod_hypot. See also the hypot function in the C99
+ * standard, which has an identical syntax and function. If you have
+ * a C99-compliant compiler, you can set Common->hypotenuse = hypot. */
+
+ /* ---------------------------------------------------------------------- */
+ /* METIS workarounds */
+ /* ---------------------------------------------------------------------- */
+
+ double metis_memory ; /* This is a parameter for CHOLMOD's interface to
+ * METIS, not a parameter to METIS itself. METIS
+ * uses an amount of memory that is difficult to estimate precisely
+ * beforehand. If it runs out of memory, it terminates your program.
+ * All routines in CHOLMOD except for CHOLMOD's interface to METIS
+ * return an error status and safely return to your program if they run
+ * out of memory. To mitigate this problem, the CHOLMOD interface
+ * can allocate a single block of memory equal in size to an empirical
+ * upper bound of METIS's memory usage times the Common->metis_memory
+ * parameter, and then immediately free it. It then calls METIS. If
+ * this pre-allocation fails, it is possible that METIS will fail as
+ * well, and so CHOLMOD returns with an out-of-memory condition without
+ * calling METIS.
+ *
+ * METIS_NodeND (used in the CHOLMOD_METIS ordering option) with its
+ * default parameter settings typically uses about (4*nz+40n+4096)
+ * times sizeof(int) memory, where nz is equal to the number of entries
+ * in A for the symmetric case or AA' if an unsymmetric matrix is
+ * being ordered (where nz includes both the upper and lower parts
+ * of A or AA'). The observed "upper bound" (with 2 exceptions),
+ * measured in an instrumented copy of METIS 4.0.1 on thousands of
+ * matrices, is (10*nz+50*n+4096) * sizeof(int). Two large matrices
+ * exceeded this bound, one by almost a factor of 2 (Gupta/gupta2).
+ *
+ * If your program is terminated by METIS, try setting metis_memory to
+ * 2.0, or even higher if needed. By default, CHOLMOD assumes that METIS
+ * does not have this problem (so that CHOLMOD will work correctly when
+ * this issue is fixed in METIS). Thus, the default value is zero.
+ * This work-around is not guaranteed anyway.
+ *
+ * If a matrix exceeds this predicted memory usage, AMD is attempted
+ * instead. It, too, may run out of memory, but if it does so it will
+ * not terminate your program.
+ */
+
+ double metis_dswitch ; /* METIS_NodeND in METIS 4.0.1 gives a seg */
+ size_t metis_nswitch ; /* fault with one matrix of order n = 3005 and
+ * nz = 6,036,025. This is a very dense graph.
+ * The workaround is to use AMD instead of METIS for matrices of dimension
+ * greater than Common->metis_nswitch (default 3000) or more and with
+ * density of Common->metis_dswitch (default 0.66) or more.
+ * cholmod_nested_dissection has no problems with the same matrix, even
+ * though it uses METIS_NodeComputeSeparator on this matrix. If this
+ * seg fault does not affect you, set metis_nswitch to zero or less,
+ * and CHOLMOD will not switch to AMD based just on the density of the
+ * matrix (it will still switch to AMD if the metis_memory parameter
+ * causes the switch).
+ */
+
+ /* ---------------------------------------------------------------------- */
+ /* workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* CHOLMOD has several routines that take less time than the size of
+ * workspace they require. Allocating and initializing the workspace would
+ * dominate the run time, unless workspace is allocated and initialized
+ * just once. CHOLMOD allocates this space when needed, and holds it here
+ * between calls to CHOLMOD. cholmod_start sets these pointers to NULL
+ * (which is why it must be the first routine called in CHOLMOD).
+ * cholmod_finish frees the workspace (which is why it must be the last
+ * call to CHOLMOD).
+ */
+
+ size_t nrow ; /* size of Flag and Head */
+ UF_long mark ; /* mark value for Flag array */
+ size_t iworksize ; /* size of Iwork. Upper bound: 6*nrow+ncol */
+ size_t xworksize ; /* size of Xwork, in bytes.
+ * maxrank*nrow*sizeof(double) for update/downdate.
+ * 2*nrow*sizeof(double) otherwise */
+
+ /* initialized workspace: contents needed between calls to CHOLMOD */
+ void *Flag ; /* size nrow, an integer array. Kept cleared between
+ * calls to cholmod rouines (Flag [i] < mark) */
+
+ void *Head ; /* size nrow+1, an integer array. Kept cleared between
+ * calls to cholmod routines (Head [i] = EMPTY) */
+
+ void *Xwork ; /* a double array. Its size varies. It is nrow for
+ * most routines (cholmod_rowfac, cholmod_add,
+ * cholmod_aat, cholmod_norm, cholmod_ssmult) for the real case, twice
+ * that when the input matrices are complex or zomplex. It is of size
+ * 2*nrow for cholmod_rowadd and cholmod_rowdel. For cholmod_updown,
+ * its size is maxrank*nrow where maxrank is 2, 4, or 8. Kept cleared
+ * between calls to cholmod (set to zero). */
+
+ /* uninitialized workspace, contents not needed between calls to CHOLMOD */
+ void *Iwork ; /* size iworksize, 2*nrow+ncol for most routines,
+ * up to 6*nrow+ncol for cholmod_analyze. */
+
+ int itype ; /* If CHOLMOD_LONG, Flag, Head, and Iwork are UF_long.
+ * Otherwise all three arrays are int. */
+
+ int dtype ; /* double or float */
+
+ /* Common->itype and Common->dtype are used to define the types of all
+ * sparse matrices, triplet matrices, dense matrices, and factors
+ * created using this Common struct. The itypes and dtypes of all
+ * parameters to all CHOLMOD routines must match. */
+
+ int no_workspace_reallocate ; /* this is an internal flag, used as a
+ * precaution by cholmod_analyze. It is normally false. If true,
+ * cholmod_allocate_work is not allowed to reallocate any workspace;
+ * they must use the existing workspace in Common (Iwork, Flag, Head,
+ * and Xwork). Added for CHOLMOD v1.1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics */
+ /* ---------------------------------------------------------------------- */
+
+ /* fl and lnz are set only in cholmod_analyze and cholmod_rowcolcounts,
+ * in the Cholesky modudle. modfl is set only in the Modify module. */
+
+ int status ; /* error code */
+ double fl ; /* LL' flop count from most recent analysis */
+ double lnz ; /* fundamental nz in L */
+ double anz ; /* nonzeros in tril(A) if A is symmetric/lower,
+ * triu(A) if symmetric/upper, or tril(A*A') if
+ * unsymmetric, in last call to cholmod_analyze. */
+ double modfl ; /* flop count from most recent update/downdate/
+ * rowadd/rowdel (excluding flops to modify the
+ * solution to Lx=b, if computed) */
+ size_t malloc_count ; /* # of objects malloc'ed minus the # free'd*/
+ size_t memory_usage ; /* peak memory usage in bytes */
+ size_t memory_inuse ; /* current memory usage in bytes */
+
+ double nrealloc_col ; /* # of column reallocations */
+ double nrealloc_factor ;/* # of factor reallocations due to col. reallocs */
+ double ndbounds_hit ; /* # of times diagonal modified by dbound */
+
+ double rowfacfl ; /* # of flops in last call to cholmod_rowfac */
+ double aatfl ; /* # of flops to compute A(:,f)*A(:,f)' */
+
+ /* ---------------------------------------------------------------------- */
+ /* future expansion */
+ /* ---------------------------------------------------------------------- */
+
+ /* To allow CHOLMOD to be updated without recompiling the user application,
+ * additional space is set aside here for future statistics, parameters,
+ * and workspace. Note: additional entries were added in v1.1 to the
+ * method array, above, and thus v1.0 and v1.1 are not binary compatible.
+ *
+ * v1.1 to the current version are binary compatible.
+ */
+
+ double other1 [16] ;
+ UF_long other2 [16] ;
+ int other3 [13] ; /* reduced from size 16 in v1.1. */
+
+ int prefer_binary ; /* cholmod_read_triplet converts a symmetric
+ * pattern-only matrix into a real matrix. If
+ * prefer_binary is FALSE, the diagonal entries are set to 1 + the degree
+ * of the row/column, and off-diagonal entries are set to -1 (resulting
+ * in a positive definite matrix if the diagonal is zero-free). Most
+ * symmetric patterns are the pattern a positive definite matrix. If
+ * this parameter is TRUE, then the matrix is returned with a 1 in each
+ * entry, instead. Default: FALSE. Added in v1.3. */
+
+ /* control parameter (added for v1.2): */
+ int default_nesdis ; /* Default: FALSE. If FALSE, then the default
+ * ordering strategy (when Common->nmethods == 0)
+ * is to try the given ordering (if present), AMD, and then METIS if AMD
+ * reports high fill-in. If Common->default_nesdis is TRUE then NESDIS
+ * is used instead in the default strategy. */
+
+ /* statistic (added for v1.2): */
+ int called_nd ; /* TRUE if the last call to
+ * cholmod_analyze called NESDIS or METIS. */
+
+ size_t other4 [16] ;
+ void *other5 [16] ;
+
+} cholmod_common ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_start: first call to CHOLMOD */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_start
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_start (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_finish: last call to CHOLMOD */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_finish
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_finish (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_defaults: restore default parameters */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_defaults
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_defaults (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_maxrank: return valid maximum rank for update/downdate */
+/* -------------------------------------------------------------------------- */
+
+size_t cholmod_maxrank /* returns validated value of Common->maxrank */
+(
+ /* ---- input ---- */
+ size_t n, /* A and L will have n rows */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+size_t cholmod_l_maxrank (size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_work: allocate workspace in Common */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_allocate_work
+(
+ /* ---- input ---- */
+ size_t nrow, /* size: Common->Flag (nrow), Common->Head (nrow+1) */
+ size_t iworksize, /* size of Common->Iwork */
+ size_t xworksize, /* size of Common->Xwork */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_allocate_work (size_t, size_t, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_work: free workspace in Common */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_work
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_work (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_clear_flag: clear Flag workspace in Common */
+/* -------------------------------------------------------------------------- */
+
+UF_long cholmod_clear_flag
+(
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_clear_flag (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_error: called when CHOLMOD encounters an error */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_error
+(
+ /* ---- input ---- */
+ int status, /* error status */
+ char *file, /* name of source code file where error occured */
+ int line, /* line number in source code file where error occured*/
+ char *message, /* error message */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_error (int, char *, int, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_dbound: for internal use in CHOLMOD only */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_dbound /* returns modified diagonal entry of D or L */
+(
+ /* ---- input ---- */
+ double dj, /* diagonal entry of D for LDL' or L for LL' */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_dbound (double, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_hypot: compute sqrt (x*x + y*y) accurately */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_hypot
+(
+ /* ---- input ---- */
+ double x, double y
+) ;
+
+double cholmod_l_hypot (double, double) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_divcomplex: complex division, c = a/b */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_divcomplex /* return 1 if divide-by-zero, 0 otherise */
+(
+ /* ---- input ---- */
+ double ar, double ai, /* real and imaginary parts of a */
+ double br, double bi, /* real and imaginary parts of b */
+ /* ---- output --- */
+ double *cr, double *ci /* real and imaginary parts of c */
+) ;
+
+int cholmod_l_divcomplex (double, double, double, double, double *, double *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_sparse ================================================== */
+/* ========================================================================== */
+
+/* A sparse matrix stored in compressed-column form. */
+
+typedef struct cholmod_sparse_struct
+{
+ size_t nrow ; /* the matrix is nrow-by-ncol */
+ size_t ncol ;
+ size_t nzmax ; /* maximum number of entries in the matrix */
+
+ /* pointers to int or UF_long: */
+ void *p ; /* p [0..ncol], the column pointers */
+ void *i ; /* i [0..nzmax-1], the row indices */
+
+ /* for unpacked matrices only: */
+ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each col. In
+ * packed form, the nonzero pattern of column j is in
+ * A->i [A->p [j] ... A->p [j+1]-1]. In unpacked form, column j is in
+ * A->i [A->p [j] ... A->p [j]+A->nz[j]-1] instead. In both cases, the
+ * numerical values (if present) are in the corresponding locations in
+ * the array x (or z if A->xtype is CHOLMOD_ZOMPLEX). */
+
+ /* pointers to double or float: */
+ void *x ; /* size nzmax or 2*nzmax, if present */
+ void *z ; /* size nzmax, if present */
+
+ int stype ; /* Describes what parts of the matrix are considered:
+ *
+ * 0: matrix is "unsymmetric": use both upper and lower triangular parts
+ * (the matrix may actually be symmetric in pattern and value, but
+ * both parts are explicitly stored and used). May be square or
+ * rectangular.
+ * >0: matrix is square and symmetric, use upper triangular part.
+ * Entries in the lower triangular part are ignored.
+ * <0: matrix is square and symmetric, use lower triangular part.
+ * Entries in the upper triangular part are ignored.
+ *
+ * Note that stype>0 and stype<0 are different for cholmod_sparse and
+ * cholmod_triplet. See the cholmod_triplet data structure for more
+ * details.
+ */
+
+ int itype ; /* CHOLMOD_INT: p, i, and nz are int.
+ * CHOLMOD_INTLONG: p is UF_long, i and nz are int.
+ * CHOLMOD_LONG: p, i, and nz are UF_long. */
+
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z are double or float */
+ int sorted ; /* TRUE if columns are sorted, FALSE otherwise */
+ int packed ; /* TRUE if packed (nz ignored), FALSE if unpacked
+ * (nz is required) */
+
+} cholmod_sparse ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_sparse: allocate a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_allocate_sparse
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */
+ int packed, /* TRUE if A will be packed, FALSE otherwise */
+ int stype, /* stype of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_allocate_sparse (size_t, size_t, size_t, int, int,
+ int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_sparse: free a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_sparse
+(
+ /* ---- in/out --- */
+ cholmod_sparse **A, /* matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_sparse (cholmod_sparse **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_sparse: change the size (# entries) of sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_sparse
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in A */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to reallocate */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_sparse ( size_t, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_nnz: return number of nonzeros in a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+UF_long cholmod_nnz
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_nnz (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_speye: sparse identity matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_speye
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_speye (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_spzeros: sparse zero matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_spzeros
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_spzeros (size_t, size_t, size_t, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_transpose: transpose a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Return A' or A.' The "values" parameter is 0, 1, or 2 to denote the pattern
+ * transpose, the array transpose (A.'), and the complex conjugate transpose
+ * (A').
+ */
+
+cholmod_sparse *cholmod_transpose
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_transpose (cholmod_sparse *, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_transpose_unsym: transpose an unsymmetric sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
+ * already allocated. See cholmod_transpose for a simpler routine. */
+
+int cholmod_transpose_unsym
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ int *Perm, /* size nrow, if present (can be NULL) */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_transpose_unsym (cholmod_sparse *, int, UF_long *, UF_long *,
+ size_t, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_transpose_sym: transpose a symmetric sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
+ * See cholmod_transpose for a simpler routine. */
+
+int cholmod_transpose_sym
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ int *Perm, /* size nrow, if present (can be NULL) */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A' or A(p,p)' */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_transpose_sym (cholmod_sparse *, int, UF_long *, cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ptranspose: transpose a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if
+ * A is unsymmetric. */
+
+cholmod_sparse *cholmod_ptranspose
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_ptranspose (cholmod_sparse *, int, UF_long *,
+ UF_long *, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sort: sort row indices in each column of sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_sort
+(
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to sort */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_sort (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_band: C = tril (triu (A,k1), k2) */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_band
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to extract band matrix from */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_band (cholmod_sparse *, UF_long, UF_long, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_band_inplace: A = tril (triu (A,k1), k2) */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_band_inplace
+(
+ /* ---- input ---- */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix from which entries not in band are removed */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_band_inplace (UF_long, UF_long, int, cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_aat: C = A*A' or A(:,f)*A(:,f)' */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_aat
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag),
+ * -2: pattern only, no diagonal, add 50%+n extra
+ * space to C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_aat (cholmod_sparse *, UF_long *, size_t, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_sparse: C = A, create an exact copy of a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_copy_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_copy_sparse (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy: C = A, with possible change of stype */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_copy
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ int stype, /* requested stype of C */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_copy (cholmod_sparse *, int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_add: C = alpha*A + beta*B */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_add
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to add */
+ cholmod_sparse *B, /* matrix to add */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for B */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE, sort columns of C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_add (cholmod_sparse *, cholmod_sparse *, double *,
+ double *, int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sparse_xtype: change the xtype of a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_sparse_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (pattern, real, complex, zomplex) */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* sparse matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_sparse_xtype (int, cholmod_sparse *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_factor ================================================== */
+/* ========================================================================== */
+
+/* A symbolic and numeric factorization, either simplicial or supernodal.
+ * In all cases, the row indices in the columns of L are kept sorted. */
+
+typedef struct cholmod_factor_struct
+{
+ /* ---------------------------------------------------------------------- */
+ /* for both simplicial and supernodal factorizations */
+ /* ---------------------------------------------------------------------- */
+
+ size_t n ; /* L is n-by-n */
+
+ size_t minor ; /* If the factorization failed, L->minor is the column
+ * at which it failed (in the range 0 to n-1). A value
+ * of n means the factorization was successful or
+ * the matrix has not yet been factorized. */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic ordering and analysis */
+ /* ---------------------------------------------------------------------- */
+
+ void *Perm ; /* size n, permutation used */
+ void *ColCount ; /* size n, column counts for simplicial L */
+
+ /* ---------------------------------------------------------------------- */
+ /* simplicial factorization */
+ /* ---------------------------------------------------------------------- */
+
+ size_t nzmax ; /* size of i and x */
+
+ void *p ; /* p [0..ncol], the column pointers */
+ void *i ; /* i [0..nzmax-1], the row indices */
+ void *x ; /* x [0..nzmax-1], the numerical values */
+ void *z ;
+ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each column.
+ * i [p [j] ... p [j]+nz[j]-1] contains the row indices,
+ * and the numerical values are in the same locatins
+ * in x. The value of i [p [k]] is always k. */
+
+ void *next ; /* size ncol+2. next [j] is the next column in i/x */
+ void *prev ; /* size ncol+2. prev [j] is the prior column in i/x.
+ * head of the list is ncol+1, and the tail is ncol. */
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L->x is shared with the simplicial data structure. L->x has
+ * size L->nzmax for a simplicial factor, and size L->xsize for a supernodal
+ * factor. */
+
+ size_t nsuper ; /* number of supernodes */
+ size_t ssize ; /* size of s, integer part of supernodes */
+ size_t xsize ; /* size of x, real part of supernodes */
+ size_t maxcsize ; /* size of largest update matrix */
+ size_t maxesize ; /* max # of rows in supernodes, excl. triangular part */
+
+ void *super ; /* size nsuper+1, first col in each supernode */
+ void *pi ; /* size nsuper+1, pointers to integer patterns */
+ void *px ; /* size nsuper+1, pointers to real parts */
+ void *s ; /* size ssize, integer part of supernodes */
+
+ /* ---------------------------------------------------------------------- */
+ /* factorization type */
+ /* ---------------------------------------------------------------------- */
+
+ int ordering ; /* ordering method used */
+
+ int is_ll ; /* TRUE if LL', FALSE if LDL' */
+ int is_super ; /* TRUE if supernodal, FALSE if simplicial */
+ int is_monotonic ; /* TRUE if columns of L appear in order 0..n-1.
+ * Only applicable to simplicial numeric types. */
+
+ /* There are 8 types of factor objects that cholmod_factor can represent
+ * (only 6 are used):
+ *
+ * Numeric types (xtype is not CHOLMOD_PATTERN)
+ * --------------------------------------------
+ *
+ * simplicial LDL': (is_ll FALSE, is_super FALSE). Stored in compressed
+ * column form, using the simplicial components above (nzmax, p, i,
+ * x, z, nz, next, and prev). The unit diagonal of L is not stored,
+ * and D is stored in its place. There are no supernodes.
+ *
+ * simplicial LL': (is_ll TRUE, is_super FALSE). Uses the same storage
+ * scheme as the simplicial LDL', except that D does not appear.
+ * The first entry of each column of L is the diagonal entry of
+ * that column of L.
+ *
+ * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used.
+ * FUTURE WORK: add support for supernodal LDL'
+ *
+ * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal factor,
+ * using the supernodal components described above (nsuper, ssize,
+ * xsize, maxcsize, maxesize, super, pi, px, s, x, and z).
+ *
+ *
+ * Symbolic types (xtype is CHOLMOD_PATTERN)
+ * -----------------------------------------
+ *
+ * simplicial LDL': (is_ll FALSE, is_super FALSE). Nothing is present
+ * except Perm and ColCount.
+ *
+ * simplicial LL': (is_ll TRUE, is_super FALSE). Identical to the
+ * simplicial LDL', except for the is_ll flag.
+ *
+ * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used.
+ * FUTURE WORK: add support for supernodal LDL'
+ *
+ * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal symbolic
+ * factorization. The simplicial symbolic information is present
+ * (Perm and ColCount), as is all of the supernodal factorization
+ * except for the numerical values (x and z).
+ */
+
+ int itype ; /* The integer arrays are Perm, ColCount, p, i, nz,
+ * next, prev, super, pi, px, and s. If itype is
+ * CHOLMOD_INT, all of these are int arrays.
+ * CHOLMOD_INTLONG: p, pi, px are UF_long, others int.
+ * CHOLMOD_LONG: all integer arrays are UF_long. */
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z double or float */
+
+} cholmod_factor ;
+
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_factor: allocate a factor (symbolic LL' or LDL') */
+/* -------------------------------------------------------------------------- */
+
+cholmod_factor *cholmod_allocate_factor
+(
+ /* ---- input ---- */
+ size_t n, /* L is n-by-n */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_allocate_factor (size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_factor: free a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_factor
+(
+ /* ---- in/out --- */
+ cholmod_factor **L, /* factor to free, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_factor (cholmod_factor **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_factor: change the # entries in a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_factor
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_factor (size_t, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_change_factor: change the type of factor (e.g., LDL' to LL') */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_change_factor
+(
+ /* ---- input ---- */
+ int to_xtype, /* to CHOLMOD_PATTERN, _REAL, _COMPLEX, _ZOMPLEX */
+ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */
+ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */
+ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */
+ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_change_factor ( int, int, int, int, int, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_pack_factor: pack the columns of a factor */
+/* -------------------------------------------------------------------------- */
+
+/* Pack the columns of a simplicial factor. Unlike cholmod_change_factor,
+ * it can pack the columns of a factor even if they are not stored in their
+ * natural order (non-monotonic). */
+
+int cholmod_pack_factor
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_pack_factor (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_column: resize a single column of a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_column
+(
+ /* ---- input ---- */
+ size_t j, /* the column to reallocate */
+ size_t need, /* required size of column j */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_column (size_t, size_t, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factor_to_sparse: create a sparse matrix copy of a factor */
+/* -------------------------------------------------------------------------- */
+
+/* Only operates on numeric factors, not symbolic ones */
+
+cholmod_sparse *cholmod_factor_to_sparse
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to copy, converted to symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_factor_to_sparse (cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_factor: create a copy of a factor */
+/* -------------------------------------------------------------------------- */
+
+cholmod_factor *cholmod_copy_factor
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_copy_factor (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factor_xtype: change the xtype of a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_factor_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (real, complex, or zomplex) */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_factor_xtype (int, cholmod_factor *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_dense =================================================== */
+/* ========================================================================== */
+
+/* A dense matrix in column-oriented form. It has no itype since it contains
+ * no integers. Entry in row i and column j is located in x [i+j*d].
+ */
+
+typedef struct cholmod_dense_struct
+{
+ size_t nrow ; /* the matrix is nrow-by-ncol */
+ size_t ncol ;
+ size_t nzmax ; /* maximum number of entries in the matrix */
+ size_t d ; /* leading dimension (d >= nrow must hold) */
+ void *x ; /* size nzmax or 2*nzmax, if present */
+ void *z ; /* size nzmax, if present */
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z double or float */
+
+} cholmod_dense ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_dense: allocate a dense matrix (contents uninitialized) */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_allocate_dense
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ size_t d, /* leading dimension */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_allocate_dense (size_t, size_t, size_t, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_zeros: allocate a dense matrix and set it to zero */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_zeros
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_zeros (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ones: allocate a dense matrix and set it to all ones */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_ones
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_ones (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_eye: allocate a dense matrix and set it to the identity matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_eye
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_eye (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_dense: free a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_dense
+(
+ /* ---- in/out --- */
+ cholmod_dense **X, /* dense matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_dense (cholmod_dense **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sparse_to_dense: create a dense matrix copy of a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_sparse_to_dense
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_sparse_to_dense (cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_dense_to_sparse: create a sparse matrix copy of a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_dense_to_sparse
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ int values, /* TRUE if values to be copied, FALSE otherwise */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_dense_to_sparse (cholmod_dense *, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_dense: create a copy of a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_copy_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_copy_dense (cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_dense2: copy a dense matrix (pre-allocated) */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_copy_dense2
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* ---- output --- */
+ cholmod_dense *Y, /* copy of matrix X */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_copy_dense2 (cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_dense_xtype: change the xtype of a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_dense_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (real, complex,or zomplex) */
+ /* ---- in/out --- */
+ cholmod_dense *X, /* dense matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_dense_xtype (int, cholmod_dense *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_triplet ================================================= */
+/* ========================================================================== */
+
+/* A sparse matrix stored in triplet form. */
+
+typedef struct cholmod_triplet_struct
+{
+ size_t nrow ; /* the matrix is nrow-by-ncol */
+ size_t ncol ;
+ size_t nzmax ; /* maximum number of entries in the matrix */
+ size_t nnz ; /* number of nonzeros in the matrix */
+
+ void *i ; /* i [0..nzmax-1], the row indices */
+ void *j ; /* j [0..nzmax-1], the column indices */
+ void *x ; /* size nzmax or 2*nzmax, if present */
+ void *z ; /* size nzmax, if present */
+
+ int stype ; /* Describes what parts of the matrix are considered:
+ *
+ * 0: matrix is "unsymmetric": use both upper and lower triangular parts
+ * (the matrix may actually be symmetric in pattern and value, but
+ * both parts are explicitly stored and used). May be square or
+ * rectangular.
+ * >0: matrix is square and symmetric. Entries in the lower triangular
+ * part are transposed and added to the upper triangular part when
+ * the matrix is converted to cholmod_sparse form.
+ * <0: matrix is square and symmetric. Entries in the upper triangular
+ * part are transposed and added to the lower triangular part when
+ * the matrix is converted to cholmod_sparse form.
+ *
+ * Note that stype>0 and stype<0 are different for cholmod_sparse and
+ * cholmod_triplet. The reason is simple. You can permute a symmetric
+ * triplet matrix by simply replacing a row and column index with their
+ * new row and column indices, via an inverse permutation. Suppose
+ * P = L->Perm is your permutation, and Pinv is an array of size n.
+ * Suppose a symmetric matrix A is represent by a triplet matrix T, with
+ * entries only in the upper triangular part. Then the following code:
+ *
+ * Ti = T->i ;
+ * Tj = T->j ;
+ * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ;
+ * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ;
+ * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ;
+ *
+ * creates the triplet form of C=P*A*P'. However, if T initially
+ * contains just the upper triangular entries (T->stype = 1), after
+ * permutation it has entries in both the upper and lower triangular
+ * parts. These entries should be transposed when constructing the
+ * cholmod_sparse form of A, which is what cholmod_triplet_to_sparse
+ * does. Thus:
+ *
+ * C = cholmod_triplet_to_sparse (T, 0, &Common) ;
+ *
+ * will return the matrix C = P*A*P'.
+ *
+ * Since the triplet matrix T is so simple to generate, it's quite easy
+ * to remove entries that you do not want, prior to converting T to the
+ * cholmod_sparse form. So if you include these entries in T, CHOLMOD
+ * assumes that there must be a reason (such as the one above). Thus,
+ * no entry in a triplet matrix is ever ignored.
+ */
+
+ int itype ; /* CHOLMOD_LONG: i and j are UF_long. Otherwise int. */
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z are double or float */
+
+} cholmod_triplet ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_triplet: allocate a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_allocate_triplet
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of T */
+ size_t ncol, /* # of columns of T */
+ size_t nzmax, /* max # of nonzeros of T */
+ int stype, /* stype of T */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_allocate_triplet (size_t, size_t, size_t, int, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_triplet: free a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_triplet
+(
+ /* ---- in/out --- */
+ cholmod_triplet **T, /* triplet matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_triplet (cholmod_triplet **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_triplet: change the # of entries in a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_triplet
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in T */
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_triplet (size_t, cholmod_triplet *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sparse_to_triplet: create a triplet matrix copy of a sparse matrix*/
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_sparse_to_triplet
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_sparse_to_triplet (cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_triplet_to_sparse: create a sparse matrix copy of a triplet matrix*/
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_triplet_to_sparse
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ size_t nzmax, /* allocate at least this much space in output matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_triplet_to_sparse (cholmod_triplet *, size_t,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_triplet: create a copy of a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_copy_triplet
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_copy_triplet (cholmod_triplet *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_triplet_xtype: change the xtype of a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_triplet_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (pattern, real, complex,or zomplex)*/
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_triplet_xtype (int, cholmod_triplet *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_memory ================================================== */
+/* ========================================================================== */
+
+/* The user may make use of these, just like malloc and free. You can even
+ * malloc an object and safely free it with cholmod_free, and visa versa
+ * (except that the memory usage statistics will be corrupted). These routines
+ * do differ from malloc and free. If cholmod_free is given a NULL pointer,
+ * for example, it does nothing (unlike the ANSI free). cholmod_realloc does
+ * not return NULL if given a non-NULL pointer and a nonzero size, even if it
+ * fails (it returns the original pointer and sets an error code in
+ * Common->status instead).
+ *
+ * CHOLMOD keeps track of the amount of memory it has allocated, and so the
+ * cholmod_free routine also takes the size of the object being freed. This
+ * is only used for statistics. If you, the user of CHOLMOD, pass the wrong
+ * size, the only consequence is that the memory usage statistics will be
+ * corrupted.
+ */
+
+void *cholmod_malloc /* returns pointer to the newly malloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_malloc (size_t, size_t, cholmod_common *) ;
+
+void *cholmod_calloc /* returns pointer to the newly calloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_calloc (size_t, size_t, cholmod_common *) ;
+
+void *cholmod_free /* always returns NULL */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to free */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_free (size_t, size_t, void *, cholmod_common *) ;
+
+void *cholmod_realloc /* returns pointer to reallocated block */
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated block */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to realloc */
+ size_t *n, /* current size on input, nnew on output if successful*/
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_realloc (size_t, size_t, void *, size_t *, cholmod_common *) ;
+
+int cholmod_realloc_multiple
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated blocks */
+ int nint, /* number of int/UF_long blocks */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* ---- in/out --- */
+ void **I, /* int or UF_long block */
+ void **J, /* int or UF_long block */
+ void **X, /* complex, double, or float block */
+ void **Z, /* zomplex case only: double or float block */
+ size_t *n, /* current size of the I,J,X,Z blocks on input,
+ * nnew on output if successful */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_realloc_multiple (size_t, int, int, void **, void **, void **,
+ void **, size_t *, cholmod_common *) ;
+
+/* ========================================================================== */
+/* === symmetry types ======================================================= */
+/* ========================================================================== */
+
+#define CHOLMOD_MM_RECTANGULAR 1
+#define CHOLMOD_MM_UNSYMMETRIC 2
+#define CHOLMOD_MM_SYMMETRIC 3
+#define CHOLMOD_MM_HERMITIAN 4
+#define CHOLMOD_MM_SKEW_SYMMETRIC 5
+#define CHOLMOD_MM_SYMMETRIC_POSDIAG 6
+#define CHOLMOD_MM_HERMITIAN_POSDIAG 7
+
+/* ========================================================================== */
+/* === Numerical relop macros =============================================== */
+/* ========================================================================== */
+
+/* These macros correctly handle the NaN case.
+ *
+ * CHOLMOD_IS_NAN(x):
+ * True if x is NaN. False otherwise. The commonly-existing isnan(x)
+ * function could be used, but it's not in Kernighan & Ritchie 2nd edition
+ * (ANSI C89). It may appear in <math.h>, but I'm not certain about
+ * portability. The expression x != x is true if and only if x is NaN,
+ * according to the IEEE 754 floating-point standard.
+ *
+ * CHOLMOD_IS_ZERO(x):
+ * True if x is zero. False if x is nonzero, NaN, or +/- Inf.
+ * This is (x == 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_NONZERO(x):
+ * True if x is nonzero, NaN, or +/- Inf. False if x zero.
+ * This is (x != 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_LT_ZERO(x):
+ * True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf.
+ * This is (x < 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_GT_ZERO(x):
+ * True if x is > zero or +Inf. False if x is <= 0, NaN, or -Inf.
+ * This is (x > 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_LE_ZERO(x):
+ * True if x is <= zero or -Inf. False if x is > 0, NaN, or +Inf.
+ * This is (x <= 0) if the compiler is IEEE 754 compliant.
+ */
+
+#ifdef CHOLMOD_WINDOWS
+
+/* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */
+/* violates the IEEE 754 floating-point standard in a bizarre way. */
+/* If you're using an IEEE 754-compliant compiler, then x != x is true */
+/* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */
+/* So either way, this macro safely detects a NaN. */
+#define CHOLMOD_IS_NAN(x) (((x) != (x)) || (((x) < (x))))
+#define CHOLMOD_IS_ZERO(x) (((x) == 0.) && !CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_NONZERO(x) (((x) != 0.) || CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_LT_ZERO(x) (((x) < 0.) && !CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_GT_ZERO(x) (((x) > 0.) && !CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_LE_ZERO(x) (((x) <= 0.) && !CHOLMOD_IS_NAN(x))
+
+#else
+
+/* These all work properly, according to the IEEE 754 standard ... except on */
+/* a PC with windows. Works fine in Linux on the same PC... */
+#define CHOLMOD_IS_NAN(x) ((x) != (x))
+#define CHOLMOD_IS_ZERO(x) ((x) == 0.)
+#define CHOLMOD_IS_NONZERO(x) ((x) != 0.)
+#define CHOLMOD_IS_LT_ZERO(x) ((x) < 0.)
+#define CHOLMOD_IS_GT_ZERO(x) ((x) > 0.)
+#define CHOLMOD_IS_LE_ZERO(x) ((x) <= 0.)
+
+#endif
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_internal.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_internal.h
new file mode 100644
index 0000000..0cabd5a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_internal.h
@@ -0,0 +1,385 @@
+/* ========================================================================== */
+/* === Include/cholmod_internal.h =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_internal.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_internal.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD internal include file.
+ *
+ * This file contains internal definitions for CHOLMOD, not meant to be included
+ * in user code. They define macros that are not prefixed with CHOLMOD_. This
+ * file can safely #include'd in user code if you want to make use of the
+ * macros defined here, and don't mind the possible name conflicts with your
+ * code, however.
+ *
+ * Required by all CHOLMOD routines. Not required by any user routine that
+ * uses CHOLMOMD. Unless debugging is enabled, this file does not require any
+ * CHOLMOD module (not even the Core module).
+ *
+ * If debugging is enabled, all CHOLMOD modules require the Check module.
+ * Enabling debugging requires that this file be editted. Debugging cannot be
+ * enabled with a compiler flag. This is because CHOLMOD is exceedingly slow
+ * when debugging is enabled. Debugging is meant for development of CHOLMOD
+ * itself, not by users of CHOLMOD.
+ */
+
+#ifndef CHOLMOD_INTERNAL_H
+#define CHOLMOD_INTERNAL_H
+
+/* ========================================================================== */
+/* === large file I/O ======================================================= */
+/* ========================================================================== */
+
+/* Definitions for large file I/O must come before any other #includes. If
+ * this causes problems (may not be portable to all platforms), then compile
+ * CHOLMOD with -DNLARGEFILE. You must do this for MATLAB 6.5 and earlier,
+ * for example. */
+
+#include "cholmod_io64.h"
+
+/* ========================================================================== */
+/* === debugging and basic includes ========================================= */
+/* ========================================================================== */
+
+/* turn off debugging */
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/* Uncomment this line to enable debugging. CHOLMOD will be very slow.
+#undef NDEBUG
+ */
+
+#if !defined(NPRINT) || !defined(NDEBUG)
+#include <stdio.h>
+#endif
+
+#include <stddef.h>
+#include <math.h>
+#include <limits.h>
+#include <float.h>
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === basic definitions ==================================================== */
+/* ========================================================================== */
+
+/* Some non-conforming compilers insist on defining TRUE and FALSE. */
+#undef TRUE
+#undef FALSE
+#define TRUE 1
+#define FALSE 0
+#define BOOLEAN(x) ((x) ? TRUE : FALSE)
+
+/* NULL should already be defined, but ensure it is here. */
+#ifndef NULL
+#define NULL ((void *) 0)
+#endif
+
+/* FLIP is a "negation about -1", and is used to mark an integer i that is
+ * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY
+ * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i
+ * for all integers i. UNFLIP (i) is >= EMPTY. */
+#define EMPTY (-1)
+#define FLIP(i) (-(i)-2)
+#define UNFLIP(i) (((i) < EMPTY) ? FLIP (i) : (i))
+
+/* MAX and MIN are not safe to use for NaN's */
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MAX3(a,b,c) (((a) > (b)) ? (MAX (a,c)) : (MAX (b,c)))
+#define MAX4(a,b,c,d) (((a) > (b)) ? (MAX3 (a,c,d)) : (MAX3 (b,c,d)))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define IMPLIES(p,q) (!(p) || (q))
+
+/* find the sign: -1 if x < 0, 1 if x > 0, zero otherwise.
+ * Not safe for NaN's */
+#define SIGN(x) (((x) < 0) ? (-1) : (((x) > 0) ? 1 : 0))
+
+/* round up an integer x to a multiple of s */
+#define ROUNDUP(x,s) ((s) * (((x) + ((s) - 1)) / (s)))
+
+#define ERROR(status,msg) \
+ CHOLMOD(error) (status, __FILE__, __LINE__, msg, Common)
+
+/* Check a pointer and return if null. Set status to invalid, unless the
+ * status is already "out of memory" */
+#define RETURN_IF_NULL(A,result) \
+{ \
+ if ((A) == NULL) \
+ { \
+ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \
+ { \
+ ERROR (CHOLMOD_INVALID, "argument missing") ; \
+ } \
+ return (result) ; \
+ } \
+}
+
+/* Return if Common is NULL or invalid */
+#define RETURN_IF_NULL_COMMON(result) \
+{ \
+ if (Common == NULL) \
+ { \
+ return (result) ; \
+ } \
+ if (Common->itype != ITYPE || Common->dtype != DTYPE) \
+ { \
+ Common->status = CHOLMOD_INVALID ; \
+ return (result) ; \
+ } \
+}
+
+#define IS_NAN(x) CHOLMOD_IS_NAN(x)
+#define IS_ZERO(x) CHOLMOD_IS_ZERO(x)
+#define IS_NONZERO(x) CHOLMOD_IS_NONZERO(x)
+#define IS_LT_ZERO(x) CHOLMOD_IS_LT_ZERO(x)
+#define IS_GT_ZERO(x) CHOLMOD_IS_GT_ZERO(x)
+#define IS_LE_ZERO(x) CHOLMOD_IS_LE_ZERO(x)
+
+/* 1e308 is a huge number that doesn't take many characters to print in a
+ * file, in CHOLMOD/Check/cholmod_read and _write. Numbers larger than this
+ * are interpretted as Inf, since sscanf doesn't read in Inf's properly.
+ * This assumes IEEE double precision arithmetic. DBL_MAX would be a little
+ * better, except that it takes too many digits to print in a file. */
+#define HUGE_DOUBLE 1e308
+
+/* ========================================================================== */
+/* === int/UF_long and double/float definitions ============================= */
+/* ========================================================================== */
+
+/* CHOLMOD is designed for 3 types of integer variables:
+ *
+ * (1) all integers are int
+ * (2) most integers are int, some are UF_long
+ * (3) all integers are UF_long
+ *
+ * and two kinds of floating-point values:
+ *
+ * (1) double
+ * (2) float
+ *
+ * the complex types (ANSI-compatible complex, and MATLAB-compatable zomplex)
+ * are based on the double or float type, and are not selected here. They
+ * are typically selected via template routines.
+ *
+ * This gives 6 different modes in which CHOLMOD can be compiled (only the
+ * first two are currently supported):
+ *
+ * DINT double, int prefix: cholmod_
+ * DLONG double, UF_long prefix: cholmod_l_
+ * DMIX double, mixed int/UF_long prefix: cholmod_m_
+ * SINT float, int prefix: cholmod_si_
+ * SLONG float, UF_long prefix: cholmod_sl_
+ * SMIX float, mixed int/log prefix: cholmod_sm_
+ *
+ * These are selected with compile time flags (-DDLONG, for example). If no
+ * flag is selected, the default is DINT.
+ *
+ * All six versions use the same include files. The user-visible include files
+ * are completely independent of which int/UF_long/double/float version is being
+ * used. The integer / real types in all data structures (sparse, triplet,
+ * dense, common, and triplet) are defined at run-time, not compile-time, so
+ * there is only one "cholmod_sparse" data type. Void pointers are used inside
+ * that data structure to point to arrays of the proper type. Each data
+ * structure has an itype and dtype field which determines the kind of basic
+ * types used. These are defined in Include/cholmod_core.h.
+ *
+ * FUTURE WORK: support all six types (float, and mixed int/UF_long)
+ *
+ * UF_long is normally defined as long. However, for WIN64 it is __int64.
+ * It can also be redefined for other platforms, by modifying UFconfig.h.
+ */
+
+#include "UFconfig.h"
+
+/* -------------------------------------------------------------------------- */
+/* Size_max: the largest value of size_t */
+/* -------------------------------------------------------------------------- */
+
+#define Size_max ((size_t) (-1))
+
+/* routines for doing arithmetic on size_t, and checking for overflow */
+size_t cholmod_add_size_t (size_t a, size_t b, int *ok) ;
+size_t cholmod_mult_size_t (size_t a, size_t k, int *ok) ;
+size_t cholmod_l_add_size_t (size_t a, size_t b, int *ok) ;
+size_t cholmod_l_mult_size_t (size_t a, size_t k, int *ok) ;
+
+/* -------------------------------------------------------------------------- */
+/* double, UF_long */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DLONG
+#define Real double
+#define Int UF_long
+#define Int_max UF_long_max
+#define CHOLMOD(name) cholmod_l_ ## name
+#define LONG
+#define DOUBLE
+#define ITYPE CHOLMOD_LONG
+#define DTYPE CHOLMOD_DOUBLE
+#define ID UF_long_id
+
+/* -------------------------------------------------------------------------- */
+/* double, int/UF_long */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (DMIX)
+#error "mixed int/UF_long not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* single, int */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (SINT)
+#error "single-precision not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* single, UF_long */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (SLONG)
+#error "single-precision not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* single, int/UF_long */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (SMIX)
+#error "single-precision not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* double, int: this is the default */
+/* -------------------------------------------------------------------------- */
+
+#else
+
+#ifndef DINT
+#define DINT
+#endif
+#define INT
+#define DOUBLE
+
+#define Real double
+#define Int int
+#define Int_max INT_MAX
+#define CHOLMOD(name) cholmod_ ## name
+#define ITYPE CHOLMOD_INT
+#define DTYPE CHOLMOD_DOUBLE
+#define ID "%d"
+
+#endif
+
+
+/* ========================================================================== */
+/* === real/complex arithmetic ============================================== */
+/* ========================================================================== */
+
+#include "cholmod_complexity.h"
+
+/* ========================================================================== */
+/* === Architecture and BLAS ================================================ */
+/* ========================================================================== */
+
+#include "cholmod_blas.h"
+
+/* ========================================================================== */
+/* === debugging definitions ================================================ */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+#include <assert.h>
+#include "cholmod.h"
+
+/* The cholmod_dump routines are in the Check module. No CHOLMOD routine
+ * calls the cholmod_check_* or cholmod_print_* routines in the Check module,
+ * since they use Common workspace that may already be in use. Instead, they
+ * use the cholmod_dump_* routines defined there, which allocate their own
+ * workspace if they need it. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+/* double, int */
+EXTERN int cholmod_dump ;
+EXTERN int cholmod_dump_malloc ;
+UF_long cholmod_dump_sparse (cholmod_sparse *, char *, cholmod_common *) ;
+int cholmod_dump_factor (cholmod_factor *, char *, cholmod_common *) ;
+int cholmod_dump_triplet (cholmod_triplet *, char *, cholmod_common *) ;
+int cholmod_dump_dense (cholmod_dense *, char *, cholmod_common *) ;
+int cholmod_dump_subset (int *, size_t, size_t, char *, cholmod_common *) ;
+int cholmod_dump_perm (int *, size_t, size_t, char *, cholmod_common *) ;
+int cholmod_dump_parent (int *, size_t, char *, cholmod_common *) ;
+void cholmod_dump_init (char *, cholmod_common *) ;
+int cholmod_dump_mem (char *, UF_long, cholmod_common *) ;
+void cholmod_dump_real (char *, Real *, UF_long, UF_long, int, int,
+ cholmod_common *) ;
+void cholmod_dump_super (UF_long, int *, int *, int *, int *, double *, int,
+ cholmod_common *) ;
+int cholmod_dump_partition (UF_long, int *, int *, int *, int *, UF_long,
+ cholmod_common *) ;
+int cholmod_dump_work(int, int, UF_long, cholmod_common *) ;
+
+/* double, UF_long */
+EXTERN int cholmod_l_dump ;
+EXTERN int cholmod_l_dump_malloc ;
+UF_long cholmod_l_dump_sparse (cholmod_sparse *, char *, cholmod_common *) ;
+int cholmod_l_dump_factor (cholmod_factor *, char *, cholmod_common *) ;
+int cholmod_l_dump_triplet (cholmod_triplet *, char *, cholmod_common *) ;
+int cholmod_l_dump_dense (cholmod_dense *, char *, cholmod_common *) ;
+int cholmod_l_dump_subset (UF_long *, size_t, size_t, char *,
+ cholmod_common *) ;
+int cholmod_l_dump_perm (UF_long *, size_t, size_t, char *, cholmod_common *) ;
+int cholmod_l_dump_parent (UF_long *, size_t, char *, cholmod_common *) ;
+void cholmod_l_dump_init (char *, cholmod_common *) ;
+int cholmod_l_dump_mem (char *, UF_long, cholmod_common *) ;
+void cholmod_l_dump_real (char *, Real *, UF_long, UF_long, int, int,
+ cholmod_common *) ;
+void cholmod_l_dump_super (UF_long, UF_long *, UF_long *, UF_long *, UF_long *,
+ double *, int, cholmod_common *) ;
+int cholmod_l_dump_partition (UF_long, UF_long *, UF_long *, UF_long *,
+ UF_long *, UF_long, cholmod_common *) ;
+int cholmod_l_dump_work(int, int, UF_long, cholmod_common *) ;
+
+#define DEBUG_INIT(s) { CHOLMOD(dump_init)(s, Common) ; }
+#define ASSERT(expression) (assert (expression))
+
+#define PRK(k,params) \
+{ \
+ if (CHOLMOD(dump) >= (k) && Common->print_function != NULL) \
+ { \
+ (Common->print_function) params ; \
+ } \
+}
+
+#define PRINT0(params) PRK (0, params)
+#define PRINT1(params) PRK (1, params)
+#define PRINT2(params) PRK (2, params)
+#define PRINT3(params) PRK (3, params)
+#define PRINTM(params) PRK (CHOLMOD(dump_malloc), params)
+
+#define DEBUG(statement) statement
+
+#else
+
+/* Debugging disabled (the normal case) */
+#define PRK(k,params)
+#define DEBUG_INIT(s)
+#define PRINT0(params)
+#define PRINT1(params)
+#define PRINT2(params)
+#define PRINT3(params)
+#define PRINTM(params)
+#define ASSERT(expression)
+#define DEBUG(statement)
+#endif
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_io64.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_io64.h
new file mode 100644
index 0000000..98bf2b3
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_io64.h
@@ -0,0 +1,46 @@
+/* ========================================================================== */
+/* === Include/cholmod_io64 ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_io64.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_io64.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Definitions required for large file I/O, which must come before any other
+ * #includes. These are not used if -DNLARGEFILE is defined at compile time.
+ * Large file support may not be portable across all platforms and compilers;
+ * if you encounter an error here, compile your code with -DNLARGEFILE. In
+ * particular, you must use -DNLARGEFILE for MATLAB 6.5 or earlier (which does
+ * not have the io64.h include file).
+ */
+
+#ifndef CHOLMOD_IO_H
+#define CHOLMOD_IO_H
+
+/* skip all of this if NLARGEFILE is defined at the compiler command line */
+#ifndef NLARGEFILE
+
+#if defined(MATLAB_MEX_FILE) || defined(MATHWORKS)
+
+/* CHOLMOD is being compiled as a MATLAB MEX file, or for use inside MATLAB */
+#include "io64.h"
+
+#else
+
+/* CHOLMOD is being compiled in a stand-alone library */
+#undef _LARGEFILE64_SOURCE
+#define _LARGEFILE64_SOURCE
+#undef _FILE_OFFSET_BITS
+#define _FILE_OFFSET_BITS 64
+
+#endif
+
+#endif
+
+#endif
+
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_matrixops.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_matrixops.h
new file mode 100644
index 0000000..59f19da
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_matrixops.h
@@ -0,0 +1,235 @@
+/* ========================================================================== */
+/* === Include/cholmod_matrixops.h ========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_matrixops.h.
+ * Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_matrixops.h is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD MatrixOps module.
+ *
+ * Basic operations on sparse and dense matrices.
+ *
+ * cholmod_drop A = entries in A with abs. value >= tol
+ * cholmod_norm_dense s = norm (X), 1-norm, inf-norm, or 2-norm
+ * cholmod_norm_sparse s = norm (A), 1-norm or inf-norm
+ * cholmod_horzcat C = [A,B]
+ * cholmod_scale A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s)
+ * cholmod_sdmult Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y
+ * cholmod_ssmult C = A*B
+ * cholmod_submatrix C = A (i,j), where i and j are arbitrary vectors
+ * cholmod_vertcat C = [A ; B]
+ *
+ * A, B, C: sparse matrices (cholmod_sparse)
+ * X, Y: dense matrices (cholmod_dense)
+ * s: scalar or vector
+ *
+ * Requires the Core module. Not required by any other CHOLMOD module.
+ */
+
+#ifndef CHOLMOD_MATRIXOPS_H
+#define CHOLMOD_MATRIXOPS_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_drop: drop entries with small absolute value */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_drop
+(
+ /* ---- input ---- */
+ double tol, /* keep entries with absolute value > tol */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to drop entries from */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_drop (double, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_norm_dense: s = norm (X), 1-norm, inf-norm, or 2-norm */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_norm_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to compute the norm of */
+ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_norm_dense (cholmod_dense *, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_norm_sparse: s = norm (A), 1-norm or inf-norm */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_norm_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to compute the norm of */
+ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_norm_sparse (cholmod_sparse *, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_horzcat: C = [A,B] */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_horzcat
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to concatenate */
+ cholmod_sparse *B, /* right matrix to concatenate */
+ int values, /* if TRUE compute the numerical values of C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_horzcat (cholmod_sparse *, cholmod_sparse *, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_scale: A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s) */
+/* -------------------------------------------------------------------------- */
+
+/* scaling modes, selected by the scale input parameter: */
+#define CHOLMOD_SCALAR 0 /* A = s*A */
+#define CHOLMOD_ROW 1 /* A = diag(s)*A */
+#define CHOLMOD_COL 2 /* A = A*diag(s) */
+#define CHOLMOD_SYM 3 /* A = diag(s)*A*diag(s) */
+
+int cholmod_scale
+(
+ /* ---- input ---- */
+ cholmod_dense *S, /* scale factors (scalar or vector) */
+ int scale, /* type of scaling to compute */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to scale */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_scale (cholmod_dense *, int, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sdmult: Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y */
+/* -------------------------------------------------------------------------- */
+
+/* Sparse matrix times dense matrix */
+
+int cholmod_sdmult
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to multiply */
+ int transpose, /* use A if 0, or A' if 1, or A.' if -1 */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for Y */
+ cholmod_dense *X, /* dense matrix to multiply */
+ /* ---- in/out --- */
+ cholmod_dense *Y, /* resulting dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_sdmult (cholmod_sparse *, int, double *, double *,
+ cholmod_dense *, cholmod_dense *Y, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ssmult: C = A*B */
+/* -------------------------------------------------------------------------- */
+
+/* Sparse matrix times sparse matrix */
+
+cholmod_sparse *cholmod_ssmult
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to multiply */
+ cholmod_sparse *B, /* right matrix to multiply */
+ int stype, /* requested stype of C */
+ int values, /* TRUE: do numerical values, FALSE: pattern only */
+ int sorted, /* if TRUE then return C with sorted columns */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_ssmult (cholmod_sparse *, cholmod_sparse *, int, int,
+ int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_submatrix: C = A (r,c), where i and j are arbitrary vectors */
+/* -------------------------------------------------------------------------- */
+
+/* rsize < 0 denotes ":" in MATLAB notation, or more precisely 0:(A->nrow)-1.
+ * In this case, r can be NULL. An rsize of zero, or r = NULL and rsize >= 0,
+ * denotes "[ ]" in MATLAB notation (the empty set).
+ * Similar rules hold for csize.
+ */
+
+cholmod_sparse *cholmod_submatrix
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to subreference */
+ int *rset, /* set of row indices, duplicates OK */
+ UF_long rsize, /* size of r; rsize < 0 denotes ":" */
+ int *cset, /* set of column indices, duplicates OK */
+ UF_long csize, /* size of c; csize < 0 denotes ":" */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE then return C with sorted columns */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_submatrix (cholmod_sparse *, UF_long *, UF_long,
+ UF_long *, UF_long, int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_vertcat: C = [A ; B] */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_vertcat
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to concatenate */
+ cholmod_sparse *B, /* right matrix to concatenate */
+ int values, /* if TRUE compute the numerical values of C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_vertcat (cholmod_sparse *, cholmod_sparse *, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_symmetry: determine if a sparse matrix is symmetric */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_symmetry
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ int option,
+ /* ---- output ---- */
+ int *xmatched,
+ int *pmatched,
+ int *nzoffdiag,
+ int *nzdiag,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_symmetry (cholmod_sparse *, int, UF_long *, UF_long *, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_modify.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_modify.h
new file mode 100644
index 0000000..bb7dd5a
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_modify.h
@@ -0,0 +1,304 @@
+/* ========================================================================== */
+/* === Include/cholmod_modify.h ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_modify.h.
+ * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager
+ * CHOLMOD/Include/cholmod_modify.h is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Modify module.
+ *
+ * Sparse Cholesky modification routines: update / downdate / rowadd / rowdel.
+ * Can also modify a corresponding solution to Lx=b when L is modified. This
+ * module is most useful when applied on a Cholesky factorization computed by
+ * the Cholesky module, but it does not actually require the Cholesky module.
+ * The Core module can create an identity Cholesky factorization (LDL' where
+ * L=D=I) that can then by modified by these routines.
+ *
+ * Primary routines:
+ * -----------------
+ *
+ * cholmod_updown multiple rank update/downdate
+ * cholmod_rowadd add a row to an LDL' factorization
+ * cholmod_rowdel delete a row from an LDL' factorization
+ *
+ * Secondary routines:
+ * -------------------
+ *
+ * cholmod_updown_solve update/downdate, and modify solution to Lx=b
+ * cholmod_updown_mark update/downdate, and modify solution to partial Lx=b
+ * cholmod_updown_mask update/downdate for LPDASA
+ * cholmod_rowadd_solve add a row, and update solution to Lx=b
+ * cholmod_rowadd_mark add a row, and update solution to partial Lx=b
+ * cholmod_rowdel_solve delete a row, and downdate Lx=b
+ * cholmod_rowdel_mark delete a row, and downdate solution to partial Lx=b
+ *
+ * Requires the Core module. Not required by any other CHOLMOD module.
+ */
+
+#ifndef CHOLMOD_MODIFY_H
+#define CHOLMOD_MODIFY_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown: multiple rank update/downdate */
+/* -------------------------------------------------------------------------- */
+
+/* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC'
+ * (a downdate). The factor object L need not be an LDL' factorization; it
+ * is converted to one if it isn't. */
+
+int cholmod_updown
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown (int, cholmod_sparse *, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown_solve: update/downdate, and modify solution to Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_updown, except that it also updates/downdates the
+ * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not
+ * need as input to this routine, but a sparse change to b is (DeltaB). Only
+ * entries in DeltaB corresponding to columns modified in L are accessed; the
+ * rest must be zero. */
+
+int cholmod_updown_solve
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown_solve (int, cholmod_sparse *, cholmod_factor *,
+ cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown_mark: update/downdate, and modify solution to partial Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_updown_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. See cholmod_updown.c for
+ * a description of colmark. */
+
+int cholmod_updown_mark
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown_mark (int, cholmod_sparse *, UF_long *, cholmod_factor *,
+ cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown_mask: update/downdate, for LPDASA */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_updown_mark, except has an additional "mask"
+ * argument. This routine is an "expert" routine. It is meant for use in
+ * LPDASA only. See cholmod_updown.c for a description of mask. */
+
+int cholmod_updown_mask
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ int *mask, /* size n */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown_mask (int, cholmod_sparse *, UF_long *, UF_long *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowadd: add a row to an LDL' factorization (a rank-2 update) */
+/* -------------------------------------------------------------------------- */
+
+/* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth
+ * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n)
+ * accordingly. The kth row and column of L must originally be equal to the
+ * kth row and column of the identity matrix. The kth row/column of L is
+ * computed as the factorization of the kth row/column of the matrix to
+ * factorize, which is provided as a single n-by-1 sparse matrix R. */
+
+int cholmod_rowadd
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowadd (size_t, cholmod_sparse *, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowadd_solve: add a row, and update solution to Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowadd, and also updates the solution to Lx=b
+ * See cholmod_updown for a description of how Lx=b is updated. There is on
+ * additional parameter: bk specifies the new kth entry of b. */
+
+int cholmod_rowadd_solve
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ double bk [2], /* kth entry of the right-hand-side b */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowadd_solve (size_t, cholmod_sparse *, double *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowadd_mark: add a row, and update solution to partial Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowadd_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. */
+
+int cholmod_rowadd_mark
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ double bk [2], /* kth entry of the right hand side, b */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowadd_mark (size_t, cholmod_sparse *, double *, UF_long *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowdel: delete a row from an LDL' factorization (a rank-2 update) */
+/* -------------------------------------------------------------------------- */
+
+/* Sets the kth row and column of L to be the kth row and column of the identity
+ * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time,
+ * the caller can optionally provide the nonzero pattern (or an upper bound) of
+ * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want
+ * CHOLMOD to determine this itself, which is easier for the caller, but takes
+ * a little more time.
+ */
+
+int cholmod_rowdel
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowdel (size_t, cholmod_sparse *, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowdel_solve: delete a row, and downdate Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b.
+ * When row/column k of A is "deleted" from the system A*y=b, this can induce
+ * a change to x, in addition to changes arising when L and b are modified.
+ * If this is the case, the kth entry of y is required as input (yk) */
+
+int cholmod_rowdel_solve
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ double yk [2], /* kth entry in the solution to A*y=b */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowdel_solve (size_t, cholmod_sparse *, double *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowdel_mark: delete a row, and downdate solution to partial Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowdel_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. */
+
+int cholmod_rowdel_mark
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ double yk [2], /* kth entry in the solution to A*y=b */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowdel_mark (size_t, cholmod_sparse *, double *, UF_long *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_partition.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_partition.h
new file mode 100644
index 0000000..1adbc46
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_partition.h
@@ -0,0 +1,233 @@
+/* ========================================================================== */
+/* === Include/cholmod_partition.h ========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_partition.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_partition.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Partition module.
+ *
+ * Graph partitioning and graph-partition-based orderings. Includes an
+ * interface to CCOLAMD and CSYMAMD, constrained minimum degree ordering
+ * methods which order a matrix following constraints determined via nested
+ * dissection.
+ *
+ * cholmod_nested_dissection CHOLMOD nested dissection ordering
+ * cholmod_metis METIS nested dissection ordering (METIS_NodeND)
+ * cholmod_ccolamd interface to CCOLAMD ordering
+ * cholmod_csymamd interface to CSYMAMD ordering
+ * cholmod_camd interface to CAMD ordering
+ * cholmod_bisect graph partitioner (currently based on METIS)
+ * cholmod_metis_bisector direct interface to METIS_NodeComputeSeparator
+ *
+ * Requires the Core and Cholesky modules, and three packages: METIS, CAMD,
+ * and CCOLAMD. Optionally used by the Cholesky module.
+ *
+ * Note that METIS does not have a version that uses UF_long integers. If you
+ * try to use cholmod_nested_dissection, cholmod_metis, cholmod_bisect, or
+ * cholmod_metis_bisector on a matrix that is too large, an error code will be
+ * returned. METIS does have an "idxtype", which could be redefined as UF_long,
+ * if you wish to edit METIS or use compile-time flags to redefine idxtype.
+ */
+
+#ifndef CHOLMOD_PARTITION_H
+#define CHOLMOD_PARTITION_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_nested_dissection */
+/* -------------------------------------------------------------------------- */
+
+/* Order A, AA', or A(:,f)*A(:,f)' using CHOLMOD's nested dissection method
+ * (METIS's node bisector applied recursively to compute the separator tree
+ * and constraint sets, followed by CCOLAMD using the constraints). Usually
+ * finds better orderings than METIS_NodeND, but takes longer.
+ */
+
+UF_long cholmod_nested_dissection /* returns # of components */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ int *CParent, /* size A->nrow. On output, CParent [c] is the parent
+ * of component c, or EMPTY if c is a root, and where
+ * c is in the range 0 to # of components minus 1 */
+ int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is
+ * in component c */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_nested_dissection (cholmod_sparse *, UF_long *, size_t,
+ UF_long *, UF_long *, UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_metis */
+/* -------------------------------------------------------------------------- */
+
+/* Order A, AA', or A(:,f)*A(:,f)' using METIS_NodeND. */
+
+int cholmod_metis
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with etree or coletree postorder */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_metis (cholmod_sparse *, UF_long *, size_t, int, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ccolamd */
+/* -------------------------------------------------------------------------- */
+
+/* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */
+
+int cholmod_ccolamd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the
+ * constraint set c. c must be >= 0. The # of
+ * constraint sets is max (Cmember) + 1. If Cmember is
+ * NULL, then it is interpretted as Cmember [i] = 0 for
+ * all i */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_ccolamd (cholmod_sparse *, UF_long *, size_t, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_csymamd */
+/* -------------------------------------------------------------------------- */
+
+/* Order A using CSYMAMD. */
+
+int cholmod_csymamd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ /* ---- output --- */
+ int *Cmember, /* size nrow. see cholmod_ccolamd above */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_csymamd (cholmod_sparse *, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_camd */
+/* -------------------------------------------------------------------------- */
+
+/* Order A using CAMD. */
+
+int cholmod_camd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Cmember, /* size nrow. see cholmod_ccolamd above */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_camd (cholmod_sparse *, UF_long *, size_t, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_bisect */
+/* -------------------------------------------------------------------------- */
+
+/* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'. */
+
+UF_long cholmod_bisect /* returns # of nodes in separator */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to bisect */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int compress, /* if TRUE, compress the graph first */
+ /* ---- output --- */
+ int *Partition, /* size A->nrow. Node i is in the left graph if
+ * Partition [i] = 0, the right graph if 1, and in the
+ * separator if 2. */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_bisect (cholmod_sparse *, UF_long *, size_t, int, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_metis_bisector */
+/* -------------------------------------------------------------------------- */
+
+/* Find a set of nodes that bisects the graph of A or AA' (direct interface
+ * to METIS_NodeComputeSeparator). */
+
+UF_long cholmod_metis_bisector /* returns separator size */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to bisect */
+ int *Anw, /* size A->nrow, node weights */
+ int *Aew, /* size nz, edge weights */
+ /* ---- output --- */
+ int *Partition, /* size A->nrow. see cholmod_bisect above. */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_metis_bisector (cholmod_sparse *, UF_long *, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_collapse_septree */
+/* -------------------------------------------------------------------------- */
+
+/* Collapse nodes in a separator tree. */
+
+UF_long cholmod_collapse_septree
+(
+ /* ---- input ---- */
+ size_t n, /* # of nodes in the graph */
+ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */
+ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */
+ size_t nd_small, /* collapse if #nodes in subtree < nd_small */
+ /* ---- in/out --- */
+ int *CParent, /* size ncomponents; from cholmod_nested_dissection */
+ int *Cmember, /* size n; from cholmod_nested_dissection */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_collapse_septree (size_t, size_t, double, size_t, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_supernodal.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_supernodal.h
new file mode 100644
index 0000000..cfb483e
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_supernodal.h
@@ -0,0 +1,147 @@
+/* ========================================================================== */
+/* === Include/cholmod_supernodal.h ========================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_supernodal.h.
+ * Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_supernodal.h is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Supernodal module.
+ *
+ * Supernodal analysis, factorization, and solve. The simplest way to use
+ * these routines is via the Cholesky module. It does not provide any
+ * fill-reducing orderings, but does accept the orderings computed by the
+ * Cholesky module. It does not require the Cholesky module itself, however.
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_super_symbolic supernodal symbolic analysis
+ * cholmod_super_numeric supernodal numeric factorization
+ * cholmod_super_lsolve supernodal Lx=b solve
+ * cholmod_super_ltsolve supernodal L'x=b solve
+ *
+ * Prototypes for the BLAS and LAPACK routines that CHOLMOD uses are listed
+ * below, including how they are used in CHOLMOD.
+ *
+ * BLAS routines:
+ * --------------
+ * dtrsv solve Lx=b or L'x=b, L non-unit diagonal, x and b stride-1
+ * dtrsm solve LX=B or L'X=b, L non-unit diagonal
+ * dgemv y=y-A*x or y=y-A'*x (x and y stride-1)
+ * dgemm C=A*B', C=C-A*B, or C=C-A'*B
+ * dsyrk C=tril(A*A')
+ *
+ * LAPACK routines:
+ * ----------------
+ * dpotrf LAPACK: A=chol(tril(A))
+ *
+ * Requires the Core module, and two external packages: LAPACK and the BLAS.
+ * Optionally used by the Cholesky module.
+ */
+
+#ifndef CHOLMOD_SUPERNODAL_H
+#define CHOLMOD_SUPERNODAL_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_symbolic */
+/* -------------------------------------------------------------------------- */
+
+/* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric
+ * factorization. The user need not call this directly; cholmod_analyze is
+ * a "simple" wrapper for this routine.
+ */
+
+int cholmod_super_symbolic
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ int *Parent, /* elimination tree */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* simplicial symbolic on input,
+ * supernodal symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_symbolic (cholmod_sparse *, cholmod_sparse *, UF_long *,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_numeric */
+/* -------------------------------------------------------------------------- */
+
+/* Computes the numeric LL' factorization of A, AA', or A(:,f)*A(:,f)' using
+ * a BLAS-based supernodal method. The user need not call this directly;
+ * cholmod_factorize is a "simple" wrapper for this routine.
+ */
+
+int cholmod_super_numeric
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ double beta [2], /* beta*I is added to diagonal of matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_numeric (cholmod_sparse *, cholmod_sparse *, double *,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_lsolve */
+/* -------------------------------------------------------------------------- */
+
+/* Solve Lx=b where L is from a supernodal numeric factorization. The user
+ * need not call this routine directly. cholmod_solve is a "simple" wrapper
+ * for this routine. */
+
+int cholmod_super_lsolve
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_lsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_ltsolve */
+/* -------------------------------------------------------------------------- */
+
+/* Solve L'x=b where L is from a supernodal numeric factorization. The user
+ * need not call this routine directly. cholmod_solve is a "simple" wrapper
+ * for this routine. */
+
+int cholmod_super_ltsolve
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the backsolve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to L'x=b on output */
+ /* ---- workspace */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_ltsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *,
+ cholmod_common *) ;
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Include/cholmod_template.h b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_template.h
new file mode 100644
index 0000000..aa45b4d
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Include/cholmod_template.h
@@ -0,0 +1,238 @@
+/* ========================================================================== */
+/* === Include/cholmod_template.h =========================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* undefine current xtype macros, and then define macros for current type */
+/* -------------------------------------------------------------------------- */
+
+#undef TEMPLATE
+#undef XTYPE
+#undef XTYPE2
+#undef XTYPE_OK
+#undef ENTRY_IS_NONZERO
+#undef ENTRY_IS_ZERO
+#undef ENTRY_IS_ONE
+#undef IMAG_IS_NONZERO
+
+#undef ASSEMBLE
+#undef ASSIGN
+#undef ASSIGN_CONJ
+#undef ASSIGN2
+#undef ASSIGN2_CONJ
+#undef ASSIGN_REAL
+#undef MULT
+#undef MULTADD
+#undef ADD
+#undef ADD_REAL
+#undef MULTSUB
+#undef MULTADDCONJ
+#undef MULTSUBCONJ
+#undef LLDOT
+#undef CLEAR
+#undef DIV
+#undef DIV_REAL
+#undef MULT_REAL
+#undef CLEAR_IMAG
+#undef LDLDOT
+#undef PREFIX
+
+#undef ENTRY_SIZE
+
+#undef XPRINT0
+#undef XPRINT1
+#undef XPRINT2
+#undef XPRINT3
+
+/* -------------------------------------------------------------------------- */
+/* pattern */
+/* -------------------------------------------------------------------------- */
+
+
+#ifdef PATTERN
+
+#define PREFIX p_
+#define TEMPLATE(name) P_TEMPLATE(name)
+#define XTYPE CHOLMOD_PATTERN
+#define XTYPE2 CHOLMOD_REAL
+#define XTYPE_OK(type) (TRUE)
+#define ENTRY_IS_NONZERO(ax,az,q) (TRUE)
+#define ENTRY_IS_ZERO(ax,az,q) (FALSE)
+#define ENTRY_IS_ONE(ax,az,q) (TRUE)
+#define IMAG_IS_NONZERO(ax,az,q) (FALSE)
+#define ENTRY_SIZE 0
+
+#define ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) P_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) P_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) P_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) P_PRINT(3,x,z,p)
+
+/* -------------------------------------------------------------------------- */
+/* real */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (REAL)
+
+#define PREFIX r_
+#define TEMPLATE(name) R_TEMPLATE(name)
+#define XTYPE CHOLMOD_REAL
+#define XTYPE2 CHOLMOD_REAL
+#define XTYPE_OK(type) R_XTYPE_OK(type)
+#define ENTRY_IS_NONZERO(ax,az,q) R_IS_NONZERO(ax,az,q)
+#define ENTRY_IS_ZERO(ax,az,q) R_IS_ZERO(ax,az,q)
+#define ENTRY_IS_ONE(ax,az,q) R_IS_ONE(ax,az,q)
+#define IMAG_IS_NONZERO(ax,az,q) (FALSE)
+#define ENTRY_SIZE 1
+
+#define ASSEMBLE(x,z,p,ax,az,q) R_ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q) R_ASSIGN_REAL(x,p,ax,q)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb) R_MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb) R_MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb) R_ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r) R_ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) R_MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ R_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ R_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q) R_LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p) R_CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p) R_CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q) R_DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r) R_DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r) R_MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r) R_LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) R_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) R_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) R_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) R_PRINT(3,x,z,p)
+
+/* -------------------------------------------------------------------------- */
+/* complex */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (COMPLEX)
+
+#define PREFIX c_
+
+#ifdef NCONJUGATE
+#define TEMPLATE(name) CT_TEMPLATE(name)
+#else
+#define TEMPLATE(name) C_TEMPLATE(name)
+#endif
+
+#define ASSEMBLE(x,z,p,ax,az,q) C_ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q) C_ASSIGN_REAL(x,p,ax,q)
+#define XTYPE CHOLMOD_COMPLEX
+#define XTYPE2 CHOLMOD_COMPLEX
+#define XTYPE_OK(type) C_XTYPE_OK(type)
+#define ENTRY_IS_NONZERO(ax,az,q) C_IS_NONZERO(ax,az,q)
+#define ENTRY_IS_ZERO(ax,az,q) C_IS_ZERO(ax,az,q)
+#define ENTRY_IS_ONE(ax,az,q) C_IS_ONE(ax,az,q)
+#define IMAG_IS_NONZERO(ax,az,q) C_IMAG_IS_NONZERO(ax,az,q)
+#define ENTRY_SIZE 2
+
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb) C_MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb) C_MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb) C_ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r) C_ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) C_MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ C_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ C_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q) C_LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p) C_CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p) C_CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q) C_DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r) C_DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r) C_MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r) C_LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) C_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) C_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) C_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) C_PRINT(3,x,z,p)
+
+/* -------------------------------------------------------------------------- */
+/* zomplex */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (ZOMPLEX)
+
+#define PREFIX z_
+
+#ifdef NCONJUGATE
+#define TEMPLATE(name) ZT_TEMPLATE(name)
+#else
+#define TEMPLATE(name) Z_TEMPLATE(name)
+#endif
+
+#define ASSEMBLE(x,z,p,ax,az,q) Z_ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q) Z_ASSIGN_REAL(x,p,ax,q)
+#define XTYPE CHOLMOD_ZOMPLEX
+#define XTYPE2 CHOLMOD_ZOMPLEX
+#define XTYPE_OK(type) Z_XTYPE_OK(type)
+#define ENTRY_IS_NONZERO(ax,az,q) Z_IS_NONZERO(ax,az,q)
+#define ENTRY_IS_ZERO(ax,az,q) Z_IS_ZERO(ax,az,q)
+#define ENTRY_IS_ONE(ax,az,q) Z_IS_ONE(ax,az,q)
+#define IMAG_IS_NONZERO(ax,az,q) Z_IMAG_IS_NONZERO(ax,az,q)
+#define ENTRY_SIZE 1
+
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb) Z_MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb) Z_MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb) Z_ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r) Z_ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) Z_MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ Z_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ Z_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q) Z_LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p) Z_CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p) Z_CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q) Z_DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r) Z_DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r) Z_MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r) Z_LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) Z_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) Z_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) Z_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) Z_PRINT(3,x,z,p)
+
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Lib/Makefile b/src/C/SuiteSparse/CHOLMOD/Lib/Makefile
new file mode 100644
index 0000000..117f869
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Lib/Makefile
@@ -0,0 +1,473 @@
+#===============================================================================
+# CHOLOMD/Lib/Makefile: for compiling the CHOLMOD library
+#===============================================================================
+
+default: all
+
+ccode: all
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG)
+
+all: libcholmod.a
+
+library: libcholmod.a
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libcholmod.a
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+# ../Include/ directory contains all include files:
+#-------------------------------------------------------------------------------
+
+INC = ../Include/cholmod.h \
+ ../Include/cholmod_blas.h \
+ ../Include/cholmod_check.h \
+ ../Include/cholmod_cholesky.h \
+ ../Include/cholmod_complexity.h \
+ ../Include/cholmod_config.h \
+ ../Include/cholmod_core.h \
+ ../Include/cholmod_internal.h \
+ ../Include/cholmod_matrixops.h \
+ ../Include/cholmod_modify.h \
+ ../Include/cholmod_partition.h \
+ ../Include/cholmod_supernodal.h \
+ ../Include/cholmod_template.h
+
+#-------------------------------------------------------------------------------
+# The 7 CHOLMOD library modules (int, double)
+#-------------------------------------------------------------------------------
+
+CORE = cholmod_aat.o cholmod_add.o cholmod_band.o \
+ cholmod_change_factor.o cholmod_common.o cholmod_complex.o \
+ cholmod_copy.o cholmod_dense.o cholmod_error.o cholmod_factor.o \
+ cholmod_memory.o cholmod_sparse.o \
+ cholmod_transpose.o cholmod_triplet.o
+
+CHECK = cholmod_check.o cholmod_read.o cholmod_write.o
+
+CHOLESKY = cholmod_amd.o cholmod_analyze.o cholmod_colamd.o \
+ cholmod_etree.o cholmod_factorize.o cholmod_postorder.o \
+ cholmod_rcond.o cholmod_resymbol.o cholmod_rowcolcounts.o \
+ cholmod_rowfac.o cholmod_solve.o cholmod_spsolve.o
+
+MATRIXOPS = cholmod_drop.o cholmod_horzcat.o cholmod_norm.o \
+ cholmod_scale.o cholmod_sdmult.o cholmod_ssmult.o \
+ cholmod_submatrix.o cholmod_vertcat.o cholmod_symmetry.o
+
+PARTITION = cholmod_ccolamd.o cholmod_csymamd.o \
+ cholmod_metis.o cholmod_nesdis.o cholmod_camd.o
+
+MODIFY = cholmod_rowadd.o cholmod_rowdel.o cholmod_updown.o
+
+SUPERNODAL = cholmod_super_numeric.o cholmod_super_solve.o \
+ cholmod_super_symbolic.o
+
+DI = $(CORE) $(CHECK) $(CHOLESKY) $(MATRIXOPS) $(MODIFY) $(SUPERNODAL) \
+ $(PARTITION)
+
+#-------------------------------------------------------------------------------
+# CHOLMOD library modules (long, double)
+#-------------------------------------------------------------------------------
+
+LCORE = cholmod_l_aat.o cholmod_l_add.o cholmod_l_band.o \
+ cholmod_l_change_factor.o cholmod_l_common.o cholmod_l_complex.o \
+ cholmod_l_copy.o cholmod_l_dense.o cholmod_l_error.o \
+ cholmod_l_factor.o cholmod_l_memory.o \
+ cholmod_l_sparse.o cholmod_l_transpose.o cholmod_l_triplet.o
+
+LCHECK = cholmod_l_check.o cholmod_l_read.o cholmod_l_write.o
+
+LCHOLESKY = cholmod_l_amd.o cholmod_l_analyze.o cholmod_l_colamd.o \
+ cholmod_l_etree.o cholmod_l_factorize.o cholmod_l_postorder.o \
+ cholmod_l_rcond.o cholmod_l_resymbol.o cholmod_l_rowcolcounts.o \
+ cholmod_l_rowfac.o cholmod_l_solve.o cholmod_l_spsolve.o
+
+LMATRIXOPS = cholmod_l_drop.o cholmod_l_horzcat.o cholmod_l_norm.o \
+ cholmod_l_scale.o cholmod_l_sdmult.o cholmod_l_ssmult.o \
+ cholmod_l_submatrix.o cholmod_l_vertcat.o cholmod_l_symmetry.o
+
+LPARTITION = cholmod_l_ccolamd.o cholmod_l_csymamd.o \
+ cholmod_l_metis.o cholmod_l_nesdis.o cholmod_l_camd.o
+
+LMODIFY = cholmod_l_rowadd.o cholmod_l_rowdel.o cholmod_l_updown.o
+
+LSUPERNODAL = cholmod_l_super_numeric.o cholmod_l_super_solve.o \
+ cholmod_l_super_symbolic.o
+
+DL = $(LCORE) $(LCHECK) $(LCHOLESKY) $(LMATRIXOPS) $(LMODIFY) $(LSUPERNODAL) \
+ $(LPARTITION)
+
+#-------------------------------------------------------------------------------
+
+# to compile just the double/int version, use OBJ = $(DI)
+OBJ = $(DI) $(DL)
+
+libcholmod.a: $(OBJ)
+ $(AR) libcholmod.a $(OBJ)
+ $(RANLIB) libcholmod.a
+
+$(OBJ): $(INC)
+
+I = -I../../AMD/Include -I../../AMD/Source -I../../COLAMD \
+ -I$(METIS_PATH)/Lib -I../../CCOLAMD -I../../CAMD/Include -I../Include \
+ -I../../UFconfig
+
+
+#-------------------------------------------------------------------------------
+# Check Module:
+#-------------------------------------------------------------------------------
+
+cholmod_check.o: ../Check/cholmod_check.c
+ $(C) -c $(I) $<
+
+cholmod_read.o: ../Check/cholmod_read.c
+ $(C) -c $(I) $<
+
+cholmod_write.o: ../Check/cholmod_write.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_check.o: ../Check/cholmod_check.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_read.o: ../Check/cholmod_read.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_write.o: ../Check/cholmod_write.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# Core Module:
+#-------------------------------------------------------------------------------
+
+cholmod_common.o: ../Core/cholmod_common.c
+ $(C) -c $(I) $<
+
+cholmod_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c
+ $(C) -c $(I) $<
+
+cholmod_factor.o: ../Core/cholmod_factor.c
+ $(C) -c $(I) $<
+
+cholmod_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c
+ $(C) -c $(I) $<
+
+cholmod_memory.o: ../Core/cholmod_memory.c
+ $(C) -c $(I) $<
+
+cholmod_sparse.o: ../Core/cholmod_sparse.c
+ $(C) -c $(I) $<
+
+cholmod_complex.o: ../Core/cholmod_complex.c
+ $(C) -c $(I) $<
+
+cholmod_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c
+ $(C) -c $(I) $<
+
+cholmod_band.o: ../Core/cholmod_band.c
+ $(C) -c $(I) $<
+
+cholmod_copy.o: ../Core/cholmod_copy.c
+ $(C) -c $(I) $<
+
+cholmod_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c
+ $(C) -c $(I) $<
+
+cholmod_error.o: ../Core/cholmod_error.c
+ $(C) -c $(I) $<
+
+cholmod_aat.o: ../Core/cholmod_aat.c
+ $(C) -c $(I) $<
+
+cholmod_add.o: ../Core/cholmod_add.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_common.o: ../Core/cholmod_common.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_factor.o: ../Core/cholmod_factor.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_memory.o: ../Core/cholmod_memory.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_sparse.o: ../Core/cholmod_sparse.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_complex.o: ../Core/cholmod_complex.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_band.o: ../Core/cholmod_band.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_copy.o: ../Core/cholmod_copy.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_error.o: ../Core/cholmod_error.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_aat.o: ../Core/cholmod_aat.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_add.o: ../Core/cholmod_add.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# Cholesky Module:
+#-------------------------------------------------------------------------------
+
+cholmod_amd.o: ../Cholesky/cholmod_amd.c
+ $(C) -c $(I) $<
+
+cholmod_analyze.o: ../Cholesky/cholmod_analyze.c
+ $(C) -c $(I) $<
+
+cholmod_colamd.o: ../Cholesky/cholmod_colamd.c
+ $(C) -c $(I) $<
+
+cholmod_etree.o: ../Cholesky/cholmod_etree.c
+ $(C) -c $(I) $<
+
+cholmod_factorize.o: ../Cholesky/cholmod_factorize.c
+ $(C) -c $(I) $<
+
+cholmod_postorder.o: ../Cholesky/cholmod_postorder.c
+ $(C) -c $(I) $<
+
+cholmod_rcond.o: ../Cholesky/cholmod_rcond.c
+ $(C) -c $(I) $<
+
+cholmod_resymbol.o: ../Cholesky/cholmod_resymbol.c
+ $(C) -c $(I) $<
+
+cholmod_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c
+ $(C) -c $(I) $<
+
+cholmod_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c
+ $(C) -c $(I) $<
+
+cholmod_spsolve.o: ../Cholesky/cholmod_spsolve.c
+ $(C) -c $(I) $<
+
+cholmod_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_amd.o: ../Cholesky/cholmod_amd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_analyze.o: ../Cholesky/cholmod_analyze.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_colamd.o: ../Cholesky/cholmod_colamd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_etree.o: ../Cholesky/cholmod_etree.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_factorize.o: ../Cholesky/cholmod_factorize.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_postorder.o: ../Cholesky/cholmod_postorder.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rcond.o: ../Cholesky/cholmod_rcond.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_resymbol.o: ../Cholesky/cholmod_resymbol.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_spsolve.o: ../Cholesky/cholmod_spsolve.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+# Partition Module:
+#-------------------------------------------------------------------------------
+
+cholmod_ccolamd.o: ../Partition/cholmod_ccolamd.c
+ $(C) -c $(I) $<
+
+cholmod_csymamd.o: ../Partition/cholmod_csymamd.c
+ $(C) -c $(I) $<
+
+cholmod_camd.o: ../Partition/cholmod_camd.c
+ $(C) -c $(I) $<
+
+cholmod_metis.o: ../Partition/cholmod_metis.c
+ $(C) -c $(I) $<
+
+cholmod_nesdis.o: ../Partition/cholmod_nesdis.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_ccolamd.o: ../Partition/cholmod_ccolamd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_csymamd.o: ../Partition/cholmod_csymamd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_camd.o: ../Partition/cholmod_camd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_metis.o: ../Partition/cholmod_metis.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_nesdis.o: ../Partition/cholmod_nesdis.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# MatrixOps Module:
+#-------------------------------------------------------------------------------
+
+cholmod_horzcat.o: ../MatrixOps/cholmod_horzcat.c
+ $(C) -c $(I) $<
+
+cholmod_norm.o: ../MatrixOps/cholmod_norm.c
+ $(C) -c $(I) $<
+
+cholmod_scale.o: ../MatrixOps/cholmod_scale.c
+ $(C) -c $(I) $<
+
+cholmod_drop.o: ../MatrixOps/cholmod_drop.c
+ $(C) -c $(I) $<
+
+cholmod_sdmult.o: ../MatrixOps/cholmod_sdmult.c \
+ ../MatrixOps/t_cholmod_sdmult.c
+ $(C) -c $(I) $<
+
+cholmod_ssmult.o: ../MatrixOps/cholmod_ssmult.c
+ $(C) -c $(I) $<
+
+cholmod_submatrix.o: ../MatrixOps/cholmod_submatrix.c
+ $(C) -c $(I) $<
+
+cholmod_vertcat.o: ../MatrixOps/cholmod_vertcat.c
+ $(C) -c $(I) $<
+
+cholmod_symmetry.o: ../MatrixOps/cholmod_symmetry.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_horzcat.o: ../MatrixOps/cholmod_horzcat.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_norm.o: ../MatrixOps/cholmod_norm.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_scale.o: ../MatrixOps/cholmod_scale.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_drop.o: ../MatrixOps/cholmod_drop.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_sdmult.o: ../MatrixOps/cholmod_sdmult.c \
+ ../MatrixOps/t_cholmod_sdmult.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_ssmult.o: ../MatrixOps/cholmod_ssmult.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_submatrix.o: ../MatrixOps/cholmod_submatrix.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_vertcat.o: ../MatrixOps/cholmod_vertcat.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_symmetry.o: ../MatrixOps/cholmod_symmetry.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+# Modify Module:
+#-------------------------------------------------------------------------------
+
+cholmod_rowadd.o: ../Modify/cholmod_rowadd.c
+ $(C) -c $(I) $<
+
+cholmod_rowdel.o: ../Modify/cholmod_rowdel.c
+ $(C) -c $(I) $<
+
+cholmod_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_rowadd.o: ../Modify/cholmod_rowadd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rowdel.o: ../Modify/cholmod_rowdel.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# Supernodal Module:
+#-------------------------------------------------------------------------------
+
+cholmod_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c
+ $(C) -c $(I) $<
+
+cholmod_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c
+ $(C) -c $(I) $<
+
+cholmod_super_solve.o: ../Supernodal/cholmod_super_solve.c \
+ ../Supernodal/t_cholmod_super_solve.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_super_solve.o: ../Supernodal/cholmod_super_solve.c \
+ ../Supernodal/t_cholmod_super_solve.c
+ $(C) -DDLONG -c $(I) $< -o $@
diff --git a/src/C/SuiteSparse/CHOLMOD/Makefile b/src/C/SuiteSparse/CHOLMOD/Makefile
new file mode 100644
index 0000000..1916688
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Makefile
@@ -0,0 +1,59 @@
+#-------------------------------------------------------------------------------
+# CHOLMOD Makefile
+#-------------------------------------------------------------------------------
+
+# Note: If you do not have METIS, or do not wish to use it in CHOLMOD, you must
+# compile CHOLMOD with the -DNPARTITION flag. See ../UFconfig/UFconfig.mk.
+
+default: all
+
+include ../UFconfig/UFconfig.mk
+
+# Compile the C-callable libraries and the Demo programs.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile the C-callable libraries only.
+library:
+ ( cd Lib ; $(MAKE) )
+
+# Remove all files not in the original distribution
+purge:
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Tcov ; $(MAKE) purge )
+ ( cd Lib ; $(MAKE) purge )
+# ( cd Valgrind ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+# Remove all files not in the original distribution, except keep the
+# compiled libraries.
+clean:
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Tcov ; $(MAKE) clean )
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Valgrind ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+
+distclean: purge
+
+ccode: all
+
+# Compile the MATLAB mexFunctions (you can also use cholmod_make.m in MATLAB)
+mex:
+ ( cd MATLAB ; $(MAKE) )
+
+# Run the test coverage suite. Takes about 40 minutes on a 3.2GHz Pentium.
+# Requires Linux (gcc, gcov).
+cov:
+ ( cd Tcov ; $(MAKE) go )
+
+# Run the test coverage suite using Valgrind. This takes a *** long *** time.
+valgrind:
+ ( cd Valgrind ; $(MAKE) )
+
+# Compile the C-callable libraries and the Demo programs.
+demo:
+ ( cd Demo ; $(MAKE) )
+
diff --git a/src/C/SuiteSparse/CHOLMOD/README.txt b/src/C/SuiteSparse/CHOLMOD/README.txt
new file mode 100644
index 0000000..61f0131
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/README.txt
@@ -0,0 +1,76 @@
+CHOLMOD: a sparse CHOLesky MODification package
+-----------------------------------------------
+
+ CHOLMOD is a set of routines for factorizing sparse symmetric positive
+ definite matrices of the form A or AA', updating/downdating a sparse
+ Cholesky factorization, solving linear systems, updating/downdating
+ the solution to the triangular system Lx=b, and many other sparse matrix
+ functions for both symmetric and unsymmetric matrices. Its supernodal
+ Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains
+ a substantial fraction of the peak performance of the BLAS. Both real and
+ complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both
+ C and MATLAB interfaces. This code works on Microsoft Windows and many
+ versions of Unix and Linux.
+
+Version 1.4, Dec 12, 2006. Copyright (c) 2005-2006.
+
+Some Modules of CHOLMOD are copyrighted by the University of Florida (the
+Core and Partition Modules). The rest are copyrighted by the authors:
+Timothy A. Davis (all of them), and William W. Hager (the Modify Module).
+
+CHOLMOD relies on several other packages: AMD, CAMD, COLAMD, CCOLAMD, UFconfig,
+METIS, the BLAS, and LAPACK. All but METIS, the BLAS, and LAPACK are part of
+SuiteSparse.
+
+AMD is authored by T. Davis, Iain Duff, and Patrick Amestoy.
+COLAMD is authored by T. Davis and Stefan Larimore, with algorithmic design
+in collaboration with John Gilbert and Esmond Ng.
+CCOLAMD is authored by T. Davis and Siva Rajamanickam.
+CAMD is authored by T. Davis and Y. Chen.
+
+LAPACK and the BLAS are authored by Jack Dongarra and many others.
+LAPACK is available at http://www.netlib.org/lapack
+
+METIS is authored by George Karypis, Univ. of Minnesota. Its use in CHOLMOD
+is optional. See http://www-users.cs.umn.edu/~karypis/metis.
+Place a copy of the metis-4.0 directory in the same directory that
+contains the CHOLMOD, AMD, COLAMD, and CCOLAMD directories. Then do:
+ cd metis-4.0 ; make
+You may then compile CHOLMOD.
+
+The CHOLMOD, AMD, COLAMD, CCOLAMD, and UFconfig directories must all reside
+in a common parent directory. To compile all these libraries,
+edit UFconfig/UFconfig.mk to reflect your environment (C compiler, location
+of the BLAS, and so on) and then type "make" in either the CHOLMOD directory
+or in the parent directory of CHOLMOD. See each package for more details on
+how to compile them.
+
+For use in MATLAB (on any system, including Windows): start MATLAB,
+cd to the CHOLMOD/MATLAB directory, and type cholmod_make in the MATLAB
+Command Window. This is the best way to compile CHOLMOD for MATLAB; it
+provides a workaround for a METIS design feature, in which METIS terminates
+your program (and thus MATLAB) if it runs out of memory. Using cholmod_make
+also ensures your mexFunctions are compiled with -fexceptions, so that
+exceptions are handled properly (when hitting control-C in the MATLAB command
+window, for example).
+
+ NOTE: DO NOT ATTEMPT TO USE THIS CODE IN 64-BIT MATLAB (v7.3).
+ It is not yet ported to that version of MATLAB.
+
+On the Pentium, do NOT use the Intel MKL BLAS prior to MKL Version 8.0 with
+CHOLMOD. Older versions (prior to 8.0) have a bug in dgemm when computing
+A*B'. The bug generates a NaN result, when the inputs are well-defined. Use
+the Goto BLAS or the MKL v8.0 BLAS instead. The Goto BLAS is faster and more
+reliable. See http://www.tacc.utexas.edu/~kgoto/ or
+http://www.cs.utexas.edu/users/flame/goto/.
+Sadly, the Intel MKL BLAS 7.x is the default for MATLAB 7.0.4. See
+http://www.mathworks.com/support/bugreports/details.html?rp=252103 for more
+details. To workaround this problem on Linux, set environment variable
+BLAS_VERSION to libmkl_p3.so:libguide.so. On Windows, set environment variable
+BLAS_VERSION to mkl_p3.dll. Better yet, get MATLAB 7sp3 (MATLAB 7.1) or later.
+
+Acknowledgements: this work was supported in part by the National Science
+Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia National
+Laboratories (Dept. of Energy) which supported the development of CHOLMOD's
+Partition Module.
+
diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/License.txt b/src/C/SuiteSparse/CHOLMOD/Supernodal/License.txt
new file mode 100644
index 0000000..668c929
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/Supernodal Module.
+Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Supernodal module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_numeric.c b/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_numeric.c
new file mode 100644
index 0000000..28c6abc
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_numeric.c
@@ -0,0 +1,295 @@
+/* ========================================================================== */
+/* === Supernodal/cholmod_super_numeric ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Computes the Cholesky factorization of A+beta*I or A*F+beta*I. Only the
+ * the lower triangular part of A+beta*I or A*F+beta*I is accessed. The
+ * matrices A and F must already be permuted according to the fill-reduction
+ * permutation L->Perm. cholmod_factorize is an "easy" wrapper for this code
+ * which applies that permutation. beta is real.
+ *
+ * Symmetric case: A is a symmetric (lower) matrix. F is not accessed.
+ * With a fill-reducing permutation, A(p,p) should be passed instead, where is
+ * p is L->Perm.
+ *
+ * Unsymmetric case: A is unsymmetric, and F must be present. Normally, F=A'.
+ * With a fill-reducing permutation, A(p,f) and A(p,f)' should be passed as A
+ * and F, respectively, where f is a list of the subset of the columns of A.
+ *
+ * The input factorization L must be supernodal (L->is_super is TRUE). It can
+ * either be symbolic or numeric. In the first case, L has been analyzed by
+ * cholmod_analyze or cholmod_super_symbolic, but the matrix has not yet been
+ * numerically factorized. The numerical values are allocated here and the
+ * factorization is computed. In the second case, a prior matrix has been
+ * analyzed and numerically factorized, and a new matrix is being factorized.
+ * The numerical values of L are replaced with the new numerical factorization.
+ *
+ * L->is_ll is ignored, and set to TRUE. This routine always computes an LL'
+ * factorization. Supernodal LDL' factorization is not (yet) supported.
+ * FUTURE WORK: perform a supernodal LDL' factorization if L->is_ll is FALSE.
+ *
+ * Uses BLAS routines dsyrk, dgemm, dtrsm, and the LAPACK routine dpotrf.
+ * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm.
+ *
+ * If the matrix is not positive definite the routine returns TRUE, but sets
+ * Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the column at
+ * which the failure occurred. The supernode containing the non-positive
+ * diagonal entry is set to zero (this includes columns to the left of L->minor
+ * in the same supernode), as are all subsequent supernodes.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow + 4*nsuper).
+ * Allocates temporary space of size L->maxcsize * sizeof(double)
+ * (twice that for the complex/zomplex case).
+ *
+ * If L is supernodal symbolic on input, it is converted to a supernodal numeric
+ * factor on output, with an xtype of real if A is real, or complex if A is
+ * complex or zomplex. If L is supernodal numeric on input, its xtype must
+ * match A (except that L can be complex and A zomplex). The xtype of A and F
+ * must match.
+ */
+
+#ifndef NSUPERNODAL
+
+#include "cholmod_internal.h"
+#include "cholmod_supernodal.h"
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_super_numeric.c"
+#define COMPLEX
+#include "t_cholmod_super_numeric.c"
+#define ZOMPLEX
+#include "t_cholmod_super_numeric.c"
+
+/* ========================================================================== */
+/* === cholmod_super_numeric ================================================ */
+/* ========================================================================== */
+
+/* Returns TRUE if successful, or if the matrix is not positive definite.
+ * Returns FALSE if out of memory, inputs are invalid, or other fatal error
+ * occurs.
+ */
+
+int CHOLMOD(super_numeric)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ double beta [2], /* beta*I is added to diagonal of matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *C ;
+ Int *Super, *Map, *SuperMap ;
+ size_t maxcsize ;
+ Int nsuper, n, i, k, s, stype, nrow ;
+ int ok = TRUE, symbolic ;
+ size_t t, w ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_COMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype < 0)
+ {
+ if (A->nrow != A->ncol || A->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid dimensions") ;
+ return (FALSE) ;
+ }
+ }
+ else if (stype == 0)
+ {
+ if (A->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid dimensions") ;
+ return (FALSE) ;
+ }
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->nrow != F->ncol || A->ncol != F->nrow || F->stype != 0)
+ {
+ ERROR (CHOLMOD_INVALID, "F invalid") ;
+ return (FALSE) ;
+ }
+ if (A->xtype != F->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "A and F must have same xtype") ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ /* symmetric upper case not suppored */
+ ERROR (CHOLMOD_INVALID, "symmetric upper case not supported") ;
+ return (FALSE) ;
+ }
+ if (!(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID, "L not supernodal") ;
+ return (FALSE) ;
+ }
+ if (L->xtype != CHOLMOD_PATTERN)
+ {
+ if (! ((A->xtype == CHOLMOD_REAL && L->xtype == CHOLMOD_REAL)
+ || (A->xtype == CHOLMOD_COMPLEX && L->xtype == CHOLMOD_COMPLEX)
+ || (A->xtype == CHOLMOD_ZOMPLEX && L->xtype == CHOLMOD_COMPLEX)))
+ {
+ ERROR (CHOLMOD_INVALID, "complex type mismatch") ;
+ return (FALSE) ;
+ }
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace in Common */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = L->nsuper ;
+ maxcsize = L->maxcsize ;
+ nrow = A->nrow ;
+ n = nrow ;
+
+ PRINT1 (("nsuper "ID" maxcsize %g\n", nsuper, (double) maxcsize)) ;
+ ASSERT (nsuper >= 0 && maxcsize > 0) ;
+
+ /* w = 2*n + 4*nsuper */
+ w = CHOLMOD(mult_size_t) (n, 2, &ok) ;
+ t = CHOLMOD(mult_size_t) (nsuper, 4, &ok) ;
+ w = CHOLMOD(add_size_t) (w, t, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, w, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the current factor L and allocate numerical part, if needed */
+ /* ---------------------------------------------------------------------- */
+
+ Super = L->super ;
+ symbolic = (L->xtype == CHOLMOD_PATTERN) ;
+ if (symbolic)
+ {
+ /* convert to supernodal numeric by allocating L->x */
+ CHOLMOD(change_factor) (
+ (A->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : CHOLMOD_COMPLEX,
+ TRUE, TRUE, TRUE, TRUE, L, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* the factor L remains in symbolic supernodal form */
+ return (FALSE) ;
+ }
+ }
+ ASSERT (L->dtype == DTYPE) ;
+ ASSERT (L->xtype == CHOLMOD_REAL || L->xtype == CHOLMOD_COMPLEX) ;
+
+ /* supernodal LDL' is not supported */
+ L->is_ll = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get more workspace */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_dense) (maxcsize, 1, maxcsize, L->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ int status = Common->status ;
+ if (symbolic)
+ {
+ /* Change L back to symbolic, since the numeric values are not
+ * initialized. This cannot fail. */
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE,
+ L, Common) ;
+ }
+ /* the factor L is now back to the form it had on input */
+ Common->status = status ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ SuperMap = Common->Iwork ; /* size n (i/i/l) */
+ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */
+ for (i = 0 ; i < n ; i++)
+ {
+ Map [i] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the mapping of nodes to relaxed supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* SuperMap [k] = s if column k is contained in supernode s */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ PRINT1 (("Super ["ID"] "ID" ncols "ID"\n",
+ s, Super[s], Super[s+1]-Super[s]));
+ for (k = Super [s] ; k < Super [s+1] ; k++)
+ {
+ SuperMap [k] = s ;
+ PRINT2 (("relaxed SuperMap ["ID"] = "ID"\n", k, SuperMap [k])) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal numerical factorization, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ ok = r_cholmod_super_numeric (A, F, beta, L, C, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_super_numeric (A, F, beta, L, C, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* This operates on complex L, not zomplex */
+ ok = z_cholmod_super_numeric (A, F, beta, L, C, Common) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear Common workspace, free temp workspace C, and return */
+ /* ---------------------------------------------------------------------- */
+
+ /* Flag array was used as workspace, clear it */
+ Common->mark = EMPTY ;
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ CHOLMOD(free_dense) (&C, Common) ;
+ return (ok) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_solve.c b/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_solve.c
new file mode 100644
index 0000000..58191f0
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_solve.c
@@ -0,0 +1,221 @@
+/* ========================================================================== */
+/* === Supernodal/cholmod_super_solve ======================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Solve Lx=b or L'x=b for a supernodal factorization. These routines do not
+ * apply the permutation L->Perm. See cholmod_solve for a more general
+ * interface that performs that operation.
+ */
+
+#ifndef NSUPERNODAL
+
+#include "cholmod_internal.h"
+#include "cholmod_supernodal.h"
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_super_solve.c"
+#define COMPLEX
+#include "t_cholmod_super_solve.c"
+
+/* ========================================================================== */
+/* === cholmod_super_lsolve ================================================= */
+/* ========================================================================== */
+
+/* Solve Lx=b where x and b are of size n-by-nrhs. b is overwritten by the
+ * solution x. On input, b is stored in col-major order with leading dimension
+ * of d, and on output x is stored in the same manner.
+ *
+ * The contents of the workspace E are undefined on both input and output.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(super_lsolve)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (E, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ if (L->xtype != X->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (L->xtype != E->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (X->d < X->nrow || L->n != X->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ;
+ return (FALSE) ;
+ }
+ if (E->nzmax < X->ncol * (L->maxesize))
+ {
+ ERROR (CHOLMOD_INVALID, "workspace E not large enough") ;
+ return (FALSE) ;
+ }
+ if (!(L->is_ll) || !(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID, "L not supernodal") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ;
+ if (L->n == 0 || X->ncol == 0)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Lx=b using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ ok = r_cholmod_super_lsolve (L, X, E, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_super_lsolve (L, X, E, Common) ;
+ break ;
+ }
+
+ if (CHECK_BLAS_INT && !ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_super_ltsolve ================================================ */
+/* ========================================================================== */
+
+/* Solve L'x=b where x and b are of size n-by-nrhs. b is overwritten by the
+ * solution x. On input, b is stored in col-major order with leading dimension
+ * of d, and on output x is stored in the same manner.
+ *
+ * The contents of the workspace E are undefined on both input and output.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(super_ltsolve)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the backsolve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to L'x=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (E, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ if (L->xtype != X->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (L->xtype != E->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (X->d < X->nrow || L->n != X->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ;
+ return (FALSE) ;
+ }
+ if (E->nzmax < X->ncol * (L->maxesize))
+ {
+ ERROR (CHOLMOD_INVALID, "workspace E not large enough") ;
+ return (FALSE) ;
+ }
+ if (!(L->is_ll) || !(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID, "L not supernodal") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ;
+ if (L->n == 0 || X->ncol == 0)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Lx=b using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ ok = r_cholmod_super_ltsolve (L, X, E, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_super_ltsolve (L, X, E, Common) ;
+ break ;
+ }
+
+ if (CHECK_BLAS_INT && !ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+
+ return (ok) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_symbolic.c b/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_symbolic.c
new file mode 100644
index 0000000..d41aa60
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/cholmod_super_symbolic.c
@@ -0,0 +1,794 @@
+/* ========================================================================== */
+/* === Supernodal/cholmod_super_symbolic ==================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Supernodal symbolic analysis of the LL' factorization of A, A*A',
+ * A(:,f)*A(:,f)'.
+ *
+ * This routine must be preceded by a simplicial symbolic analysis
+ * (cholmod_rowcolcounts). See cholmod_analyze.c for an example of how to use
+ * this routine.
+ *
+ * The user need not call this directly; cholmod_analyze is a "simple" wrapper
+ * for this routine.
+ *
+ * Symmetric case:
+ *
+ * A is stored in column form, with entries stored in the upper triangular
+ * part. Entries in the lower triangular part are ignored.
+ *
+ * Unsymmetric case:
+ *
+ * A is stored in column form. If F is equal to the transpose of A, then
+ * A*A' is analyzed. F can include a subset of the columns of A
+ * (F=A(:,f)'), in which case F*F' is analyzed.
+ *
+ * Requires Parent and L->ColCount to be defined on input; these are the
+ * simplicial Parent and ColCount arrays as computed by cholmod_rowcolcounts.
+ * Does not use L->Perm; the input matrices A and F must already be properly
+ * permuted. Allocates and computes the supernodal pattern of L (L->super,
+ * L->pi, L->px, and L->s). Does not allocate the real part (L->x).
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NSUPERNODAL
+
+#include "cholmod_internal.h"
+#include "cholmod_supernodal.h"
+
+
+/* ========================================================================== */
+/* === subtree ============================================================== */
+/* ========================================================================== */
+
+/* In the symmetric case, traverse the kth row subtree from the nonzeros in
+ * A (0:k,k) and add the new entries found to the pattern of the kth row of L.
+ *
+ * In the unsymmetric case, the nonzero pattern of A*F is computed one column at
+ * one column at a time. The kth column is A*F(:,k), or the set union of all
+ * columns A(:,j) for which F(j,k) is nonzero. This routine is called once
+ * for each entry j. Only the upper triangular part is needed, so only
+ * A (0:k,j) is accessed.
+ *
+ * Only adds column indices corresponding to the leading columns of each
+ * relaxed supernode.
+ */
+
+static void subtree
+(
+ /* inputs, not modified: */
+ Int j, /* j = k for symmetric case */
+ Int k,
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Anz [ ],
+ Int SuperMap [ ],
+ Int Sparent [ ],
+ Int mark,
+
+ /* input/output: */
+ Int Flag [ ],
+ Int Ls [ ],
+ Int Lpi2 [ ]
+)
+{
+ Int p, pend, i, si ;
+ p = Ap [j] ;
+ pend = (Anz == NULL) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i < k)
+ {
+ /* (i,k) is an entry in the upper triangular part of A or A*F'.
+ * symmetric case: A(i,k) is nonzero (j=k).
+ * unsymmetric case: A(i,j) and F(j,k) are both nonzero.
+ *
+ * Column i is in supernode si = SuperMap [i]. Follow path from si
+ * to root of supernodal etree, stopping at the first flagged
+ * supernode. The root of the row subtree is supernode SuperMap[k],
+ * which is flagged already. This traversal will stop there, or it
+ * might stop earlier if supernodes have been flagged by previous
+ * calls to this routine for the same k. */
+ for (si = SuperMap [i] ; Flag [si] < mark ; si = Sparent [si])
+ {
+ ASSERT (si <= SuperMap [k]) ;
+ Ls [Lpi2 [si]++] = k ;
+ Flag [si] = mark ;
+ }
+ }
+ }
+}
+
+
+/* clear workspace used by cholmod_super_symbolic */
+#define FREE_WORKSPACE \
+{ \
+ CHOLMOD(clear_flag) (Common) ; \
+ for (k = 0 ; k <= nfsuper ; k++) \
+ { \
+ Head [k] = EMPTY ; \
+ } \
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \
+} \
+
+
+/* ========================================================================== */
+/* === cholmod_super_symbolic =============================================== */
+/* ========================================================================== */
+
+/* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric
+ * factorization. The user need not call this directly; cholmod_analyze is
+ * a "simple" wrapper for this routine.
+ *
+ * workspace: Flag (nrow), Head (nrow), Iwork (2*nrow),
+ * and temporary space of size 3*nfsuper*sizeof(Int), where nfsuper <= n
+ * is the number of fundamental supernodes.
+ */
+
+int CHOLMOD(super_symbolic)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ Int *Parent, /* elimination tree */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* simplicial symbolic on input,
+ * supernodal symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double zrelax0, zrelax1, zrelax2, xxsize ;
+ Int *Wi, *Wj, *Super, *Snz, *Ap, *Ai, *Flag, *Head, *Ls, *Lpi, *Lpx, *Fnz,
+ *Sparent, *Anz, *SuperMap, *Merged, *Nscol, *Zeros, *Fp, *Fj,
+ *ColCount, *Lpi2, *Lsuper, *Iwork ;
+ Int nsuper, d, n, j, k, s, mark, parent, p, pend, k1, k2, packed, nscol,
+ nsrow, ndrow1, ndrow2, stype, ssize, xsize, sparent, plast, slast,
+ csize, maxcsize, ss, nscol0, nscol1, ns, nfsuper, newzeros, totzeros,
+ merge, snext, esize, maxesize, nrelax0, nrelax1, nrelax2 ;
+ size_t w ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_PATTERN, FALSE) ;
+ stype = A->stype ;
+ if (stype < 0)
+ {
+ /* invalid symmetry; symmetric lower form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+ if (stype == 0)
+ {
+ /* F must be present in the unsymmetric case */
+ RETURN_IF_NULL (F, FALSE) ;
+ ASSERT (CHOLMOD(dump_sparse) (F, "Fsup", Common) >= 0) ;
+ }
+ if (L->is_super)
+ {
+ /* L must be a simplicial symbolic factor */
+ ERROR (CHOLMOD_INVALID, "L must be symbolic on input") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "Asup", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+
+ /* w = 5*n */
+ w = CHOLMOD(mult_size_t) (n, 5, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, w, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* A is now either A or triu(A(p,p)) for the symmetric case. It is either
+ * A or A(p,f) for the unsymmetric case (both in column form). It can be
+ * either packed or unpacked, and either sorted or unsorted. Entries in
+ * the lower triangular part may be present if A is symmetric, but these
+ * are ignored. */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+
+ if (stype != 0)
+ {
+ /* F not accessed */
+ Fp = NULL ;
+ Fj = NULL ;
+ Fnz = NULL ;
+ packed = TRUE ;
+ }
+ else
+ {
+ /* F = A(:,f) or A(p,f) in packed row form, either sorted or unsorted */
+ Fp = F->p ;
+ Fj = F->i ;
+ Fnz = F->nz ;
+ packed = F->packed ;
+ }
+
+ ColCount = L->ColCount ;
+
+ nrelax0 = Common->nrelax [0] ;
+ nrelax1 = Common->nrelax [1] ;
+ nrelax2 = Common->nrelax [2] ;
+
+ zrelax0 = Common->zrelax [0] ;
+ zrelax1 = Common->zrelax [1] ;
+ zrelax2 = Common->zrelax [2] ;
+
+ zrelax0 = IS_NAN (zrelax0) ? 0 : zrelax0 ;
+ zrelax1 = IS_NAN (zrelax1) ? 0 : zrelax1 ;
+ zrelax2 = IS_NAN (zrelax2) ? 0 : zrelax2 ;
+
+ ASSERT (CHOLMOD(dump_parent) (Parent, n, "Parent", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Sparent, Snz, and Merged could be allocated later, of size nfsuper */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size n (i/l/l). Lpi2 is i/l/l */
+ Wj = Iwork + n ; /* size n (i/l/l). Zeros is i/l/l */
+ Sparent = Iwork + 2*((size_t) n) ; /* size nfsuper <= n [ */
+ Snz = Iwork + 3*((size_t) n) ; /* size nfsuper <= n [ */
+ Merged = Iwork + 4*((size_t) n) ; /* size nfsuper <= n [ */
+
+ Flag = Common->Flag ; /* size n */
+ Head = Common->Head ; /* size n+1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the fundamental supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* count the number of children of each node, using Wi [ */
+ for (j = 0 ; j < n ; j++)
+ {
+ Wi [j] = 0 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ Wi [parent]++ ;
+ }
+ }
+
+ Super = Head ; /* use Head [0..nfsuper] as workspace for Super list ( */
+
+ /* column 0 always starts a new supernode */
+ nfsuper = (n == 0) ? 0 : 1 ; /* number of fundamental supernodes */
+ Super [0] = 0 ;
+
+ for (j = 1 ; j < n ; j++)
+ {
+ /* check if j starts new supernode, or in the same supernode as j-1 */
+ if (Parent [j-1] != j /* parent of j-1 is not j */
+ || (ColCount [j-1] != ColCount [j] + 1) /* j-1 not subset of j*/
+ || Wi [j] > 1) /* j has more than one child */
+ {
+ /* j is the leading node of a supernode */
+ Super [nfsuper++] = j ;
+ }
+ }
+ Super [nfsuper] = n ;
+
+ /* contents of Wi no longer needed for child count ] */
+
+ Nscol = Wi ; /* use Wi as size-nfsuper workspace for Nscol [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the mapping of fundamental nodes to supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ SuperMap = Wj ; /* use Wj as workspace for SuperMap [ */
+
+ /* SuperMap [k] = s if column k is contained in supernode s */
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ for (k = Super [s] ; k < Super [s+1] ; k++)
+ {
+ SuperMap [k] = s ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the fundamental supernodal etree */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ j = Super [s+1] - 1 ; /* last node in supernode s */
+ parent = Parent [j] ; /* parent of last node */
+ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ;
+ PRINT1 (("Sparent ["ID"] = "ID"\n", s, Sparent [s])) ;
+ }
+
+ /* contents of Wj no longer needed as workspace for SuperMap ]
+ * SuperMap will be recomputed below, for the relaxed supernodes. */
+
+ Zeros = Wj ; /* use Wj for Zeros, workspace of size nfsuper [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* relaxed amalgamation */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ Merged [s] = EMPTY ; /* s not merged into another */
+ Nscol [s] = Super [s+1] - Super [s] ; /* # of columns in s */
+ Zeros [s] = 0 ; /* # of zero entries in s */
+ ASSERT (s <= Super [s]) ;
+ Snz [s] = ColCount [Super [s]] ; /* # of entries in leading col of s */
+ PRINT2 (("lnz ["ID"] "ID"\n", s, Snz [s])) ;
+ }
+
+ for (s = nfsuper-2 ; s >= 0 ; s--)
+ {
+ /* should supernodes s and s+1 merge into a new node s? */
+ PRINT1 (("\n========= Check relax of s "ID" and s+1 "ID"\n", s, s+1)) ;
+
+ ss = Sparent [s] ;
+ if (ss == EMPTY)
+ {
+ PRINT1 (("s "ID" is a root, no merge with s+1 = "ID"\n", s, s+1)) ;
+ continue ;
+ }
+
+ /* find the current parent of s (perform path compression as needed) */
+ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = Merged [ss]) ;
+ sparent = ss ;
+ PRINT2 (("Current sparent of s "ID" is "ID"\n", s, sparent)) ;
+
+ /* ss is the current parent of s */
+ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = snext)
+ {
+ snext = Merged [ss] ;
+ PRINT2 (("ss "ID" is dead, merged into snext "ID"\n", ss, snext)) ;
+ Merged [ss] = sparent ;
+ }
+
+ /* if s+1 is not the current parent of s, do not merge */
+ if (sparent != s+1)
+ {
+ continue ;
+ }
+
+ nscol0 = Nscol [s] ; /* # of columns in s */
+ nscol1 = Nscol [s+1] ; /* # of columns in s+1 */
+ ns = nscol0 + nscol1 ;
+ PRINT2 (("ns "ID" nscol0 "ID" nscol1 "ID"\n", ns, nscol0, nscol1)) ;
+
+ totzeros = Zeros [s+1] ; /* current # of zeros in s+1 */
+
+ /* determine if supernodes s and s+1 should merge */
+ if (ns <= nrelax0)
+ {
+ PRINT2 (("ns is tiny ("ID"), so go ahead and merge\n", ns)) ;
+ merge = TRUE ;
+ }
+ else
+ {
+ /* use double to avoid integer overflow */
+ double lnz0 = Snz [s] ; /* # entries in leading column of s */
+ double lnz1 = Snz [s+1] ; /* # entries in leading column of s+1 */
+ double xnewzeros = nscol0 * (lnz1 + nscol0 - lnz0) ;
+
+ /* use Int for the final update of Zeros [s] below */
+ newzeros = nscol0 * (Snz [s+1] + nscol0 - Snz [s]) ;
+ ASSERT (newzeros == xnewzeros) ;
+
+ PRINT2 (("lnz0 %g lnz1 %g xnewzeros %g\n", lnz0, lnz1, xnewzeros)) ;
+ if (xnewzeros == 0)
+ {
+ /* no new zeros, so go ahead and merge */
+ PRINT2 (("no new fillin, so go ahead and merge\n")) ;
+ merge = TRUE ;
+ }
+ else
+ {
+ /* # of zeros if merged */
+ double xtotzeros = ((double) totzeros) + xnewzeros ;
+
+ /* xtotsize: total size of merged supernode, if merged: */
+ double xns = (double) ns ;
+ double xtotsize = (xns * (xns+1) / 2) + xns * (lnz1 - nscol1) ;
+ double z = xtotzeros / xtotsize ;
+
+ Int totsize ;
+ totsize = (ns * (ns+1) / 2) + ns * (Snz [s+1] - nscol1) ;
+
+ PRINT2 (("oldzeros "ID" newzeros "ID" xtotsize %g z %g\n",
+ Zeros [s+1], newzeros, xtotsize, z)) ;
+
+ /* use Int for the final update of Zeros [s] below */
+ totzeros += newzeros ;
+
+ /* do not merge if supernode would become too big
+ * (Int overflow). Continue computing; not (yet) an error. */
+ /* fl.pt. compare, but no NaN's can occur here */
+ merge = ((ns <= nrelax1 && z < zrelax0) ||
+ (ns <= nrelax2 && z < zrelax1) ||
+ (z < zrelax2)) &&
+ (xtotsize < Int_max / sizeof (double)) ;
+
+ }
+ }
+
+ if (merge)
+ {
+ PRINT1 (("Merge node s ("ID") and s+1 ("ID")\n", s, s+1)) ;
+ Zeros [s] = totzeros ;
+ Merged [s+1] = s ;
+ Snz [s] = nscol0 + Snz [s+1] ;
+ Nscol [s] += Nscol [s+1] ;
+ }
+ }
+
+ /* contents of Wj no longer needed for Zeros ] */
+ /* contents of Wi no longer needed for Nscol ] */
+ /* contents of Sparent no longer needed (recomputed below) */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the relaxed supernode list */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = 0 ;
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ if (Merged [s] == EMPTY)
+ {
+ PRINT1 (("live supernode: "ID" snz "ID"\n", s, Snz [s])) ;
+ Super [nsuper] = Super [s] ;
+ Snz [nsuper] = Snz [s] ;
+ nsuper++ ;
+ }
+ }
+ Super [nsuper] = n ;
+ PRINT1 (("Fundamental supernodes: "ID" relaxed "ID"\n", nfsuper, nsuper)) ;
+
+ /* Merged no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the mapping of relaxed nodes to supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Wj as workspace for SuperMap { */
+
+ /* SuperMap [k] = s if column k is contained in supernode s */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ for (k = Super [s] ; k < Super [s+1] ; k++)
+ {
+ SuperMap [k] = s ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the relaxed supernodal etree */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ j = Super [s+1] - 1 ; /* last node in supernode s */
+ parent = Parent [j] ; /* parent of last node */
+ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ;
+ PRINT1 (("new Sparent ["ID"] = "ID"\n", s, Sparent [s])) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the size of L->s and L->x */
+ /* ---------------------------------------------------------------------- */
+
+ ssize = 0 ;
+ xsize = 0 ;
+ xxsize = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ nscol = Super [s+1] - Super [s] ;
+ nsrow = Snz [s] ;
+ ASSERT (nscol > 0) ;
+ ssize += nsrow ;
+ xsize += nscol * nsrow ;
+ /* also compute xsize in double to guard against Int overflow */
+ xxsize += ((double) nscol) * ((double) nsrow) ;
+ if (xxsize > Int_max)
+ {
+ /* Int overflow, clear workspace and return */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ FREE_WORKSPACE ;
+ return (FALSE) ;
+ }
+ ASSERT (ssize > 0 && xsize > 0) ;
+ }
+ xsize = MAX (1, xsize) ;
+ ssize = MAX (1, ssize) ;
+ PRINT1 (("ix sizes: "ID" "ID" nsuper "ID"\n", ssize, xsize, nsuper)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate L (all except real part L->x) */
+ /* ---------------------------------------------------------------------- */
+
+ L->ssize = ssize ;
+ L->xsize = xsize ;
+ L->nsuper = nsuper ;
+
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L, Common);
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory; L is still a valid simplicial symbolic factor */
+ FREE_WORKSPACE ;
+ return (FALSE) ;
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "L to symbolic super", Common)) ;
+ ASSERT (L->is_ll && L->xtype == CHOLMOD_PATTERN && L->is_super) ;
+
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Ls [0] = 0 ; /* flag for cholmod_check_factor; supernodes are defined */
+ Lsuper = L->super ;
+
+ /* copy the list of relaxed supernodes into the final list in L */
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ Lsuper [s] = Super [s] ;
+ }
+
+ /* Head no longer needed as workspace for fundamental Super list ) */
+
+ Super = Lsuper ; /* Super is now the list of relaxed supernodes */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct column pointers of relaxed supernodal pattern (L->pi) */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ Lpi [s] = p ;
+ p += Snz [s] ;
+ PRINT1 (("Snz ["ID"] = "ID", Super ["ID"] = "ID"\n",
+ s, Snz [s], s, Super[s])) ;
+ }
+ Lpi [nsuper] = p ;
+ ASSERT ((Int) (L->ssize) == MAX (1,p)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct pointers for supernodal values (L->px) */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ nscol = Super [s+1] - Super [s] ; /* number of columns in s */
+ nsrow = Snz [s] ; /* # of rows, incl triangular part*/
+ Lpx [s] = p ; /* pointer to numerical part of s */
+ p += nscol * nsrow ;
+ }
+ Lpx [s] = p ;
+ ASSERT ((Int) (L->xsize) == MAX (1,p)) ;
+
+ /* Snz no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic analysis to construct the relaxed supernodal pattern (L->s) */
+ /* ---------------------------------------------------------------------- */
+
+ Lpi2 = Wi ; /* copy Lpi into Lpi2, using Wi as workspace for Lpi2 [ */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ Lpi2 [s] = Lpi [s] ;
+ }
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ /* sth supernode is in columns k1 to k2-1.
+ * compute nonzero pattern of L (k1:k2-1,:). */
+
+ /* place rows k1 to k2-1 in leading column of supernode s */
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ PRINT1 (("=========>>> Supernode "ID" k1 "ID" k2-1 "ID"\n",
+ s, k1, k2-1)) ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ Ls [Lpi2 [s]++] = k ;
+ }
+
+ /* compute nonzero pattern each row k1 to k2-1 */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ /* compute row k of L. In the symmetric case, the pattern of L(k,:)
+ * is the set of nodes reachable in the supernodal etree from any
+ * row i in the nonzero pattern of A(0:k,k). In the unsymmetric
+ * case, the pattern of the kth column of A*A' is the set union
+ * of all columns A(0:k,j) for each nonzero F(j,k). */
+
+ /* clear the Flag array and mark the current supernode */
+ mark = CHOLMOD(clear_flag) (Common) ;
+ Flag [s] = mark ;
+ ASSERT (s == SuperMap [k]) ;
+
+ /* traverse the row subtree for each nonzero in A or AA' */
+ if (stype != 0)
+ {
+ subtree (k, k, Ap, Ai, Anz, SuperMap, Sparent, mark,
+ Flag, Ls, Lpi2) ;
+ }
+ else
+ {
+ /* for each nonzero in F (k,:) do */
+ p = Fp [k] ;
+ pend = (packed) ? (Fp [k+1]) : (p + Fnz [k]) ;
+ for ( ; p < pend ; p++)
+ {
+ subtree (Fj [p], k, Ap, Ai, Anz, SuperMap, Sparent, mark,
+ Flag, Ls, Lpi2) ;
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ PRINT1 (("Lpi2[s] "ID" Lpi[s+1] "ID"\n", Lpi2 [s], Lpi [s+1])) ;
+ ASSERT (Lpi2 [s] == Lpi [s+1]) ;
+ CHOLMOD(dump_super) (s, Super, Lpi, Ls, NULL, NULL, 0, Common) ;
+ }
+#endif
+
+ /* contents of Wi no longer needed for Lpi2 ] */
+ /* Sparent no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the largest update matrix (L->maxcsize) */
+ /* ---------------------------------------------------------------------- */
+
+ /* maxcsize could be determined before L->s is allocated and defined, which
+ * would mean that all memory requirements for both the symbolic and numeric
+ * factorizations could be computed using O(nnz(A)+O(n)) space. However, it
+ * would require a lot of extra work. The analysis phase, above, would need
+ * to be duplicated, but with Ls not kept; instead, the algorithm would keep
+ * track of the current s and slast for each supernode d, and update them
+ * when a new row index appears in supernode d. An alternative would be to
+ * do this computation only if the allocation of L->s failed, in which case
+ * the following code would be skipped.
+ *
+ * The csize for a supernode is the size of its largest contribution to
+ * a subsequent ancestor supernode. For example, suppose the rows of #'s
+ * in the figure below correspond to the columns of a subsequent supernode,
+ * and the dots are the entries in that ancestore.
+ *
+ * c
+ * c c
+ * c c c
+ * x x x
+ * x x x
+ * # # # .
+ * # # # . .
+ * * * * . .
+ * * * * . .
+ * * * * . .
+ * . .
+ *
+ * Then for this update, the csize is 3-by-2, or 6, because there are 3
+ * rows of *'s which is the number of rows in the update, and there are
+ * 2 rows of #'s, which is the number columns in the update. The csize
+ * of a supernode is the largest such contribution for any ancestor
+ * supernode. maxcsize, for the whole matrix, has a rough upper bound of
+ * the maximum size of any supernode. This bound is loose, because the
+ * the contribution must be less than the size of the ancestor supernodal
+ * that it's updating. maxcsize of a completely dense matrix, with one
+ * supernode, is zero.
+ *
+ * maxesize is the column dimension for the workspace E needed for the
+ * solve. E is of size nrhs-by-maxesize, where the nrhs is the number of
+ * columns in the right-hand-side. The maxesize is the largest esize of
+ * any supernode. The esize of a supernode is the number of row indices
+ * it contains, excluding the column indices of the supernode itself.
+ * For the following example, esize is 4:
+ *
+ * c
+ * c c
+ * c c c
+ * x x x
+ * x x x
+ * x x x
+ * x x x
+ *
+ * maxesize can be no bigger than n.
+ */
+
+ maxcsize = 1 ;
+ maxesize = 1 ;
+
+ /* do not need to guard csize against Int overflow if xsize is OK */
+
+ for (d = 0 ; d < nsuper ; d++)
+ {
+ nscol = Super [d+1] - Super [d] ;
+ p = Lpi [d] + nscol ;
+ plast = p ;
+ pend = Lpi [d+1] ;
+ esize = pend - p ;
+ maxesize = MAX (maxesize, esize) ;
+ slast = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ;
+ for ( ; p <= pend ; p++)
+ {
+ s = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ;
+ if (s != slast)
+ {
+ /* row i is the start of a new supernode */
+ ndrow1 = p - plast ;
+ ndrow2 = pend - plast ;
+ csize = ndrow2 * ndrow1 ;
+ PRINT1 (("Supernode "ID" ancestor "ID" C: "ID"-by-"ID" csize "
+ ""ID"\n", d, slast, ndrow1, ndrow2, csize)) ;
+ maxcsize = MAX (maxcsize, csize) ;
+ plast = p ;
+ slast = s ;
+ }
+ }
+ }
+ PRINT1 (("max csize "ID"\n", maxcsize)) ;
+
+ /* Wj no longer needed for SuperMap } */
+
+ L->maxcsize = maxcsize ;
+ L->maxesize = maxesize ;
+ L->is_super = TRUE ;
+ ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_ll) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal symbolic factorization is complete */
+ /* ---------------------------------------------------------------------- */
+
+ FREE_WORKSPACE ;
+ return (TRUE) ;
+}
+#endif
diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/gpl.txt b/src/C/SuiteSparse/CHOLMOD/Supernodal/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
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diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_numeric.c b/src/C/SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_numeric.c
new file mode 100644
index 0000000..4757721
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_numeric.c
@@ -0,0 +1,741 @@
+/* ========================================================================== */
+/* === Supernodal/t_cholmod_super_numeric =================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_super_numeric. All xtypes supported, except
+ * that a zomplex A and F result in a complex L (there is no supernodal
+ * zomplex L).
+ */
+
+/* ========================================================================== */
+/* === complex arithmetic =================================================== */
+/* ========================================================================== */
+
+#include "cholmod_template.h"
+
+#undef L_ENTRY
+#undef L_CLEAR
+#undef L_ASSIGN
+#undef L_MULTADD
+#undef L_ASSEMBLE
+#undef L_ASSEMBLESUB
+
+#ifdef REAL
+
+/* -------------------------------------------------------------------------- */
+/* A, F, and L are all real */
+/* -------------------------------------------------------------------------- */
+
+#define L_ENTRY 1
+#define L_CLEAR(Lx,p) Lx [p] = 0
+#define L_ASSIGN(Lx,q, Ax,Az,p) Lx [q] = Ax [p]
+#define L_MULTADD(Lx,q, Ax,Az,p, f) Lx [q] += Ax [p] * f [0]
+#define L_ASSEMBLE(Lx,q,b) Lx [q] += b [0]
+#define L_ASSEMBLESUB(Lx,q,C,p) Lx [q] -= C [p]
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* A and F are complex or zomplex, L and C are complex */
+/* -------------------------------------------------------------------------- */
+
+#define L_ENTRY 2
+#define L_CLEAR(Lx,p) Lx [2*(p)] = 0 ; Lx [2*(p)+1] = 0
+#define L_ASSEMBLE(Lx,q,b) Lx [2*(q)] += b [0] ;
+#define L_ASSEMBLESUB(Lx,q,C,p) \
+ Lx [2*(q) ] -= C [2*(p) ] ; \
+ Lx [2*(q)+1] -= C [2*(p)+1] ;
+
+#ifdef COMPLEX
+
+/* -------------------------------------------------------------------------- */
+/* A, F, L, and C are all complex */
+/* -------------------------------------------------------------------------- */
+
+#define L_ASSIGN(Lx,q, Ax,Az,p) \
+ Lx [2*(q) ] = Ax [2*(p) ] ; \
+ Lx [2*(q)+1] = Ax [2*(p)+1]
+
+#define L_MULTADD(Lx,q, Ax,Az,p, f) \
+ Lx [2*(q) ] += Ax [2*(p) ] * f [0] - Ax [2*(p)+1] * f [1] ; \
+ Lx [2*(q)+1] += Ax [2*(p)+1] * f [0] + Ax [2*(p) ] * f [1]
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* A and F are zomplex, L and C is complex */
+/* -------------------------------------------------------------------------- */
+
+#define L_ASSIGN(Lx,q, Ax,Az,p) \
+ Lx [2*(q) ] = Ax [p] ; \
+ Lx [2*(q)+1] = Az [p] ;
+
+#define L_MULTADD(Lx,q, Ax,Az,p, f) \
+ Lx [2*(q) ] += Ax [p] * f [0] - Az [p] * f [1] ; \
+ Lx [2*(q)+1] += Az [p] * f [0] + Ax [p] * f [1]
+
+#endif
+#endif
+
+
+/* ========================================================================== */
+/* === t_cholmod_super_numeric ============================================== */
+/* ========================================================================== */
+
+/* This function returns FALSE only if integer overflow occurs in the BLAS.
+ * It returns TRUE otherwise whether or not the matrix is positive definite. */
+
+static int TEMPLATE (cholmod_super_numeric)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ double beta [2], /* beta*I is added to diagonal of matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization */
+ /* -- workspace -- */
+ cholmod_dense *Cwork, /* size (L->maxcsize)-by-1 */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double one [2], zero [2], fjk [2] ;
+ double *Lx, *Ax, *Fx, *Az, *Fz, *C ;
+ Int *Super, *Head, *Ls, *Lpi, *Lpx, *Map, *SuperMap, *RelativeMap, *Next,
+ *Lpos, *Fp, *Fi, *Fnz, *Ap, *Ai, *Anz, *Iwork, *Next_save, *Lpos_save ;
+ Int nsuper, n, j, i, k, s, p, pend, k1, k2, nscol, psi, psx, psend, nsrow,
+ pj, d, kd1, kd2, info, ndcol, ndrow, pdi, pdx, pdend, pdi1, pdi2, pdx1,
+ ndrow1, ndrow2, px, dancestor, sparent, dnext, nsrow2, ndrow3, pk, pf,
+ pfend, stype, Apacked, Fpacked, q, imap, repeat_supernode, nscol2, ss,
+ nscol_new = 0 ;
+
+ /* If integer overflow occurs in the BLAS, Common->status is set to
+ * CHOLMOD_TOO_LARGE, and the contents of Lx are undefined. */
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = L->nsuper ;
+ n = L->n ;
+
+ C = Cwork->x ; /* workspace of size L->maxcsize */
+
+ one [0] = 1.0 ; /* ALPHA for *syrk, *herk, *gemm, and *trsm */
+ one [1] = 0. ;
+
+ zero [0] = 0. ; /* BETA for *syrk, *herk, and *gemm */
+ zero [1] = 0. ;
+
+ Iwork = Common->Iwork ;
+ SuperMap = Iwork ; /* size n (i/i/l) */
+ RelativeMap = Iwork + n ; /* size n (i/i/l) */
+ Next = Iwork + 2*((size_t) n) ; /* size nsuper*/
+ Lpos = Iwork + 2*((size_t) n) + nsuper ; /* size nsuper*/
+ Next_save = Iwork + 2*((size_t) n) + 2*((size_t) nsuper) ;/* size nsuper*/
+ Lpos_save = Iwork + 2*((size_t) n) + 3*((size_t) nsuper) ;/* size nsuper*/
+
+ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */
+ Head = Common->Head ; /* size n+1, only Head [0..nsuper-1] used */
+
+ Ls = L->s ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+
+ Super = L->super ;
+
+ Lx = L->x ;
+
+ stype = A->stype ;
+
+ if (stype != 0)
+ {
+ /* F not accessed */
+ Fp = NULL ;
+ Fi = NULL ;
+ Fx = NULL ;
+ Fz = NULL ;
+ Fnz = NULL ;
+ Fpacked = TRUE ;
+ }
+ else
+ {
+ Fp = F->p ;
+ Fi = F->i ;
+ Fx = F->x ;
+ Fz = F->z ;
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ Apacked = A->packed ;
+
+ /* clear the Map so that changes in the pattern of A can be detected */
+ for (i = 0 ; i < n ; i++)
+ {
+ Map [i] = EMPTY ;
+ }
+
+ /* If the matrix is not positive definite, the supernode s containing the
+ * first zero or negative diagonal entry of L is repeated (but factorized
+ * only up to just before the problematic diagonal entry). The purpose is
+ * to provide MATLAB with [R,p]=chol(A); columns 1 to p-1 of L=R' are
+ * required, where L(p,p) is the problematic diagonal entry. The
+ * repeat_supernode flag tells us whether this is the repeated supernode.
+ * Once supernode s is repeated, the factorization is terminated. */
+ repeat_supernode = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the size of supernode s */
+ /* ------------------------------------------------------------------ */
+
+ k1 = Super [s] ; /* s contains columns k1 to k2-1 of L */
+ k2 = Super [s+1] ;
+ nscol = k2 - k1 ; /* # of columns in all of s */
+ psi = Lpi [s] ; /* pointer to first row of s in Ls */
+ psx = Lpx [s] ; /* pointer to first row of s in Lx */
+ psend = Lpi [s+1] ; /* pointer just past last row of s in Ls */
+ nsrow = psend - psi ; /* # of rows in all of s */
+
+ PRINT1 (("====================================================\n"
+ "S "ID" k1 "ID" k2 "ID" nsrow "ID" nscol "ID" psi "ID" psend "
+ ""ID" psx "ID"\n", s, k1, k2, nsrow, nscol, psi, psend, psx)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* zero the supernode s */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT ((size_t) (psx + nsrow*nscol) <= L->xsize) ;
+
+ pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */
+ for (p = psx ; p < pend ; p++)
+ {
+ /* Lx [p] = 0 ; */
+ L_CLEAR (Lx,p) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* construct the scattered Map for supernode s */
+ /* ------------------------------------------------------------------ */
+
+ /* If row i is the kth row in s, then Map [i] = k. Similarly, if
+ * column j is the kth column in s, then Map [j] = k. */
+
+ for (k = 0 ; k < nsrow ; k++)
+ {
+ PRINT1 ((" "ID" map "ID"\n", Ls [psi+k], k)) ;
+ Map [Ls [psi + k]] = k ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* copy matrix into supernode s (lower triangular part only) */
+ /* ------------------------------------------------------------------ */
+
+ pk = psx ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ if (stype != 0)
+ {
+ /* copy the kth column of A into the supernode */
+ p = Ap [k] ;
+ pend = (Apacked) ? (Ap [k+1]) : (p + Anz [k]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* row i of L is located in row Map [i] of s */
+ i = Ai [p] ;
+ if (i >= k)
+ {
+ /* This test is here simply to avoid a segfault. If
+ * the test is false, the numeric factorization of A
+ * is undefined. It does not detect all invalid
+ * entries, only some of them (when debugging is
+ * enabled, and Map is cleared after each step, then
+ * all entries not in the pattern of L are detected). */
+ imap = Map [i] ;
+ if (imap >= 0 && imap < nsrow)
+ {
+ /* Lx [Map [i] + pk] = Ax [p] ; */
+ L_ASSIGN (Lx,(imap+pk), Ax,Az,p) ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* copy the kth column of A*F into the supernode */
+ pf = Fp [k] ;
+ pfend = (Fpacked) ? (Fp [k+1]) : (p + Fnz [k]) ;
+ for ( ; pf < pfend ; pf++)
+ {
+ j = Fi [pf] ;
+
+ /* fjk = Fx [pf] ; */
+ L_ASSIGN (fjk,0, Fx,Fz,pf) ;
+
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= k)
+ {
+ /* See the discussion of imap above. */
+ imap = Map [i] ;
+ if (imap >= 0 && imap < nsrow)
+ {
+ /* Lx [Map [i] + pk] += Ax [p] * fjk ; */
+ L_MULTADD (Lx,(imap+pk), Ax,Az,p, fjk) ;
+ }
+ }
+ }
+ }
+ }
+ pk += nsrow ; /* advance to the next column of the supernode */
+ }
+
+ /* add beta to the diagonal of the supernode, if nonzero */
+ if (beta [0] != 0.0)
+ {
+ /* note that only the real part of beta is used */
+ pk = psx ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ /* Lx [pk] += beta [0] ; */
+ L_ASSEMBLE (Lx,pk, beta) ;
+ pk += nsrow + 1 ; /* advance to the next diagonal entry */
+ }
+ }
+
+ PRINT1 (("Supernode with just A: repeat: "ID"\n", repeat_supernode)) ;
+ DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+ PRINT1 (("\n\n")) ;
+
+ /* ------------------------------------------------------------------ */
+ /* save/restore the list of supernodes */
+ /* ------------------------------------------------------------------ */
+
+ if (!repeat_supernode)
+ {
+ /* Save the list of pending descendants in case s is not positive
+ * definite. Also save Lpos for each descendant d, so that we can
+ * find which part of d is used to update s. */
+ for (d = Head [s] ; d != EMPTY ; d = Next [d])
+ {
+ Lpos_save [d] = Lpos [d] ;
+ Next_save [d] = Next [d] ;
+ }
+ }
+ else
+ {
+ /* s is not positive definite, and is being repeated. Restore
+ * the list of supernodes. This can be done with pointer assignment
+ * because all 4 arrays are held within Common->Iwork. */
+ Lpos = Lpos_save ;
+ Next = Next_save ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* update supernode s with each pending descendant d */
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ for (d = Head [s] ; d != EMPTY ; d = Next [d])
+ {
+ PRINT1 (("\nWill update "ID" with Child: "ID"\n", s, d)) ;
+ DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+ }
+ PRINT1 (("\nNow factorizing supernode "ID":\n", s)) ;
+#endif
+
+ for (d = Head [s] ; d != EMPTY ; d = dnext)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* get the size of supernode d */
+ /* -------------------------------------------------------------- */
+
+ kd1 = Super [d] ; /* d contains cols kd1 to kd2-1 of L */
+ kd2 = Super [d+1] ;
+ ndcol = kd2 - kd1 ; /* # of columns in all of d */
+ pdi = Lpi [d] ; /* pointer to first row of d in Ls */
+ pdx = Lpx [d] ; /* pointer to first row of d in Lx */
+ pdend = Lpi [d+1] ; /* pointer just past last row of d in Ls */
+ ndrow = pdend - pdi ; /* # rows in all of d */
+
+ PRINT1 (("Child: ")) ;
+ DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+
+ /* -------------------------------------------------------------- */
+ /* find the range of rows of d that affect rows k1 to k2-1 of s */
+ /* -------------------------------------------------------------- */
+
+ p = Lpos [d] ; /* offset of 1st row of d affecting s */
+ pdi1 = pdi + p ; /* ptr to 1st row of d affecting s in Ls */
+ pdx1 = pdx + p ; /* ptr to 1st row of d affecting s in Lx */
+
+ /* there must be at least one row remaining in d to update s */
+ ASSERT (pdi1 < pdend) ;
+ PRINT1 (("Lpos[d] "ID" pdi1 "ID" Ls[pdi1] "ID"\n",
+ Lpos[d], pdi1, Ls [pdi1])) ;
+ ASSERT (Ls [pdi1] >= k1 && Ls [pdi1] < k2) ;
+
+ for (pdi2 = pdi1 ; pdi2 < pdend && Ls [pdi2] < k2 ; pdi2++) ;
+ ndrow1 = pdi2 - pdi1 ; /* # rows in first part of d */
+ ndrow2 = pdend - pdi1 ; /* # rows in remaining d */
+
+ /* rows Ls [pdi1 ... pdi2-1] are in the range k1 to k2-1. Since d
+ * affects s, this set cannot be empty. */
+ ASSERT (pdi1 < pdi2 && pdi2 <= pdend) ;
+ PRINT1 (("ndrow1 "ID" ndrow2 "ID"\n", ndrow1, ndrow2)) ;
+ DEBUG (for (p = pdi1 ; p < pdi2 ; p++)
+ PRINT1 (("Ls["ID"] "ID"\n", p, Ls[p]))) ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the update matrix C for this supernode d */
+ /* -------------------------------------------------------------- */
+
+ /* C = L (k1:n-1, kd1:kd2-1) * L (k1:k2-1, kd1:kd2-1)', except
+ * that k1:n-1 refers to all of the rows in L, but many of the
+ * rows are all zero. Supernode d holds columns kd1 to kd2-1 of L.
+ * Nonzero rows in the range k1:k2-1 are in the list
+ * Ls [pdi1 ... pdi2-1], of size ndrow1. Nonzero rows in the range
+ * k2:n-1 are in the list Ls [pdi2 ... pdend], of size ndrow2. Let
+ * L1 = L (Ls [pdi1 ... pdi2-1], kd1:kd2-1), and let
+ * L2 = L (Ls [pdi2 ... pdend], kd1:kd2-1). C is ndrow2-by-ndcol.
+ * Let C1 be the first ndrow1 rows of C and let C2 be the last
+ * ndrow2-ndrow1 rows of C. Only the lower triangular part of C1
+ * needs to be computed since C1 is symmetric.
+ */
+
+ /* maxcsize is the largest size of C for all pairs (d,s) */
+ ASSERT (ndrow2 * ndrow1 <= ((Int) L->maxcsize)) ;
+
+ /* compute leading ndrow1-by-ndrow1 lower triangular block of C,
+ * C1 = L1*L1' */
+
+#ifdef REAL
+ BLAS_dsyrk ("L", "N",
+ ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */
+ zero, /* BETA: 0 */
+ C, ndrow2) ; /* C, LDC: C1 */
+#else
+ BLAS_zherk ("L", "N",
+ ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */
+ zero, /* BETA: 0 */
+ C, ndrow2) ; /* C, LDC: C1 */
+#endif
+
+ /* compute remaining (ndrow3-ndrow1)-by-ndrow1 block of C,
+ * C2 = L2*L1' */
+ ndrow3 = ndrow2 - ndrow1 ;
+ if (ndrow3 > 0)
+ {
+
+#ifdef REAL
+ BLAS_dgemm ("N", "C",
+ ndrow3, ndrow1, ndcol, /* M, N, K */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */
+ ndrow,
+ Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */
+ ndrow,
+ zero, /* BETA: 0 */
+ C + L_ENTRY*ndrow1, /* C, LDC: C2 */
+ ndrow2) ;
+#else
+ BLAS_zgemm ("N", "C",
+ ndrow3, ndrow1, ndcol, /* M, N, K */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */
+ ndrow,
+ Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */
+ ndrow,
+ zero, /* BETA: 0 */
+ C + L_ENTRY*ndrow1, /* C, LDC: C2 */
+ ndrow2) ;
+#endif
+
+ }
+
+ DEBUG (CHOLMOD(dump_real) ("C", C, ndrow2, ndrow1, TRUE, L_ENTRY,
+ Common)) ;
+
+ /* -------------------------------------------------------------- */
+ /* construct relative map to assemble d into s */
+ /* -------------------------------------------------------------- */
+
+ for (i = 0 ; i < ndrow2 ; i++)
+ {
+ RelativeMap [i] = Map [Ls [pdi1 + i]] ;
+ ASSERT (RelativeMap [i] >= 0 && RelativeMap [i] < nsrow) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* assemble C into supernode s using the relative map */
+ /* -------------------------------------------------------------- */
+
+ pj = 0 ;
+ for (j = 0 ; j < ndrow1 ; j++) /* cols k1:k2-1 */
+ {
+ ASSERT (RelativeMap [j] == Map [Ls [pdi1 + j]]) ;
+ ASSERT (RelativeMap [j] >= 0 && RelativeMap [j] < nscol) ;
+ px = psx + RelativeMap [j] * nsrow ;
+ for (i = j ; i < ndrow2 ; i++) /* rows k1:n-1 */
+ {
+ ASSERT (RelativeMap [i] == Map [Ls [pdi1 + i]]) ;
+ ASSERT (RelativeMap [i] >= j && RelativeMap [i] < nsrow) ;
+ /* Lx [px + RelativeMap [i]] -= C [i + pj] ; */
+ q = px + RelativeMap [i] ;
+ L_ASSEMBLESUB (Lx,q, C, i+pj) ;
+ }
+ pj += ndrow2 ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* prepare this supernode d for its next ancestor */
+ /* -------------------------------------------------------------- */
+
+ dnext = Next [d] ;
+
+ if (!repeat_supernode)
+ {
+ /* If node s is being repeated, Head [dancestor] has already
+ * been cleared (set to EMPTY). It must remain EMPTY. The
+ * dancestor will not be factorized since the factorization
+ * terminates at node s. */
+ Lpos [d] = pdi2 - pdi ;
+ if (Lpos [d] < ndrow)
+ {
+ dancestor = SuperMap [Ls [pdi2]] ;
+ ASSERT (dancestor > s && dancestor < nsuper) ;
+ /* place d in the link list of its next ancestor */
+ Next [d] = Head [dancestor] ;
+ Head [dancestor] = d ;
+ }
+ }
+ }
+
+ PRINT1 (("\nSupernode with contributions A: repeat: "ID"\n",
+ repeat_supernode)) ;
+ DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+ PRINT1 (("\n\n")) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factorize diagonal block of supernode s in LL' */
+ /* ------------------------------------------------------------------ */
+
+ /* The current supernode s is ready to factorize. It has been updated
+ * by all descendant supernodes. Let S = the current supernode, which
+ * holds rows k1:n-1 and columns k1:k2-1 of the updated matrix. It
+ * splits into two parts: the square diagonal block S1, and the
+ * rectangular part S2. Here, S1 is factorized into L1*L1' and
+ * overwritten by S1.
+ *
+ * If supernode s is being repeated, only factorize it up to but not
+ * including the column containing the problematic entry.
+ */
+
+ nscol2 = (repeat_supernode) ? (nscol_new) : (nscol) ;
+
+#ifdef REAL
+ LAPACK_dpotrf ("L",
+ nscol2, /* N: nscol2 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */
+ info) ; /* INFO */
+#else
+ LAPACK_zpotrf ("L",
+ nscol2, /* N: nscol2 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */
+ info) ; /* INFO */
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* check if the matrix is not positive definite */
+ /* ------------------------------------------------------------------ */
+
+ if (repeat_supernode)
+ {
+ /* the leading part has been refactorized; it must have succeeded */
+ info = 0 ;
+
+ /* zero out the rest of this supernode */
+ p = psx + nsrow * nscol_new ;
+ pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */
+ for ( ; p < pend ; p++)
+ {
+ /* Lx [p] = 0 ; */
+ L_CLEAR (Lx,p) ;
+ }
+ }
+
+ /* info is set to one in LAPACK_*potrf if blas_ok is FALSE. It is
+ * set to zero in dpotrf/zpotrf if the factorization was successful. */
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+
+ if (info != 0)
+ {
+ /* Matrix is not positive definite. dpotrf/zpotrf do NOT report an
+ * error if the diagonal of L has NaN's, only if it has a zero. */
+ if (Common->status == CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "matrix not positive definite") ;
+ }
+
+ /* L->minor is the column of L that contains a zero or negative
+ * diagonal term. */
+ L->minor = k1 + info - 1 ;
+
+ /* clear the link lists of all subsequent supernodes */
+ for (ss = s+1 ; ss < nsuper ; ss++)
+ {
+ Head [ss] = EMPTY ;
+ }
+
+ /* zero this supernode, and all remaining supernodes */
+ pend = L->xsize ;
+ for (p = psx ; p < pend ; p++)
+ {
+ /* Lx [p] = 0. ; */
+ L_CLEAR (Lx,p) ;
+ }
+
+ /* If L is indefinite, it still contains useful information.
+ * Supernodes 0 to s-1 are valid, similar to MATLAB [R,p]=chol(A),
+ * where the 1-based p is identical to the 0-based L->minor. Since
+ * L->minor is in the current supernode s, it and any columns to the
+ * left of it in supernode s are also all zero. This differs from
+ * [R,p]=chol(A), which contains nonzero rows 1 to p-1. Fix this
+ * by setting repeat_supernode to TRUE, and repeating supernode s.
+ *
+ * If Common->quick_return_if_not_posdef is true, then the entire
+ * supernode s is not factorized; it is left as all zero.
+ */
+
+ if (info == 1 || Common->quick_return_if_not_posdef)
+ {
+ /* If the first column of supernode s contains a zero or
+ * negative diagonal entry, then it is already properly set to
+ * zero. Also, info will be 1 if integer overflow occured in
+ * the BLAS. */
+ Head [s] = EMPTY ;
+ return (Common->status >= CHOLMOD_OK) ;
+ }
+ else
+ {
+ /* Repeat supernode s, but only factorize it up to but not
+ * including the column containing the problematic diagonal
+ * entry. */
+ repeat_supernode = TRUE ;
+ s-- ;
+ nscol_new = info - 1 ;
+ continue ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* compute the subdiagonal block and prepare supernode for its parent */
+ /* ------------------------------------------------------------------ */
+
+ nsrow2 = nsrow - nscol2 ;
+ if (nsrow2 > 0)
+ {
+ /* The current supernode is columns k1 to k2-1 of L. Let L1 be the
+ * diagonal block (factorized by dpotrf/zpotrf above; rows/cols
+ * k1:k2-1), and L2 be rows k2:n-1 and columns k1:k2-1 of L. The
+ * triangular system to solve is L2*L1' = S2, where S2 is
+ * overwritten with L2. More precisely, L2 = S2 / L1' in MATLAB
+ * notation.
+ */
+
+#ifdef REAL
+ BLAS_dtrsm ("R", "L", "C", "N",
+ nsrow2, nscol2, /* M, N */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */
+ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */
+ nsrow) ;
+#else
+ BLAS_ztrsm ("R", "L", "C", "N",
+ nsrow2, nscol2, /* M, N */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */
+ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */
+ nsrow) ;
+#endif
+
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+
+ if (!repeat_supernode)
+ {
+ /* Lpos [s] is offset of first row of s affecting its parent */
+ Lpos [s] = nscol ;
+ sparent = SuperMap [Ls [psi + nscol]] ;
+ ASSERT (sparent != EMPTY) ;
+ ASSERT (Ls [psi + nscol] >= Super [sparent]) ;
+ ASSERT (Ls [psi + nscol] < Super [sparent+1]) ;
+ ASSERT (SuperMap [Ls [psi + nscol]] == sparent) ;
+ ASSERT (sparent > s && sparent < nsuper) ;
+ /* place s in link list of its parent */
+ Next [s] = Head [sparent] ;
+ Head [sparent] = s ;
+ }
+ }
+
+ Head [s] = EMPTY ; /* link list for supernode s no longer needed */
+
+ /* clear the Map (debugging only, to detect changes in pattern of A) */
+ DEBUG (for (k = 0 ; k < nsrow ; k++) Map [Ls [psi + k]] = EMPTY) ;
+ DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+
+ if (repeat_supernode)
+ {
+ /* matrix is not positive definite; finished clean-up for supernode
+ * containing negative diagonal */
+ return (Common->status >= CHOLMOD_OK) ;
+ }
+ }
+
+ /* success; matrix is positive definite */
+ L->minor = n ;
+ return (Common->status >= CHOLMOD_OK) ;
+}
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_solve.c b/src/C/SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_solve.c
new file mode 100644
index 0000000..2f5e792
--- /dev/null
+++ b/src/C/SuiteSparse/CHOLMOD/Supernodal/t_cholmod_super_solve.c
@@ -0,0 +1,430 @@
+/* ========================================================================== */
+/* === Supernodal/t_cholmod_super_solve ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_super_solve. Supports real or complex L. */
+
+#include "cholmod_template.h"
+
+static int TEMPLATE (cholmod_super_lsolve)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Xx, *Ex ;
+ double minus_one [2], one [2] ;
+ Int *Lpi, *Lpx, *Ls, *Super ;
+ Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s,
+ nsrow2, n, ps2, j, i, d, nrhs ;
+
+ /* If integer overflow occurs in the BLAS, Common->status is set to
+ * CHOLMOD_TOO_LARGE in the caller, and the contents of X are undefined. */
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrhs = X->ncol ;
+ Ex = E->x ;
+ Xx = X->x ;
+ n = L->n ;
+ d = X->d ;
+
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+ Lx = L->x ;
+ minus_one [0] = -1.0 ;
+ minus_one [1] = 0 ;
+ one [0] = 1.0 ;
+ one [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Lx=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrhs == 1)
+ {
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal.
+ * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of
+ * nsrow. x1 is nscol-by-nsrow, with leading dimension n.
+ * E is nsrow2-by-1, with leading dimension nsrow2.
+ */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */
+ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ;
+ }
+
+#ifdef REAL
+
+ /* solve L1*x1 (that is, x1 = L1\x1) */
+ BLAS_dtrsv ("L", "N", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+ /* E = E - L2*x1 */
+ BLAS_dgemv ("N",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */
+ one, /* BETA: 1 */
+ Ex, 1) ; /* Y, INCY: E */
+
+#else
+
+ /* solve L1*x1 (that is, x1 = L1\x1) */
+ BLAS_ztrsv ("L", "N", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+ /* E = E - L2*x1 */
+ BLAS_zgemv ("N",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */
+ one, /* BETA: 1 */
+ Ex, 1) ; /* Y, INCY: E */
+
+#endif
+
+ /* scatter E back into X */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ /* Xx [Ls [ps2 + ii]] = Ex [ii] ; */
+ ASSIGN (Xx,-,Ls [ps2 + ii], Ex,-,ii) ;
+ }
+ }
+ }
+ else
+ {
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ i = Ls [ps2 + ii] ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */
+ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ;
+ }
+ }
+
+#ifdef REAL
+
+ /* solve L1*x1 */
+ BLAS_dtrsm ("L", "L", "N", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+ /* E = E - L2*x1 */
+ if (nsrow2 > 0)
+ {
+ BLAS_dgemm ("N", "N",
+ nsrow2, nrhs, nscol, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */
+ one, /* BETA: 1 */
+ Ex, nsrow2) ; /* C, LDC: E */
+ }
+
+#else
+
+ /* solve L1*x1 */
+ BLAS_ztrsm ("L", "L", "N", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+ /* E = E - L2*x1 */
+ if (nsrow2 > 0)
+ {
+ BLAS_zgemm ("N", "N",
+ nsrow2, nrhs, nscol, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */
+ one, /* BETA: 1 */
+ Ex, nsrow2) ; /* C, LDC: E */
+ }
+
+#endif
+
+ /* scatter E back into X */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ i = Ls [ps2 + ii] ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ /* Xx [i + j*d] = Ex [ii + j*nsrow2] ; */
+ ASSIGN (Xx,-,i+j*d, Ex,-,ii+j*nsrow2) ;
+ }
+ }
+ }
+ }
+
+ Common->status = CHOLMOD_OK ;
+ return (blas_ok) ;
+}
+
+
+static int TEMPLATE (cholmod_super_ltsolve)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Xx, *Ex ;
+ double minus_one [2], one [2] ;
+ Int *Lpi, *Lpx, *Ls, *Super ;
+ Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s,
+ nsrow2, n, ps2, j, i, d, nrhs ;
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrhs = X->ncol ;
+ Ex = E->x ;
+ Xx = X->x ;
+ n = L->n ;
+ d = X->d ;
+
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+ Lx = L->x ;
+ minus_one [0] = -1.0 ;
+ minus_one [1] = 0 ;
+ one [0] = 1.0 ;
+ one [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve L'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrhs == 1)
+ {
+
+ for (s = nsuper-1 ; s >= 0 ; s--)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal.
+ * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of
+ * nsrow. x1 is nscol-by-nsrow, with leading dimension n.
+ * E is nsrow2-by-1, with leading dimension nsrow2.
+ */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */
+ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ;
+ }
+
+#ifdef REAL
+
+ /* x1 = x1 - L2'*E */
+ BLAS_dgemv ("C",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, 1, /* X, INCX: Ex */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */
+
+ /* solve L1'*x1 */
+ BLAS_dtrsv ("L", "C", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+#else
+
+ /* x1 = x1 - L2'*E */
+ BLAS_zgemv ("C",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, 1, /* X, INCX: Ex */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */
+
+ /* solve L1'*x1 */
+ BLAS_ztrsv ("L", "C", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+#endif
+
+ }
+ }
+ else
+ {
+
+ for (s = nsuper-1 ; s >= 0 ; s--)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ i = Ls [ps2 + ii] ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */
+ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ;
+ }
+ }
+
+#ifdef REAL
+
+ /* x1 = x1 - L2'*E */
+ if (nsrow2 > 0)
+ {
+ BLAS_dgemm ("C", "N",
+ nscol, nrhs, nsrow2, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, nsrow2, /* B, LDB: E */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */
+ }
+
+ /* solve L1'*x1 */
+ BLAS_dtrsm ("L", "L", "C", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+#else
+
+ /* x1 = x1 - L2'*E */
+ if (nsrow2 > 0)
+ {
+ BLAS_zgemm ("C", "N",
+ nscol, nrhs, nsrow2, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, nsrow2, /* B, LDB: E */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */
+ }
+
+ /* solve L1'*x1 */
+ BLAS_ztrsm ("L", "L", "C", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+#endif
+
+ }
+ }
+
+ Common->status = CHOLMOD_OK ;
+ return (blas_ok) ;
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/src/C/SuiteSparse/COLAMD/ChangeLog b/src/C/SuiteSparse/COLAMD/ChangeLog
new file mode 100644
index 0000000..e16e946
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/ChangeLog
@@ -0,0 +1,123 @@
+Dec 12, 2006, version 2.5.2
+
+ * minor MATLAB cleanup. MATLAB functions renamed colamd2 and symamd2,
+ so that they do not conflict with the built-in versions. Note that
+ the MATLAB built-in functions colamd and symamd are identical to
+ the colamd and symamd functions here.
+
+Aug 31, 2006: Version 2.5.1
+
+ * minor change to colamd.m and symamd.m, to use etree instead
+ of sparsfun.
+
+Apr. 30, 2006: Version 2.5
+
+ * colamd_recommended modified, to do more careful integer overflow
+ checking. It now returns size_t, not int. colamd_l_recommended
+ also returns size_t. A zero is returned if an error occurs. A
+ postive return value denotes success. In v2.4 and earlier,
+ -1 was returned on error (an int or long).
+
+ * long replaced with UF_long integer, which is long except on WIN64.
+
+Nov 15, 2005:
+
+ * minor editting of comments; version number (2.4) unchanged.
+
+Changes from Version 2.3 to 2.4 (Aug 30, 2005)
+
+ * Makefile now relies on ../UFconfig/UFconfig.mk
+
+ * changed the dense row/col detection. The meaning of the knobs
+ has thus changed.
+
+ * added an option to turn off aggressive absorption. It was
+ always on in versions 2.3 and earlier.
+
+ * added a #define'd version number
+
+ * added a function pointer (colamd_printf) for COLAMD's printing.
+
+ * added a -DNPRINT option, to turn off printing at compile-time.
+
+ * added a check for integer overflow in colamd_recommended
+
+ * minor changes to allow for more simpler 100% test coverage
+
+ * bug fix. If symamd v2.3 fails to allocate its copy of the input
+ matrix, then it erroneously frees a calloc'd workspace twice.
+ This bug has no effect on the MATLAB symamd mexFunction, since
+ mxCalloc terminates the mexFunction if it fails to allocate
+ memory. Similarly, UMFPACK is not affected because it does not
+ use symamd. The bug has no effect on the colamd ordering
+ routine in v2.3.
+
+Changes from Version 2.2 to 2.3 (Sept. 8, 2003)
+
+ * removed the call to the MATLAB spparms ('spumoni') function.
+ This can take a lot of time if you are ordering many small
+ matrices. Only affects the MATLAB interface (colamdmex.c,
+ symamdmex.c, colamdtestmex.c, and symamdtestmex.c). The
+ usage of the optional 2nd argument to the colamd and symamd
+ mexFunctions was changed accordingly.
+
+Changes from Version 2.1 to 2.2 (Sept. 23, 2002)
+
+ * extensive testing routines added (colamd_test.m, colamdtestmex.c,
+ and symamdtestmex.c), and the Makefile modified accordingly.
+
+ * a few typos in the comments corrected
+
+ * use of the MATLAB "flops" command removed from colamd_demo, and an
+ m-file routine luflops.m added.
+
+ * an explicit typecast from unsigned to int added, for COLAMD_C and
+ COLAMD_R in colamd.h.
+
+ * #include <stdio.h> added to colamd_example.c
+
+
+Changes from Version 2.0 to 2.1 (May 4, 2001)
+
+ * TRUE and FALSE are predefined on some systems, so they are defined
+ here only if not already defined.
+
+ * web site changed
+
+ * UNIX Makefile modified, to handle the case if "." is not in your path.
+
+
+Changes from Version 1.0 to 2.0 (January 31, 2000)
+
+ No bugs were found in version 1.1. These changes merely add new
+ functionality.
+
+ * added the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro.
+
+ * moved the output statistics, from A, to a separate output argument.
+ The arguments changed for the C-callable routines.
+
+ * added colamd_report and symamd_report.
+
+ * added a C-callable symamd routine. Formerly, symamd was only
+ available as a mexFunction from MATLAB.
+
+ * added error-checking to symamd. Formerly, it assumed its input
+ was error-free.
+
+ * added the optional stats and knobs arguments to the symamd mexFunction
+
+ * deleted colamd_help. A help message is still available from
+ "help colamd" and "help symamd" in MATLAB.
+
+ * deleted colamdtree.m and symamdtree.m. Now, colamd.m and symamd.m
+ also do the elimination tree post-ordering. The Version 1.1
+ colamd and symamd mexFunctions, which do not do the post-
+ ordering, are now visible as colamdmex and symamdmex from
+ MATLAB. Essentialy, the post-ordering is now the default
+ behavior of colamd.m and symamd.m, to match the behavior of
+ colmmd and symmmd. The post-ordering is only available in the
+ MATLAB interface, not the C-callable interface.
+
+ * made a slight change to the dense row/column detection in symamd,
+ to match the stated specifications.
diff --git a/src/C/SuiteSparse/COLAMD/Contents.m b/src/C/SuiteSparse/COLAMD/Contents.m
new file mode 100644
index 0000000..5639549
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/Contents.m
@@ -0,0 +1,18 @@
+% COLAMD, column approximate minimum degree ordering
+%
+% Primary:
+% colamd2 - Column approximate minimum degree permutation.
+% symamd2 - SYMAMD Symmetric approximate minimum degree permutation.
+%
+% helper and test functions:
+% colamd_demo - demo for colamd, column approx minimum degree ordering algorithm
+% colamd_make - compiles COLAMD2 and SYMAMD2 for MATLAB
+% colamd_test - test colamd2 and symamd2
+% luflops - compute the flop count for sparse LU factorization
+%
+% Example:
+% p = colamd2 (A)
+%
+
+% Copyright 2006, Timothy A. Davis
+
diff --git a/src/C/SuiteSparse/COLAMD/Makefile b/src/C/SuiteSparse/COLAMD/Makefile
new file mode 100644
index 0000000..07a2518
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/Makefile
@@ -0,0 +1,51 @@
+
+default: libcolamd.a colamd_example colamd_l_example
+
+include ../UFconfig/UFconfig.mk
+
+I = -I../UFconfig
+
+colamd_example: colamd_example.c libcolamd.a
+ $(CC) $(CFLAGS) $(I) -o colamd_example colamd_example.c libcolamd.a -lm
+ - ./colamd_example > my_colamd_example.out
+ - diff colamd_example.out my_colamd_example.out
+
+colamd_l_example: colamd_l_example.c libcolamd.a
+ $(CC) $(CFLAGS) $(I) -o colamd_l_example colamd_l_example.c libcolamd.a -lm
+ - ./colamd_l_example > my_colamd_l_example.out
+ - diff colamd_example.out my_colamd_example.out
+
+purge: distclean
+
+distclean: clean2
+ - $(RM) libcolamd.a
+
+clean2: clean
+ - $(RM) *.o *.dll colamd_example colamd_l_example
+ - $(RM) colamd2mex.mex* symamd2mex.mex*
+ - $(RM) colamdtestmex.mex* symamdtestmex.mex*
+ - $(RM) my_colamd_example.out my_colamd_l_example.out
+
+# Compiles the MATLAB-callable routines
+mex: colamdmex.c symamdmex.c libcolamd.a
+ $(MEX) -output colamd2mex $(I) colamdmex.c libcolamd.a
+ $(MEX) -output symamd2mex $(I) symamdmex.c libcolamd.a
+
+# Compiles the extensive test code
+test: mex colamdtestmex.c symamdtestmex.c libcolamd.a
+ $(MEX) $(I) colamdtestmex.c libcolamd.a
+ $(MEX) $(I) symamdtestmex.c libcolamd.a
+
+# creates libcolamd.a, a C-callable COLAMD library
+libcolamd.a: colamd.c colamd_global.c colamd.h
+ $(CC) $(CFLAGS) $(I) -c colamd_global.c
+ $(CC) $(CFLAGS) $(I) -c colamd.c
+ $(CC) $(CFLAGS) $(I) -c colamd.c -DDLONG -o colamd_l.o
+ $(AR) libcolamd.a colamd.o colamd_l.o colamd_global.o
+
+ccode: libcolamd.a
+
+library: libcolamd.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/src/C/SuiteSparse/COLAMD/README.txt b/src/C/SuiteSparse/COLAMD/README.txt
new file mode 100644
index 0000000..5561ec3
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/README.txt
@@ -0,0 +1,108 @@
+The COLAMD ordering method - Version 2.6
+-------------------------------------------------------------------------------
+
+The COLAMD column approximate minimum degree ordering algorithm computes
+a permutation vector P such that the LU factorization of A (:,P)
+tends to be sparser than that of A. The Cholesky factorization of
+(A (:,P))'*(A (:,P)) will also tend to be sparser than that of A'*A.
+SYMAMD is a symmetric minimum degree ordering method based on COLAMD,
+available as a MATLAB-callable function. It constructs a matrix M such
+that M'*M has the same pattern as A, and then uses COLAMD to compute a column
+ordering of M. Colamd and symamd tend to be faster and generate better
+orderings than their MATLAB counterparts, colmmd and symmmd.
+
+To compile and test the colamd m-files and mexFunctions, just unpack the
+COLAMD/ directory from the COLAMD.tar.gz file, and run MATLAB from
+within that directory. Next, type colamd_test to compile and test colamd
+and symamd. This will work on any computer with MATLAB (Unix, PC, or Mac).
+Alternatively, type "make" (in Unix) to compile and run a simple example C
+code, without using MATLAB.
+
+Colamd is a built-in routine in MATLAB, available from The
+Mathworks, Inc. Under most cases, the compiled COLAMD from Versions 2.0
+through 2.6 do not differ. Colamd Versions 2.2 and 2.3 differ only in their
+mexFunction interaces to MATLAB. v2.4 fixes a bug in the symamd routine in
+v2.3. The bug (in v2.3 and earlier) has no effect on the MATLAB symamd
+mexFunction. v2.5 adds additional checks for integer overflow, so that
+the "int" version can be safely used with 64-bit pointers. Refer to the
+ChangeLog for more details.
+
+ NOTE: DO NOT ATTEMPT TO USE THIS CODE IN 64-BIT MATLAB (v7.3).
+ It is not yet ported to that version of MATLAB.
+
+To use colamd and symamd within an application written in C, all you need are
+colamd.c, colamd_global.c, and colamd.h, which are the C-callable
+colamd/symamd codes. See colamd.c for more information on how to call
+colamd from a C program.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+ Copyright (c) 1998-2006, Timothy A. Davis, All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+
+Related papers:
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column
+ minimum degree ordering algorithm, ACM Transactions on Mathematical
+ Software, vol. 30, no. 3., pp. 353-376, 2004.
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD,
+ an approximate column minimum degree ordering algorithm, ACM
+ Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380,
+ 2004.
+
+ "An approximate minimum degree column ordering algorithm",
+ S. I. Larimore, MS Thesis, Dept. of Computer and Information
+ Science and Engineering, University of Florida, Gainesville, FL,
+ 1998. CISE Tech Report TR-98-016. Available at
+ ftp://ftp.cise.ufl.edu/cis/tech-reports/tr98/tr98-016.ps
+ via anonymous ftp.
+
+ Approximate Deficiency for Ordering the Columns of a Matrix,
+ J. L. Kern, Senior Thesis, Dept. of Computer and Information
+ Science and Engineering, University of Florida, Gainesville, FL,
+ 1999. Available at http://www.cise.ufl.edu/~davis/Kern/kern.ps
+
+
+Authors: Stefan I. Larimore and Timothy A. Davis, University of Florida,
+in collaboration with John Gilbert, Xerox PARC (now at UC Santa Barbara),
+and Esmong Ng, Lawrence Berkeley National Laboratory (much of this work
+he did while at Oak Ridge National Laboratory).
+
+COLAMD files
+
+ colamd.c: the primary colamd computational kernel.
+
+ colamd.h: include file for colamd/symamd library.
+
+ colamd.m: the MATLAB interface to colamd.
+
+ colamd_demo.m: MATLAB demo file for colamd and symamd
+ (also compiles the colamdmex and symamdmex mexFunctions).
+
+ colamdmex.c: colamd mexFunction for use in MATLAB.
+
+ colamd_example.c: example C main program that calls colamd and symamd.
+
+ colamd_example.out: output of colamd_example.c.
+
+ Makefile: Makefile for colamd_example.c
+
+ symamd.m: the MATLAB interface to symamd.
+
+ symamdmex.c: symamd mexFunction for use in MATLAB.
+
+ README: this file
+
+ ChangeLog: a log of changes since Version 1.0.
+
+ colamd_test.m: test code
+
+ colamdtestmex.c: test code
+
+ luflops.m: test code
+
+ symamdtestmex.c: test code
diff --git a/src/C/SuiteSparse/COLAMD/colamd.c b/src/C/SuiteSparse/COLAMD/colamd.c
new file mode 100644
index 0000000..abf67e7
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd.c
@@ -0,0 +1,3611 @@
+/* ========================================================================== */
+/* === colamd/symamd - a sparse matrix column ordering algorithm ============ */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD
+
+ colamd: an approximate minimum degree column ordering algorithm,
+ for LU factorization of symmetric or unsymmetric matrices,
+ QR factorization, least squares, interior point methods for
+ linear programming problems, and other related problems.
+
+ symamd: an approximate minimum degree ordering algorithm for Cholesky
+ factorization of symmetric matrices.
+
+ Purpose:
+
+ Colamd computes a permutation Q such that the Cholesky factorization of
+ (AQ)'(AQ) has less fill-in and requires fewer floating point operations
+ than A'A. This also provides a good ordering for sparse partial
+ pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
+ factorization, and P is computed during numerical factorization via
+ conventional partial pivoting with row interchanges. Colamd is the
+ column ordering method used in SuperLU, part of the ScaLAPACK library.
+ It is also available as built-in function in MATLAB Version 6,
+ available from MathWorks, Inc. (http://www.mathworks.com). This
+ routine can be used in place of colmmd in MATLAB.
+
+ Symamd computes a permutation P of a symmetric matrix A such that the
+ Cholesky factorization of PAP' has less fill-in and requires fewer
+ floating point operations than A. Symamd constructs a matrix M such
+ that M'M has the same nonzero pattern of A, and then orders the columns
+ of M using colmmd. The column ordering of M is then returned as the
+ row and column ordering P of A.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Copyright and License:
+
+ Copyright (c) 1998-2006, Timothy A. Davis, All Rights Reserved.
+ COLAMD is also available under alternate licenses, contact T. Davis
+ for details.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.c
+ file. It requires the colamd.h file. It is required by the colamdmex.c
+ and symamdmex.c files, for the MATLAB interface to colamd and symamd.
+ Appears as ACM Algorithm 836.
+
+ See the ChangeLog file for changes since Version 1.0.
+
+ References:
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column
+ minimum degree ordering algorithm, ACM Transactions on Mathematical
+ Software, vol. 30, no. 3., pp. 353-376, 2004.
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD,
+ an approximate column minimum degree ordering algorithm, ACM
+ Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380,
+ 2004.
+
+*/
+
+/* ========================================================================== */
+/* === Description of user-callable routines ================================ */
+/* ========================================================================== */
+
+/* COLAMD includes both int and UF_long versions of all its routines. The
+ * description below is for the int version. For UF_long, all int arguments
+ * become UF_long. UF_long is normally defined as long, except for WIN64.
+
+ ----------------------------------------------------------------------------
+ colamd_recommended:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ size_t colamd_recommended (int nnz, int n_row, int n_col) ;
+ size_t colamd_l_recommended (UF_long nnz, UF_long n_row,
+ UF_long n_col) ;
+
+ Purpose:
+
+ Returns recommended value of Alen for use by colamd. Returns 0
+ if any input argument is negative. The use of this routine
+ is optional. Not needed for symamd, which dynamically allocates
+ its own memory.
+
+ Note that in v2.4 and earlier, these routines returned int or long.
+ They now return a value of type size_t.
+
+ Arguments (all input arguments):
+
+ int nnz ; Number of nonzeros in the matrix A. This must
+ be the same value as p [n_col] in the call to
+ colamd - otherwise you will get a wrong value
+ of the recommended memory to use.
+
+ int n_row ; Number of rows in the matrix A.
+
+ int n_col ; Number of columns in the matrix A.
+
+ ----------------------------------------------------------------------------
+ colamd_set_defaults:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ colamd_set_defaults (double knobs [COLAMD_KNOBS]) ;
+ colamd_l_set_defaults (double knobs [COLAMD_KNOBS]) ;
+
+ Purpose:
+
+ Sets the default parameters. The use of this routine is optional.
+
+ Arguments:
+
+ double knobs [COLAMD_KNOBS] ; Output only.
+
+ NOTE: the meaning of the dense row/col knobs has changed in v2.4
+
+ knobs [0] and knobs [1] control dense row and col detection:
+
+ Colamd: rows with more than
+ max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n_col))
+ entries are removed prior to ordering. Columns with more than
+ max (16, knobs [COLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col)))
+ entries are removed prior to
+ ordering, and placed last in the output column ordering.
+
+ Symamd: uses only knobs [COLAMD_DENSE_ROW], which is knobs [0].
+ Rows and columns with more than
+ max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n))
+ entries are removed prior to ordering, and placed last in the
+ output ordering.
+
+ COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
+ respectively, in colamd.h. Default values of these two knobs
+ are both 10. Currently, only knobs [0] and knobs [1] are
+ used, but future versions may use more knobs. If so, they will
+ be properly set to their defaults by the future version of
+ colamd_set_defaults, so that the code that calls colamd will
+ not need to change, assuming that you either use
+ colamd_set_defaults, or pass a (double *) NULL pointer as the
+ knobs array to colamd or symamd.
+
+ knobs [2]: aggressive absorption
+
+ knobs [COLAMD_AGGRESSIVE] controls whether or not to do
+ aggressive absorption during the ordering. Default is TRUE.
+
+
+ ----------------------------------------------------------------------------
+ colamd:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ int colamd (int n_row, int n_col, int Alen, int *A, int *p,
+ double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS]) ;
+ UF_long colamd_l (UF_long n_row, UF_long n_col, UF_long Alen,
+ UF_long *A, UF_long *p, double knobs [COLAMD_KNOBS],
+ UF_long stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Computes a column ordering (Q) of A such that P(AQ)=LU or
+ (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ operations than factorizing the unpermuted matrix A or A'A,
+ respectively.
+
+ Returns:
+
+ TRUE (1) if successful, FALSE (0) otherwise.
+
+ Arguments:
+
+ int n_row ; Input argument.
+
+ Number of rows in the matrix A.
+ Restriction: n_row >= 0.
+ Colamd returns FALSE if n_row is negative.
+
+ int n_col ; Input argument.
+
+ Number of columns in the matrix A.
+ Restriction: n_col >= 0.
+ Colamd returns FALSE if n_col is negative.
+
+ int Alen ; Input argument.
+
+ Restriction (see note):
+ Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col
+ Colamd returns FALSE if these conditions are not met.
+
+ Note: this restriction makes an modest assumption regarding
+ the size of the two typedef's structures in colamd.h.
+ We do, however, guarantee that
+
+ Alen >= colamd_recommended (nnz, n_row, n_col)
+
+ will be sufficient. Note: the macro version does not check
+ for integer overflow, and thus is not recommended. Use
+ the colamd_recommended routine instead.
+
+ int A [Alen] ; Input argument, undefined on output.
+
+ A is an integer array of size Alen. Alen must be at least as
+ large as the bare minimum value given above, but this is very
+ low, and can result in excessive run time. For best
+ performance, we recommend that Alen be greater than or equal to
+ colamd_recommended (nnz, n_row, n_col), which adds
+ nnz/5 to the bare minimum value given above.
+
+ On input, the row indices of the entries in column c of the
+ matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices
+ in a given column c need not be in ascending order, and
+ duplicate row indices may be be present. However, colamd will
+ work a little faster if both of these conditions are met
+ (Colamd puts the matrix into this format, if it finds that the
+ the conditions are not met).
+
+ The matrix is 0-based. That is, rows are in the range 0 to
+ n_row-1, and columns are in the range 0 to n_col-1. Colamd
+ returns FALSE if any row index is out of range.
+
+ The contents of A are modified during ordering, and are
+ undefined on output.
+
+ int p [n_col+1] ; Both input and output argument.
+
+ p is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the matrix A. Column c of
+ the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ for all c in the range 0 to n_col-1. The value p [n_col] is
+ thus the total number of entries in the pattern of the matrix A.
+ Colamd returns FALSE if these conditions are not met.
+
+ On output, if colamd returns TRUE, the array p holds the column
+ permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
+ the first column index in the new ordering, and p [n_col-1] is
+ the last. That is, p [k] = j means that column j of A is the
+ kth pivot column, in AQ, where k is in the range 0 to n_col-1
+ (p [0] = j means that column j of A is the first column in AQ).
+
+ If colamd returns FALSE, then no permutation is returned, and
+ p is undefined on output.
+
+ double knobs [COLAMD_KNOBS] ; Input argument.
+
+ See colamd_set_defaults for a description.
+
+ int stats [COLAMD_STATS] ; Output argument.
+
+ Statistics on the ordering, and error status.
+ See colamd.h for related definitions.
+ Colamd returns FALSE if stats is not present.
+
+ stats [0]: number of dense or empty rows ignored.
+
+ stats [1]: number of dense or empty columns ignored (and
+ ordered last in the output permutation p)
+ Note that a row can become "empty" if it
+ contains only "dense" and/or "empty" columns,
+ and similarly a column can become "empty" if it
+ only contains "dense" and/or "empty" rows.
+
+ stats [2]: number of garbage collections performed.
+ This can be excessively high if Alen is close
+ to the minimum required value.
+
+ stats [3]: status code. < 0 is an error code.
+ > 1 is a warning or notice.
+
+ 0 OK. Each column of the input matrix contained
+ row indices in increasing order, with no
+ duplicates.
+
+ 1 OK, but columns of input matrix were jumbled
+ (unsorted columns or duplicate entries). Colamd
+ had to do some extra work to sort the matrix
+ first and remove duplicate entries, but it
+ still was able to return a valid permutation
+ (return value of colamd was TRUE).
+
+ stats [4]: highest numbered column that
+ is unsorted or has duplicate
+ entries.
+ stats [5]: last seen duplicate or
+ unsorted row index.
+ stats [6]: number of duplicate or
+ unsorted row indices.
+
+ -1 A is a null pointer
+
+ -2 p is a null pointer
+
+ -3 n_row is negative
+
+ stats [4]: n_row
+
+ -4 n_col is negative
+
+ stats [4]: n_col
+
+ -5 number of nonzeros in matrix is negative
+
+ stats [4]: number of nonzeros, p [n_col]
+
+ -6 p [0] is nonzero
+
+ stats [4]: p [0]
+
+ -7 A is too small
+
+ stats [4]: required size
+ stats [5]: actual size (Alen)
+
+ -8 a column has a negative number of entries
+
+ stats [4]: column with < 0 entries
+ stats [5]: number of entries in col
+
+ -9 a row index is out of bounds
+
+ stats [4]: column with bad row index
+ stats [5]: bad row index
+ stats [6]: n_row, # of rows of matrx
+
+ -10 (unused; see symamd.c)
+
+ -999 (unused; see symamd.c)
+
+ Future versions may return more statistics in the stats array.
+
+ Example:
+
+ See http://www.cise.ufl.edu/research/sparse/colamd/example.c
+ for a complete example.
+
+ To order the columns of a 5-by-4 matrix with 11 nonzero entries in
+ the following nonzero pattern
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ with default knobs and no output statistics, do the following:
+
+ #include "colamd.h"
+ #define ALEN 100
+ int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ;
+ int p [ ] = {0, 3, 5, 9, 11} ;
+ int stats [COLAMD_STATS] ;
+ colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ;
+
+ The permutation is returned in the array p, and A is destroyed.
+
+ ----------------------------------------------------------------------------
+ symamd:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ int symamd (int n, int *A, int *p, int *perm,
+ double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS],
+ void (*allocate) (size_t, size_t), void (*release) (void *)) ;
+ UF_long symamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm,
+ double knobs [COLAMD_KNOBS], UF_long stats [COLAMD_STATS],
+ void (*allocate) (size_t, size_t), void (*release) (void *)) ;
+
+ Purpose:
+
+ The symamd routine computes an ordering P of a symmetric sparse
+ matrix A such that the Cholesky factorization PAP' = LL' remains
+ sparse. It is based on a column ordering of a matrix M constructed
+ so that the nonzero pattern of M'M is the same as A. The matrix A
+ is assumed to be symmetric; only the strictly lower triangular part
+ is accessed. You must pass your selected memory allocator (usually
+ calloc/free or mxCalloc/mxFree) to symamd, for it to allocate
+ memory for the temporary matrix M.
+
+ Returns:
+
+ TRUE (1) if successful, FALSE (0) otherwise.
+
+ Arguments:
+
+ int n ; Input argument.
+
+ Number of rows and columns in the symmetrix matrix A.
+ Restriction: n >= 0.
+ Symamd returns FALSE if n is negative.
+
+ int A [nnz] ; Input argument.
+
+ A is an integer array of size nnz, where nnz = p [n].
+
+ The row indices of the entries in column c of the matrix are
+ held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a
+ given column c need not be in ascending order, and duplicate
+ row indices may be present. However, symamd will run faster
+ if the columns are in sorted order with no duplicate entries.
+
+ The matrix is 0-based. That is, rows are in the range 0 to
+ n-1, and columns are in the range 0 to n-1. Symamd
+ returns FALSE if any row index is out of range.
+
+ The contents of A are not modified.
+
+ int p [n+1] ; Input argument.
+
+ p is an integer array of size n+1. On input, it holds the
+ "pointers" for the column form of the matrix A. Column c of
+ the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ for all c in the range 0 to n-1. The value p [n] is
+ thus the total number of entries in the pattern of the matrix A.
+ Symamd returns FALSE if these conditions are not met.
+
+ The contents of p are not modified.
+
+ int perm [n+1] ; Output argument.
+
+ On output, if symamd returns TRUE, the array perm holds the
+ permutation P, where perm [0] is the first index in the new
+ ordering, and perm [n-1] is the last. That is, perm [k] = j
+ means that row and column j of A is the kth column in PAP',
+ where k is in the range 0 to n-1 (perm [0] = j means
+ that row and column j of A are the first row and column in
+ PAP'). The array is used as a workspace during the ordering,
+ which is why it must be of length n+1, not just n.
+
+ double knobs [COLAMD_KNOBS] ; Input argument.
+
+ See colamd_set_defaults for a description.
+
+ int stats [COLAMD_STATS] ; Output argument.
+
+ Statistics on the ordering, and error status.
+ See colamd.h for related definitions.
+ Symamd returns FALSE if stats is not present.
+
+ stats [0]: number of dense or empty row and columns ignored
+ (and ordered last in the output permutation
+ perm). Note that a row/column can become
+ "empty" if it contains only "dense" and/or
+ "empty" columns/rows.
+
+ stats [1]: (same as stats [0])
+
+ stats [2]: number of garbage collections performed.
+
+ stats [3]: status code. < 0 is an error code.
+ > 1 is a warning or notice.
+
+ 0 OK. Each column of the input matrix contained
+ row indices in increasing order, with no
+ duplicates.
+
+ 1 OK, but columns of input matrix were jumbled
+ (unsorted columns or duplicate entries). Symamd
+ had to do some extra work to sort the matrix
+ first and remove duplicate entries, but it
+ still was able to return a valid permutation
+ (return value of symamd was TRUE).
+
+ stats [4]: highest numbered column that
+ is unsorted or has duplicate
+ entries.
+ stats [5]: last seen duplicate or
+ unsorted row index.
+ stats [6]: number of duplicate or
+ unsorted row indices.
+
+ -1 A is a null pointer
+
+ -2 p is a null pointer
+
+ -3 (unused, see colamd.c)
+
+ -4 n is negative
+
+ stats [4]: n
+
+ -5 number of nonzeros in matrix is negative
+
+ stats [4]: # of nonzeros (p [n]).
+
+ -6 p [0] is nonzero
+
+ stats [4]: p [0]
+
+ -7 (unused)
+
+ -8 a column has a negative number of entries
+
+ stats [4]: column with < 0 entries
+ stats [5]: number of entries in col
+
+ -9 a row index is out of bounds
+
+ stats [4]: column with bad row index
+ stats [5]: bad row index
+ stats [6]: n_row, # of rows of matrx
+
+ -10 out of memory (unable to allocate temporary
+ workspace for M or count arrays using the
+ "allocate" routine passed into symamd).
+
+ Future versions may return more statistics in the stats array.
+
+ void * (*allocate) (size_t, size_t)
+
+ A pointer to a function providing memory allocation. The
+ allocated memory must be returned initialized to zero. For a
+ C application, this argument should normally be a pointer to
+ calloc. For a MATLAB mexFunction, the routine mxCalloc is
+ passed instead.
+
+ void (*release) (size_t, size_t)
+
+ A pointer to a function that frees memory allocated by the
+ memory allocation routine above. For a C application, this
+ argument should normally be a pointer to free. For a MATLAB
+ mexFunction, the routine mxFree is passed instead.
+
+
+ ----------------------------------------------------------------------------
+ colamd_report:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ colamd_report (int stats [COLAMD_STATS]) ;
+ colamd_l_report (UF_long stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Prints the error status and statistics recorded in the stats
+ array on the standard error output (for a standard C routine)
+ or on the MATLAB output (for a mexFunction).
+
+ Arguments:
+
+ int stats [COLAMD_STATS] ; Input only. Statistics from colamd.
+
+
+ ----------------------------------------------------------------------------
+ symamd_report:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ symamd_report (int stats [COLAMD_STATS]) ;
+ symamd_l_report (UF_long stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Prints the error status and statistics recorded in the stats
+ array on the standard error output (for a standard C routine)
+ or on the MATLAB output (for a mexFunction).
+
+ Arguments:
+
+ int stats [COLAMD_STATS] ; Input only. Statistics from symamd.
+
+
+*/
+
+/* ========================================================================== */
+/* === Scaffolding code definitions ======================================== */
+/* ========================================================================== */
+
+/* Ensure that debugging is turned off: */
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/* turn on debugging by uncommenting the following line
+ #undef NDEBUG
+*/
+
+/*
+ Our "scaffolding code" philosophy: In our opinion, well-written library
+ code should keep its "debugging" code, and just normally have it turned off
+ by the compiler so as not to interfere with performance. This serves
+ several purposes:
+
+ (1) assertions act as comments to the reader, telling you what the code
+ expects at that point. All assertions will always be true (unless
+ there really is a bug, of course).
+
+ (2) leaving in the scaffolding code assists anyone who would like to modify
+ the code, or understand the algorithm (by reading the debugging output,
+ one can get a glimpse into what the code is doing).
+
+ (3) (gasp!) for actually finding bugs. This code has been heavily tested
+ and "should" be fully functional and bug-free ... but you never know...
+
+ The code will become outrageously slow when debugging is
+ enabled. To control the level of debugging output, set an environment
+ variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging,
+ you should see the following message on the standard output:
+
+ colamd: debug version, D = 1 (THIS WILL BE SLOW!)
+
+ or a similar message for symamd. If you don't, then debugging has not
+ been enabled.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include <limits.h>
+#include <math.h>
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#include "matrix.h"
+#endif /* MATLAB_MEX_FILE */
+
+#if !defined (NPRINT) || !defined (NDEBUG)
+#include <stdio.h>
+#endif
+
+#ifndef NULL
+#define NULL ((void *) 0)
+#endif
+
+/* ========================================================================== */
+/* === int or UF_long ======================================================= */
+/* ========================================================================== */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#ifdef DLONG
+
+#define Int UF_long
+#define ID UF_long_id
+#define Int_MAX UF_long_max
+
+#define COLAMD_recommended colamd_l_recommended
+#define COLAMD_set_defaults colamd_l_set_defaults
+#define COLAMD_MAIN colamd_l
+#define SYMAMD_MAIN symamd_l
+#define COLAMD_report colamd_l_report
+#define SYMAMD_report symamd_l_report
+
+#else
+
+#define Int int
+#define ID "%d"
+#define Int_MAX INT_MAX
+
+#define COLAMD_recommended colamd_recommended
+#define COLAMD_set_defaults colamd_set_defaults
+#define COLAMD_MAIN colamd
+#define SYMAMD_MAIN symamd
+#define COLAMD_report colamd_report
+#define SYMAMD_report symamd_report
+
+#endif
+
+/* ========================================================================== */
+/* === Row and Column structures ============================================ */
+/* ========================================================================== */
+
+/* User code that makes use of the colamd/symamd routines need not directly */
+/* reference these structures. They are used only for colamd_recommended. */
+
+typedef struct Colamd_Col_struct
+{
+ Int start ; /* index for A of first row in this column, or DEAD */
+ /* if column is dead */
+ Int length ; /* number of rows in this column */
+ union
+ {
+ Int thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ Int parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ Int score ; /* the score used to maintain heap, if col is alive */
+ Int order ; /* pivot ordering of this column, if col is dead */
+ } shared2 ;
+ union
+ {
+ Int headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ Int hash ; /* hash value, if col is not in a degree list */
+ Int prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ Int degree_next ; /* next column, if col is in a degree list */
+ Int hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+} Colamd_Col ;
+
+typedef struct Colamd_Row_struct
+{
+ Int start ; /* index for A of first col in this row */
+ Int length ; /* number of principal columns in this row */
+ union
+ {
+ Int degree ; /* number of principal & non-principal columns in row */
+ Int p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ Int mark ; /* for computing set differences and marking dead rows*/
+ Int first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+} Colamd_Row ;
+
+/* ========================================================================== */
+/* === Definitions ========================================================== */
+/* ========================================================================== */
+
+/* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */
+#define PUBLIC
+#define PRIVATE static
+
+#define DENSE_DEGREE(alpha,n) \
+ ((Int) MAX (16.0, (alpha) * sqrt ((double) (n))))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+#define ONES_COMPLEMENT(r) (-(r)-1)
+
+/* -------------------------------------------------------------------------- */
+/* Change for version 2.1: define TRUE and FALSE only if not yet defined */
+/* -------------------------------------------------------------------------- */
+
+#ifndef TRUE
+#define TRUE (1)
+#endif
+
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+#define EMPTY (-1)
+
+/* Row and column status */
+#define ALIVE (0)
+#define DEAD (-1)
+
+/* Column status */
+#define DEAD_PRINCIPAL (-1)
+#define DEAD_NON_PRINCIPAL (-2)
+
+/* Macros for row and column status update and checking. */
+#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
+#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
+#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
+#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
+#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
+#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
+#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
+#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
+#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
+
+/* ========================================================================== */
+/* === Colamd reporting mechanism =========================================== */
+/* ========================================================================== */
+
+#if defined (MATLAB_MEX_FILE) || defined (MATHWORKS)
+/* In MATLAB, matrices are 1-based to the user, but 0-based internally */
+#define INDEX(i) ((i)+1)
+#else
+/* In C, matrices are 0-based and indices are reported as such in *_report */
+#define INDEX(i) (i)
+#endif
+
+/* All output goes through the PRINTF macro. */
+#define PRINTF(params) { if (colamd_printf != NULL) (void) colamd_printf params ; }
+
+/* ========================================================================== */
+/* === Prototypes of PRIVATE routines ======================================= */
+/* ========================================================================== */
+
+PRIVATE Int init_rows_cols
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int p [],
+ Int stats [COLAMD_STATS]
+) ;
+
+PRIVATE void init_scoring
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ double knobs [COLAMD_KNOBS],
+ Int *p_n_row2,
+ Int *p_n_col2,
+ Int *p_max_deg
+) ;
+
+PRIVATE Int find_ordering
+(
+ Int n_row,
+ Int n_col,
+ Int Alen,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int n_col2,
+ Int max_deg,
+ Int pfree,
+ Int aggressive
+) ;
+
+PRIVATE void order_children
+(
+ Int n_col,
+ Colamd_Col Col [],
+ Int p []
+) ;
+
+PRIVATE void detect_super_cols
+(
+
+#ifndef NDEBUG
+ Int n_col,
+ Colamd_Row Row [],
+#endif /* NDEBUG */
+
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int row_start,
+ Int row_length
+) ;
+
+PRIVATE Int garbage_collection
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int *pfree
+) ;
+
+PRIVATE Int clear_mark
+(
+ Int tag_mark,
+ Int max_mark,
+ Int n_row,
+ Colamd_Row Row []
+) ;
+
+PRIVATE void print_report
+(
+ char *method,
+ Int stats [COLAMD_STATS]
+) ;
+
+/* ========================================================================== */
+/* === Debugging prototypes and definitions ================================= */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+#include <assert.h>
+
+/* colamd_debug is the *ONLY* global variable, and is only */
+/* present when debugging */
+
+PRIVATE Int colamd_debug = 0 ; /* debug print level */
+
+#define DEBUG0(params) { PRINTF (params) ; }
+#define DEBUG1(params) { if (colamd_debug >= 1) PRINTF (params) ; }
+#define DEBUG2(params) { if (colamd_debug >= 2) PRINTF (params) ; }
+#define DEBUG3(params) { if (colamd_debug >= 3) PRINTF (params) ; }
+#define DEBUG4(params) { if (colamd_debug >= 4) PRINTF (params) ; }
+
+#ifdef MATLAB_MEX_FILE
+#define ASSERT(expression) (mxAssert ((expression), ""))
+#else
+#define ASSERT(expression) (assert (expression))
+#endif /* MATLAB_MEX_FILE */
+
+PRIVATE void colamd_get_debug /* gets the debug print level from getenv */
+(
+ char *method
+) ;
+
+PRIVATE void debug_deg_lists
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+) ;
+
+PRIVATE void debug_mark
+(
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+) ;
+
+PRIVATE void debug_matrix
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+) ;
+
+PRIVATE void debug_structures
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+) ;
+
+#else /* NDEBUG */
+
+/* === No debugging ========================================================= */
+
+#define DEBUG0(params) ;
+#define DEBUG1(params) ;
+#define DEBUG2(params) ;
+#define DEBUG3(params) ;
+#define DEBUG4(params) ;
+
+#define ASSERT(expression)
+
+#endif /* NDEBUG */
+
+/* ========================================================================== */
+/* === USER-CALLABLE ROUTINES: ============================================== */
+/* ========================================================================== */
+
+/* ========================================================================== */
+/* === colamd_recommended =================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd_recommended routine returns the suggested size for Alen. This
+ value has been determined to provide good balance between the number of
+ garbage collections and the memory requirements for colamd. If any
+ argument is negative, or if integer overflow occurs, a 0 is returned as an
+ error condition. 2*nnz space is required for the row and column
+ indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is
+ required for the Col and Row arrays, respectively, which are internal to
+ colamd (roughly 6*n_col + 4*n_row). An additional n_col space is the
+ minimal amount of "elbow room", and nnz/5 more space is recommended for
+ run time efficiency.
+
+ Alen is approximately 2.2*nnz + 7*n_col + 4*n_row + 10.
+
+ This function is not needed when using symamd.
+*/
+
+/* add two values of type size_t, and check for integer overflow */
+static size_t t_add (size_t a, size_t b, int *ok)
+{
+ (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ;
+ return ((*ok) ? (a + b) : 0) ;
+}
+
+/* compute a*k where k is a small integer, and check for integer overflow */
+static size_t t_mult (size_t a, size_t k, int *ok)
+{
+ size_t i, s = 0 ;
+ for (i = 0 ; i < k ; i++)
+ {
+ s = t_add (s, a, ok) ;
+ }
+ return (s) ;
+}
+
+/* size of the Col and Row structures */
+#define COLAMD_C(n_col,ok) \
+ ((t_mult (t_add (n_col, 1, ok), sizeof (Colamd_Col), ok) / sizeof (Int)))
+
+#define COLAMD_R(n_row,ok) \
+ ((t_mult (t_add (n_row, 1, ok), sizeof (Colamd_Row), ok) / sizeof (Int)))
+
+
+PUBLIC size_t COLAMD_recommended /* returns recommended value of Alen. */
+(
+ /* === Parameters ======================================================= */
+
+ Int nnz, /* number of nonzeros in A */
+ Int n_row, /* number of rows in A */
+ Int n_col /* number of columns in A */
+)
+{
+ size_t s, c, r ;
+ int ok = TRUE ;
+ if (nnz < 0 || n_row < 0 || n_col < 0)
+ {
+ return (0) ;
+ }
+ s = t_mult (nnz, 2, &ok) ; /* 2*nnz */
+ c = COLAMD_C (n_col, &ok) ; /* size of column structures */
+ r = COLAMD_R (n_row, &ok) ; /* size of row structures */
+ s = t_add (s, c, &ok) ;
+ s = t_add (s, r, &ok) ;
+ s = t_add (s, n_col, &ok) ; /* elbow room */
+ s = t_add (s, nnz/5, &ok) ; /* elbow room */
+ ok = ok && (s < Int_MAX) ;
+ return (ok ? s : 0) ;
+}
+
+
+/* ========================================================================== */
+/* === colamd_set_defaults ================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd_set_defaults routine sets the default values of the user-
+ controllable parameters for colamd and symamd:
+
+ Colamd: rows with more than max (16, knobs [0] * sqrt (n_col))
+ entries are removed prior to ordering. Columns with more than
+ max (16, knobs [1] * sqrt (MIN (n_row,n_col))) entries are removed
+ prior to ordering, and placed last in the output column ordering.
+
+ Symamd: Rows and columns with more than max (16, knobs [0] * sqrt (n))
+ entries are removed prior to ordering, and placed last in the
+ output ordering.
+
+ knobs [0] dense row control
+
+ knobs [1] dense column control
+
+ knobs [2] if nonzero, do aggresive absorption
+
+ knobs [3..19] unused, but future versions might use this
+
+*/
+
+PUBLIC void COLAMD_set_defaults
+(
+ /* === Parameters ======================================================= */
+
+ double knobs [COLAMD_KNOBS] /* knob array */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+
+ if (!knobs)
+ {
+ return ; /* no knobs to initialize */
+ }
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [COLAMD_DENSE_ROW] = 10 ;
+ knobs [COLAMD_DENSE_COL] = 10 ;
+ knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/
+}
+
+
+/* ========================================================================== */
+/* === symamd =============================================================== */
+/* ========================================================================== */
+
+PUBLIC Int SYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n, /* number of rows and columns of A */
+ Int A [], /* row indices of A */
+ Int p [], /* column pointers of A */
+ Int perm [], /* output permutation, size n+1 */
+ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ Int stats [COLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),
+ /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *)
+ /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *count ; /* length of each column of M, and col pointer*/
+ Int *mark ; /* mark array for finding duplicate entries */
+ Int *M ; /* row indices of matrix M */
+ size_t Mlen ; /* length of M */
+ Int n_row ; /* number of rows in M */
+ Int nnz ; /* number of entries in A */
+ Int i ; /* row index of A */
+ Int j ; /* column index of A */
+ Int k ; /* row index of M */
+ Int mnz ; /* number of nonzeros in M */
+ Int pp ; /* index into a column of A */
+ Int last_row ; /* last row seen in the current column */
+ Int length ; /* number of nonzeros in a column */
+
+ double cknobs [COLAMD_KNOBS] ; /* knobs for colamd */
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs for colamd */
+
+#ifndef NDEBUG
+ colamd_get_debug ("symamd") ;
+#endif /* NDEBUG */
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ DEBUG0 (("symamd: stats not present\n")) ;
+ return (FALSE) ;
+ }
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+ if (!A)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ DEBUG0 (("symamd: A not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ DEBUG0 (("symamd: p not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (n < 0) /* n must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n ;
+ DEBUG0 (("symamd: n negative %d\n", n)) ;
+ return (FALSE) ;
+ }
+
+ nnz = p [n] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ DEBUG0 (("symamd: number of entries negative %d\n", nnz)) ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ DEBUG0 (("symamd: p[0] not zero %d\n", p [0])) ;
+ return (FALSE) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ COLAMD_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ /* === Allocate count and mark ========================================== */
+
+ count = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
+ if (!count)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ;
+ DEBUG0 (("symamd: allocate count (size %d) failed\n", n+1)) ;
+ return (FALSE) ;
+ }
+
+ mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
+ if (!mark)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ;
+ (*release) ((void *) count) ;
+ DEBUG0 (("symamd: allocate mark (size %d) failed\n", n+1)) ;
+ return (FALSE) ;
+ }
+
+ /* === Compute column counts of M, check if A is valid ================== */
+
+ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (i = 0 ; i < n ; i++)
+ {
+ mark [i] = -1 ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ last_row = -1 ;
+
+ length = p [j+1] - p [j] ;
+ if (length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = j ;
+ stats [COLAMD_INFO2] = length ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG0 (("symamd: col %d negative length %d\n", j, length)) ;
+ return (FALSE) ;
+ }
+
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ if (i < 0 || i >= n)
+ {
+ /* row index i, in column j, is out of bounds */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = j ;
+ stats [COLAMD_INFO2] = i ;
+ stats [COLAMD_INFO3] = n ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG0 (("symamd: row %d col %d out of bounds\n", i, j)) ;
+ return (FALSE) ;
+ }
+
+ if (i <= last_row || mark [i] == j)
+ {
+ /* row index is unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
+ stats [COLAMD_INFO1] = j ;
+ stats [COLAMD_INFO2] = i ;
+ (stats [COLAMD_INFO3]) ++ ;
+ DEBUG1 (("symamd: row %d col %d unsorted/duplicate\n", i, j)) ;
+ }
+
+ if (i > j && mark [i] != j)
+ {
+ /* row k of M will contain column indices i and j */
+ count [i]++ ;
+ count [j]++ ;
+ }
+
+ /* mark the row as having been seen in this column */
+ mark [i] = j ;
+
+ last_row = i ;
+ }
+ }
+
+ /* v2.4: removed free(mark) */
+
+ /* === Compute column pointers of M ===================================== */
+
+ /* use output permutation, perm, for column pointers of M */
+ perm [0] = 0 ;
+ for (j = 1 ; j <= n ; j++)
+ {
+ perm [j] = perm [j-1] + count [j-1] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ count [j] = perm [j] ;
+ }
+
+ /* === Construct M ====================================================== */
+
+ mnz = perm [n] ;
+ n_row = mnz / 2 ;
+ Mlen = COLAMD_recommended (mnz, n_row, n) ;
+ M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ;
+ DEBUG0 (("symamd: M is %d-by-%d with %d entries, Mlen = %g\n",
+ n_row, n, mnz, (double) Mlen)) ;
+
+ if (!M)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG0 (("symamd: allocate M (size %g) failed\n", (double) Mlen)) ;
+ return (FALSE) ;
+ }
+
+ k = 0 ;
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK)
+ {
+ /* Matrix is OK */
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (p [j+1] - p [j] >= 0) ;
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i > j)
+ {
+ /* row k of M contains column indices i and j */
+ M [count [i]++] = k ;
+ M [count [j]++] = k ;
+ k++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */
+ DEBUG0 (("symamd: Duplicates in A.\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ mark [i] = -1 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (p [j+1] - p [j] >= 0) ;
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i > j && mark [i] != j)
+ {
+ /* row k of M contains column indices i and j */
+ M [count [i]++] = k ;
+ M [count [j]++] = k ;
+ k++ ;
+ mark [i] = j ;
+ }
+ }
+ }
+ /* v2.4: free(mark) moved below */
+ }
+
+ /* count and mark no longer needed */
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ; /* v2.4: free (mark) moved here */
+ ASSERT (k == n_row) ;
+
+ /* === Adjust the knobs for M =========================================== */
+
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ cknobs [i] = knobs [i] ;
+ }
+
+ /* there are no dense rows in M */
+ cknobs [COLAMD_DENSE_ROW] = -1 ;
+ cknobs [COLAMD_DENSE_COL] = knobs [COLAMD_DENSE_ROW] ;
+
+ /* === Order the columns of M =========================================== */
+
+ /* v2.4: colamd cannot fail here, so the error check is removed */
+ (void) COLAMD_MAIN (n_row, n, (Int) Mlen, M, perm, cknobs, stats) ;
+
+ /* Note that the output permutation is now in perm */
+
+ /* === get the statistics for symamd from colamd ======================== */
+
+ /* a dense column in colamd means a dense row and col in symamd */
+ stats [COLAMD_DENSE_ROW] = stats [COLAMD_DENSE_COL] ;
+
+ /* === Free M =========================================================== */
+
+ (*release) ((void *) M) ;
+ DEBUG0 (("symamd: done.\n")) ;
+ return (TRUE) ;
+
+}
+
+/* ========================================================================== */
+/* === colamd =============================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd routine computes a column ordering Q of a sparse matrix
+ A such that the LU factorization P(AQ) = LU remains sparse, where P is
+ selected via partial pivoting. The routine can also be viewed as
+ providing a permutation Q such that the Cholesky factorization
+ (AQ)'(AQ) = LL' remains sparse.
+*/
+
+PUBLIC Int COLAMD_MAIN /* returns TRUE if successful, FALSE otherwise*/
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* length of A */
+ Int A [], /* row indices of A */
+ Int p [], /* pointers to columns in A */
+ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ Int stats [COLAMD_STATS] /* output statistics and error codes */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ; /* loop index */
+ Int nnz ; /* nonzeros in A */
+ size_t Row_size ; /* size of Row [], in integers */
+ size_t Col_size ; /* size of Col [], in integers */
+ size_t need ; /* minimum required length of A */
+ Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */
+ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int ngarbage ; /* number of garbage collections performed */
+ Int max_deg ; /* maximum row degree */
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
+ Int aggressive ; /* do aggressive absorption */
+ int ok ;
+
+#ifndef NDEBUG
+ colamd_get_debug ("colamd") ;
+#endif /* NDEBUG */
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ DEBUG0 (("colamd: stats not present\n")) ;
+ return (FALSE) ;
+ }
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+ if (!A) /* A is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ DEBUG0 (("colamd: A not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ DEBUG0 (("colamd: p not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
+ stats [COLAMD_INFO1] = n_row ;
+ DEBUG0 (("colamd: nrow negative %d\n", n_row)) ;
+ return (FALSE) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n_col ;
+ DEBUG0 (("colamd: ncol negative %d\n", n_col)) ;
+ return (FALSE) ;
+ }
+
+ nnz = p [n_col] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ;
+ return (FALSE) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ COLAMD_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ aggressive = (knobs [COLAMD_AGGRESSIVE] != FALSE) ;
+
+ /* === Allocate the Row and Col arrays from array A ===================== */
+
+ ok = TRUE ;
+ Col_size = COLAMD_C (n_col, &ok) ; /* size of Col array of structs */
+ Row_size = COLAMD_R (n_row, &ok) ; /* size of Row array of structs */
+
+ /* need = 2*nnz + n_col + Col_size + Row_size ; */
+ need = t_mult (nnz, 2, &ok) ;
+ need = t_add (need, n_col, &ok) ;
+ need = t_add (need, Col_size, &ok) ;
+ need = t_add (need, Row_size, &ok) ;
+
+ if (!ok || need > (size_t) Alen || need > Int_MAX)
+ {
+ /* not enough space in array A to perform the ordering */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
+ stats [COLAMD_INFO1] = need ;
+ stats [COLAMD_INFO2] = Alen ;
+ DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen));
+ return (FALSE) ;
+ }
+
+ Alen -= Col_size + Row_size ;
+ Col = (Colamd_Col *) &A [Alen] ;
+ Row = (Colamd_Row *) &A [Alen + Col_size] ;
+
+ /* === Construct the row and column data structures ===================== */
+
+ if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
+ {
+ /* input matrix is invalid */
+ DEBUG0 (("colamd: Matrix invalid\n")) ;
+ return (FALSE) ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+ n_col2, max_deg, 2*nnz, aggressive) ;
+
+ /* === Order the non-principal columns ================================== */
+
+ order_children (n_col, Col, p) ;
+
+ /* === Return statistics in stats ======================================= */
+
+ stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;
+ stats [COLAMD_DENSE_COL] = n_col - n_col2 ;
+ stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
+ DEBUG0 (("colamd: done.\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === colamd_report ======================================================== */
+/* ========================================================================== */
+
+PUBLIC void COLAMD_report
+(
+ Int stats [COLAMD_STATS]
+)
+{
+ print_report ("colamd", stats) ;
+}
+
+
+/* ========================================================================== */
+/* === symamd_report ======================================================== */
+/* ========================================================================== */
+
+PUBLIC void SYMAMD_report
+(
+ Int stats [COLAMD_STATS]
+)
+{
+ print_report ("symamd", stats) ;
+}
+
+
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns FALSE if the matrix is invalid,
+ TRUE otherwise. Not user-callable.
+*/
+
+PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A, of size Alen */
+ Int p [], /* pointers to columns in A, of size n_col+1 */
+ Int stats [COLAMD_STATS] /* colamd statistics */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int col ; /* a column index */
+ Int row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *rp ; /* a row pointer */
+ Int *rp_end ; /* a pointer to the end of a row */
+ Int last_row ; /* previous row */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+ if (Col [col].length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = Col [col].length ;
+ DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ;
+ return (FALSE) ;
+ }
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = EMPTY ;
+ Col [col].shared4.degree_next = EMPTY ;
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ last_row = -1 ;
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ stats [COLAMD_INFO3] = n_row ;
+ DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ;
+ return (FALSE) ;
+ }
+
+ if (row <= last_row || Row [row].shared2.mark == col)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ (stats [COLAMD_INFO3]) ++ ;
+ DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col));
+ }
+
+ if (Row [row].shared2.mark != col)
+ {
+ Row [row].length++ ;
+ }
+ else
+ {
+ /* this is a repeated entry in the column, */
+ /* it will be removed */
+ Col [col].length-- ;
+ }
+
+ /* mark the row as having been seen in this column */
+ Row [row].shared2.mark = col ;
+
+ last_row = row ;
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ Row [0].shared2.mark = -1 ;
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ /* === Create row form ================================================== */
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
+ {
+ /* if cols jumbled, watch for repeated row indices */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+ if (Row [row].shared2.mark != col)
+ {
+ A [(Row [row].shared1.p)++] = col ;
+ Row [row].shared2.mark = col ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* if cols not jumbled, we don't need the mark (this is faster) */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* === See if we need to re-create columns ============================== */
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
+ {
+ DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ;
+
+#ifndef NDEBUG
+ /* make sure column lengths are correct */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p [col] = Col [col].length ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ p [*rp++]-- ;
+ }
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ ASSERT (p [col] == 0) ;
+ }
+ /* now p is all zero (different than when debugging is turned off) */
+#endif /* NDEBUG */
+
+ /* === Compute col pointers ========================================= */
+
+ /* col form of the matrix starts at A [0]. */
+ /* Note, we may have a gap between the col form and the row */
+ /* form if there were duplicate entries, if so, it will be */
+ /* removed upon the first garbage collection */
+ Col [0].start = 0 ;
+ p [0] = Col [0].start ;
+ for (col = 1 ; col < n_col ; col++)
+ {
+ /* note that the lengths here are for pruned columns, i.e. */
+ /* no duplicate row indices will exist for these columns */
+ Col [col].start = Col [col-1].start + Col [col-1].length ;
+ p [col] = Col [col].start ;
+ }
+
+ /* === Re-create col form =========================================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ A [(p [*rp++])++] = row ;
+ }
+ }
+ }
+
+ /* === Done. Matrix is not (or no longer) jumbled ====================== */
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+
+PRIVATE void init_scoring
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameters */
+ Int *p_n_row2, /* number of non-dense, non-empty rows */
+ Int *p_n_col2, /* number of non-dense, non-empty columns */
+ Int *p_max_deg /* maximum row degree */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int c ; /* a column index */
+ Int r, row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int deg ; /* degree of a row or column */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *new_cp ; /* new column pointer */
+ Int col_length ; /* length of pruned column */
+ Int score ; /* current column score */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int dense_row_count ; /* remove rows with more entries than this */
+ Int dense_col_count ; /* remove cols with more entries than this */
+ Int min_score ; /* smallest column score */
+ Int max_deg ; /* maximum row degree */
+ Int next_col ; /* Used to add to degree list.*/
+
+#ifndef NDEBUG
+ Int debug_count ; /* debug only. */
+#endif /* NDEBUG */
+
+ /* === Extract knobs ==================================================== */
+
+ /* Note: if knobs contains a NaN, this is undefined: */
+ if (knobs [COLAMD_DENSE_ROW] < 0)
+ {
+ /* only remove completely dense rows */
+ dense_row_count = n_col-1 ;
+ }
+ else
+ {
+ dense_row_count = DENSE_DEGREE (knobs [COLAMD_DENSE_ROW], n_col) ;
+ }
+ if (knobs [COLAMD_DENSE_COL] < 0)
+ {
+ /* only remove completely dense columns */
+ dense_col_count = n_row-1 ;
+ }
+ else
+ {
+ dense_col_count =
+ DENSE_DEGREE (knobs [COLAMD_DENSE_COL], MIN (n_row, n_col)) ;
+ }
+
+ DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* === Kill empty columns =============================================== */
+
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip any dead columns */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ ASSERT (deg >= 0 && deg <= n_col) ;
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ KILL_ROW (r) ;
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = MAX (max_deg, deg) ;
+ }
+ }
+ DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial matlab score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = MIN (score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (Int) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ DEBUG2 (("Newly null killed: %d\n", c)) ;
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ else
+ {
+ /* set column length and set score */
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+#ifndef NDEBUG
+ debug_structures (n_row, n_col, Row, Col, A, n_col2) ;
+#endif /* NDEBUG */
+
+ /* === Initialize degree lists ========================================== */
+
+#ifndef NDEBUG
+ debug_count = 0 ;
+#endif /* NDEBUG */
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = EMPTY ;
+ }
+ min_score = n_col ;
+ /* place in reverse order, so low column indices are at the front */
+ /* of the lists. This is to encourage natural tie-breaking */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* only add principal columns to degree lists */
+ if (COL_IS_ALIVE (c))
+ {
+ DEBUG4 (("place %d score %d minscore %d ncol %d\n",
+ c, Col [c].shared2.score, min_score, n_col)) ;
+
+ /* === Add columns score to DList =============================== */
+
+ score = Col [c].shared2.score ;
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ ASSERT (head [score] >= EMPTY) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [c].shared3.prev = EMPTY ;
+ Col [c].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = c ;
+ }
+ head [score] = c ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, score) ;
+
+#ifndef NDEBUG
+ debug_count++ ;
+#endif /* NDEBUG */
+
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("colamd: Live cols %d out of %d, non-princ: %d\n",
+ debug_count, n_col, n_col-debug_count)) ;
+ ASSERT (debug_count == n_col2) ;
+ debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ Order the principal columns of the supercolumn form of the matrix
+ (no supercolumns on input). Uses a minimum approximate column minimum
+ degree ordering method. Not user-callable.
+*/
+
+PRIVATE Int find_ordering /* return the number of garbage collections */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int Alen, /* size of A, 2*nnz + n_col or larger */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ Int n_col2, /* Remaining columns to order */
+ Int max_deg, /* Maximum row degree */
+ Int pfree, /* index of first free slot (2*nnz on entry) */
+ Int aggressive
+)
+{
+ /* === Local variables ================================================== */
+
+ Int k ; /* current pivot ordering step */
+ Int pivot_col ; /* current pivot column */
+ Int *cp ; /* a column pointer */
+ Int *rp ; /* a row pointer */
+ Int pivot_row ; /* current pivot row */
+ Int *new_cp ; /* modified column pointer */
+ Int *new_rp ; /* modified row pointer */
+ Int pivot_row_start ; /* pointer to start of pivot row */
+ Int pivot_row_degree ; /* number of columns in pivot row */
+ Int pivot_row_length ; /* number of supercolumns in pivot row */
+ Int pivot_col_score ; /* score of pivot column */
+ Int needed_memory ; /* free space needed for pivot row */
+ Int *cp_end ; /* pointer to the end of a column */
+ Int *rp_end ; /* pointer to the end of a row */
+ Int row ; /* a row index */
+ Int col ; /* a column index */
+ Int max_score ; /* maximum possible score */
+ Int cur_score ; /* score of current column */
+ unsigned Int hash ; /* hash value for supernode detection */
+ Int head_column ; /* head of hash bucket */
+ Int first_col ; /* first column in hash bucket */
+ Int tag_mark ; /* marker value for mark array */
+ Int row_mark ; /* Row [row].shared2.mark */
+ Int set_difference ; /* set difference size of row with pivot row */
+ Int min_score ; /* smallest column score */
+ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ Int max_mark ; /* maximum value of tag_mark */
+ Int pivot_col_thickness ; /* number of columns represented by pivot col */
+ Int prev_col ; /* Used by Dlist operations. */
+ Int next_col ; /* Used by Dlist operations. */
+ Int ngarbage ; /* number of garbage collections performed */
+
+#ifndef NDEBUG
+ Int debug_d ; /* debug loop counter */
+ Int debug_step = 0 ; /* debug loop counter */
+#endif /* NDEBUG */
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */
+ tag_mark = clear_mark (0, max_mark, n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ;
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
+ {
+
+#ifndef NDEBUG
+ if (debug_step % 100 == 0)
+ {
+ DEBUG2 (("\n... Step k: %d out of n_col2: %d\n", k, n_col2)) ;
+ }
+ else
+ {
+ DEBUG3 (("\n----------Step k: %d out of n_col2: %d\n", k, n_col2)) ;
+ }
+ debug_step++ ;
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+
+ /* === Select pivot column, and order it ============================ */
+
+ /* make sure degree list isn't empty */
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (head [min_score] >= EMPTY) ;
+
+#ifndef NDEBUG
+ for (debug_d = 0 ; debug_d < min_score ; debug_d++)
+ {
+ ASSERT (head [debug_d] == EMPTY) ;
+ }
+#endif /* NDEBUG */
+
+ /* get pivot column from head of minimum degree list */
+ while (head [min_score] == EMPTY && min_score < n_col)
+ {
+ min_score++ ;
+ }
+ pivot_col = head [min_score] ;
+ ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = EMPTY ;
+ }
+
+ ASSERT (COL_IS_ALIVE (pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ k += pivot_col_thickness ;
+ ASSERT (pivot_col_thickness > 0) ;
+ DEBUG3 (("Pivot col: %d thick %d\n", pivot_col, pivot_col_thickness)) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = MIN (pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out the Row[].shared2.mark array */
+ tag_mark = clear_mark (0, max_mark, n_row, Row) ;
+
+#ifndef NDEBUG
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+
+ /* tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ;
+ /* skip if row is dead */
+ if (ROW_IS_ALIVE (row))
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && COL_IS_ALIVE (col))
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ }
+ }
+ }
+ }
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ;
+ max_deg = MAX (max_deg, pivot_row_degree) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check2\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+ DEBUG3 (("Kill row in pivot col: %d\n", row)) ;
+ KILL_ROW (row) ;
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ DEBUG3 (("Pivotal row is %d\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = EMPTY ;
+ ASSERT (pivot_row_length == 0) ;
+ }
+ ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ DEBUG3 (("Pivot row: ")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ DEBUG3 (("Col: %d\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (cur_score >= EMPTY) ;
+ if (prev_col == EMPTY)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ ASSERT (set_difference >= 0) ;
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0 && aggressive)
+ {
+ DEBUG3 (("aggressive absorption. Row: %d\n", row)) ;
+ KILL_ROW (row) ;
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k-pivot_row_degree, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Add up set differences for each column ======================= */
+
+ DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ ASSERT(row >= 0 && row < n_row) ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ DEBUG4 ((" Row %d, dead\n", row)) ;
+ continue ;
+ }
+ DEBUG4 ((" Row %d, set diff %d\n", row, row_mark-tag_mark));
+ ASSERT (row_mark >= tag_mark) ;
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = MIN (cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0)
+ {
+ DEBUG4 (("further mass elimination. Col: %d\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ KILL_PRINCIPAL_COL (col) ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ;
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ hash %= n_col + 1 ;
+
+ DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ;
+ ASSERT (((Int) hash) <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (Int) hash ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ detect_super_cols (
+
+#ifndef NDEBUG
+ n_col, Row,
+#endif /* NDEBUG */
+
+ Col, A, head, pivot_row_start, pivot_row_length) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ KILL_PRINCIPAL_COL (pivot_col) ;
+
+ /* === Clear mark =================================================== */
+
+ tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check3\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ DEBUG3 (("** Finalize scores phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ /* skip dead columns */
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = MIN (cur_score, max_score) ;
+ ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+
+ /* === Place column back in degree list ========================= */
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (head [cur_score] >= EMPTY) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = EMPTY ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, cur_score) ;
+
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if (pivot_row_degree > 0)
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ;
+ ASSERT (Row [pivot_row].length > 0) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ /* pivot row is no longer dead */
+
+ DEBUG1 (("Resurrect Pivot_row %d deg: %d\n",
+ pivot_row, pivot_row_degree)) ;
+ }
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === order_children ======================================================= */
+/* ========================================================================== */
+
+/*
+ The find_ordering routine has ordered all of the principal columns (the
+ representatives of the supercolumns). The non-principal columns have not
+ yet been ordered. This routine orders those columns by walking up the
+ parent tree (a column is a child of the column which absorbed it). The
+ final permutation vector is then placed in p [0 ... n_col-1], with p [0]
+ being the first column, and p [n_col-1] being the last. It doesn't look
+ like it at first glance, but be assured that this routine takes time linear
+ in the number of columns. Although not immediately obvious, the time
+ taken by this routine is O (n_col), that is, linear in the number of
+ columns. Not user-callable.
+*/
+
+PRIVATE void order_children
+(
+ /* === Parameters ======================================================= */
+
+ Int n_col, /* number of columns of A */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int p [] /* p [0 ... n_col-1] is the column permutation*/
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ; /* loop counter for all columns */
+ Int c ; /* column index */
+ Int parent ; /* index of column's parent */
+ Int order ; /* column's order */
+
+ /* === Order each non-principal column ================================== */
+
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* find an un-ordered non-principal column */
+ ASSERT (COL_IS_DEAD (i)) ;
+ if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == EMPTY)
+ {
+ parent = i ;
+ /* once found, find its principal parent */
+ do
+ {
+ parent = Col [parent].shared1.parent ;
+ } while (!COL_IS_DEAD_PRINCIPAL (parent)) ;
+
+ /* now, order all un-ordered non-principal columns along path */
+ /* to this parent. collapse tree at the same time */
+ c = i ;
+ /* get order of parent */
+ order = Col [parent].shared2.order ;
+
+ do
+ {
+ ASSERT (Col [c].shared2.order == EMPTY) ;
+
+ /* order this column */
+ Col [c].shared2.order = order++ ;
+ /* collaps tree */
+ Col [c].shared1.parent = parent ;
+
+ /* get immediate parent of this column */
+ c = Col [c].shared1.parent ;
+
+ /* continue until we hit an ordered column. There are */
+ /* guarranteed not to be anymore unordered columns */
+ /* above an ordered column */
+ } while (Col [c].shared2.order == EMPTY) ;
+
+ /* re-order the super_col parent to largest order for this group */
+ Col [parent].shared2.order = order ;
+ }
+ }
+
+ /* === Generate the permutation ========================================= */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ p [Col [c].shared2.order] = c ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ Detects supercolumns by finding matches between columns in the hash buckets.
+ Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ The columns under consideration are currently *not* in the degree lists,
+ and have already been placed in the hash buckets.
+
+ The hash bucket for columns whose hash function is equal to h is stored
+ as follows:
+
+ if head [h] is >= 0, then head [h] contains a degree list, so:
+
+ head [h] is the first column in degree bucket h.
+ Col [head [h]].headhash gives the first column in hash bucket h.
+
+ otherwise, the degree list is empty, and:
+
+ -(head [h] + 2) is the first column in hash bucket h.
+
+ For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ column" pointer. Col [c].shared3.hash is used instead as the hash number
+ for that column. The value of Col [c].shared4.hash_next is the next column
+ in the same hash bucket.
+
+ Assuming no, or "few" hash collisions, the time taken by this routine is
+ linear in the sum of the sizes (lengths) of each column whose score has
+ just been computed in the approximate degree computation.
+ Not user-callable.
+*/
+
+PRIVATE void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+#ifndef NDEBUG
+ /* these two parameters are only needed when debugging is enabled: */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+#endif /* NDEBUG */
+
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A */
+ Int head [], /* head of degree lists and hash buckets */
+ Int row_start, /* pointer to set of columns to check */
+ Int row_length /* number of columns to check */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int hash ; /* hash value for a column */
+ Int *rp ; /* pointer to a row */
+ Int c ; /* a column index */
+ Int super_c ; /* column index of the column to absorb into */
+ Int *cp1 ; /* column pointer for column super_c */
+ Int *cp2 ; /* column pointer for column c */
+ Int length ; /* length of column super_c */
+ Int prev_c ; /* column preceding c in hash bucket */
+ Int i ; /* loop counter */
+ Int *rp_end ; /* pointer to the end of the row */
+ Int col ; /* a column index in the row to check */
+ Int head_column ; /* first column in hash bucket or degree list */
+ Int first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != EMPTY ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ ASSERT (COL_IS_ALIVE (super_c)) ;
+ ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != EMPTY ; c = Col [c].shared4.hash_next)
+ {
+ ASSERT (c != super_c) ;
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ ASSERT (ROW_IS_ALIVE (*cp1)) ;
+ ASSERT (ROW_IS_ALIVE (*cp2)) ;
+ /* row indices will same order for both supercols, */
+ /* no gather scatter nessasary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ KILL_NON_PRINCIPAL_COL (c) ;
+ /* order c later, in order_children() */
+ Col [c].shared2.order = EMPTY ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > EMPTY)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = EMPTY ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = EMPTY ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ Defragments and compacts columns and rows in the workspace A. Used when
+ all avaliable memory has been used while performing row merging. Returns
+ the index of the first free position in A, after garbage collection. The
+ time taken by this routine is linear is the size of the array A, which is
+ itself linear in the number of nonzeros in the input matrix.
+ Not user-callable.
+*/
+
+PRIVATE Int garbage_collection /* returns the new value of pfree */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows */
+ Int n_col, /* number of columns */
+ Colamd_Row Row [], /* row info */
+ Colamd_Col Col [], /* column info */
+ Int A [], /* A [0 ... Alen-1] holds the matrix */
+ Int *pfree /* &A [0] ... pfree is in use */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *psrc ; /* source pointer */
+ Int *pdest ; /* destination pointer */
+ Int j ; /* counter */
+ Int r ; /* a row index */
+ Int c ; /* a column index */
+ Int length ; /* length of a row or column */
+
+#ifndef NDEBUG
+ Int debug_rows ;
+ DEBUG2 (("Defrag..\n")) ;
+ for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ;
+ debug_rows = 0 ;
+#endif /* NDEBUG */
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ ASSERT (pdest <= psrc) ;
+ Col [c].start = (Int) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (ROW_IS_ALIVE (r))
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (Int) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_DEAD (r) || (Row [r].length == 0))
+ {
+ /* This row is already dead, or is of zero length. Cannot compact
+ * a row of zero length, so kill it. NOTE: in the current version,
+ * there are no zero-length live rows. Kill the row (for the first
+ * time, or again) just to be safe. */
+ KILL_ROW (r) ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ONES_COMPLEMENT (r) ;
+#ifndef NDEBUG
+ debug_rows++ ;
+#endif /* NDEBUG */
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ONES_COMPLEMENT (*psrc) ;
+ ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ ASSERT (Row [r].length > 0) ;
+ /* move and compact the row */
+ ASSERT (pdest <= psrc) ;
+ Row [r].start = (Int) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (Int) (pdest - &A [Row [r].start]) ;
+ ASSERT (Row [r].length > 0) ;
+#ifndef NDEBUG
+ debug_rows-- ;
+#endif /* NDEBUG */
+ }
+ }
+ /* ensure we found all the rows */
+ ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((Int) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Clears the Row [].shared2.mark array, and returns the new tag_mark.
+ Return value is the new tag_mark. Not user-callable.
+*/
+
+PRIVATE Int clear_mark /* return the new value for tag_mark */
+(
+ /* === Parameters ======================================================= */
+
+ Int tag_mark, /* new value of tag_mark */
+ Int max_mark, /* max allowed value of tag_mark */
+
+ Int n_row, /* number of rows in A */
+ Colamd_Row Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ if (tag_mark <= 0 || tag_mark >= max_mark)
+ {
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+ tag_mark = 1 ;
+ }
+
+ return (tag_mark) ;
+}
+
+
+/* ========================================================================== */
+/* === print_report ========================================================= */
+/* ========================================================================== */
+
+PRIVATE void print_report
+(
+ char *method,
+ Int stats [COLAMD_STATS]
+)
+{
+
+ Int i1, i2, i3 ;
+
+ PRINTF (("\n%s version %d.%d, %s: ", method,
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE)) ;
+
+ if (!stats)
+ {
+ PRINTF (("No statistics available.\n")) ;
+ return ;
+ }
+
+ i1 = stats [COLAMD_INFO1] ;
+ i2 = stats [COLAMD_INFO2] ;
+ i3 = stats [COLAMD_INFO3] ;
+
+ if (stats [COLAMD_STATUS] >= 0)
+ {
+ PRINTF (("OK. ")) ;
+ }
+ else
+ {
+ PRINTF (("ERROR. ")) ;
+ }
+
+ switch (stats [COLAMD_STATUS])
+ {
+
+ case COLAMD_OK_BUT_JUMBLED:
+
+ PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ;
+
+ PRINTF(("%s: number of duplicate or out-of-order row indices: %d\n",
+ method, i3)) ;
+
+ PRINTF(("%s: last seen duplicate or out-of-order row index: %d\n",
+ method, INDEX (i2))) ;
+
+ PRINTF(("%s: last seen in column: %d",
+ method, INDEX (i1))) ;
+
+ /* no break - fall through to next case instead */
+
+ case COLAMD_OK:
+
+ PRINTF(("\n")) ;
+
+ PRINTF(("%s: number of dense or empty rows ignored: %d\n",
+ method, stats [COLAMD_DENSE_ROW])) ;
+
+ PRINTF(("%s: number of dense or empty columns ignored: %d\n",
+ method, stats [COLAMD_DENSE_COL])) ;
+
+ PRINTF(("%s: number of garbage collections performed: %d\n",
+ method, stats [COLAMD_DEFRAG_COUNT])) ;
+ break ;
+
+ case COLAMD_ERROR_A_not_present:
+
+ PRINTF(("Array A (row indices of matrix) not present.\n")) ;
+ break ;
+
+ case COLAMD_ERROR_p_not_present:
+
+ PRINTF(("Array p (column pointers for matrix) not present.\n")) ;
+ break ;
+
+ case COLAMD_ERROR_nrow_negative:
+
+ PRINTF(("Invalid number of rows (%d).\n", i1)) ;
+ break ;
+
+ case COLAMD_ERROR_ncol_negative:
+
+ PRINTF(("Invalid number of columns (%d).\n", i1)) ;
+ break ;
+
+ case COLAMD_ERROR_nnz_negative:
+
+ PRINTF(("Invalid number of nonzero entries (%d).\n", i1)) ;
+ break ;
+
+ case COLAMD_ERROR_p0_nonzero:
+
+ PRINTF(("Invalid column pointer, p [0] = %d, must be zero.\n", i1));
+ break ;
+
+ case COLAMD_ERROR_A_too_small:
+
+ PRINTF(("Array A too small.\n")) ;
+ PRINTF((" Need Alen >= %d, but given only Alen = %d.\n",
+ i1, i2)) ;
+ break ;
+
+ case COLAMD_ERROR_col_length_negative:
+
+ PRINTF
+ (("Column %d has a negative number of nonzero entries (%d).\n",
+ INDEX (i1), i2)) ;
+ break ;
+
+ case COLAMD_ERROR_row_index_out_of_bounds:
+
+ PRINTF
+ (("Row index (row %d) out of bounds (%d to %d) in column %d.\n",
+ INDEX (i2), INDEX (0), INDEX (i3-1), INDEX (i1))) ;
+ break ;
+
+ case COLAMD_ERROR_out_of_memory:
+
+ PRINTF(("Out of memory.\n")) ;
+ break ;
+
+ /* v2.4: internal-error case deleted */
+ }
+}
+
+
+
+
+/* ========================================================================== */
+/* === colamd debugging routines ============================================ */
+/* ========================================================================== */
+
+/* When debugging is disabled, the remainder of this file is ignored. */
+
+#ifndef NDEBUG
+
+
+/* ========================================================================== */
+/* === debug_structures ===================================================== */
+/* ========================================================================== */
+
+/*
+ At this point, all empty rows and columns are dead. All live columns
+ are "clean" (containing no dead rows) and simplicial (no supercolumns
+ yet). Rows may contain dead columns, but all live rows contain at
+ least one live column.
+*/
+
+PRIVATE void debug_structures
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+ Int c ;
+ Int *cp ;
+ Int *cp_end ;
+ Int len ;
+ Int score ;
+ Int r ;
+ Int *rp ;
+ Int *rp_end ;
+ Int deg ;
+
+ /* === Check A, Row, and Col ============================================ */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ len = Col [c].length ;
+ score = Col [c].shared2.score ;
+ DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ;
+ ASSERT (len > 0) ;
+ ASSERT (score >= 0) ;
+ ASSERT (Col [c].shared1.thickness == 1) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + len ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ }
+ }
+ else
+ {
+ i = Col [c].shared2.order ;
+ ASSERT (i >= n_col2 && i < n_col) ;
+ }
+ }
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ i = 0 ;
+ len = Row [r].length ;
+ deg = Row [r].shared1.degree ;
+ ASSERT (len > 0) ;
+ ASSERT (deg > 0) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + len ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ i++ ;
+ }
+ }
+ ASSERT (i > 0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_deg_lists ====================================================== */
+/* ========================================================================== */
+
+/*
+ Prints the contents of the degree lists. Counts the number of columns
+ in the degree list and compares it to the total it should have. Also
+ checks the row degrees.
+*/
+
+PRIVATE void debug_deg_lists
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+)
+{
+ /* === Local variables ================================================== */
+
+ Int deg ;
+ Int col ;
+ Int have ;
+ Int row ;
+
+ /* === Check the degree lists =========================================== */
+
+ if (n_col > 10000 && colamd_debug <= 0)
+ {
+ return ;
+ }
+ have = 0 ;
+ DEBUG4 (("Degree lists: %d\n", min_score)) ;
+ for (deg = 0 ; deg <= n_col ; deg++)
+ {
+ col = head [deg] ;
+ if (col == EMPTY)
+ {
+ continue ;
+ }
+ DEBUG4 (("%d:", deg)) ;
+ while (col != EMPTY)
+ {
+ DEBUG4 ((" %d", col)) ;
+ have += Col [col].shared1.thickness ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ col = Col [col].shared4.degree_next ;
+ }
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("should %d have %d\n", should, have)) ;
+ ASSERT (should == have) ;
+
+ /* === Check the row degrees ============================================ */
+
+ if (n_row > 10000 && colamd_debug <= 0)
+ {
+ return ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (ROW_IS_ALIVE (row))
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Ensures that the tag_mark is less that the maximum and also ensures that
+ each entry in the mark array is less than the tag mark.
+*/
+
+PRIVATE void debug_mark
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ /* === Check the Row marks ============================================== */
+
+ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ;
+ if (n_row > 10000 && colamd_debug <= 0)
+ {
+ return ;
+ }
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared2.mark < tag_mark) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_matrix ========================================================= */
+/* ========================================================================== */
+
+/*
+ Prints out the contents of the columns and the rows.
+*/
+
+PRIVATE void debug_matrix
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+ Int c ;
+ Int *rp ;
+ Int *rp_end ;
+ Int *cp ;
+ Int *cp_end ;
+
+ /* === Dump the rows and columns of the matrix ========================== */
+
+ if (colamd_debug < 3)
+ {
+ return ;
+ }
+ DEBUG3 (("DUMP MATRIX:\n")) ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ DEBUG3 (("Row %d alive? %d\n", r, ROW_IS_ALIVE (r))) ;
+ if (ROW_IS_DEAD (r))
+ {
+ continue ;
+ }
+ DEBUG3 (("start %d length %d degree %d\n",
+ Row [r].start, Row [r].length, Row [r].shared1.degree)) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + Row [r].length ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ DEBUG4 ((" %d col %d\n", COL_IS_ALIVE (c), c)) ;
+ }
+ }
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ DEBUG3 (("Col %d alive? %d\n", c, COL_IS_ALIVE (c))) ;
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ DEBUG3 (("start %d length %d shared1 %d shared2 %d\n",
+ Col [c].start, Col [c].length,
+ Col [c].shared1.thickness, Col [c].shared2.score)) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ DEBUG4 ((" %d row %d\n", ROW_IS_ALIVE (r), r)) ;
+ }
+ }
+}
+
+PRIVATE void colamd_get_debug
+(
+ char *method
+)
+{
+ FILE *f ;
+ colamd_debug = 0 ; /* no debug printing */
+ f = fopen ("debug", "r") ;
+ if (f == (FILE *) NULL)
+ {
+ colamd_debug = 0 ;
+ }
+ else
+ {
+ fscanf (f, "%d", &colamd_debug) ;
+ fclose (f) ;
+ }
+ DEBUG0 (("%s: debug version, D = %d (THIS WILL BE SLOW!)\n",
+ method, colamd_debug)) ;
+}
+
+#endif /* NDEBUG */
diff --git a/src/C/SuiteSparse/COLAMD/colamd.h b/src/C/SuiteSparse/COLAMD/colamd.h
new file mode 100644
index 0000000..7af4213
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd.h
@@ -0,0 +1,254 @@
+/* ========================================================================== */
+/* === colamd/symamd prototypes and definitions ============================= */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD include file
+
+ You must include this file (colamd.h) in any routine that uses colamd,
+ symamd, or the related macros and definitions.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2006, Timothy A. Davis, All Rights Reserved.
+
+ THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+
+ Permission is hereby granted to use, copy, modify, and/or distribute
+ this program, provided that the Copyright, this License, and the
+ Availability of the original version is retained on all copies and made
+ accessible to the end-user of any code or package that includes COLAMD
+ or any modified version of COLAMD.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h
+ file. It is required by the colamd.c, colamdmex.c, and symamdmex.c
+ files, and by any C code that calls the routines whose prototypes are
+ listed below, or that uses the colamd/symamd definitions listed below.
+
+*/
+
+#ifndef COLAMD_H
+#define COLAMD_H
+
+/* make it easy for C++ programs to include COLAMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === COLAMD version ======================================================= */
+/* ========================================================================== */
+
+/* COLAMD Version 2.4 and later will include the following definitions.
+ * As an example, to test if the version you are using is 2.4 or later:
+ *
+ * #ifdef COLAMD_VERSION
+ * if (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(COLAMD_VERSION) && (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4))
+ * printf ("This is version 2.4 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 2.3 and earlier of COLAMD do not include a #define'd version number.
+ */
+
+#define COLAMD_DATE "Dec 12, 2006"
+#define COLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define COLAMD_MAIN_VERSION 2
+#define COLAMD_SUB_VERSION 6
+#define COLAMD_VERSION \
+ COLAMD_VERSION_CODE(COLAMD_MAIN_VERSION,COLAMD_SUB_VERSION)
+
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..1] are currently used. */
+#define COLAMD_KNOBS 20
+
+/* number of output statistics. Only stats [0..6] are currently used. */
+#define COLAMD_STATS 20
+
+/* knobs [0] and stats [0]: dense row knob and output statistic. */
+#define COLAMD_DENSE_ROW 0
+
+/* knobs [1] and stats [1]: dense column knob and output statistic. */
+#define COLAMD_DENSE_COL 1
+
+/* knobs [2]: aggressive absorption */
+#define COLAMD_AGGRESSIVE 2
+
+/* stats [2]: memory defragmentation count output statistic */
+#define COLAMD_DEFRAG_COUNT 2
+
+/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
+#define COLAMD_STATUS 3
+
+/* stats [4..6]: error info, or info on jumbled columns */
+#define COLAMD_INFO1 4
+#define COLAMD_INFO2 5
+#define COLAMD_INFO3 6
+
+/* error codes returned in stats [3]: */
+#define COLAMD_OK (0)
+#define COLAMD_OK_BUT_JUMBLED (1)
+#define COLAMD_ERROR_A_not_present (-1)
+#define COLAMD_ERROR_p_not_present (-2)
+#define COLAMD_ERROR_nrow_negative (-3)
+#define COLAMD_ERROR_ncol_negative (-4)
+#define COLAMD_ERROR_nnz_negative (-5)
+#define COLAMD_ERROR_p0_nonzero (-6)
+#define COLAMD_ERROR_A_too_small (-7)
+#define COLAMD_ERROR_col_length_negative (-8)
+#define COLAMD_ERROR_row_index_out_of_bounds (-9)
+#define COLAMD_ERROR_out_of_memory (-10)
+#define COLAMD_ERROR_internal_error (-999)
+
+
+/* ========================================================================== */
+/* === Prototypes of user-callable routines ================================= */
+/* ========================================================================== */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+size_t colamd_recommended /* returns recommended value of Alen, */
+ /* or 0 if input arguments are erroneous */
+(
+ int nnz, /* nonzeros in A */
+ int n_row, /* number of rows in A */
+ int n_col /* number of columns in A */
+) ;
+
+size_t colamd_l_recommended /* returns recommended value of Alen, */
+ /* or 0 if input arguments are erroneous */
+(
+ UF_long nnz, /* nonzeros in A */
+ UF_long n_row, /* number of rows in A */
+ UF_long n_col /* number of columns in A */
+) ;
+
+void colamd_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */
+) ;
+
+void colamd_l_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */
+) ;
+
+int colamd /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ int n_row, /* number of rows in A */
+ int n_col, /* number of columns in A */
+ int Alen, /* size of the array A */
+ int A [], /* row indices of A, of size Alen */
+ int p [], /* column pointers of A, of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */
+ int stats [COLAMD_STATS] /* colamd output statistics and error codes */
+) ;
+
+UF_long colamd_l /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ UF_long n_row, /* number of rows in A */
+ UF_long n_col, /* number of columns in A */
+ UF_long Alen, /* size of the array A */
+ UF_long A [], /* row indices of A, of size Alen */
+ UF_long p [], /* column pointers of A, of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */
+ UF_long stats [COLAMD_STATS]/* colamd output statistics and error codes */
+) ;
+
+int symamd /* return (1) if OK, (0) otherwise */
+(
+ int n, /* number of rows and columns of A */
+ int A [], /* row indices of A */
+ int p [], /* column pointers of A */
+ int perm [], /* output permutation, size n_col+1 */
+ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ int stats [COLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),
+ /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *)
+ /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+) ;
+
+UF_long symamd_l /* return (1) if OK, (0) otherwise */
+(
+ UF_long n, /* number of rows and columns of A */
+ UF_long A [], /* row indices of A */
+ UF_long p [], /* column pointers of A */
+ UF_long perm [], /* output permutation, size n_col+1 */
+ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ UF_long stats [COLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),
+ /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *)
+ /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+) ;
+
+void colamd_report
+(
+ int stats [COLAMD_STATS]
+) ;
+
+void colamd_l_report
+(
+ UF_long stats [COLAMD_STATS]
+) ;
+
+void symamd_report
+(
+ int stats [COLAMD_STATS]
+) ;
+
+void symamd_l_report
+(
+ UF_long stats [COLAMD_STATS]
+) ;
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN int (*colamd_printf) (const char *, ...) ;
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* COLAMD_H */
diff --git a/src/C/SuiteSparse/COLAMD/colamd2.m b/src/C/SuiteSparse/COLAMD/colamd2.m
new file mode 100644
index 0000000..69348c3
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd2.m
@@ -0,0 +1,103 @@
+function [p,stats] = colamd2 (S, knobs)
+%COLAMD2 Column approximate minimum degree permutation.
+% P = COLAMD2(S) returns the column approximate minimum degree permutation
+% vector for the sparse matrix S. For a non-symmetric matrix S, S(:,P)
+% tends to have sparser LU factors than S. The Cholesky factorization of
+% S(:,P)'*S(:,P) also tends to be sparser than that of S'*S. The ordering
+% is followed by a column elimination tree post-ordering.
+%
+% Note that this function is the source code for the built-in MATLAB colamd
+% function. It has been renamed here to colamd2 to avoid a filename clash.
+% colamd and colamd2 are identical.
+%
+% See also COLAMD, AMD, SYMAMD, SYMAMD2.
+%
+% Example:
+% P = colamd2 (S)
+% [P, stats] = colamd2 (S, knobs)
+%
+% knobs is an optional one- to three-element input vector. If S is m-by-n,
+% then rows with more than max(16,knobs(1)*sqrt(n)) entries are ignored.
+% Columns with more than max(16,knobs(2)*sqrt(min(m,n))) entries are
+% removed prior to ordering, and ordered last in the output permutation P.
+% Only completely dense rows or columns are removed if knobs(1) and knobs(2)
+% are < 0, respectively. If knobs(3) is nonzero, stats and knobs are
+% printed. The default is knobs = [10 10 0]. Note that knobs differs from
+% earlier versions of colamd.
+%
+% Type the command "type colamd2" for a description of the optional stats
+% output and for the copyright information.
+%
+% Authors: S. Larimore and T. Davis, University of Florida. Developed in
+% collaboration with J. Gilbert and E. Ng.
+%
+% Acknowledgements: This work was supported by the National Science
+% Foundation, under grants DMS-9504974 and DMS-9803599.
+
+% Notice:
+%
+% Copyright 1998-2006, Timothy A. Davis, All Rights Reserved.
+%
+% See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+% file) for the License.
+%
+% Availability:
+%
+% colamd, symamd, amd, ccolamd, and csymamd are available at
+% http://www.cise.ufl.edu/research/sparse
+
+%-------------------------------------------------------------------------------
+% Perform the colamd ordering:
+%-------------------------------------------------------------------------------
+
+if (nargout <= 1 && nargin == 1)
+ p = colamd2mex (S) ;
+elseif (nargout <= 1 && nargin == 2)
+ p = colamd2mex (S, knobs) ;
+elseif (nargout == 2 && nargin == 1)
+ [p, stats] = colamd2mex (S) ;
+elseif (nargout == 2 && nargin == 2)
+ [p, stats] = colamd2mex (S, knobs) ;
+else
+ error ('MATLAB:colamd:WrongInputOrOutputNumber',...
+ 'colamd: incorrect number of input and/or output arguments') ;
+end
+
+%-------------------------------------------------------------------------------
+% column elimination tree post-ordering:
+%-------------------------------------------------------------------------------
+
+[ignore, q] = etree (S (:,p), 'col') ;
+p = p (q) ;
+
+% stats is an optional 20-element output vector that provides data about the
+% ordering and the validity of the input matrix S. Ordering statistics are
+% in stats (1:3). stats (1) and stats (2) are the number of dense or empty
+% rows and columns ignored by COLAMD and stats (3) is the number of
+% garbage collections performed on the internal data structure used by
+% COLAMD (roughly of size 2.2*nnz(S) + 4*m + 7*n integers).
+%
+% MATLAB built-in functions are intended to generate valid sparse matrices,
+% with no duplicate entries, with ascending row indices of the nonzeros
+% in each column, with a non-negative number of entries in each column (!)
+% and so on. If a matrix is invalid, then COLAMD may or may not be able
+% to continue. If there are duplicate entries (a row index appears two or
+% more times in the same column) or if the row indices in a column are out
+% of order, then COLAMD can correct these errors by ignoring the duplicate
+% entries and sorting each column of its internal copy of the matrix S (the
+% input matrix S is not repaired, however). If a matrix is invalid in other
+% ways then COLAMD cannot continue, an error message is printed, and no
+% output arguments (P or stats) are returned. COLAMD is thus a simple way
+% to check a sparse matrix to see if it's valid.
+%
+% stats (4:7) provide information if COLAMD was able to continue. The
+% matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the
+% rightmost column index that is unsorted or contains duplicate entries,
+% or zero if no such column exists. stats (6) is the last seen duplicate
+% or out-of-order row index in the column index given by stats (5), or zero
+% if no such row index exists. stats (7) is the number of duplicate or
+% out-of-order row indices.
+%
+% stats (8:20) is always zero in the current version of COLAMD (reserved
+% for future use).
+
diff --git a/src/C/SuiteSparse/COLAMD/colamd_demo.m b/src/C/SuiteSparse/COLAMD/colamd_demo.m
new file mode 100644
index 0000000..265daf4
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_demo.m
@@ -0,0 +1,178 @@
+%COLAMD_DEMO demo for colamd, column approx minimum degree ordering algorithm
+%
+% Example:
+% colamd_demo
+%
+% The following m-files and mexFunctions provide alternative sparse matrix
+% ordering methods for MATLAB. They are typically faster (sometimes much
+% faster) and typically provide better orderings than their MATLAB counterparts:
+%
+% colamd a replacement for colmmd.
+%
+% Typical usage: p = colamd (A) ;
+%
+% symamd a replacement for symmmd. Based on colamd.
+%
+% Typical usage: p = symamd (A) ;
+%
+% For a description of the methods used, see the colamd.c file.
+%
+% http://www.cise.ufl.edu/research/sparse/colamd/
+%
+% See also colamd, symamd
+
+% Minor changes: in MATLAB 7, symmmd and colmmd are flagged as "obsolete".
+% This demo checks if they exist, so it should still work when they are removed.
+
+% Copyright 2006, Timothy A. Davis, University of Florida
+
+%-------------------------------------------------------------------------------
+% Print the introduction, the help info, and compile the mexFunctions
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Colamd2/symamd2 demo.') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help colamd_demo ;
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Colamd help information:') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help colamd2 ;
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Symamd help information:') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help symamd2 ;
+
+%-------------------------------------------------------------------------------
+% Solving Ax=b
+%-------------------------------------------------------------------------------
+
+n = 100 ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Solving Ax=b for a small %d-by-%d random matrix:', n, n) ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, '\nNote: Random sparse matrices are AWFUL test cases.\n') ;
+fprintf (1, 'They''re just easy to generate in a demo.\n') ;
+
+% set up the system
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+spparms ('default') ;
+A = sprandn (n, n, 5/n) + speye (n) ;
+b = (1:n)' ;
+
+fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colamd2:\n') ;
+q = colamd2 (A) ;
+I = speye (n) ;
+Q = I (:, q) ;
+[L,U,P] = lu (A*Q) ;
+fl = luflops (L, U) ;
+x = Q * (U \ (L \ (P * b))) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+
+try
+ fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colmmd:\n') ;
+ q = colmmd (A) ;
+ I = speye (n) ;
+ Q = I (:, q) ;
+ [L,U,P] = lu (A*Q) ;
+ fl = luflops (L, U) ;
+ x = Q * (U \ (L \ (P * b))) ;
+ fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+ fprintf (1, 'residual: %e\n', ...
+ norm (A*x-b)) ;
+catch
+ fprintf (1, 'colmmd is obsolete\n') ;
+end
+
+fprintf (1, '\n\nSolving via lu (PA = LU), without regard for sparsity:\n') ;
+[L,U,P] = lu (A) ;
+fl = luflops (L, U) ;
+x = U \ (L \ (P * b)) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+
+%-------------------------------------------------------------------------------
+% Large demo for colamd2
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Large demo for colamd2 (symbolic analysis only):') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+spparms ('default') ;
+n = 1000 ;
+fprintf (1, 'Generating a random %d-by-%d sparse matrix.\n', n, n) ;
+A = sprandn (n, n, 5/n) + speye (n) ;
+
+fprintf (1, '\n\nUnordered matrix:\n') ;
+lnz = symbfact (A, 'col') ;
+fprintf (1, 'nz in Cholesky factors of A''A: %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A''A: %d\n', sum (lnz.^2)) ;
+
+tic ;
+p = colamd2 (A) ;
+t = toc ;
+lnz = symbfact (A (:,p), 'col') ;
+fprintf (1, '\n\nColamd run time: %f\n', t) ;
+fprintf (1, 'colamd2 ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ;
+
+try
+ tic ;
+ p = colmmd (A) ;
+ t = toc ;
+ lnz = symbfact (A (:,p), 'col') ;
+ fprintf (1, '\n\nColmmd run time: %f\n', t) ;
+ fprintf (1, 'colmmd ordering quality: \n') ;
+ fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ;
+ fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', ...
+ sum (lnz.^2)) ;
+catch
+ fprintf (1, 'colmmd is obsolete\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% Large demo for symamd2
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Large demo for symamd2 (symbolic analysis only):') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+
+fprintf (1, 'Generating a random symmetric %d-by-%d sparse matrix.\n', n, n) ;
+A = A+A' ;
+
+fprintf (1, '\n\nUnordered matrix:\n') ;
+lnz = symbfact (A, 'sym') ;
+fprintf (1, 'nz in Cholesky factors of A: %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A: %d\n', sum (lnz.^2)) ;
+
+tic ;
+p = symamd2 (A) ;
+t = toc ;
+lnz = symbfact (A (p,p), 'sym') ;
+fprintf (1, '\n\nSymamd run time: %f\n', t) ;
+fprintf (1, 'symamd2 ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ;
+
+try
+ tic ;
+ p = symmmd (A) ;
+ t = toc ;
+ lnz = symbfact (A (p,p), 'sym') ;
+ fprintf (1, '\n\nSymmmd run time: %f\n', t) ;
+ fprintf (1, 'symmmd ordering quality: \n') ;
+ fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ;
+ fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ;
+catch
+ fprintf (1, 'symmmd is obsolete\n') ;
+end
diff --git a/src/C/SuiteSparse/COLAMD/colamd_example.c b/src/C/SuiteSparse/COLAMD/colamd_example.c
new file mode 100644
index 0000000..fe824d8
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_example.c
@@ -0,0 +1,181 @@
+/* ========================================================================== */
+/* === colamd and symamd example ============================================ */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD example
+
+ colamd example of use, to order the columns of a 5-by-4 matrix with
+ 11 nonzero entries in the following nonzero pattern, with default knobs.
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ symamd example of use, to order the rows and columns of a 5-by-5
+ matrix with 13 nonzero entries in the following nonzero pattern,
+ with default knobs.
+
+ x x 0 0 0
+ x x x x 0
+ 0 x x 0 0
+ 0 x 0 x x
+ 0 0 0 x x
+
+ (where x denotes a nonzero value).
+
+ See http://www.cise.ufl.edu/research/sparse/colamd/ (the colamd.c file)
+ for the routines this program calls, and for the License.
+*/
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include "colamd.h"
+
+#define A_NNZ 11
+#define A_NROW 5
+#define A_NCOL 4
+#define ALEN 150
+
+#define B_NNZ 4
+#define B_N 5
+
+int main (void)
+{
+
+ /* ====================================================================== */
+ /* input matrix A definition */
+ /* ====================================================================== */
+
+ int A [ALEN] = {
+
+ 0, 1, 4, /* row indices of nonzeros in column 0 */
+ 2, 4, /* row indices of nonzeros in column 1 */
+ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */
+ 1, 3} ; /* row indices of nonzeros in column 3 */
+
+ int p [ ] = {
+
+ 0, /* column 0 is in A [0..2] */
+ 3, /* column 1 is in A [3..4] */
+ 5, /* column 2 is in A [5..8] */
+ 9, /* column 3 is in A [9..10] */
+ A_NNZ} ; /* number of nonzeros in A */
+
+ /* ====================================================================== */
+ /* input matrix B definition */
+ /* ====================================================================== */
+
+ int B [ ] = { /* Note: only strictly lower triangular part */
+ /* is included, since symamd ignores the */
+ /* diagonal and upper triangular part of B. */
+
+ 1, /* row indices of nonzeros in column 0 */
+ 2, 3, /* row indices of nonzeros in column 1 */
+ /* row indices of nonzeros in column 2 (none) */
+ 4 /* row indices of nonzeros in column 3 */
+ } ; /* row indices of nonzeros in column 4 (none) */
+
+ int q [ ] = {
+
+ 0, /* column 0 is in B [0] */
+ 1, /* column 1 is in B [1..2] */
+ 3, /* column 2 is empty */
+ 3, /* column 3 is in B [3] */
+ 4, /* column 4 is empty */
+ B_NNZ} ; /* number of nonzeros in strictly lower B */
+
+ /* ====================================================================== */
+ /* other variable definitions */
+ /* ====================================================================== */
+
+ int perm [B_N+1] ; /* note the size is N+1 */
+ int stats [COLAMD_STATS] ; /* for colamd and symamd output statistics */
+
+ int row, col, pp, length, ok ;
+
+ /* ====================================================================== */
+ /* dump the input matrix A */
+ /* ====================================================================== */
+
+ printf ("colamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ;
+ for (col = 0 ; col < A_NCOL ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ printf ("Column %d, with %d entries:\n", col, length) ;
+ for (pp = p [col] ; pp < p [col+1] ; pp++)
+ {
+ row = A [pp] ;
+ printf (" row %d\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix. Note that this destroys A and overwrites p */
+ /* ====================================================================== */
+
+ ok = colamd (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats) ;
+ colamd_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("colamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the column ordering */
+ /* ====================================================================== */
+
+ printf ("colamd column ordering:\n") ;
+ printf ("1st column: %d\n", p [0]) ;
+ printf ("2nd column: %d\n", p [1]) ;
+ printf ("3rd column: %d\n", p [2]) ;
+ printf ("4th column: %d\n", p [3]) ;
+
+ /* ====================================================================== */
+ /* dump the strictly lower triangular part of symmetric input matrix B */
+ /* ====================================================================== */
+
+ printf ("\n\nsymamd %d-by-%d input matrix:\n", B_N, B_N) ;
+ printf ("Entries in strictly lower triangular part:\n") ;
+ for (col = 0 ; col < B_N ; col++)
+ {
+ length = q [col+1] - q [col] ;
+ printf ("Column %d, with %d entries:\n", col, length) ;
+ for (pp = q [col] ; pp < q [col+1] ; pp++)
+ {
+ row = B [pp] ;
+ printf (" row %d\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix B. Note that this does not modify B or q. */
+ /* ====================================================================== */
+
+ ok = symamd (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free) ;
+ symamd_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("symamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the symmetric ordering */
+ /* ====================================================================== */
+
+ printf ("symamd column ordering:\n") ;
+ printf ("1st row/column: %d\n", perm [0]) ;
+ printf ("2nd row/column: %d\n", perm [1]) ;
+ printf ("3rd row/column: %d\n", perm [2]) ;
+ printf ("4th row/column: %d\n", perm [3]) ;
+ printf ("5th row/column: %d\n", perm [4]) ;
+
+ exit (0) ;
+}
+
diff --git a/src/C/SuiteSparse/COLAMD/colamd_example.out b/src/C/SuiteSparse/COLAMD/colamd_example.out
new file mode 100644
index 0000000..45377ca
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_example.out
@@ -0,0 +1,50 @@
+colamd 5-by-4 input matrix:
+Column 0, with 3 entries:
+ row 0
+ row 1
+ row 4
+Column 1, with 2 entries:
+ row 2
+ row 4
+Column 2, with 4 entries:
+ row 0
+ row 1
+ row 2
+ row 3
+Column 3, with 2 entries:
+ row 1
+ row 3
+
+colamd version 2.6, Dec 12, 2006: OK.
+colamd: number of dense or empty rows ignored: 0
+colamd: number of dense or empty columns ignored: 0
+colamd: number of garbage collections performed: 0
+colamd column ordering:
+1st column: 1
+2nd column: 0
+3rd column: 2
+4th column: 3
+
+
+symamd 5-by-5 input matrix:
+Entries in strictly lower triangular part:
+Column 0, with 1 entries:
+ row 1
+Column 1, with 2 entries:
+ row 2
+ row 3
+Column 2, with 0 entries:
+Column 3, with 1 entries:
+ row 4
+Column 4, with 0 entries:
+
+symamd version 2.6, Dec 12, 2006: OK.
+symamd: number of dense or empty rows ignored: 0
+symamd: number of dense or empty columns ignored: 0
+symamd: number of garbage collections performed: 0
+symamd column ordering:
+1st row/column: 0
+2nd row/column: 2
+3rd row/column: 1
+4th row/column: 3
+5th row/column: 4
diff --git a/src/C/SuiteSparse/COLAMD/colamd_global.c b/src/C/SuiteSparse/COLAMD/colamd_global.c
new file mode 100644
index 0000000..6c9dfde
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_global.c
@@ -0,0 +1,24 @@
+/* ========================================================================== */
+/* === colamd_global.c ====================================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * COLAMD, Copyright (C) 2006, Timothy A. Davis.
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Global variables for COLAMD */
+
+#ifndef NPRINT
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+int (*colamd_printf) (const char *, ...) = mexPrintf ;
+#else
+#include <stdio.h>
+int (*colamd_printf) (const char *, ...) = printf ;
+#endif
+#else
+int (*colamd_printf) (const char *, ...) = ((void *) 0) ;
+#endif
+
diff --git a/src/C/SuiteSparse/COLAMD/colamd_l_example.c b/src/C/SuiteSparse/COLAMD/colamd_l_example.c
new file mode 100644
index 0000000..9ff9aeb
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_l_example.c
@@ -0,0 +1,185 @@
+/* ========================================================================== */
+/* === colamd and symamd example ============================================ */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD example
+
+ colamd example of use, to order the columns of a 5-by-4 matrix with
+ 11 nonzero entries in the following nonzero pattern, with default knobs.
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ symamd example of use, to order the rows and columns of a 5-by-5
+ matrix with 13 nonzero entries in the following nonzero pattern,
+ with default knobs.
+
+ x x 0 0 0
+ x x x x 0
+ 0 x x 0 0
+ 0 x 0 x x
+ 0 0 0 x x
+
+ (where x denotes a nonzero value).
+
+
+ See http://www.cise.ufl.edu/research/sparse/colamd/ (the colamd.c file)
+ for the routines this program calls, and for the License.
+*/
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include "colamd.h"
+
+#define A_NNZ 11
+#define A_NROW 5
+#define A_NCOL 4
+#define ALEN 150
+
+#define B_NNZ 4
+#define B_N 5
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int main (void)
+{
+
+ /* ====================================================================== */
+ /* input matrix A definition */
+ /* ====================================================================== */
+
+ UF_long A [ALEN] = {
+
+ 0, 1, 4, /* row indices of nonzeros in column 0 */
+ 2, 4, /* row indices of nonzeros in column 1 */
+ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */
+ 1, 3} ; /* row indices of nonzeros in column 3 */
+
+ UF_long p [ ] = {
+
+ 0, /* column 0 is in A [0..2] */
+ 3, /* column 1 is in A [3..4] */
+ 5, /* column 2 is in A [5..8] */
+ 9, /* column 3 is in A [9..10] */
+ A_NNZ} ; /* number of nonzeros in A */
+
+ /* ====================================================================== */
+ /* input matrix B definition */
+ /* ====================================================================== */
+
+ UF_long B [ ] = { /* Note: only strictly lower triangular part */
+ /* is included, since symamd ignores the */
+ /* diagonal and upper triangular part of B. */
+
+ 1, /* row indices of nonzeros in column 0 */
+ 2, 3, /* row indices of nonzeros in column 1 */
+ /* row indices of nonzeros in column 2 (none) */
+ 4 /* row indices of nonzeros in column 3 */
+ } ; /* row indices of nonzeros in column 4 (none) */
+
+ UF_long q [ ] = {
+
+ 0, /* column 0 is in B [0] */
+ 1, /* column 1 is in B [1..2] */
+ 3, /* column 2 is empty */
+ 3, /* column 3 is in B [3] */
+ 4, /* column 4 is empty */
+ B_NNZ} ; /* number of nonzeros in strictly lower B */
+
+ /* ====================================================================== */
+ /* other variable definitions */
+ /* ====================================================================== */
+
+ UF_long perm [B_N+1] ; /* note the size is N+1 */
+ UF_long stats [COLAMD_STATS] ;/* for colamd and symamd output statistics */
+
+ UF_long row, col, pp, length, ok ;
+
+ /* ====================================================================== */
+ /* dump the input matrix A */
+ /* ====================================================================== */
+
+ printf ("colamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ;
+ for (col = 0 ; col < A_NCOL ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ printf ("Column %ld, with %ld entries:\n", col, length) ;
+ for (pp = p [col] ; pp < p [col+1] ; pp++)
+ {
+ row = A [pp] ;
+ printf (" row %ld\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix. Note that this destroys A and overwrites p */
+ /* ====================================================================== */
+
+ ok = colamd_l (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats) ;
+ colamd_l_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("colamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the column ordering */
+ /* ====================================================================== */
+
+ printf ("colamd_l column ordering:\n") ;
+ printf ("1st column: %ld\n", p [0]) ;
+ printf ("2nd column: %ld\n", p [1]) ;
+ printf ("3rd column: %ld\n", p [2]) ;
+ printf ("4th column: %ld\n", p [3]) ;
+
+ /* ====================================================================== */
+ /* dump the strictly lower triangular part of symmetric input matrix B */
+ /* ====================================================================== */
+
+ printf ("\n\nsymamd_l %d-by-%d input matrix:\n", B_N, B_N) ;
+ printf ("Entries in strictly lower triangular part:\n") ;
+ for (col = 0 ; col < B_N ; col++)
+ {
+ length = q [col+1] - q [col] ;
+ printf ("Column %ld, with %ld entries:\n", col, length) ;
+ for (pp = q [col] ; pp < q [col+1] ; pp++)
+ {
+ row = B [pp] ;
+ printf (" row %ld\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix B. Note that this does not modify B or q. */
+ /* ====================================================================== */
+
+ ok = symamd_l (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free) ;
+ symamd_l_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("symamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the symmetric ordering */
+ /* ====================================================================== */
+
+ printf ("symamd_l column ordering:\n") ;
+ printf ("1st row/column: %ld\n", perm [0]) ;
+ printf ("2nd row/column: %ld\n", perm [1]) ;
+ printf ("3rd row/column: %ld\n", perm [2]) ;
+ printf ("4th row/column: %ld\n", perm [3]) ;
+ printf ("5th row/column: %ld\n", perm [4]) ;
+
+ exit (0) ;
+}
+
diff --git a/src/C/SuiteSparse/COLAMD/colamd_l_example.out b/src/C/SuiteSparse/COLAMD/colamd_l_example.out
new file mode 100644
index 0000000..f088b27
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_l_example.out
@@ -0,0 +1,50 @@
+colamd 5-by-4 input matrix:
+Column 0, with 3 entries:
+ row 0
+ row 1
+ row 4
+Column 1, with 2 entries:
+ row 2
+ row 4
+Column 2, with 4 entries:
+ row 0
+ row 1
+ row 2
+ row 3
+Column 3, with 2 entries:
+ row 1
+ row 3
+
+colamd version 2.6, Dec 12, 2006: OK.
+colamd: number of dense or empty rows ignored: 0
+colamd: number of dense or empty columns ignored: 0
+colamd: number of garbage collections performed: 0
+colamd_l column ordering:
+1st column: 1
+2nd column: 0
+3rd column: 2
+4th column: 3
+
+
+symamd_l 5-by-5 input matrix:
+Entries in strictly lower triangular part:
+Column 0, with 1 entries:
+ row 1
+Column 1, with 2 entries:
+ row 2
+ row 3
+Column 2, with 0 entries:
+Column 3, with 1 entries:
+ row 4
+Column 4, with 0 entries:
+
+symamd version 2.6, Dec 12, 2006: OK.
+symamd: number of dense or empty rows ignored: 0
+symamd: number of dense or empty columns ignored: 0
+symamd: number of garbage collections performed: 0
+symamd_l column ordering:
+1st row/column: 0
+2nd row/column: 2
+3rd row/column: 1
+4th row/column: 3
+5th row/column: 4
diff --git a/src/C/SuiteSparse/COLAMD/colamd_make.m b/src/C/SuiteSparse/COLAMD/colamd_make.m
new file mode 100644
index 0000000..48d8b98
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_make.m
@@ -0,0 +1,18 @@
+function colamd_make
+%COLAMD_MAKE compiles COLAMD2 and SYMAMD2 for MATLAB
+%
+% Example:
+% colamd_make
+%
+% See also colamd, symamd
+
+% Copyright 2006, Timothy A. Davis, University of Florida
+
+
+if (~isempty (strfind (computer, '64')))
+ error ('64-bit version not yet supported') ;
+end
+
+mex -output colamd2mex -O -I../UFconfig colamdmex.c colamd.c colamd_global.c
+mex -output symamd2mex -O -I../UFconfig symamdmex.c colamd.c colamd_global.c
+fprintf ('COLAMD2 and SYMAMD2 successfully compiled.\n') ;
diff --git a/src/C/SuiteSparse/COLAMD/colamd_test.m b/src/C/SuiteSparse/COLAMD/colamd_test.m
new file mode 100644
index 0000000..cd909b6
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamd_test.m
@@ -0,0 +1,507 @@
+function colamd_test
+%COLAMD_TEST test colamd2 and symamd2
+% Example:
+% colamd_test
+%
+% COLAMD and SYMAMD testing function. Here we try to give colamd2 and symamd2
+% every possible type of matrix and erroneous input that they may encounter.
+% We want either a valid permutation returned or we want them to fail
+% gracefully.
+%
+% You are prompted as to whether or not the colamd2 and symand routines and
+% the test mexFunctions are to be compiled.
+%
+% See also colamd2, symamd2
+%
+% Tim Davis
+% http://www.cise.ufl.edu/research/sparse/colamd/
+
+% Copyright 2006, Timothy A. Davis, University of Florida
+
+
+help colamd_test
+
+s = input (...
+'Compile colamd2, symand, and the test codes? (y/n, default is yes): ', 's') ;
+
+do_compile = 1 ;
+if (~isempty (s))
+ if (s (1) == 'n' || s (1) == 'N')
+ do_compile = 0 ;
+ end
+end
+
+if (do_compile)
+ fprintf ('Compiling colamd2, symamd2, and test mexFunctions.\n') ;
+ colamd_make ;
+ cmd = 'mex -O -I../UFconfig colamdtestmex.c colamd.c colamd_global.c' ;
+ fprintf ('%s\n', cmd) ;
+ eval (cmd) ;
+ cmd = 'mex -O -I../UFconfig symamdtestmex.c colamd.c colamd_global.c' ;
+ fprintf ('%s\n', cmd) ;
+ eval (cmd) ;
+ fprintf ('Done compiling.\n') ;
+end
+
+fprintf ('\nThe following codes will be tested:\n') ;
+which colamd2
+which symamd2
+which colamdmex
+which symamdmex
+
+fprintf ('\nStarting the tests. Please be patient.\n') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+A = sprandn (500,500,0.4) ;
+
+p = colamd2 (A, [10 10 1]) ; check_perm (p, A) ;
+p = colamd2 (A, [2 7 1]) ; check_perm (p, A) ;
+p = symamd2 (A, [10 1]) ; check_perm (p, A) ;
+p = symamd2 (A, [7 1]) ; check_perm (p, A) ;
+p = symamd2 (A, [4 1]) ; check_perm (p, A) ;
+
+
+fprintf ('Null matrices') ;
+A = zeros (0,0) ;
+A = sparse (A) ;
+
+[p, stats] = colamd2 (A, [10 10 0]) ; %#ok
+check_perm (p, A) ;
+
+[p, stats] = symamd2 (A, [10 0]) ; %#ok
+check_perm (p, A) ;
+
+A = zeros (0, 100) ;
+A = sparse (A) ;
+[p, stats] = colamd2 (A, [10 10 0]) ; %#ok
+check_perm (p, A) ;
+
+A = zeros (100, 0) ;
+A = sparse (A) ;
+[p, stats] = colamd2 (A, [10 10 0]) ;
+check_perm (p, A) ;
+fprintf (' OK\n') ;
+
+
+fprintf ('Matrices with a few dense row/cols\n') ;
+
+for trial = 1:20
+
+ % random square unsymmetric matrix
+ A = rand_matrix (1000, 1000, 1, 10, 20) ;
+
+ for tol = [0:.1:2 3:20 1e6]
+
+ [p, stats] = colamd2 (A, [tol tol 0]) ; %#ok
+ check_perm (p, A) ;
+
+ B = A + A' ;
+ [p, stats] = symamd2 (B, [tol 0]) ; %#ok
+ check_perm (p, A) ;
+
+ [p, stats] = colamd2 (A, [tol 1 0]) ; %#ok
+ check_perm (p, A) ;
+
+ [p, stats] = colamd2 (A, [1 tol 0]) ; %#ok
+ check_perm (p, A) ;
+
+ fprintf ('.') ;
+
+ end
+end
+fprintf (' OK\n') ;
+
+fprintf ('General matrices\n') ;
+for trial = 1:400
+
+ % matrix of random mtype
+ mtype = irand (3) ;
+ A = rand_matrix (2000, 2000, mtype, 0, 0) ;
+ p = colamd2 (A) ;
+ check_perm (p, A) ;
+ if (mtype == 3)
+ p = symamd2 (A) ;
+ check_perm (p, A) ;
+ end
+
+ fprintf ('.') ;
+end
+fprintf (' OK\n') ;
+
+fprintf ('Test error handling with invalid inputs\n') ;
+
+% Check different erroneous input.
+for trial = 1:30
+
+ A = rand_matrix (1000, 1000, 2, 0, 0) ;
+ [m n] = size (A) ;
+
+ for err = 1:13
+
+ p = Tcolamd (A, [n n 0 0 err]) ;
+ if (p ~= -1) %#ok
+ check_perm (p, A) ;
+ end
+
+ if (err == 1)
+ % check different (valid) input args to colamd2
+ p = Acolamd (A) ;
+
+ p2 = Acolamd (A, [10 10 0 0 0]) ;
+ if (any (p ~= p2))
+ error ('colamd2: mismatch 1!') ;
+ end
+ [p2 stats] = Acolamd (A) ; %#ok
+ if (any (p ~= p2))
+ error ('colamd2: mismatch 2!') ;
+ end
+ [p2 stats] = Acolamd (A, [10 10 0 0 0]) ;
+ if (any (p ~= p2))
+ error ('colamd2: mismatch 3!') ;
+ end
+ end
+
+ B = A'*A ;
+ p = Tsymamd (B, [n 0 err]) ;
+ if (p ~= -1) %#ok
+ check_perm (p, A) ;
+ end
+
+ if (err == 1)
+
+ % check different (valid) input args to symamd2
+ p = Asymamd (B) ;
+ check_perm (p, A) ;
+ p2 = Asymamd (B, [10 0 0]) ;
+ if (any (p ~= p2))
+ error ('symamd2: mismatch 1!') ;
+ end
+ [p2 stats] = Asymamd (B) ; %#ok
+ if (any (p ~= p2))
+ error ('symamd2: mismatch 2!') ;
+ end
+ [p2 stats] = Asymamd (B, [10 0 0]) ; %#ok
+ if (any (p ~= p2))
+ error ('symamd2: mismatch 3!') ;
+ end
+ end
+
+ fprintf ('.') ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty columns\n') ;
+
+for trial = 1:400
+
+ % some are square, some are rectangular
+ n = 0 ;
+ while (n < 5)
+ A = rand_matrix (1000, 1000, irand (2), 0, 0) ;
+ [m n] = size (A) ;
+ end
+
+ % Add 5 null columns at random locations.
+ null_col = randperm (n) ;
+ null_col = sort (null_col (1:5)) ;
+ A (:, null_col) = 0 ;
+
+ % Order the matrix and make sure that the null columns are ordered last.
+ [p, stats] = colamd2 (A, [1e6 1e6 0]) ;
+ check_perm (p, A) ;
+
+% if (stats (2) ~= 5)
+% stats (2)
+% error ('colamd2: wrong number of null columns') ;
+% end
+
+ % find all null columns in A
+ null_col = find (sum (spones (A), 1) == 0) ;
+ nnull = length (null_col) ; %#ok
+ if (any (null_col ~= p ((n-4):n)))
+ error ('colamd2: Null cols are not ordered last in natural order') ;
+ end
+
+ fprintf ('.') ;
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty rows and columns\n') ;
+
+for trial = 1:400
+
+ % symmetric matrices
+ n = 0 ;
+ while (n < 5)
+ A = rand_matrix (1000, 1000, 3, 0, 0) ;
+ [m n] = size (A) ;
+ end
+
+ % Add 5 null columns and rows at random locations.
+ null_col = randperm (n) ;
+ null_col = sort (null_col (1:5)) ;
+ A (:, null_col) = 0 ;
+ A (null_col, :) = 0 ;
+
+ % Order the matrix and make sure that the null rows/cols are ordered last.
+ [p,stats] = symamd2 (A, [10 0]) ;
+ check_perm (p, A) ;
+
+ % find actual number of null rows and columns
+ Alo = tril (A, -1) ;
+ nnull = length (find (sum (Alo') == 0 & sum (Alo) == 0)) ; %#ok
+
+ if (stats (2) ~= nnull || nnull < 5)
+ error ('symamd2: wrong number of null columns') ;
+ end
+ if (any (null_col ~= p ((n-4):n)))
+ error ('symamd2: Null cols are not ordered last in natural order') ;
+ end
+
+ fprintf ('.') ;
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty rows\n') ;
+
+% Test matrices with null rows inserted.
+
+for trial = 1:400
+
+ m = 0 ;
+ while (m < 5)
+ A = rand_matrix (1000, 1000, 2, 0, 0) ;
+ [m n] = size (A) ; %#ok
+ end
+
+ % Add 5 null rows at random locations.
+ null_row = randperm (m) ;
+ null_row = sort (null_row (1:5)) ;
+ A (null_row, :) = 0 ;
+
+ p = colamd2 (A, [10 10 0]) ;
+ check_perm (p, A) ;
+ if (stats (1) ~= 5)
+ error ('colamd2: wrong number of null rows') ;
+ end
+ fprintf ('.') ;
+end
+fprintf (' OK\n') ;
+
+
+fprintf ('\ncolamd and symamd2: all tests passed\n\n') ;
+
+%-------------------------------------------------------------------------------
+
+function [p,stats] = Acolamd (S, knobs)
+% Acolamd: compare colamd2 and Tcolamd results
+
+if (nargin < 3)
+ if (nargout == 1)
+ [p] = colamd2 (S) ;
+ [p1] = Tcolamd (S, [10 10 0 0 0]) ;
+ else
+ [p, stats] = colamd2 (S) ;
+ [p1, stats1] = Tcolamd (S, [10 10 0 0 0]) ; %#ok
+ end
+else
+ if (nargout == 1)
+ [p] = colamd2 (S, knobs (1:3)) ;
+ [p1] = Tcolamd (S, knobs) ;
+ else
+ [p, stats] = colamd2 (S, knobs (1:3)) ;
+ [p1, stats1] = Tcolamd (S, knobs) ; %#ok
+ end
+end
+
+check_perm (p, S) ;
+check_perm (p1, S) ;
+
+if (any (p1 ~= p))
+ error ('Acolamd mismatch!') ;
+end
+
+
+%-------------------------------------------------------------------------------
+
+function [p,stats] = Asymamd (S, knobs)
+% Asymamd: compare symamd2 and Tsymamd results
+
+if (nargin < 3)
+ if (nargout == 1)
+ [p] = symamd2 (S) ;
+ [p1] = Tsymamd (S, [10 0 0]) ;
+ else
+ [p, stats] = symamd2 (S) ;
+ [p1, stats1] = Tsymamd (S, [10 0 0]) ; %#ok
+ end
+else
+ if (nargout == 1)
+ [p] = symamd2 (S, knobs (1:2)) ;
+ [p1] = Tsymamd (S, knobs) ;
+ else
+ [p, stats] = symamd2 (S, knobs (1:2)) ;
+ [p1, stats1] = Tsymamd (S, knobs) ; %#ok
+ end
+end
+
+if (any (p1 ~= p))
+ error ('Asymamd mismatch!') ;
+end
+
+
+%-------------------------------------------------------------------------------
+
+function check_perm (p, A)
+% check_perm: check for a valid permutation vector
+
+if (isempty (A) && isempty (p)) %#ok
+ % empty permutation vectors of empty matrices are OK
+ return
+end
+
+if (isempty (p))
+ error ('bad permutation: cannot be empty') ;
+end
+
+[m n] = size (A) ;
+[pm pn] = size (p) ;
+if (pn == 1)
+ % force p to be a row vector
+ p = p' ;
+ [pm pn] = size (p) ;
+end
+
+if (n ~= pn)
+ error ('bad permutation: wrong size') ;
+end
+
+if (pm ~= 1) ;
+ % p must be a vector
+ error ('bad permutation: not a vector') ;
+else
+ if (any (sort (p) - (1:pn)))
+ error ('bad permutation') ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+
+function i = irand (n)
+% irand: return a random integer between 1 and n
+i = min (n, 1 + floor (rand * n)) ;
+
+%-------------------------------------------------------------------------------
+
+function A = rand_matrix (nmax, mmax, mtype, drows, dcols)
+% rand_matrix: return a random sparse matrix
+%
+% A = rand_matrix (nmax, mmax, mtype, drows, dcols)
+%
+% A binary matrix of random size, at most nmax-by-mmax, with drows dense rows
+% and dcols dense columns.
+%
+% mtype 1: square unsymmetric (mmax is ignored)
+% mtype 2: rectangular
+% mtype 3: symmetric (mmax is ignored)
+
+n = irand (nmax) ;
+if (mtype ~= 2)
+ % square
+ m = n ;
+else
+ m = irand (mmax) ;
+end
+
+A = sprand (m, n, 10 / max (m,n)) ;
+
+if (drows > 0)
+ % add dense rows
+ for k = 1:drows
+ i = irand (m) ;
+ nz = irand (n) ;
+ p = randperm (n) ;
+ p = p (1:nz) ;
+ A (i,p) = 1 ;
+ end
+end
+
+if (dcols > 0)
+ % add dense cols
+ for k = 1:dcols
+ j = irand (n) ;
+ nz = irand (m) ;
+ p = randperm (m) ;
+ p = p (1:nz) ;
+ A (p,j) = 1 ;
+ end
+end
+
+A = spones (A) ;
+
+% ensure that there are no empty columns
+d = find (full (sum (A)) == 0) ; %#ok
+A (m,d) = 1 ; %#ok
+
+% ensure that there are no empty rows
+d = find (full (sum (A,2)) == 0) ; %#ok
+A (d,n) = 1 ; %#ok
+
+if (mtype == 3)
+ % symmetric
+ A = A + A' + speye (n) ;
+end
+
+A = spones (A) ;
+
+%-------------------------------------------------------------------------------
+
+function [p,stats] = Tcolamd (S, knobs)
+% Tcolamd: run colamd2 in a testing mode
+
+if (nargout <= 1 && nargin == 1)
+ p = colamdtestmex (S) ;
+elseif (nargout <= 1 && nargin == 2)
+ p = colamdtestmex (S, knobs) ;
+elseif (nargout == 2 && nargin == 1)
+ [p, stats] = colamdtestmex (S) ;
+elseif (nargout == 2 && nargin == 2)
+ [p, stats] = colamdtestmex (S, knobs) ;
+else
+ error ('colamd2: incorrect number of input and/or output arguments') ;
+end
+
+if (p (1) ~= -1)
+ [ignore, q] = etree (S (:,p), 'col') ;
+ p = p (q) ;
+ check_perm (p, S) ;
+end
+
+%-------------------------------------------------------------------------------
+
+function [p, stats] = Tsymamd (S, knobs)
+% Tsymamd: run symamd2 in a testing mode
+
+if (nargout <= 1 && nargin == 1)
+ p = symamdtestmex (S) ;
+elseif (nargout <= 1 && nargin == 2)
+ p = symamdtestmex (S, knobs) ;
+elseif (nargout == 2 && nargin == 1)
+ [p, stats] = symamdtestmex (S) ;
+elseif (nargout == 2 && nargin == 2)
+ [p, stats] = symamdtestmex (S, knobs) ;
+else
+ error ('symamd2: incorrect number of input and/or output arguments') ;
+end
+
+if (p (1) ~= -1)
+ [ignore, q] = etree (S (p,p)) ;
+ p = p (q) ;
+ check_perm (p, S) ;
+end
diff --git a/src/C/SuiteSparse/COLAMD/colamdmex.c b/src/C/SuiteSparse/COLAMD/colamdmex.c
new file mode 100644
index 0000000..d5ae3fd
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamdmex.c
@@ -0,0 +1,219 @@
+/* ========================================================================== */
+/* === colamd mexFunction =================================================== */
+/* ========================================================================== */
+
+/* Usage:
+
+ P = colamd2 (A) ;
+ [ P, stats ] = colamd2 (A, knobs) ;
+
+ see colamd.m for a description.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2006, Timothy A. Davis, All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamdmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+
+/* ========================================================================== */
+/* === colamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ int *A ; /* colamd's copy of the matrix, and workspace */
+ int *p ; /* colamd's copy of the column pointers */
+ int Alen ; /* size of A */
+ int n_col ; /* number of columns of A */
+ int n_row ; /* number of rows of A */
+ int nnz ; /* number of entries in A */
+ int full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ int i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ int spumoni ; /* verbosity variable */
+ int stats [COLAMD_STATS] ; /* stats for colamd */
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "colamd: incorrect number of input and/or output arguments") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) knobs [COLAMD_DENSE_COL] = in_knobs [1] ;
+ if (i > 2) spumoni = (int) (in_knobs [2] != 0) ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\ncolamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows with > max(16,%g*sqrt(size(A,2)))"
+ " entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, only completely dense rows removed\n",
+ in_knobs [0]) ;
+ }
+ if (knobs [COLAMD_DENSE_COL] >= 0)
+ {
+ mexPrintf ("knobs(2): %g, cols with > max(16,%g*sqrt(min(size(A)))"
+ " entries removed\n", in_knobs [1], knobs [COLAMD_DENSE_COL]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(2): %g, only completely dense columns removed\n",
+ in_knobs [1]) ;
+ }
+ mexPrintf ("knobs(3): %g, statistics and knobs printed\n",
+ in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("colamd: input matrix must be 2-dimensional") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for colamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+
+ /* get column pointer vector so we can find nnz */
+ p = (int *) mxCalloc (n_col+1, sizeof (int)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (int)) ;
+ nnz = p [n_col] ;
+ Alen = (int) colamd_recommended (nnz, n_row, n_col) ;
+ if (Alen == 0)
+ {
+ mexErrMsgTxt ("colamd: problem too large") ;
+ }
+
+ /* === Copy input matrix into workspace ================================= */
+
+ A = (int *) mxCalloc (Alen, sizeof (int)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (int)) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Order the columns (destroys A) =================================== */
+
+ if (!colamd (n_row, n_col, Alen, A, p, knobs, stats))
+ {
+ colamd_report (stats) ;
+ mexErrMsgTxt ("colamd error!") ;
+ }
+ mxFree (A) ;
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* colamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = p [i] + 1 ;
+ }
+ mxFree (p) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni is set */
+ if (spumoni)
+ {
+ colamd_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
diff --git a/src/C/SuiteSparse/COLAMD/colamdtestmex.c b/src/C/SuiteSparse/COLAMD/colamdtestmex.c
new file mode 100644
index 0000000..fe3a4c4
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/colamdtestmex.c
@@ -0,0 +1,576 @@
+/* ========================================================================== */
+/* === colamdtest mexFunction =============================================== */
+/* ========================================================================== */
+
+/* COLAMD test function
+
+ This MATLAB mexFunction is for testing only. It is not meant for
+ production use. See colamdmex.c instead.
+
+ Usage:
+
+ [ P, stats ] = colamdtest (A, knobs) ;
+
+ See colamd.m for a description. knobs is required.
+
+ knobs (1) dense row control
+ knobs (2) dense column control
+ knobs (3) spumoni
+ knobs (4) for testing only. Controls the workspace used by
+ colamd.
+
+ knobs (5) for testing only. Controls how the input matrix is
+ jumbled prior to calling colamd, to test its error
+ handling capability.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2006, Timothy A. Davis, All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the
+ http://www.cise.ufl.edu/research/sparse/colamd/colamdtestmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+
+static void dump_matrix
+(
+ int A [ ],
+ int p [ ],
+ int n_row,
+ int n_col,
+ int Alen,
+ int limit
+) ;
+
+/* ========================================================================== */
+/* === colamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ int *A ; /* colamd's copy of the matrix, and workspace */
+ int *p ; /* colamd's copy of the column pointers */
+ int Alen ; /* size of A */
+ int n_col ; /* number of columns of A */
+ int n_row ; /* number of rows of A */
+ int nnz ; /* number of entries in A */
+ int full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ int i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ int spumoni ; /* verbosity variable */
+ int stats2 [COLAMD_STATS] ; /* stats for colamd */
+
+ int *cp, *cp_end, result, col, length ;
+ int *stats ;
+ stats = stats2 ;
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "colamd: incorrect number of input and/or output arguments") ;
+ }
+
+ if (nrhs != 2)
+ {
+ mexErrMsgTxt ("colamdtest: knobs are required") ;
+ }
+ /* for testing we require all 5 knobs */
+ if (mxGetNumberOfElements (prhs [1]) != 5)
+ {
+ mexErrMsgTxt ("colamd: must have all 5 knobs for testing") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) knobs [COLAMD_DENSE_COL] = in_knobs [1] ;
+ if (i > 2) spumoni = (int) in_knobs [2] ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\ncolamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows with > max(16,%g*sqrt(size(A,2)))"
+ " entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, only completely dense rows removed\n",
+ in_knobs [0]) ;
+ }
+ if (knobs [COLAMD_DENSE_COL] >= 0)
+ {
+ mexPrintf ("knobs(2): %g, cols with > max(16,%g*sqrt(min(size(A)))"
+ " entries removed\n", in_knobs [1], knobs [COLAMD_DENSE_COL]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(2): %g, only completely dense columns removed\n",
+ in_knobs [1]) ;
+ }
+ mexPrintf ("knobs(3): %g, statistics and knobs printed\n",
+ in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("colamd: input matrix must be 2-dimensional") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for colamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+
+ /* get column pointer vector so we can find nnz */
+ p = (int *) mxCalloc (n_col+1, sizeof (int)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (int)) ;
+ nnz = p [n_col] ;
+ Alen = (int) colamd_recommended (nnz, n_row, n_col) ;
+ if (Alen == 0)
+ {
+ mexErrMsgTxt ("colamd: problem too large") ;
+ }
+
+
+/* === Modify size of Alen if testing ======================================= */
+
+/*
+ knobs [3] amount of workspace given to colamd.
+ < 0 : TIGHT memory
+ > 0 : MIN + knob [3] - 1
+ == 0 : RECOMMENDED memory
+*/
+
+/* Here only for testing */
+/* size of the Col and Row structures */
+#define COLAMD_C(n_col) (((n_col) + 1) * 24 / sizeof (int))
+#define COLAMD_R(n_row) (((n_row) + 1) * 16 / sizeof (int))
+#ifdef MIN
+#undef MIN
+#endif
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define COLAMD_MIN_MEMORY(nnz,n_row,n_col) \
+ (2 * (nnz) + COLAMD_C (n_col) + COLAMD_R (n_row))
+
+ /* get knob [3], if negative */
+ if (in_knobs [3] < 0)
+ {
+ Alen = COLAMD_MIN_MEMORY (nnz, n_row, n_col) + n_col ;
+ }
+ else if (in_knobs [3] > 0)
+ {
+ Alen = COLAMD_MIN_MEMORY (nnz, n_row, n_col) + in_knobs [3] - 1 ;
+ }
+
+ /* otherwise, we use the recommended amount set above */
+
+ /* === Copy input matrix into workspace ================================= */
+
+ A = (int *) mxCalloc (Alen, sizeof (int)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (int)) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+
+/* === Jumble matrix ======================================================== */
+
+/*
+ knobs [4] FOR TESTING ONLY: Specifies how to jumble matrix
+ 0 : No jumbling
+ 1 : Make n_row less than zero
+ 2 : Make first pointer non-zero
+ 3 : Make column pointers not non-decreasing
+ 4 : Make a column pointer greater or equal to Alen
+ 5 : Make row indices not strictly increasing
+ 6 : Make a row index greater or equal to n_row
+ 7 : Set A = NULL
+ 8 : Set p = NULL
+ 9 : Repeat row index
+ 10: make row indices not sorted
+ 11: jumble columns massively (note this changes
+ the pattern of the matrix A.)
+ 12: Set stats = NULL
+ 13: Make n_col less than zero
+*/
+
+ /* jumble appropriately */
+ switch ((int) in_knobs [4])
+ {
+
+ case 0 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: no errors expected\n") ;
+ }
+ result = 1 ; /* no errors */
+ break ;
+
+ case 1 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: nrow out of range\n") ;
+ }
+ result = 0 ; /* nrow out of range */
+ n_row = -1 ;
+ break ;
+
+ case 2 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: p [0] nonzero\n") ;
+ }
+ result = 0 ; /* p [0] must be zero */
+ p [0] = 1 ;
+ break ;
+
+ case 3 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: negative length last column\n") ;
+ }
+ result = (n_col == 0) ; /* p must be monotonically inc. */
+ p [n_col] = p [0] ;
+ break ;
+
+ case 4 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: Alen too small\n") ;
+ }
+ result = 0 ; /* out of memory */
+ p [n_col] = Alen ;
+ break ;
+
+ case 5 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: row index out of range (-1)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = -1 ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 6 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: row index out of range (n_row)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Changing A[nnz-1] from %d to %d\n",
+ A [nnz-1], n_row) ;
+ }
+ result = 0 ;
+ A [nnz-1] = n_row ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 7 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: A not present\n") ;
+ }
+ result = 0 ; /* A not present */
+ A = (int *) NULL ;
+ break ;
+
+ case 8 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: p not present\n") ;
+ }
+ result = 0 ; /* p not present */
+ p = (int *) NULL ;
+ break ;
+
+ case 9 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: duplicate row index\n") ;
+ }
+ result = 1 ; /* duplicate row index */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ A [p [col]] = A [p [col] + 1] ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Made duplicate row %d in col %d\n",
+ A [p [col] + 1], col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, col+2) ;
+ }
+ break ;
+
+ case 10 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: unsorted column\n") ;
+ }
+ result = 1 ; /* jumbled columns */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ i = A[p [col]] ;
+ A [p [col]] = A[p [col] + 1] ;
+ A [p [col] + 1] = i ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Unsorted column %d \n", col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, col+2) ;
+ }
+ break ;
+
+ case 11 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: massive jumbling\n") ;
+ }
+ result = 1 ; /* massive jumbling, but no errors */
+ srand (1) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ cp = &A [p [i]] ;
+ cp_end = &A [p [i+1]] ;
+ while (cp < cp_end)
+ {
+ *cp++ = rand() % n_row ;
+ }
+ }
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, n_col) ;
+ }
+ break ;
+
+ case 12 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: stats not present\n") ;
+ }
+ result = 0 ; /* stats not present */
+ stats = (int *) NULL ;
+ break ;
+
+ case 13 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: ncol out of range\n") ;
+ }
+ result = 0 ; /* ncol out of range */
+ n_col = -1 ;
+ break ;
+
+ }
+
+
+ /* === Order the columns (destroys A) =================================== */
+
+ if (!colamd (n_row, n_col, Alen, A, p, knobs, stats))
+ {
+
+ /* return p = -1 if colamd failed */
+ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ out_perm [0] = -1 ;
+ mxFree (p) ;
+ mxFree (A) ;
+
+ if (spumoni > 0 || result)
+ {
+ colamd_report (stats) ;
+ }
+
+ if (result)
+ {
+ mexErrMsgTxt ("colamd should have returned TRUE\n") ;
+ }
+
+ return ;
+ /* mexErrMsgTxt ("colamd error!") ; */
+ }
+
+ if (!result)
+ {
+ colamd_report (stats) ;
+ mexErrMsgTxt ("colamd should have returned FALSE\n") ;
+ }
+ mxFree (A) ;
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* colamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = p [i] + 1 ;
+ }
+ mxFree (p) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni > 0 */
+ if (spumoni > 0)
+ {
+ colamd_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
+
+
+static void dump_matrix
+(
+ int A [ ],
+ int p [ ],
+ int n_row,
+ int n_col,
+ int Alen,
+ int limit
+)
+{
+ int col, k, row ;
+
+ mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ;
+
+ for (col = 0 ; col < MIN (n_col, limit) ; col++)
+ {
+ mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n",
+ col, p [col], p [col+1], p [col+1] - p [col]) ;
+ for (k = p [col] ; k < p [col+1] ; k++)
+ {
+ row = A [k] ;
+ mexPrintf (" %d", row) ;
+ }
+ mexPrintf ("\n") ;
+ }
+}
diff --git a/src/C/SuiteSparse/COLAMD/lesser.txt b/src/C/SuiteSparse/COLAMD/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/lesser.txt
@@ -0,0 +1,504 @@
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+
+
diff --git a/src/C/SuiteSparse/COLAMD/luflops.m b/src/C/SuiteSparse/COLAMD/luflops.m
new file mode 100644
index 0000000..0f6f46d
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/luflops.m
@@ -0,0 +1,35 @@
+function fl = luflops (L, U)
+%LUFLOPS compute the flop count for sparse LU factorization
+%
+% Example:
+% fl = luflops (L,U)
+%
+% Given a sparse LU factorization (L and U), return the flop count required
+% by a conventional LU factorization algorithm to compute it. L and U can
+% be either sparse or full matrices. L must be lower triangular and U must
+% be upper triangular. Do not attempt to use this on the permuted L from
+% [L,U] = lu (A). Instead, use [L,U,P] = lu (A) or [L,U,P,Q] = lu (A).
+%
+% Note that there is a subtle undercount in this estimate. Suppose A is
+% completely dense, but during LU factorization exact cancellation occurs,
+% causing some of the entries in L and U to become identically zero. The
+% flop count returned by this routine is an undercount. There is a simple
+% way to fix this (L = spones (L) + spones (tril (A))), but the fix is partial.
+% It can also occur that some entry in L is a "symbolic" fill-in (zero in
+% A, but a fill-in entry and thus must be computed), but numerically
+% zero. The only way to get a reliable LU factorization would be to do a
+% purely symbolic factorization of A. This cannot be done with
+% symbfact (A, 'col').
+%
+% See NA Digest, Vol 00, #50, Tuesday, Dec. 5, 2000
+%
+% See also symbfact
+%
+
+% Copyright 2006, Timothy A. Davis, University of Florida
+
+
+Lnz = full (sum (spones (L))) - 1 ; % off diagonal nz in cols of L
+Unz = full (sum (spones (U')))' - 1 ; % off diagonal nz in rows of U
+fl = 2*Lnz*Unz + sum (Lnz) ;
+
diff --git a/src/C/SuiteSparse/COLAMD/symamd2.m b/src/C/SuiteSparse/COLAMD/symamd2.m
new file mode 100644
index 0000000..2ec705c
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/symamd2.m
@@ -0,0 +1,103 @@
+function [p, stats] = symamd2 (S, knobs)
+%SYMAMD Symmetric approximate minimum degree permutation.
+% P = SYMAMD2(S) for a symmetric positive definite matrix S, returns the
+% permutation vector p such that S(p,p) tends to have a sparser Cholesky
+% factor than S. Sometimes SYMAMD works well for symmetric indefinite
+% matrices too. The matrix S is assumed to be symmetric; only the
+% strictly lower triangular part is referenced. S must be square.
+% Note that p = amd(S) is much faster and generates comparable orderings.
+% The ordering is followed by an elimination tree post-ordering.
+%
+% Note that this function is source code for the built-in MATLAB symamd
+% function. It has been renamed here to symamd2 to avoid a filename clash.
+% symamd and symamd2 are identical.
+%
+% See also SYMAMD, AMD, COLAMD, COLAMD2.
+%
+% Example:
+% P = symamd2 (S)
+% [P, stats] = symamd2 (S, knobs)
+%
+% knobs is an optional one- to two-element input vector. If S is n-by-n,
+% then rows and columns with more than max(16,knobs(1)*sqrt(n)) entries are
+% removed prior to ordering, and ordered last in the output permutation P.
+% No rows/columns are removed if knobs(1)<0. If knobs(2) is nonzero, stats
+% and knobs are printed. The default is knobs = [10 0]. Note that knobs
+% differs from earlier versions of symamd.
+%
+% Type the command "type symamd2" for a description of the optional stats
+% output and for the copyright information.
+%
+% Authors: S. Larimore and T. Davis, University of Florida. Developed in
+% collaboration with J. Gilbert and E. Ng.
+%
+% Acknowledgements: This work was supported by the National Science
+% Foundation, under grants DMS-9504974 and DMS-9803599.
+
+% Notice:
+%
+% Copyright 1998-2006, Timothy A. Davis, All Rights Reserved.
+%
+% See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+% file) for the License.
+%
+% Availability:
+%
+% colamd, symamd, amd, ccolamd, and csymamd are available at
+% http://www.cise.ufl.edu/research/sparse
+
+%-------------------------------------------------------------------------------
+% perform the symamd ordering:
+%-------------------------------------------------------------------------------
+
+if (nargout <= 1 && nargin == 1)
+ p = symamd2mex (S) ;
+elseif (nargout <= 1 && nargin == 2)
+ p = symamd2mex (S, knobs) ;
+elseif (nargout == 2 && nargin == 1)
+ [p, stats] = symamd2mex (S) ;
+elseif (nargout == 2 && nargin == 2)
+ [p, stats] = symamd2mex (S, knobs) ;
+else
+ error('MATLAB:symamd:WrongInputOrOutputNumber',...
+ 'symamd: incorrect number of input and/or output arguments.') ;
+end
+
+%-------------------------------------------------------------------------------
+% symmetric elimination tree post-ordering:
+%-------------------------------------------------------------------------------
+
+[ignore, q] = etree (S (p,p)) ;
+p = p (q) ;
+
+
+% stats is an optional 20-element output vector that provides data about the
+% ordering and the validity of the input matrix S. Ordering statistics are
+% in stats (1:3). stats (1) = stats (2) is the number of dense or empty
+% rows and columns ignored by SYMAMD and stats (3) is the number of
+% garbage collections performed on the internal data structure used by
+% SYMAMD (roughly of size 8.4*nnz(tril(S,-1)) + 9*n integers).
+%
+% MATLAB built-in functions are intended to generate valid sparse matrices,
+% with no duplicate entries, with ascending row indices of the nonzeros
+% in each column, with a non-negative number of entries in each column (!)
+% and so on. If a matrix is invalid, then SYMAMD may or may not be able
+% to continue. If there are duplicate entries (a row index appears two or
+% more times in the same column) or if the row indices in a column are out
+% of order, then SYMAMD can correct these errors by ignoring the duplicate
+% entries and sorting each column of its internal copy of the matrix S (the
+% input matrix S is not repaired, however). If a matrix is invalid in other
+% ways then SYMAMD cannot continue, an error message is printed, and no
+% output arguments (P or stats) are returned. SYMAMD is thus a simple way
+% to check a sparse matrix to see if it's valid.
+%
+% stats (4:7) provide information if SYMAMD was able to continue. The
+% matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the
+% rightmost column index that is unsorted or contains duplicate entries,
+% or zero if no such column exists. stats (6) is the last seen duplicate
+% or out-of-order row index in the column index given by stats (5), or zero
+% if no such row index exists. stats (7) is the number of duplicate or
+% out-of-order row indices.
+%
+% stats (8:20) is always zero in the current version of SYMAMD (reserved
+% for future use).
diff --git a/src/C/SuiteSparse/COLAMD/symamdmex.c b/src/C/SuiteSparse/COLAMD/symamdmex.c
new file mode 100644
index 0000000..74ed936
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/symamdmex.c
@@ -0,0 +1,200 @@
+/* ========================================================================== */
+/* === symamd mexFunction =================================================== */
+/* ========================================================================== */
+
+/* SYMAMD mexFunction
+
+ Usage:
+
+ P = symamd2 (A) ;
+ [ P, stats ] = symamd2 (A, knobs) ;
+
+ See symamd.m for a description.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2006, Timothy A. Davis. All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/symamdmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === symamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ int *perm ; /* column ordering of M and ordering of A */
+ int *A ; /* row indices of input matrix A */
+ int *p ; /* column pointers of input matrix A */
+ int n_col ; /* number of columns of A */
+ int n_row ; /* number of rows of A */
+ int full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ int i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ int spumoni ; /* verbosity variable */
+ int stats [COLAMD_STATS] ; /* stats for symamd */
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "symamd: incorrect number of input and/or output arguments.") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) spumoni = (int) (in_knobs [1] != 0) ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\nsymamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows/cols with > "
+ "max(16,%g*sqrt(size(A,2))) entries removed\n",
+ in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ;
+ }
+ mexPrintf ("knobs(2): %g, statistics and knobs printed\n",
+ in_knobs [1]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("symamd: input matrix must be 2-dimensional.") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for symamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+ if (n_col != n_row)
+ {
+ mexErrMsgTxt ("symamd: matrix must be square.") ;
+ }
+
+ A = mxGetIr (Ainput) ;
+ p = mxGetJc (Ainput) ;
+ perm = (int *) mxCalloc (n_col+1, sizeof (int)) ;
+
+ /* === Order the rows and columns of A (does not destroy A) ============= */
+
+ if (!symamd (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree))
+ {
+ symamd_report (stats) ;
+ mexErrMsgTxt ("symamd error!") ;
+ }
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* symamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = perm [i] + 1 ;
+ }
+ mxFree (perm) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni is set */
+ if (spumoni)
+ {
+ symamd_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
diff --git a/src/C/SuiteSparse/COLAMD/symamdtestmex.c b/src/C/SuiteSparse/COLAMD/symamdtestmex.c
new file mode 100644
index 0000000..75c946e
--- /dev/null
+++ b/src/C/SuiteSparse/COLAMD/symamdtestmex.c
@@ -0,0 +1,542 @@
+/* ========================================================================== */
+/* === symamdtest mexFunction =============================================== */
+/* ========================================================================== */
+
+/* SYMAMD test function
+
+ This MATLAB mexFunction is for testing only. It is not meant for
+ production use. See symamdmex.c instead.
+
+ Usage:
+
+ [ P, stats ] = symamdtest (A, knobs) ;
+
+ See symamd.m for a description. knobs is required.
+
+ knobs (1) dense row control
+ knobs (2) spumoni
+ knobs (3) for testing only. Controls how the input matrix is
+ jumbled prior to calling symamd, to test its error
+ handling capability.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2006, Timothy A. Davis. All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the
+ http://www.cise.ufl.edu/research/sparse/colamd/symamdtestmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+
+static void dump_matrix
+(
+ int A [ ],
+ int p [ ],
+ int n_row,
+ int n_col,
+ int Alen,
+ int limit
+) ;
+
+/* ========================================================================== */
+/* === symamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ int *perm ; /* column ordering of M and ordering of A */
+ int *A ; /* row indices of input matrix A */
+ int *p ; /* column pointers of input matrix A */
+ int n_col ; /* number of columns of A */
+ int n_row ; /* number of rows of A */
+ int full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ int i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ int spumoni ; /* verbosity variable */
+ int stats2 [COLAMD_STATS] ; /* stats for symamd */
+
+ int *cp, *cp_end, result, nnz, col, length ;
+ int *stats ;
+ stats = stats2 ;
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "symamd: incorrect number of input and/or output arguments.") ;
+ }
+
+ if (nrhs != 2)
+ {
+ mexErrMsgTxt ("symamdtest: knobs are required") ;
+ }
+ /* for testing we require all 3 knobs */
+ if (mxGetNumberOfElements (prhs [1]) != 3)
+ {
+ mexErrMsgTxt ("symamdtest: must have all 3 knobs for testing") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) spumoni = (int) in_knobs [1] ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\nsymamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows/cols with > "
+ "max(16,%g*sqrt(size(A,2))) entries removed\n",
+ in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ;
+ }
+ mexPrintf ("knobs(2): %g, statistics and knobs printed\n",
+ in_knobs [1]) ;
+ mexPrintf ("Testing %d\n", in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("symamd: input matrix must be 2-dimensional.") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for symamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+ if (n_col != n_row)
+ {
+ mexErrMsgTxt ("symamd: matrix must be square.") ;
+ }
+
+ /* p = mxGetJc (Ainput) ; */
+ p = (int *) mxCalloc (n_col+1, sizeof (int)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (int)) ;
+
+ nnz = p [n_col] ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: nnz %d\n", nnz) ;
+ }
+
+ /* A = mxGetIr (Ainput) ; */
+ A = (int *) mxCalloc (nnz+1, sizeof (int)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (int)) ;
+
+ perm = (int *) mxCalloc (n_col+1, sizeof (int)) ;
+
+/* === Jumble matrix ======================================================== */
+
+
+/*
+ knobs [2] FOR TESTING ONLY: Specifies how to jumble matrix
+ 0 : No jumbling
+ 1 : (no errors)
+ 2 : Make first pointer non-zero
+ 3 : Make column pointers not non-decreasing
+ 4 : (no errors)
+ 5 : Make row indices not strictly increasing
+ 6 : Make a row index greater or equal to n_row
+ 7 : Set A = NULL
+ 8 : Set p = NULL
+ 9 : Repeat row index
+ 10: make row indices not sorted
+ 11: jumble columns massively (note this changes
+ the pattern of the matrix A.)
+ 12: Set stats = NULL
+ 13: Make n_col less than zero
+*/
+
+ /* jumble appropriately */
+ switch ((int) in_knobs [2])
+ {
+
+ case 0 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: no errors expected\n") ;
+ }
+ result = 1 ; /* no errors */
+ break ;
+
+ case 1 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: no errors expected (1)\n") ;
+ }
+ result = 1 ;
+ break ;
+
+ case 2 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: p [0] nonzero\n") ;
+ }
+ result = 0 ; /* p [0] must be zero */
+ p [0] = 1 ;
+ break ;
+
+ case 3 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: negative length last column\n") ;
+ }
+ result = (n_col == 0) ; /* p must be monotonically inc. */
+ p [n_col] = p [0] ;
+ break ;
+
+ case 4 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: no errors expected (4)\n") ;
+ }
+ result = 1 ;
+ break ;
+
+ case 5 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: row index out of range (-1)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = -1 ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 6 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: row index out of range (ncol)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = n_col ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 7 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: A not present\n") ;
+ }
+ result = 0 ; /* A not present */
+ A = (int *) NULL ;
+ break ;
+
+ case 8 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: p not present\n") ;
+ }
+ result = 0 ; /* p not present */
+ p = (int *) NULL ;
+ break ;
+
+ case 9 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: duplicate row index\n") ;
+ }
+ result = 1 ; /* duplicate row index */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ A [p [col+1]-2] = A [p [col+1] - 1] ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Made duplicate row %d in col %d\n",
+ A [p [col+1] - 1], col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, col+2) ;
+ }
+ break ;
+
+ case 10 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: unsorted column\n") ;
+ }
+ result = 1 ; /* jumbled columns */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ i = A[p [col]] ;
+ A [p [col]] = A[p [col] + 1] ;
+ A [p [col] + 1] = i ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Unsorted column %d \n", col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, col+2) ;
+ }
+ break ;
+
+ case 11 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: massive jumbling\n") ;
+ }
+ result = 1 ; /* massive jumbling, but no errors */
+ srand (1) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ cp = &A [p [i]] ;
+ cp_end = &A [p [i+1]] ;
+ while (cp < cp_end)
+ {
+ *cp++ = rand() % n_row ;
+ }
+ }
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, n_col) ;
+ }
+ break ;
+
+ case 12 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: stats not present\n") ;
+ }
+ result = 0 ; /* stats not present */
+ stats = (int *) NULL ;
+ break ;
+
+ case 13 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: ncol out of range\n") ;
+ }
+ result = 0 ; /* ncol out of range */
+ n_col = -1 ;
+ break ;
+
+ }
+
+ /* === Order the rows and columns of A (does not destroy A) ============= */
+
+ if (!symamd (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree))
+ {
+
+ /* return p = -1 if colamd failed */
+ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ out_perm [0] = -1 ;
+ mxFree (p) ;
+ mxFree (A) ;
+
+ if (spumoni > 0 || result)
+ {
+ symamd_report (stats) ;
+ }
+
+ if (result)
+ {
+ mexErrMsgTxt ("symamd should have returned TRUE\n") ;
+ }
+
+ return ;
+ /* mexErrMsgTxt ("symamd error!") ; */
+ }
+
+ if (!result)
+ {
+ symamd_report (stats) ;
+ mexErrMsgTxt ("symamd should have returned FALSE\n") ;
+ }
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* symamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = perm [i] + 1 ;
+ }
+ mxFree (perm) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni > 0 */
+ if (spumoni > 0)
+ {
+ symamd_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
+
+
+#ifdef MIN
+#undef MIN
+#endif
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+
+static void dump_matrix
+(
+ int A [ ],
+ int p [ ],
+ int n_row,
+ int n_col,
+ int Alen,
+ int limit
+)
+{
+ int col, k, row ;
+
+ mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ;
+
+ if (!A)
+ {
+ mexPrintf ("A not present\n") ;
+ return ;
+ }
+
+ if (!p)
+ {
+ mexPrintf ("p not present\n") ;
+ return ;
+ }
+
+ for (col = 0 ; col < MIN (n_col, limit) ; col++)
+ {
+ mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n",
+ col, p [col], p [col+1], p [col+1] - p [col]) ;
+ for (k = p [col] ; k < p [col+1] ; k++)
+ {
+ row = A [k] ;
+ mexPrintf (" %d", row) ;
+ }
+ mexPrintf ("\n") ;
+ }
+}
diff --git a/src/C/SuiteSparse/Contents.m b/src/C/SuiteSparse/Contents.m
new file mode 100644
index 0000000..b1c7cce
--- /dev/null
+++ b/src/C/SuiteSparse/Contents.m
@@ -0,0 +1,134 @@
+% Welcome to SuiteSparse : a Suite of Sparse matrix packages, containing a
+% collection of sparse matrix packages authored or co-authored by Tim Davis.
+% Only the primary MATLAB functions are listed below.
+%
+% Example:
+% SuiteSparse_install - compiles and installs all of SuiteSparse, and runs
+% several demos and tests.
+%
+%-------------------
+% Ordering methods:
+%-------------------
+%
+% amd - approximate minimum degree ordering.
+% colamd - column approximate minimum degree ordering.
+% symamd - symmetrix approximate min degree ordering based on colamd.
+% camd - constrained amd.
+% ccolamd - constrained colamd.
+% csymamd - constrained symamd.
+%
+%---------------------------------------------------------------
+% CHOLMOD: a sparse supernodal Cholesky update/downdate package:
+%---------------------------------------------------------------
+%
+% cholmod - computes x=A\b when A is symmetric and positive definite.
+% chol2 - same as MATLAB chol(sparse(A)), just faster.
+% lchol - computes an LL' factorization.
+% ldlchol - computes an LDL' factorization.
+% ldlupdate - updates an LDL' factorization.
+% resymbol - recomputes symbolic LL or LDL' factorization.
+% ldlsolve - solves Ax=b using an LDL' factorization.
+% ldlsplit - splits LD into L and D.
+% metis - interface to METIS node-nested-dissection.
+% nesdis - interface to CHOLMOD's nested-dissection (based on METIS).
+% septree - prune a separator tree.
+% bisect - interface to METIS' node bisector.
+% analyze - order and analyze using CHOLMOD.
+% etree2 - same as MATLAB "etree", just faster and more reliable.
+% sparse2 - same as MATLAB "sparse", just faster.
+% symbfact2 - same as MATLAB "symbfact", just faster and more reliable.
+% sdmult - same as MATLAB S*F or S'*F (S sparse, F full), just faster.
+% ldl_normest - compute error in LDL' factorization.
+% lu_normest - compute error in LU factorization.
+% mread - read a sparse matrix in Matrix Market format
+% mwrite - write a sparse matrix in Matrix Market format
+% spsym - determine the symmetry of a sparse matrix
+%
+%------------------------------------------
+% CSPARSE: a Concise Sparse matrix package:
+%------------------------------------------
+%
+% Matrices used in CSparse must in general be either sparse and real,
+% or dense vectors. Ordering methods can accept any sparse matrix.
+%
+% cs_add - sparse matrix addition.
+% cs_amd - approximate minimum degree ordering.
+% cs_chol - sparse Cholesky factorization.
+% cs_cholsol - solve A*x=b using a sparse Cholesky factorization.
+% cs_counts - column counts for sparse Cholesky factor L.
+% cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation.
+% cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix.
+% cs_droptol - remove small entries from a sparse matrix.
+% cs_esep - find an edge separator of a symmetric matrix A
+% cs_etree - elimination tree of A or A'*A.
+% cs_gaxpy - sparse matrix times vector.
+% cs_lsolve - solve a sparse lower triangular system L*x=b.
+% cs_ltsolve - solve a sparse upper triangular system L'*x=b.
+% cs_lu - sparse LU factorization, with fill-reducing ordering.
+% cs_lusol - solve Ax=b using LU factorization.
+% cs_make - compiles CSparse for use in MATLAB.
+% cs_multiply - sparse matrix multiply.
+% cs_nd - generalized nested dissection ordering.
+% cs_nsep - find a node separator of a symmetric matrix A.
+% cs_permute - permute a sparse matrix.
+% cs_print - print the contents of a sparse matrix.
+% cs_qr - sparse QR factorization.
+% cs_qleft - apply Householder vectors on the left.
+% cs_qright - apply Householder vectors on the right.
+% cs_qrsol - solve a sparse least-squares problem.
+% cs_randperm - random permutation.
+% cs_sep - convert an edge separator into a node separator.
+% cs_scc - strongly-connected components of a square sparse matrix.
+% cs_scc2 - cs_scc, or connected components of a bipartite graph.
+% cs_sparse - convert a triplet form into a sparse matrix.
+% cs_sqr - symbolic sparse QR factorization.
+% cs_symperm - symmetric permutation of a symmetric matrix.
+% cs_transpose - transpose a real sparse matrix.
+% cs_updown - rank-1 update/downdate of a sparse Cholesky factorization.
+% cs_usolve - solve a sparse upper triangular system U*x=b.
+% cs_utsolve - solve a sparse lower triangular system U'*x=b.
+% cspy - plot a sparse matrix in color.
+% ccspy - plot the connected components of a matrix.
+%
+%-------------------------------
+% LDL: Sparse LDL factorization:
+%-------------------------------
+%
+% ldlsparse - LDL' factorization of a real, sparse, symmetric matrix.
+% ldlrow - an m-file description of the algorithm used by LDL.
+%
+%-----------------------------------------------
+% UMFPACK: the Unsymmetric MultiFrontal Package:
+%-----------------------------------------------
+%
+% umfpack - computes x=A\b, x=A/b, or lu (A) for a sparse matrix A
+% umfpack_details - details on all the options for using umfpack in MATLAB
+% umfpack_report - prints optional control settings and statistics
+% umfpack_btf - factorize A using a block triangular form
+% umfpack_solve - x = A\b or x = b/A
+% lu_normest - estimates norm (L*U-A,1) without forming L*U-A
+% (duplicate of CHOLMOD/lu_normest, for completeness)
+% luflop - given L and U, computes # of flops required
+%
+%------------------------------------------------------
+% RBio: read/write matrices in Rutherford/Boeing format
+%------------------------------------------------------
+%
+% RBread - read a sparse matrix from a Rutherford/Boeing file
+% RBreade - read a symmetric finite-element matrix from a R/B file
+% RBtype - determine the Rutherford/Boeing type of a sparse matrix
+% RBwrite - write a sparse matrix to a Rutherford/Boeing file
+%
+%-------------------------------------------------------------------------------
+%
+% For help on compiling SuiteSparse or the demos, testing functions, etc.,
+% please see the help for each individual package.
+%
+% NOTE: None of the packages above have yet been ported to 64-bit MATLAB.
+% Do not attempt to use these in 64-bit MATLAB.
+%
+% Copyright 2006, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+help SuiteSparse
diff --git a/src/C/SuiteSparse/Makefile b/src/C/SuiteSparse/Makefile
new file mode 100644
index 0000000..dafd591
--- /dev/null
+++ b/src/C/SuiteSparse/Makefile
@@ -0,0 +1,93 @@
+#-------------------------------------------------------------------------------
+# Makefile for all UF sparse matrix packages
+#-------------------------------------------------------------------------------
+
+include UFconfig/UFconfig.mk
+
+# Compile the default rules for each package
+default:
+ ( cd UFconfig/xerbla ; $(MAKE) )
+ ( cd metis-4.0 ; $(MAKE) )
+ ( cd AMD ; $(MAKE) )
+ ( cd CAMD ; $(MAKE) )
+ ( cd COLAMD ; $(MAKE) )
+ ( cd BTF ; $(MAKE) )
+ ( cd KLU ; $(MAKE) )
+ ( cd LDL ; $(MAKE) )
+ ( cd CCOLAMD ; $(MAKE) )
+ ( cd UMFPACK ; $(MAKE) )
+ ( cd CHOLMOD ; $(MAKE) )
+ ( cd CSparse ; $(MAKE) )
+ ( cd CXSparse ; $(MAKE) )
+# ( cd LPDASA ; $(MAKE) )
+# ( cd PARAKLETE ; $(MAKE) )
+
+library: default
+
+# Compile the MATLAB mexFunctions
+mex:
+ ( cd AMD ; $(MAKE) mex )
+ ( cd CAMD ; $(MAKE) mex )
+ ( cd COLAMD ; $(MAKE) mex )
+ ( cd BTF ; $(MAKE) mex )
+ ( cd KLU ; $(MAKE) mex )
+ ( cd LDL ; $(MAKE) mex )
+ ( cd CCOLAMD ; $(MAKE) mex )
+ ( cd CHOLMOD ; $(MAKE) mex )
+ ( cd UMFPACK ; $(MAKE) mex )
+ ( cd CSparse ; $(MAKE) mex )
+ ( cd RBio ; $(MAKE) )
+ ( cd UFcollection ; $(MAKE) )
+
+# Remove all files not in the original distribution
+purge:
+ ( cd UFconfig/xerbla ; $(MAKE) purge )
+ ( cd metis-4.0 ; $(MAKE) realclean )
+ ( cd AMD ; $(MAKE) purge )
+ ( cd CAMD ; $(MAKE) purge )
+ ( cd COLAMD ; $(MAKE) purge )
+ ( cd BTF ; $(MAKE) purge )
+ ( cd KLU ; $(MAKE) purge )
+ ( cd LDL ; $(MAKE) purge )
+ ( cd CCOLAMD ; $(MAKE) purge )
+ ( cd UMFPACK ; $(MAKE) purge )
+ ( cd CHOLMOD ; $(MAKE) purge )
+ ( cd CSparse ; $(MAKE) purge )
+ ( cd CXSparse ; $(MAKE) purge )
+ ( cd RBio ; $(MAKE) purge )
+ ( cd UFcollection ; $(MAKE) purge )
+# ( cd LPDASA ; $(MAKE) purge )
+# ( cd PARAKLETE ; $(MAKE) purge )
+
+# Remove all files not in the original distribution, but keep the libraries
+clean:
+ ( cd UFconfig/xerbla ; $(MAKE) clean )
+ ( cd metis-4.0 ; $(MAKE) clean )
+ ( cd AMD ; $(MAKE) clean )
+ ( cd CAMD ; $(MAKE) clean )
+ ( cd COLAMD ; $(MAKE) clean )
+ ( cd BTF ; $(MAKE) clean )
+ ( cd KLU ; $(MAKE) clean )
+ ( cd LDL ; $(MAKE) clean )
+ ( cd CCOLAMD ; $(MAKE) clean )
+ ( cd UMFPACK ; $(MAKE) clean )
+ ( cd CHOLMOD ; $(MAKE) clean )
+ ( cd CSparse ; $(MAKE) clean )
+ ( cd CXSparse ; $(MAKE) clean )
+ ( cd RBio ; $(MAKE) clean )
+ ( cd UFcollection ; $(MAKE) clean )
+# ( cd LPDASA ; $(MAKE) clean )
+# ( cd PARAKLETE ; $(MAKE) clean )
+
+distclean: purge
+
+# Create CXSparse from CSparse. Note that the CXSparse directory should
+# initially not exist.
+cx:
+ ( cd CSparse ; $(MAKE) purge )
+ ( cd CXSparse_newfiles ; tar cfv - * | gzip -9 > ../CXSparse_newfiles.tar.gz )
+ ./CSparse_to_CXSparse CSparse CXSparse CXSparse_newfiles.tar.gz
+ ( cd CXSparse/Demo ; $(MAKE) )
+ ( cd CXSparse/Demo ; $(MAKE) > cs_demo.out )
+ ( cd CXSparse ; $(MAKE) purge )
+
diff --git a/src/C/SuiteSparse/README.txt b/src/C/SuiteSparse/README.txt
new file mode 100644
index 0000000..a87e1ea
--- /dev/null
+++ b/src/C/SuiteSparse/README.txt
@@ -0,0 +1,120 @@
+SuiteSparse: A Suite of Sparse matrix packages
+
+------------------
+SuiteSparse/README
+------------------
+
+================================================================================
+QUICK START FOR MATLAB USERS: unzip the SuiteSparse.zip file, then in the
+MATLAB Command Window, cd to the SuiteSparse directory and type
+SuiteSparse_install. All packages will be compiled, and several demos will be
+run.
+================================================================================
+
+All codes, below, are stable except KLU and BTF. KLU and BTF are "beta", but
+robust enough for production use. They merely are still in development, and
+are missing a few minor features to make them "1.0". Thus the "beta". They
+are bug-free as far as I know, and are in use in commercial circuit simulation
+packages.
+
+Nov, 2006. SuiteSparse version 2.3. Note that SuiteSparse is now given
+its own version number, rather than merely a date of release.
+
+UF suite of sparse matrix algorithms:
+
+ AMD approximate minimum degree ordering
+
+ CAMD constrained column approximate minimum degree ordering
+
+ COLAMD column approximate minimum degree ordering
+
+ CCOLAMD constrained column approximate minimum degree ordering
+
+ BTF permutation to block triangular form (beta)
+
+ KLU sparse LU factorization, primarily for circuit simulation.
+ Requires AMD, COLAMD, and BTF (beta). Optionally
+ uses CHOLMOD, CCOLAMD, and METIS.
+
+ UMFPACK sparse LU factorization. Requires AMD and the BLAS.
+
+ CHOLMOD sparse Cholesky factorization. Requires AMD, COLAMD, CCOLAMD,
+ METIS, the BLAS, and LAPACK.
+
+ UFconfig configuration file for all the above packages. The
+ UFconfig/UFconfig.mk is included in the Makefile's of all
+ packages. CSparse and CXSparse do not use UFconfig.
+
+ CSparse a concise sparse matrix package, developed for my upcoming
+ book, "Direct Methods for Sparse Linear Systems", to be
+ published by SIAM.
+
+ CXSparse CSparse Extended. Includes support for complex matrices
+ and both int or long integers.
+
+ RBio read/write sparse matrices in Rutherford/Boeing format
+
+ UFcollection toolbox for managing the UF Sparse Matrix Collection
+
+ LPDASA LP dual active set algorithm (to appear)
+
+
+See http://www.netlib.org/blas for the Fortran reference BLAS (slow, but they
+work). See http://www.tacc.utexas.edu/~kgoto/ or
+http://www.cs.utexas.edu/users/flame/goto/ for an optimized BLAS.
+See http://www.netlib.org/lapack for LAPACK. The UFconfig/UFconfig.mk
+file assumes the Goto BLAS; change -lgoto to -l(your BLAS library here),
+if you have another BLAS (-lblas, for example).
+
+CHOLMOD requires METIS 4.0.1 (http://www-users.cs.umn.edu/~karypis/metis)
+by default. Place a copy of the metis-4.0 directory in the same directory
+(SuiteSparse) containing this README file. cd to metis-4.0 and edit the
+Makefile.in file. I recommend making these changes to metis-4.0/Makefile.in:
+
+CC = gcc
+OPTFLAGS = -O3
+COPTIONS = -fexceptions -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE
+
+then type "make". You can now compile CHOLMOD. First,
+edit the UFconfig/UFconfig.mk file (see that file for instructions), if
+necessary. Next, type "make" in this directory to compile all packages in
+this distribution. CHOLMOD can be compiled without METIS (use -DNPARTITION).
+
+Refer to each package for license, copyright, and author information. All
+codes are authored or co-authored by Timothy A. Davis, CISE Dept., Univ. of
+Florida. email: my last name @ cise dot ufl dot edu.
+
+To compile each package, cd to the top-level directory (AMD, COLAMD, etc)
+and type "make". Type "make clean" in the same directory to remove all but
+the compiled libraries. Type "make distclean" to remove all files not in
+the original distribution. Alternatively, just type "make" in this directory.
+
+If you intend on compiling the MATLAB mexFunction interfaces, UFconfig.mk
+should use
+
+ CFLAGS = -O3 -fexceptions
+
+(for Linux), to ensure that exceptions are properly caught. See your
+default MATLAB mexopts.sh file for how to do this for other systems
+(type the command "mex -v"). Alternatively, you can use the various M-files
+in each package to compile them from within the MATLAB Command Window, or
+just type "SuiteSparse_install" in the MATLAB Command Window when MATLAB's
+working directory is this one. That is the only way to compile these packages
+for Windows, unless you have Cygwin or wish to write your own MS Visual Studio
+scripts.
+
+--------------------------------------------------------------------------------
+
+To turn on debugging (for development only, not needed by the typical user):
+
+SuiteSparse/UFconfig/UFconfig.mk
+ change CFLAGS = -O to CFLAGS = -g
+
+To turn on debugging, add the line "#undef NDEBUG" in the following files.
+To turn off debugging, remove that line.
+
+ SuiteSparse/CHOLMOD/Include/cholmod_internal.h
+ SuiteSparse/AMD/Source/amd_internal.h
+ SuiteSparse/CAMD/Source/camd_internal.h
+ SuiteSparse/CCOLAMD/ccolmod.c
+ SuiteSparse/COLAMD/colamd.c
diff --git a/src/C/SuiteSparse/README_cvxopt b/src/C/SuiteSparse/README_cvxopt
new file mode 100644
index 0000000..83bc799
--- /dev/null
+++ b/src/C/SuiteSparse/README_cvxopt
@@ -0,0 +1,28 @@
+This is the January 30, 2007 (version 2.4.0) distribution of the
+SuiteSparse package, with the following files and directories removed.
+
+AMD/Demo
+AMD/MATLAB
+BTF
+CAMD
+CCOLAMD
+CHOLMOD/Demo
+CHOLMOD/MATLAB
+CHOLMOD/MatrixOps
+CHOLMOD/Modify
+CHOLMOD/Partition
+CHOLMOD/Tcov
+CHOLMOD/Valgrind
+CSparse
+Csparse_to_CXsparse
+CXSparse
+CXSparse_newfiles
+CXSparse_newfiles.tar.gz
+KLU
+LDL
+RBio
+SuiteSparse_install.m
+UFcollection
+UMFPACK/Demo
+UMFPACK/MATLAB
+UMFPACK/Tcov
diff --git a/src/C/SuiteSparse/UFconfig/README.txt b/src/C/SuiteSparse/UFconfig/README.txt
new file mode 100644
index 0000000..b505181
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/README.txt
@@ -0,0 +1,25 @@
+This file contains configuration settings for
+all many of the software packages that I develop or
+co-author:
+
+ Package Version Description
+ ------- ------- -----------
+ AMD 1.2 or later approximate minimum degree ordering
+ CAMD any
+ COLAMD 2.4 or later column approximate minimum degree ordering
+ CCOLAMD any constrained approximate minimum degree ordering
+ UMFPACK 4.5 or later sparse LU factorization, with the BLAS
+ CXSparse any
+ CHOLMOD any sparse Cholesky factorization, update/downdate
+ KLU 1.0 or later sparse LU factorization, BLAS-free
+ BTF 1.0 or later permutation to block triangular form
+ LDL any concise sparse LDL'
+ LPDASA any LP Dual Active Set Algorithm
+
+In addition, the xerbla/ directory contains Fortan and C versions
+of the BLAS/LAPACK xerbla routine, which is called when an invalid
+input is passed to the BLAS or LAPACK. The xerbla provided here
+does not print any message, so the entire Fortran I/O library does
+not need to be linked into a C application. Most versions of the
+BLAS contain xerbla, but those from K. Goto do not. Use this if
+you need too.
diff --git a/src/C/SuiteSparse/UFconfig/UFconfig.h b/src/C/SuiteSparse/UFconfig/UFconfig.h
new file mode 100644
index 0000000..051a40f
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/UFconfig.h
@@ -0,0 +1,115 @@
+/* ========================================================================== */
+/* === UFconfig.h =========================================================== */
+/* ========================================================================== */
+
+/* Configuration file for SuiteSparse: a Suite of Sparse matrix packages
+ * (AMD, COLAMD, CCOLAMD, CAMD, CHOLMOD, UMFPACK, CXSparse, and others).
+ *
+ * UFconfig.h provides the definition of the long integer. On most systems,
+ * a C program can be compiled in LP64 mode, in which long's and pointers are
+ * both 64-bits, and int's are 32-bits. Windows 64, however, uses the LLP64
+ * model, in which int's and long's are 32-bits, and long long's and pointers
+ * are 64-bits.
+ *
+ * SuiteSparse packages that include long integer versions are
+ * intended for the LP64 mode. However, as a workaround for Windows 64
+ * (and perhaps other systems), the long integer can be redefined.
+ *
+ * If _WIN64 is defined, then the __int64 type is used instead of long.
+ *
+ * The long integer can also be defined at compile time. For example, this
+ * could be added to UFconfig.mk:
+ *
+ * CFLAGS = -O -D'UF_long=long long' -D'UF_long_max=9223372036854775801' \
+ * -D'UF_long_id="%lld"'
+ *
+ * This file defines UF_long as either long (on all but _WIN64) or
+ * __int64 on Windows 64. The intent is that a UF_long is always a 64-bit
+ * integer in a 64-bit code. ptrdiff_t might be a better choice than long;
+ * it is always the same size as a pointer.
+ *
+ * This file also defines the SUITESPARSE_VERSION and related definitions.
+ *
+ * Copyright (c) 2006, University of Florida. No licensing restrictions
+ * apply to this file or to the UFconfig directory. Author: Timothy A. Davis.
+ */
+
+#ifndef _UFCONFIG_H
+#define _UFCONFIG_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <limits.h>
+
+/* ========================================================================== */
+/* === UF_long ============================================================== */
+/* ========================================================================== */
+
+#ifndef UF_long
+
+#ifdef _WIN64
+
+#define UF_long __int64
+#define UF_long_max _I64_MAX
+#define UF_long_id "%I64d"
+
+#else
+
+#define UF_long long
+#define UF_long_max LONG_MAX
+#define UF_long_id "%ld"
+
+#endif
+#endif
+
+/* ========================================================================== */
+/* === SuiteSparse version ================================================== */
+/* ========================================================================== */
+
+/* SuiteSparse is not a package itself, but a collection of packages, some of
+ * which must be used together (UMFPACK requires AMD, CHOLMOD requires AMD,
+ * COLAMD, CAMD, and CCOLAMD, etc). A version number is provided here for the
+ * collection itself. The versions of packages within each version of
+ * SuiteSparse are meant to work together. Combining one packge from one
+ * version of SuiteSparse, with another package from another version of
+ * SuiteSparse, may or may not work.
+ *
+ * SuiteSparse Version 2.4 contains the following packages:
+ *
+ * AMD version 2.0.4
+ * CAMD version 2.1.3
+ * COLAMD version 2.6.0
+ * CCOLAMD version 2.5.2
+ * CHOLMOD version 1.4.0
+ * CSparse version 2.0.7
+ * CXSparse version 2.0.7
+ * KLU version 0.11
+ * BTF version 0.11
+ * LDL version 1.3.4
+ * UFconfig version number is the same as SuiteSparse
+ * UMFPACK version 5.0.3
+ * RBio version 1.0.0
+ * UFcollection version 1.0.1
+ *
+ * Other package dependencies:
+ * BLAS required by CHOLMOD and UMFPACK
+ * LAPACK required by CHOLMOD
+ * METIS 4.0.1 required by CHOLMOD (optional)
+ */
+
+#define SUITESPARSE_DATE "Dec 13, 2006"
+#define SUITESPARSE_VER_CODE(main,sub) ((main) * 1000 + (sub))
+#define SUITESPARSE_MAIN_VERSION 2
+#define SUITESPARSE_SUB_VERSION 4
+#define SUITESPARSE_SUBSUB_VERSION 0
+#define SUITESPARSE_VERSION \
+ SUITESPARSE_VER_CODE(SUITESPARSE_MAIN_VERSION,SUITESPARSE_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+
+#endif
diff --git a/src/C/SuiteSparse/UFconfig/UFconfig.mk b/src/C/SuiteSparse/UFconfig/UFconfig.mk
new file mode 100644
index 0000000..61dcbee
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/UFconfig.mk
@@ -0,0 +1,298 @@
+#===============================================================================
+# UFconfig.mk: common configuration file for the SuiteSparse
+#===============================================================================
+
+# This file contains all configuration settings for all packages authored or
+# co-authored by Tim Davis at the University of Florida:
+#
+# Package Version Description
+# ------- ------- -----------
+# AMD 1.2 or later approximate minimum degree ordering
+# COLAMD 2.4 or later column approximate minimum degree ordering
+# CCOLAMD 1.0 or later constrained column approximate minimum degree ordering
+# CAMD any constrained approximate minimum degree ordering
+# UMFPACK 4.5 or later sparse LU factorization, with the BLAS
+# CHOLMOD any sparse Cholesky factorization, update/downdate
+# KLU 0.8 or later sparse LU factorization, BLAS-free
+# BTF 0.8 or later permutation to block triangular form
+# LDL 1.2 or later concise sparse LDL'
+# LPDASA any linear program solve (dual active set algorithm)
+#
+# The UFconfig directory and the above packages should all appear in a single
+# directory, in order for the Makefile's within each package to find this file.
+#
+# To enable an option of the form "# OPTION = ...", edit this file and
+# delete the "#" in the first column of the option you wish to use.
+
+#------------------------------------------------------------------------------
+# Generic configuration
+#------------------------------------------------------------------------------
+
+# C compiler and compiler flags: These will normally not give you optimal
+# performance. You should select the optimization parameters that are best
+# for your system. On Linux, use "CFLAGS = -O3 -fexceptions" for example.
+CC = cc
+CFLAGS = -O
+
+# ranlib, and ar, for generating libraries
+RANLIB = ranlib
+AR = ar cr
+
+# delete and rename a file
+RM = rm -f
+MV = mv -f
+
+# Fortran compiler (not normally required)
+F77 = f77
+F77FLAGS = -O
+F77LIB =
+
+# C and Fortran libraries
+LIB = -lm
+
+# For compiling MATLAB mexFunctions
+MEX = mex -O
+
+# Which version of MAKE you are using (default is "make")
+# MAKE = make
+# MAKE = gmake
+
+#------------------------------------------------------------------------------
+# BLAS and LAPACK configuration:
+#------------------------------------------------------------------------------
+
+# UMFPACK and CHOLMOD both require the BLAS. CHOLMOD also requires LAPACK.
+# See Kazushige Goto's BLAS at http://www.cs.utexas.edu/users/flame/goto/ or
+# http://www.tacc.utexas.edu/~kgoto/ for the best BLAS to use with CHOLMOD.
+# LAPACK is at http://www.netlib.org/lapack/ . You can use the standard
+# Fortran LAPACK along with Goto's BLAS to obtain very good performance.
+# CHOLMOD gets a peak numeric factorization rate of 3.6 Gflops on a 3.2 GHz
+# Pentium 4 (512K cache, 4GB main memory) with the Goto BLAS, and 6 Gflops
+# on a 2.5Ghz dual-core AMD Opteron.
+
+# These settings will probably not work, since there is no fixed convention for
+# naming the BLAS and LAPACK library (*.a or *.so) files. Assume the Goto
+# BLAS are available.
+BLAS = -lgoto -lgfortran -lgfortranbegin
+LAPACK = -llapack
+
+# The BLAS might not contain xerbla, an error-handling routine for LAPACK and
+# the BLAS. Also, the standard xerbla requires the Fortran I/O library, and
+# stops the application program if an error occurs. A C version of xerbla
+# distributed with this software (UFconfig/xerbla/libcerbla.a) includes a
+# Fortran-callable xerbla routine that prints nothing and does not stop the
+# application program. This is optional.
+# XERBLA = ../../UFconfig/xerbla/libcerbla.a
+
+# If you wish to use the XERBLA in LAPACK and/or the BLAS instead,
+# use this option:
+XERBLA =
+
+# If you wish to use the Fortran UFconfig/xerbla/xerbla.f instead, use this:
+# XERBLA = ../../UFconfig/xerbla/libxerbla.a
+
+#------------------------------------------------------------------------------
+# METIS, optionally used by CHOLMOD
+#------------------------------------------------------------------------------
+
+# If you do not have METIS, or do not wish to use it in CHOLMOD, you must
+# compile CHOLMOD with the -DNPARTITION flag. You must also use the
+# "METIS =" option, below.
+
+# The path is relative to where it is used, in CHOLMOD/Lib, CHOLMOD/MATLAB, etc.
+# You may wish to use an absolute path. METIS is optional. Compile
+# CHOLMOD with -DNPARTITION if you do not wish to use METIS.
+METIS_PATH = ../../metis-4.0
+METIS = ../../metis-4.0/libmetis.a
+
+# If you use CHOLMOD_CONFIG = -DNPARTITION then you must use the following
+# options:
+# METIS_PATH =
+# METIS =
+
+#------------------------------------------------------------------------------
+# UMFPACK configuration:
+#------------------------------------------------------------------------------
+
+# Configuration flags for UMFPACK. See UMFPACK/Source/umf_config.h for details.
+#
+# -DNBLAS do not use the BLAS. UMFPACK will be very slow.
+# -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by
+# LAPACK and the BLAS (defaults to 'int')
+# -DNSUNPERF do not use the Sun Perf. Library (default is use it on Solaris)
+# -DNPOSIX do not use POSIX routines sysconf and times.
+# -DGETRUSAGE use getrusage
+# -DNO_TIMER do not use any timing routines
+# -DNRECIPROCAL do not multiply by the reciprocal
+# -DNO_DIVIDE_BY_ZERO do not divide by zero
+
+UMFPACK_CONFIG =
+
+#------------------------------------------------------------------------------
+# CHOLMOD configuration
+#------------------------------------------------------------------------------
+
+# CHOLMOD Library Modules, which appear in libcholmod.a:
+# Core requires: none
+# Check requires: Core
+# Cholesky requires: Core, AMD, COLAMD. optional: Partition, Supernodal
+# MatrixOps requires: Core
+# Modify requires: Core
+# Partition requires: Core, CCOLAMD, METIS. optional: Cholesky
+# Supernodal requires: Core, BLAS, LAPACK
+#
+# CHOLMOD test/demo Modules (all are GNU GPL, do not appear in libcholmod.a):
+# Tcov requires: Core, Check, Cholesky, MatrixOps, Modify, Supernodal
+# optional: Partition
+# Valgrind same as Tcov
+# Demo requires: Core, Check, Cholesky, MatrixOps, Supernodal
+# optional: Partition
+#
+# Configuration flags:
+# -DNCHECK do not include the Check module. License GNU LGPL
+# -DNCHOLESKY do not include the Cholesky module. License GNU LGPL
+# -DNPARTITION do not include the Partition module. License GNU LGPL
+# also do not include METIS.
+# -DNGPL do not include any GNU GPL Modules in the CHOLMOD library:
+# -DNMATRIXOPS do not include the MatrixOps module. License GNU GPL
+# -DNMODIFY do not include the Modify module. License GNU GPL
+# -DNSUPERNODAL do not include the Supernodal module. License GNU GPL
+#
+# -DNPRINT do not print anything.
+# -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by
+# LAPACK and the BLAS (defaults to 'int')
+# -DNSUNPERF for Solaris only. If defined, do not use the Sun
+# Performance Library
+
+CHOLMOD_CONFIG =
+
+#------------------------------------------------------------------------------
+# Linux
+#------------------------------------------------------------------------------
+
+# Using default compilers:
+# CC = gcc
+# CFLAGS = -O3
+
+# alternatives:
+# CFLAGS = -g -fexceptions \
+ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi
+# CFLAGS = -O3 -fexceptions \
+ -Wall -W -Werror -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi
+CFLAGS = -O3 -fexceptions -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE
+# CFLAGS = -O3
+
+# consider:
+# -fforce-addr -fmove-all-movables -freduce-all-givs -ftsp-ordering
+# -frename-registers -ffast-math -funroll-loops
+
+# Using the Goto BLAS:
+# BLAS = -lgoto -lfrtbegin -lg2c $(XERBLA) -lpthread
+
+# Using Intel's icc and ifort compilers:
+# (does not work for mexFunctions unless you add a mexopts.sh file)
+# F77 = ifort
+# CC = icc
+# CFLAGS = -O3 -xN -vec_report=0
+# CFLAGS = -g
+# old (broken): CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0
+
+# 64bit:
+# F77FLAGS = -O -m64
+# CFLAGS = -O3 -fexceptions -m64
+# BLAS = -lgoto64 -lfrtbegin -lg2c -lpthread $(XERBLA)
+# LAPACK = -llapack64
+
+
+# SUSE Linux 10.1, AMD Opteron
+# F77 = gfortran
+# BLAS = -lgoto_opteron64 -lgfortran
+
+# SUSE Linux 10.1, Intel Pentium
+# F77 = gfortran
+# BLAS = -lgoto -lgfortran
+
+#------------------------------------------------------------------------------
+# Solaris
+#------------------------------------------------------------------------------
+
+# 32-bit
+# CFLAGS = -KPIC -dalign -xc99=%none -Xc -xlibmieee -xO5 -xlibmil
+
+# 64-bit
+# CFLAGS = -KPIC -dalign -xc99=%none -Xc -xlibmieee -xO5 -xlibmil -xarch=v9
+
+# BLAS = -xlic_lib=sunperf
+# LAPACK =
+
+#------------------------------------------------------------------------------
+# Compaq Alpha
+#------------------------------------------------------------------------------
+
+# 64-bit mode only
+# CFLAGS = -O2 -std1
+# BLAS = -ldxml
+# LAPACK =
+
+#------------------------------------------------------------------------------
+# Macintosh
+#------------------------------------------------------------------------------
+
+# CC = gcc
+# CFLAGS = -O3 -fno-common -no-cpp-precomp -fexceptions
+# LIB = -lstdc++
+# BLAS = -framework Accelerate
+# LAPACK = -framework Accelerate
+
+#------------------------------------------------------------------------------
+# IBM RS 6000
+#------------------------------------------------------------------------------
+
+# BLAS = -lessl
+# LAPACK =
+
+# 32-bit mode:
+# CFLAGS = -O4 -qipa -qmaxmem=16384 -qproto
+# F77FLAGS = -O4 -qipa -qmaxmem=16384
+
+# 64-bit mode:
+# CFLAGS = -O4 -qipa -qmaxmem=16384 -q64 -qproto
+# F77FLAGS = -O4 -qipa -qmaxmem=16384 -q64
+# AR = ar -X64
+
+#------------------------------------------------------------------------------
+# SGI IRIX
+#------------------------------------------------------------------------------
+
+# BLAS = -lscsl
+# LAPACK =
+
+# 32-bit mode
+# CFLAGS = -O
+
+# 64-bit mode (32 bit int's and 64-bit long's):
+# CFLAGS = -64
+# F77FLAGS = -64
+
+# SGI doesn't have ranlib
+# RANLIB = echo
+
+#------------------------------------------------------------------------------
+# AMD Opteron (64 bit)
+#------------------------------------------------------------------------------
+
+# BLAS = -lgoto_opteron64 -lg2c
+# LAPACK = -llapack_opteron64
+
+# SUSE Linux 10.1, AMD Opteron
+# F77 = gfortran
+# BLAS = -lgoto_opteron64 -lgfortran
+# LAPACK = -llapack_opteron64
+
+#------------------------------------------------------------------------------
+# remove object files and profile output
+#------------------------------------------------------------------------------
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.tcov *.gcov gmon.out *.bak *.d
diff --git a/src/C/SuiteSparse/UFconfig/xerbla/Makefile b/src/C/SuiteSparse/UFconfig/xerbla/Makefile
new file mode 100644
index 0000000..7eb2d58
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/xerbla/Makefile
@@ -0,0 +1,31 @@
+# Makefile for null-output xerbla
+
+default: ccode
+
+include ../UFconfig.mk
+
+ccode: libcerbla.a
+
+fortran: libxerbla.a
+
+all: libxerbla.a libcerbla.a
+
+# Fortran version:
+libxerbla.a: xerbla.f
+ $(F77) $(F77FLAGS) -c xerbla.f
+ $(AR) libxerbla.a xerbla.o
+ - $(RM) xerbla.o
+
+# C version:
+libcerbla.a: xerbla.c xerbla.h
+ $(CC) $(CFLAGS) -c xerbla.c
+ $(AR) libcerbla.a xerbla.o
+ - $(RM) xerbla.o
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.o *.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/src/C/SuiteSparse/UFconfig/xerbla/xerbla.c b/src/C/SuiteSparse/UFconfig/xerbla/xerbla.c
new file mode 100644
index 0000000..5107f03
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/xerbla/xerbla.c
@@ -0,0 +1,12 @@
+
+void xerbla_ (char *srname, int *info)
+{
+ /* do nothing */ ;
+}
+
+
+void xerbla (char *srname, int *info)
+{
+ /* do nothing */ ;
+}
+
diff --git a/src/C/SuiteSparse/UFconfig/xerbla/xerbla.f b/src/C/SuiteSparse/UFconfig/xerbla/xerbla.f
new file mode 100644
index 0000000..4272004
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/xerbla/xerbla.f
@@ -0,0 +1,46 @@
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* -- LAPACK auxiliary routine (version 3.0) --
+* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
+* Courant Institute, Argonne National Lab, and Rice University
+* September 30, 1994
+*
+* .. Scalar Arguments ..
+ CHARACTER*6 SRNAME
+ INTEGER INFO
+* ..
+*
+* Purpose
+* =======
+*
+* XERBLA is an error handler for the LAPACK routines.
+* It is called by an LAPACK routine if an input parameter has an
+* invalid value. A message is printed and execution stops.
+*
+* Installers may consider modifying the STOP statement in order to
+* call system-specific exception-handling facilities.
+*
+* Arguments
+* =========
+*
+* SRNAME (input) CHARACTER*6
+* The name of the routine which called XERBLA.
+*
+* INFO (input) INTEGER
+* The position of the invalid parameter in the parameter list
+* of the calling routine.
+*
+* =====================================================================
+*
+* .. Executable Statements ..
+*
+***** WRITE( *, FMT = 9999 )SRNAME, INFO
+*
+***** STOP
+*
+***** 9999 FORMAT( ' ** On entry to ', A6, ' parameter number ', I2, ' had ',
+***** $ 'an illegal value' )
+*
+* End of XERBLA
+*
+ END
diff --git a/src/C/SuiteSparse/UFconfig/xerbla/xerbla.h b/src/C/SuiteSparse/UFconfig/xerbla/xerbla.h
new file mode 100644
index 0000000..b332eb3
--- /dev/null
+++ b/src/C/SuiteSparse/UFconfig/xerbla/xerbla.h
@@ -0,0 +1,2 @@
+void xerbla_ (char *srname, int *info) ;
+void xerbla (char *srname, int *info) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/ChangeLog b/src/C/SuiteSparse/UMFPACK/Doc/ChangeLog
new file mode 100644
index 0000000..4ecbfd7
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/ChangeLog
@@ -0,0 +1,452 @@
+Dec 12, 2006: version 5.0.3
+
+ * minor MATLAB cleanup. Renamed umfpack mexFunction to umfpack2, to avoid
+ filename clash with the built-in version of umfpack.
+
+Dec 2, 2006, version 5.0.2
+
+ * minor change to umfpack_report_info: does not print timings less
+ than 0.001 seconds.
+
+ * bug fix for complex case when using a non-gcc compiler (simplified the
+ scaling of the pivot column). Does not affect the use of UMFPACK in
+ MATLAB.
+
+Aug 31, 2006, version 5.0.1
+
+ * Minor correction to comments in umfpack_get_numeric.h.
+
+May 5, 2006, version 5.0
+
+ * Tcov subdirectory added. This has existed since the first C version of
+ UMFPACK, but is only now included in the released version. It provides
+ a near 100% test coverage for UMFPACK. The code isn't pretty, but it
+ works.
+
+ * now uses CHOLMOD's method for interfacing to the BLAS, including the
+ BLAS_INT definition. This way, the UF_long version of UMFPACK can
+ call the int BLAS.
+
+ * revised to use AMD v2.0
+
+Apr 7, 2006
+
+ * Minor correction to UMFPACK/Source/Makefile, for those who
+ do not have GNU make. No change to version number, because
+ no code was modified.
+
+Oct 10, 2005, version 4.6
+
+ * umf_solve.c modified for the complex case. A, X, and b can be
+ split complex or unsplit. Prior version required the form of
+ A, X, and B to be identical (all split or all unsplit).
+ (Thanks to David Bateman).
+
+ * added Cygwin to architecture detection.
+
+ * added UMFPACK_SUBSUB_VERSION
+
+Aug. 30, 2005: v4.5 released
+
+ * License changed to GNU LGPL.
+
+ * The Make/ directory removed; configurations are now in ../UFconfig.
+
+ * requires AMD v1.2 or later
+
+ * added UMFPACK_MAIN_VERSION and UMFPACK_SUB_VERSION, defined as 4 and 5,
+ respectively, for version 4.5. These macros will be updated for all
+ future versions. See Include/umfpack.h for details.
+
+ * function pointers used for malloc, free, calloc, realloc, printf,
+ hypot, and complex divide. Defined in AMD/Source/amd_global.c,
+ AMD/Source/amd_internal.h, UMFPACK/Source/umfpack_global.c,
+ and UMFPACK/Include/umfpack_global.h.
+ Compile-time dependence on The MathWorks "util.h", ut* routines
+ and ut* macros removed.
+
+Jan. 28, 2005: v4.4 released
+
+ * bug fix: when Qinit is provided to umfpack_*_qsymbolic,
+ only the symmetric and unsymmetric strategies are now permitted.
+ The auto and 2-by-2 strategies are not allowed. In v4.3 and
+ earlier, providing Qinit and requesting the symmetric strategy
+ did not always work (you got the unsymmetric strategy instead).
+ This does not affect umfpack_*_symbolic, which computes its own
+ ordering and can use all 4 strategies (auto, symmetric, unsymmetric,
+ and 2-by-2).
+
+ * umfpack_get_determinant added. (Thanks to David Bateman).
+
+ * packed complex case added for all routines (previously only used in
+ umfpack_report_vector). This allows arrays of ANSI C/C++ complex
+ type to be passed directly to UMFPACK.
+
+ * added umf_multicomple.c to assist in the compilation of UMFPACK
+ in Microsoft Visual Studio, which does not have the required
+ flexibility of the Unix "make" command.
+
+ * local variable declarations reordered to encourage double-word
+ alignment of double's and Entry's, for better performance.
+
+ * note that with the exception of the behavior when a user-provided
+ ordering is passed to umfpack_*_qsymbolic, versions 4.1 through 4.4
+ have comparable performance (ordering quality, memory usage,
+ and run time). v4.1 is much better than v4.0 in performance.
+
+Jan. 11, 2005: v4.3.1 released
+
+ * bug fix in umf_solve. This bug is only the 4th one found in the C
+ versions of UMFPACK to date (Version 3.0 to 4.3.1, from March 2001 to
+ Jan. 2005, excluding workarounds for quirky compilers). No bugs have
+ been reported in the last Fortran version of UMFPACK (MA38, or UMFPACK
+ V2.2.1) since its release in Jan. 1998.
+
+ In Version 4.3, a bug in umf_solve caused iterative refinement
+ to be disabled when solving A'x=b or A.'x=b after factorizing A.
+ Modified the umfpack mexFunction to factorize A and then solve A'x=b
+ when performing the operation x=b/A (as "umfpack(b,'/',A). Note that
+ this has no effect on the use of UMFPACK in MATLAB itself, since MATLAB
+ does not use the umfpack mexFunction for x=b/A. When computing x=b/A,
+ MATLAB factorizes A' and computes x=(A'\b')' instead. The following
+ source code files changed:
+
+ UMFPACK/MATLAB/umfpackmex.c (see above)
+ UMFPACK/Source/umf_solve.c (see source code: 2 lines changed)
+ UMFPACK/Include/umfpack.h (version and date changed)
+ UMFPACK/MATLAB/umfpack_test.m (new file)
+
+Jan. 16, 2004: v4.3 released.
+
+ * user interface of v4.3 is upwardly-compatible with v4.2 and v4.1.
+ No bugs found in v4.1 (except for one workaround for an old compiler).
+ These changes add features only.
+
+ * Note that v4.0 has a bug in umf_scale_column.c. The bug was patched
+ in that version on Jan. 12, 2004. The bug does not appear in v4.1
+ and later. The bug is thus present in MATLAB 6.5, but it occurs
+ very rarely, fortunately. It can occur when dividing a nonzero entry
+ in the pivot column by the pivot value results in an underflow.
+
+ * <float.h> added to umfpackmex.c, for DBL_EPSILON. Some non-standard
+ compilers (Microsoft Visual C++) require this.
+
+ * #pragma added to umf_analyze.c, as a workaround around a bug in an
+ old Intel compiler.
+
+ * mexFunction interface to MATLAB modified. Call to mexCallMATLAB removed,
+ which can be slow. In V4.1 it was used only to get MATLAB's
+ spparms ('spumoni') value.
+
+ * The AMD mexFunction was also modified in the same way (v1.1), with
+ the call to mexCallMATLAB removed. Note that UMFPACK v4.1 through
+ v4.3 can use either AMD v1.0 or AMD v1.1.
+
+ * -DNO_DIVIDE_BY_ZERO option added. If this non-default option is enabled
+ at compile time, and if the pivot value is zero, then no division
+ occurs (zeros on the diagonal of U are treated as if they were equal
+ to one). By default, the division by zero does occur.
+
+ * -DNO_TIMER option added. If this non-default option is enabled at
+ compile time, then no timers (times ( ), clock ( ), getrusage ( ))
+ are used.
+
+V4.2: A special release for COMSOL, Inc., only (FEMLAB)
+
+ * drop tolerance added. A few new parameters in the Control array are used,
+ and a few new Info entries.
+
+May 6, 2003: V4.1 released.
+
+ * No bugs were found in the prior version, Version 4.0. New features
+ added only. Major changes throughout the code. User interface
+ nearly unchanged, however.
+
+ * Version 4.1 is upward-compatible with Version 4.0. The calling
+ sequence of some user-callable routines in Version 4.0 have changed
+ in this version. The routines umfpack_*_symbolic, umfpack_*_qsymbolic,
+ umfpack_*_get_symbolic, and umfpack_*_get_numeric have new arguments
+ added to them. The new arguments are optional. If you want to use
+ a calling sequence similar to v4.0, simply pass NULL pointers in
+ place of the new arguments. There are two new timing routines,
+ umfpack_tic and umfpack_toc. A new user-callable routine,
+ umfpack_*_scale, has been added.
+
+ * "auto", "unsymmetric", "symmetric", and "2-by-2" strategies added.
+ The symmetric strategy uses AMD on A+A' as the column preordering,
+ followed by a postorder of the assembly tree of A+A'. Column ordering
+ refinement is turned off, and diagonal entries are prefered as pivots.
+ V4.0 only had the unsymmetric strategy. The 2-by-2 strategy does row
+ permutations and attempts to find a zero-free diagonal while at the
+ same time maintaining structural symmetry, and then uses the
+ symmetric strategy on the permuted matrix.
+
+ * row-scaling added. The default is to divide each row by the sum of
+ the absolute values of each row. Other options are no scaling,
+ and to divide each row by the max abs value in each row.
+
+ * Matrices with upper bound memory usage greater than the maximum integer
+ (2GB for 32-bit int's) can now be factorized (assuming the actual
+ memory usage is still less than the maximum integer). With this change,
+ the UMFPACK_ERROR_problem_too_large error code is no longer returned.
+
+ * The current frontal matrix (Work->Fx) is no longer allocated as a
+ static size, via malloc. It can grow and shrink, and is allocated
+ from Numeric->Memory.
+
+ * The AMD (Version 1.0) package is now required. It is available
+ separately. To compile UMFPACK, it must appear as ../AMD if you are
+ in the main UMFPACK directory.
+
+ * The UMFPACK mexFunction now uses the internal utMalloc, utRealloc,
+ and utFree routines, by default (except on Windows).
+
+ * Three control parameters for modifying relaxed amalgamation removed.
+ These values are now fixed at compile-time.
+
+ * Many new statistics added to Info, and new control parameters added.
+
+ * The umfpack mexFunction now returns permutation matrices for P and Q,
+ not permutation vectors. It also returns the scale factors as a
+ diagonal matrix. The factorization is now L*U = P*(R\A)*Q.
+
+ * Option added for controlling the initial allocation of the workspace for
+ the current frontal matrix.
+
+ * pivot tolerance of zero treated differently. symmetric pivot tolerance
+ added.
+
+ * Makefile and GNUmakefile changed. umf_* routines with no double or
+ complex values are now compiled just twice (int and long versions)
+ rather than 4 times.
+
+ * New routines added to save and load the Numeric and Symbolic objects
+ to/from binary files.
+
+ * Simple Fortran interface added.
+
+Apr 11, 2002:
+
+ * Version 4.0 released.
+
+ * bug fix: the Microsoft compiler doesn't handle NaN's properly.
+ utIsNaN, and other ut* routines, added for MathWorks version
+ to handle this properly.
+
+Apr 1, 2002:
+
+ * bug fix: if a column was all NaN's, then UMFPACK would fail
+ to find a pivot row. umf_row_search.c and umf_internal.h
+ modified to fix this problem.
+
+Mar 9, 2002: V4.0beta released
+
+ * Map argument added to umfpack_*_triplet_to_col. New files
+ (umf_triplet.[ch]) added.
+ * minor changes made so that UMFPACK can be compiled with g++
+ * additional error checking added to umfpack_*_numeric, for
+ detecting more changes in pattern (Ap, Ai) since last
+ call to umfpack_*_symbolic
+
+Feb 21, 2002:
+
+ * User Guide explains the Makefile vs. GNUmakefile
+
+ * umf_config.h modified, so that the complex SCSL C-BLAS uses
+ (void *) arguments instead of (scsl_zomplex *). gcc generates
+ some spurious warnings (cc doesn't complain). Affects the SGI
+ IRIX only.
+
+ * ported to Compaq Alpha
+
+Feb 20, 2002: V4.0 (alpha) released.
+
+ * V4.0 not yet ported to the Compaq Alpha (V3.2 was ported).
+
+Feb 6 to Feb 19, 2002:
+
+ * Relaxed restrictions on sizes of arrays for umfpack_*_transpose and
+ umfpack_*_triplet_to_col. Size of "max(n,nz)" now just size nz.
+
+ * workspace for umfpack_*_wsolve increased in size.
+
+ * two user arrays for umfpack_*_get_symbolic increased in size,
+ by 1 (Chain_maxrows, Chain_maxcols).
+
+ * lu_normest.m added.
+
+Jan 18 to Feb 5, 2002:
+
+ * The matrix A can be complex, singular, and/or rectangular.
+ The solve step that uses the LU factors can only handle
+ matrices that are complex or real, singuluar or non-singular,
+ and *** square ***, however.
+
+ * Estimate of the condition number computed:
+ (min (abs (diag (U))) / (max (abs (diag (U)))))
+
+ * Forward/backsolves can solve with A.' as well as A'.
+
+ * char * arguments removed from user-callable routines to make it
+ easier for Fortran to call UMFPACK. No Fortran interface is (yet)
+ provided, however.
+
+ The solve codes for umfpack_*_*solve changed to #define'd
+ integers:
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Aat A.'x=b
+ UMFPACK_Pt_L P'Lx=b
+ UMFPACK_L Lx=b
+ UMFPACK_Lt_P L'Px=b
+ UMFPACK_Lat_P L.'Px=b
+ UMFPACK_Lt L'x=b
+ UMFPACK_U_Qt UQ'x=b
+ UMFPACK_U Ux=b
+ UMFPACK_Q_Ut QU'x=b
+ UMFPACK_Q_Uat QU.'x=b
+ UMFPACK_Ut U'x=b
+ UMFPACK_Uat U.'x=b
+
+ All arguments are now either int, long scalars (pass by value),
+ or int, long, double arrays (pass by reference), or void * pointers
+ (pass by value or reference). A void * pointer is of size 32 or 64
+ bits on most machines. There is no need for the caller (C or Fortran)
+ to dereference the void * pointers, so these can be treated as
+ integer*4 or integer*8 in Fortran. A Fortran interface would have to
+ have all arguments passed by reference.
+
+ * All user-callable routine names changed. The four sets are now:
+ umfpack_di_* real (double precision), int's as integers
+ umfpack_dl_* real (double precision), longs's as integers
+ umfpack_zi_* real (double precision), int's as integers
+ umfpack_zl_* real (double precision), longs's as integers
+
+ * Ptree (row preordering) and info on pivotal rows for each front
+ added to Symbolic object (extracted by umfpack_*_get_symbolic).
+ Ptree added as output argument to "umfpack (A, 'symbolic')"
+ mexFunction.
+
+ * umfpack_*_transpose can do A' or A.'
+
+ * umfpack_wsolve.c file removed (now generated from umfpack_solve.c).
+
+ * Can now extract just the diagonal of U with umfpack_*_get_numeric,
+ without having to extract the entire matrix U.
+
+ * UMFPACK_ERROR_singular_matrix (-2) removed.
+
+ * UMFPACK_WARNING_singular_matrix (1) added.
+
+ * Control [UMFPACK_PIVOT_OPTION] removed. No longer any symmetric
+ pivot option (conflicts with the handling of singular and
+ rectangular matrices).
+
+ * Iterative refinement can do Ax=b, A'x=b, or A.'x=b.
+
+ * Most floating-point operations done in macros, to support the complex
+ versions.
+
+ * Info [UMFPACK_N] is now Info [UMFPACK_NROW]
+
+ * Info [UMFPACK_NCOL], Info [UMFPACK_UDIAG_NZ], Info [UMFPACK_UDIAG_NZ]
+ added.
+
+ * umfpack_* routines with "n" as input now use two arguments,
+ n_row and n_col.
+
+ * umfpack mexFunction now explicitly transposes A for b/A. It computes
+ it using the array transpose as (A.'\b.').'
+
+January 1, 2002: UMFPACK Version 3.2 released. Submitted to ACM Trans.
+ on Mathematical Software.
+
+ * The umfpack mexFunction now returns the Info array when the matrix
+ is singular. Returned an empty array prior to this change.
+
+ * Renamed variable that conflicted with system library routines
+ (system and j1).
+
+ * Added a #ifdef MATHWORKS definition, so the built-in UMFPACK routine
+ (in a future release of MATLAB) can use the internal ut* memory
+ allocation routines, ut* assertion routine, and utPrintf.
+
+ * MAX and MIN are not defined if they are already defined.
+
+ * A bug fix in umf_kernel_init (a variable was not properly initialized).
+
+ * Removed unused variables.
+
+October 8, 2001: UMFPACK Version 3.1 released.
+
+August-October, 2001:
+
+ * added umfpack_btf M-file.
+
+ * modified the BLAS update in the frontal matrix. If there are only
+ a few pivots in remaining in the current front, then the BLAS3 update
+ is delayed to include pivots in the next front.
+
+ * Removed the special-case handling of dense columns from the numerical
+ factorization (kept it in the colamd preordering). This improves the
+ performance of UMFPACK on dense matrices by a factor of 5 or so, and
+ simplifies the code.
+
+ * Added a symmetric-preference pivoting option. The option slightly
+ (but uniformly) improves the ordering when factorizing matrices with
+ symmetric nonzero pattern. That class of matrix is better handled by
+ the symmetric-pattern multifrontal method (MA41 in the Harwell
+ Subroutine Library), however.
+
+ * Fixed the detection of integer overflow. The 32-bit version cannot
+ make use of more than 2GB of main memory (use the 64-bit version
+ in that case, instead). The 32-bit version did not correctly detect
+ when it was trying to factorize too large of a matrix.
+
+May 4, 2001:
+
+ * SGI port extended. It can now call the SCSL Scientific Library, with
+ 64-bit BLAS. Make.sgi and umf_config.h modified.
+
+April 30, 2001: UMFPACK Version 3.0 released. Changes since 3.0Beta release:
+
+ * long integer version added (umfpack_l_* user-callable routines).
+
+ * Peak memory usage in the numerical factorization reduced by a total of
+ 12n integers (8n temporary workspace used during numerical factorization,
+ and 4n for the permanent LU factors which was allocated
+ at the beginning of factorization).
+
+ * Ported to the IBM RS 6000 and Compaq Alpha, with help from Anshul Gupta
+ and Friedrich Grund, respectively.
+
+ * 64-bit version added. Uses dgemm_64, dgemv_64, and dger_64 in the Sun
+ Performance Library. 64-bit versions with the BLAS might not work on
+ any other platform, because they take int's as their integer input
+ arguments instead of long's. Unfortunately, the proposed ANSI
+ definition of the C-BLAS also uses int's as input integer arguments.
+ It ought to use long's, or include a version that uses long's, just
+ like the Sun Performance Library BLAS.
+
+ * Additional statistics returned in Info:
+ Info [UMFPACK_SIZE_OF_INT] sizeof (int)
+ Info [UMFPACK_SIZE_OF_LONG] sizeof (long)
+ Info [UMFPACK_SIZE_OF_POINTER] sizeof (void *)
+ Info [UMFPACK_SIZE_OF_ENTRY] (was Info [UMFPACK_WORD])
+ Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE] est. front matrix size
+ Info [UMFPACK_MAX_FRONT_SIZE] actual max frontal matrix size.
+ Contents of Info rearranged.
+
+ * UMFPACK_ERROR_bad_configurution error code replaced with
+ UMFPACK_ERROR_problem_too_large error code. The "bad configuration"
+ error occured when sizeof (int) < sizeof (size_t). Now, the int
+ version of UMFPACK can use 32-bit int's and 64-bit pointers, and the
+ long version can use 64-bit long's and 64-bit pointers. Both versions
+ check to see if the array sizes allocated are larger than what can be
+ accessed by an integer index variable (int or long, depending on the
+ version), and returns UMFPACK_ERROR_problem_too_large if they become
+ too large.
+
+March 15, 2001: UMFPACK Version 3.0Beta released.
+
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/License b/src/C/SuiteSparse/UMFPACK/Doc/License
new file mode 100644
index 0000000..3ee02fd
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/License
@@ -0,0 +1,38 @@
+UMFPACK Version 5.0, Copyright 1995-2006 by Timothy A. Davis.
+All Rights Reserved.
+UMFPACK is available under alternate licenses, contact T. Davis for details.
+
+UMFPACK License:
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/umfpack
+
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/Makefile b/src/C/SuiteSparse/UMFPACK/Doc/Makefile
new file mode 100644
index 0000000..41cf07e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/Makefile
@@ -0,0 +1,59 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for compiling on Unix systems (for GNU or original make)
+#-------------------------------------------------------------------------------
+
+# UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
+# All Rights Reserved. See ../Doc/License for License.
+
+default: dist
+
+include ../../UFconfig/UFconfig.mk
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+# Note that UserGuide.tex is created from UserGuide.stex, the files in
+# the ../Include directory, and the ../Demo/umfpack_simple.c file.
+purge: clean
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+ - $(RM) UserGuide.tex
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+# Create the User Guide and Quick Start Guide
+#-------------------------------------------------------------------------------
+
+UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \
+ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \
+ umfpack_get_determinant \
+ umfpack_get_symbolic umfpack_numeric umfpack_qsymbolic \
+ umfpack_report_control umfpack_report_info umfpack_report_matrix \
+ umfpack_report_numeric umfpack_report_perm umfpack_report_status \
+ umfpack_report_symbolic umfpack_report_triplet \
+ umfpack_report_vector umfpack_solve umfpack_symbolic \
+ umfpack_transpose umfpack_triplet_to_col umfpack_scale
+
+UMFPACKW = umfpack_wsolve
+
+USER = $(UMFPACKW) $(UMFPACK)
+
+SRC = $(addprefix ../Include/, $(addsuffix .h,$(USER))) ../Demo/umfpack_simple.c
+
+UserGuide.pdf: UserGuide.stex UserGuide.sed1 UserGuide.sed2 $(SRC) UserGuide.bib
+ sed -f UserGuide.sed1 < UserGuide.stex | sed -f UserGuide.sed2 \
+ | expand -8 > UserGuide.tex
+ pdflatex UserGuide
+ bibtex UserGuide
+ pdflatex UserGuide
+ pdflatex UserGuide
+
+QuickStart.pdf: QuickStart.tex
+ pdflatex QuickStart
+ pdflatex QuickStart
+
+dist: QuickStart.pdf UserGuide.pdf
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+ - $(RM) UserGuide.tex
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/QuickStart.pdf b/src/C/SuiteSparse/UMFPACK/Doc/QuickStart.pdf
new file mode 100644
index 0000000..986f282
Binary files /dev/null and b/src/C/SuiteSparse/UMFPACK/Doc/QuickStart.pdf differ
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/QuickStart.tex b/src/C/SuiteSparse/UMFPACK/Doc/QuickStart.tex
new file mode 100644
index 0000000..9958477
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/QuickStart.tex
@@ -0,0 +1,1020 @@
+%-------------------------------------------------------------------------------
+% The QuickStart.tex file.
+%-------------------------------------------------------------------------------
+
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+\begin{document}
+
+\author{Timothy A. Davis \\
+Dept. of Computer and Information Science and Engineering \\
+Univ. of Florida, Gainesville, FL}
+\title{UMFPACK Version 5.0 Quick Start Guide}
+\date{May 5, 2006}
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+ UMFPACK is a set of routines for solving unsymmetric sparse linear
+ systems, $\m{Ax}=\m{b}$, using the Unsymmetric-pattern MultiFrontal method
+ and direct sparse LU factorization. It is written in ANSI/ISO C, with a
+ MATLAB interface. UMFPACK relies on the Level-3
+ Basic Linear Algebra Subprograms (dense matrix multiply) for its
+ performance. This code works on Windows and many versions of Unix (Sun
+ Solaris, Red Hat Linux, IBM AIX, SGI IRIX, and Compaq Alpha).
+ This is a ``quick start'' guide for Unix users of the C interface.
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+UMFPACK Version 5.0, Copyright\copyright 1995-2006 by Timothy A. Davis.
+All Rights Reserved. Refer to the UMFPACK User Guide
+for the License. See \newline
+http://www.cise.ufl.edu/research/sparse/umfpack
+for the code and full documentation.
+
+%-------------------------------------------------------------------------------
+\section{Overview}
+%-------------------------------------------------------------------------------
+
+UMFPACK is a set of routines for solving systems of linear
+equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and unsymmetric.
+The sparse matrix $\m{A}$ can be square or rectangular, singular
+or non-singular, and real or complex (or any combination). Only square
+matrices $\m{A}$ can be used to solve $\m{Ax}=\m{b}$ or related systems.
+Rectangular matrices can only be factorized.
+
+UMFPACK is a built-in routine in MATLAB used by the forward and
+backslash operator, and the {\tt lu} routine.
+The following is a short
+introduction to Unix users of the C interface of UMFPACK.
+
+%-------------------------------------------------------------------------------
+
+The C-callable UMFPACK library consists of 32 user-callable routines and one
+include file. Twenty-eight of the routines come in four versions, with
+different sizes of integers and for real or complex floating-point numbers.
+This Quick Start Guide assumes you are working with real matrices
+(not complex) and with {\tt int}'s as integers (not {\tt long}'s).
+Refer to the User Guide for information about the complex and
+long integer versions. The include file {\tt umfpack.h}
+must be included in any C program that uses UMFPACK.
+
+For more details, see:
+{\em A column pre-ordering strategy for the unsymmetric-pattern multifrontal method},
+Davis, T. A.,
+ACM Trans. Math. Software, vol 30. no 2, 2004, pp. 165-195, and
+{\em Algorithm 832: {UMFPACK}, an unsymmetric-pattern multifrontal method},
+same issue, pp. 196-199.
+
+%-------------------------------------------------------------------------------
+\section{Primary routines, and a simple example}
+%-------------------------------------------------------------------------------
+
+Five primary UMFPACK routines are required to factorize $\m{A}$ or
+solve $\m{Ax}=\m{b}$. An overview of the primary features of the routines
+is given in Section~\ref{Primary}.
+Additional routines are available for passing a different column ordering
+to UMFPACK, changing default parameters, manipulating sparse matrices,
+getting the LU factors, save and loading the LU factors from a file,
+computing the determinant,
+and reporting results. See the User Guide for more information.
+
+\begin{itemize}
+\item {\tt umfpack\_di\_symbolic}:
+
+ Pre-orders the columns of $\m{A}$ to reduce fill-in and performs a
+ symbolic analysis.
+ Returns an opaque {\tt Symbolic} object as a {\tt void *}
+ pointer. The object contains the symbolic analysis and is needed for the
+ numerical factorization.
+
+\item {\tt umfpack\_di\_numeric}:
+
+ Numerically scales and then factorizes a sparse matrix
+ $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$,
+ where
+ $\m{P}$ and $\m{Q}$ are permutation matrices, $\m{R}$ is a diagonal
+ matrix of scale factors, $\m{L}$ is lower triangular with unit diagonal,
+ and $\m{U}$ is upper triangular. Requires the
+ symbolic ordering and analysis computed by {\tt umfpack\_di\_symbolic}.
+ Returns an opaque {\tt Numeric} object as a
+ {\tt void *} pointer. The object contains the numerical factorization and
+ is used by {\tt umfpack\_di\_solve}.
+
+\item {\tt umfpack\_di\_solve}:
+
+ Solves a sparse linear system ($\m{Ax}=\m{b}$, $\m{A}\tr\m{x}=\m{b}$, or
+ systems involving just $\m{L}$ or $\m{U}$), using the numeric factorization
+ computed by {\tt umfpack\_di\_numeric}.
+
+\item {\tt umfpack\_di\_free\_symbolic}:
+
+ Frees the {\tt Symbolic} object created by {\tt umfpack\_di\_symbolic}.
+
+\item {\tt umfpack\_di\_free\_numeric}:
+
+ Frees the {\tt Numeric} object created by {\tt umfpack\_di\_numeric}.
+
+\end{itemize}
+
+The matrix $\m{A}$ is represented in compressed column form, which is
+identical to the sparse matrix representation used by MATLAB. It consists
+of three arrays, where the matrix is {\tt m}-by-{\tt n},
+with {\tt nz} entries:
+
+{\footnotesize
+\begin{verbatim}
+ int Ap [n+1] ;
+ int Ai [nz] ;
+ double Ax [nz] ;
+\end{verbatim}
+}
+
+All nonzeros are entries, but an entry may be numerically zero. The row indices
+of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} ... {\tt Ap[j+1]-1]}.
+The corresponding numerical values are stored in
+ {\tt Ax[Ap[j]} ... {\tt Ap[j+1]-1]}.
+
+No duplicate row indices may be present, and the row indices in any given
+column must be sorted in ascending order. The first entry {\tt Ap[0]} must be
+zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+Except for the fact that extra zero entries can be included, there is thus a
+unique compressed column representation of any given matrix $\m{A}$.
+
+Here is a simple main program, {\tt umfpack\_simple.c}, that illustrates the
+basic usage of UMFPACK.
+
+{\footnotesize
+\begin{verbatim}
+ #include <stdio.h>
+ #include "umfpack.h"
+
+ int n = 5 ;
+ int Ap [ ] = {0, 2, 5, 9, 10, 12} ;
+ int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ;
+ double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ;
+ double b [ ] = {8., 45., -3., 3., 19.} ;
+ double x [5] ;
+
+ int main (void)
+ {
+ double *null = (double *) NULL ;
+ int i ;
+ void *Symbolic, *Numeric ;
+ (void) umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic, null, null) ;
+ (void) umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, null, null) ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+ (void) umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, null, null) ;
+ umfpack_di_free_numeric (&Numeric) ;
+ for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, x [i]) ;
+ return (0) ;
+ }
+\end{verbatim}
+}
+
+The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 & -1 & -3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1 \\
+\end{array}
+\right].
+\]
+and the solution is $\m{x} = [1 \, 2 \, 3 \, 4 \, 5]\tr$. The program uses
+default control settings and does not return any statistics about the ordering,
+factorization, or solution ({\tt Control} and {\tt Info} are both
+{\tt (double *) NULL}).
+
+For routines to manipulate a simpler ``triplet-form'' data structure for your
+sparse matrix $\m{A}$, refer to the UMFPACK User Guide.
+
+%-------------------------------------------------------------------------------
+\section{Synopsis of primary C-callable routines}
+\label{Synopsis}
+%-------------------------------------------------------------------------------
+
+The matrix $\m{A}$ is {\tt m}-by-{\tt n} with {\tt nz} entries.
+The optional {\tt umfpack\_di\_defaults} routine loads the default control
+parameters into the {\tt Control} array. The settings can then be modified
+before passing the array to the other routines. Refer to Section~\ref{Primary}
+for more details.
+
+{\footnotesize
+\begin{verbatim}
+ #include "umfpack.h"
+ int status, sys, n, m, nz, Ap [n+1], Ai [nz] ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], Ax [nz], X [n], B [n] ;
+ void *Symbolic, *Numeric ;
+
+ status = umfpack_di_symbolic (m, n, Ap, Ai, Ax, &Symbolic, Control, Info) ;
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ;
+ status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+ umfpack_di_free_numeric (&Numeric) ;
+ umfpack_di_defaults (Control) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%-------------------------------------------------------------------------------
+
+You will need to install both UMFPACK v5.0 and AMD v2.0 to use UMFPACK.
+Note that UMFPACK v5.0 cannot use AMD v1.2 or earlier.
+The {\tt UMFPACK} and {\tt AMD} subdirectories must be placed side-by-side
+within the same parent directory. AMD is a stand-alone package that
+is required by UMFPACK. UMFPACK can be compiled without the
+BLAS but your performance will be much less than what it should be.
+
+System-dependent configurations are in the {\tt UFconfig/UFconfig.mk}
+file. The default
+settings will work on most systems, except that UMFPACK will be compiled so
+that it does not use the BLAS. Sample configurations are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install both packages,
+go to the UMFPACK directory and type {\tt make}. This will compile the
+libraries ({\tt AMD/Lib/libamd.a} and {\tt UMFPACK/Lib/libumfpack.a}).
+A demo of the AMD ordering routine will be compiled and tested in
+the {\tt AMD/Demo} directory, and five demo programs will then be
+compiled and tested in the {\tt UMFPACK/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution. Expect to see a few differences, such as
+residual norms, compile-time control settings, and perhaps memory usage
+differences. The AMD and MATLAB mexFunctions for
+use in MATLAB will also be compiled. If you do not have MATLAB,
+type {\tt make lib} instead.
+
+If you compile UMFPACK and AMD and then later change the
+{\tt UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+Here are the various parameters that you can control in your
+{\tt UFconfig/UFconfig.mk} file:
+
+\begin{itemize}
+\item {\tt CC = } your C compiler, such as {\tt cc}.
+\item {\tt RANLIB = } your system's {\tt ranlib} program, if needed.
+\item {\tt CFLAGS = } optimization flags, such as {\tt -O}.
+\item {\tt UMFPACK\_CONFIG = } configuration settings, for the BLAS,
+ memory allocation routines, and timing routines.
+\item {\tt LIB = } your libraries, such as {\tt -lm} or {\tt -lblas}.
+\item {\tt RM =} the command to delete a file.
+\item {\tt MV =} the command to rename a file.
+\item {\tt MEX =} the command to compile a MATLAB mexFunction.
+\item {\tt F77 =} the command to compile a Fortran program (optional).
+\item {\tt F77FLAGS =} the Fortran compiler flags (optional).
+\item {\tt F77LIB =} the Fortran libraries (optional).
+\end{itemize}
+
+The {\tt UMFPACK\_CONFIG} string can include combinations of the following;
+most deal with how the BLAS are called:
+\begin{itemize}
+\item {\tt -DNBLAS} if you do not have any BLAS at all.
+\item {\tt -DNSUNPERF} if you are on Solaris but do not have the Sun
+ Performance Library.
+\item {\tt -DLONGBLAS} if your BLAS takes non-{\tt int} integer arguments.
+\item {\tt -DBLAS\_INT = } the integer used by the BLAS.
+
+\item {\tt -DBLAS\_NO\_UNDERSCORE}
+ for controlling how C calls the Fortran BLAS.
+ This is set automatically for Windows,
+ Sun Solaris, SGI Irix, Red Hat Linux, Compaq Alpha, and
+ AIX (the IBM RS 6000).
+
+\item {\tt -DGETRUSAGE} if you have the {\tt getrusage} function.
+\item {\tt -DNPOSIX} if you do not have the POSIX-compliant
+ {\tt sysconf} and {\tt times} routines.
+\item {\tt -DNRECIPROCAL} controls a trade-off between speed and accuracy.
+ This is off by default (speed preferred over accuracy) except when
+ compiling for MATLAB.
+\end{itemize}
+
+When you compile your program that uses the C-callable UMFPACK library,
+you need to add the both {\tt UMFPACK/Lib/libumfpack.a} and
+{\tt AMD/Lib/libamd.a}
+libraries, and you need to tell your compiler to look in the
+directories {\tt UMFPACK/Include} and {\tt AMD/Include} for include
+files. See {\tt UMFPACK/Demo/Makefile} for an example.
+You do not need to directly include any AMD include files in your
+program, unless you directly call AMD routines. You only need the
+\begin{verbatim}
+#include "umfpack.h"
+\end{verbatim}
+statement, as described in Section~\ref{Synopsis}.
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{The primary UMFPACK routines}
+\label{Primary}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_di\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+int umfpack_di_symbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+Purpose:
+
+ Given nonzero pattern of a sparse matrix A in column-oriented form,
+ umfpack_di_symbolic performs a column pre-ordering to reduce fill-in
+ (using COLAMD or AMD) and a symbolic factorization. This is required
+ before the matrix can be numerically factorized with umfpack_di_numeric.
+
+ For the following discussion, let S be the submatrix of A obtained after
+ eliminating all pivots of zero Markowitz cost. S has dimension
+ (n_row-n1-nempty_row) -by- (n_col-n1-nempty_col), where
+ n1 = Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS],
+ nempty_row = Info [UMFPACK_NEMPTY_ROW] and
+ nempty_col = Info [UMFPACK_NEMPTY_COL].
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ int n_row ; Input argument, not modified.
+ int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+
+ int Ap [n_col+1] ; Input argument, not modified.
+
+ Ap is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the sparse matrix A. Column j of
+ the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first
+ entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all
+ j in the range 0 to n_col-1. The value nz = Ap [n_col] is thus the
+ total number of entries in the pattern of the matrix A. nz must be
+ greater than or equal to zero.
+
+ int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to n_row-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Optional input argument, not modified.
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. Used only by the 2-by-2 strategy to
+ determine whether entries are "large" or "small". You do not have to
+ pass the same numerical values to umfpack_di_numeric. If Ax is not
+ present (a (double *) NULL pointer), then any entry in A is assumed to
+ be "large".
+
+ void **Symbolic ; Output argument.
+
+ **Symbolic is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Symbolic object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Only the primary parameters are listed below:
+
+ Control [UMFPACK_STRATEGY]: This is the most important control
+ parameter. It determines what kind of ordering and pivoting
+ strategy that UMFPACK should use. It is new to Version 4.1
+ There are 4 options:
+
+ UMFPACK_STRATEGY_AUTO: This is the default. The input matrix is
+ analyzed to determine how symmetric the nonzero pattern is, and
+ how many entries there are on the diagonal. It then selects one
+ of the following strategies. Refer to the User Guide for a
+ description of how the strategy is automatically selected.
+
+ UMFPACK_STRATEGY_UNSYMMETRIC: Use the unsymmetric strategy. COLAMD
+ is used to order the columns of A, followed by a postorder of
+ the column elimination tree. No attempt is made to perform
+ diagonal pivoting. The column ordering is refined during
+ factorization. This strategy was the only one provided with
+ UMFPACK V4.0.
+
+ In the numerical factorization, the
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE] parameter is ignored. A
+ pivot is selected if its magnitude is >=
+ Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the
+ largest entry in its column.
+
+ UMFPACK_STRATEGY_SYMMETRIC: Use the symmetric strategy (new to
+ Version 4.1). In this method, the approximate minimum degree
+ ordering (AMD) is applied to A+A', followed by a postorder of
+ the elimination tree of A+A'. UMFPACK attempts to perform
+ diagonal pivoting during numerical factorization. No refinement
+ of the column preordering is performed during factorization.
+
+ In the numerical factorization, a nonzero entry on the diagonal
+ is selected as the pivot if its magnitude is >= Control
+ [UMFPACK_SYM_PIVOT_TOLERANCE] (default 0.001) times the largest
+ entry in its column. If this is not acceptable, then an
+ off-diagonal pivot is selected with magnitude >= Control
+ [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry
+ in its column.
+
+ UMFPACK_STRATEGY_2BY2: a row permutation P2 is found that places
+ large entries on the diagonal. The matrix P2*A is then
+ factorized using the symmetric strategy, described above.
+ Refer to the User Guide for more information.
+
+ Control [UMFPACK_2BY2_TOLERANCE]: a diagonal entry S (k,k) is
+ considered "small" if it is < tol * max (abs (S (:,k))), where S a
+ submatrix of the scaled input matrix, with pivots of zero Markowitz
+ cost removed.
+
+ Control [UMFPACK_SCALE]: This parameter is new to V4.1. See
+ umfpack_numeric.h for a description. Only affects the 2-by-2
+ strategy. Default: UMFPACK_SCALE_SUM.
+
+ double Info [UMFPACK_INFO] ; Output argument, not defined on input.
+
+ Contains statistics about the symbolic analysis. If a (double *) NULL
+ pointer is passed, then no statistics are returned in Info (this is not
+ an error condition). The entire Info array is cleared (all entries set
+ to -1) and then the following statistics are computed (only the
+ primary statistics are listed):
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Each column of the input matrix contained row indices
+ in increasing order, with no duplicates. Only in this case
+ does umfpack_di_symbolic compute a valid symbolic factorization.
+ For the other cases below, no Symbolic object is created
+ (*Symbolic is (void *) NULL).
+
+ UMFPACK_ERROR_n_nonpositive
+
+ n is less than or equal to zero.
+
+ UMFPACK_ERROR_invalid_matrix
+
+ Number of entries in the matrix is negative, Ap [0] is nonzero,
+ a column has a negative number of entries, a row index is out of
+ bounds, or the columns of input matrix were jumbled (unsorted
+ columns or duplicate entries).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to perform the symbolic analysis. If the
+ analysis requires more than 2GB of memory and you are using
+ the 32-bit ("int") version of UMFPACK, then you are guaranteed
+ to run out of memory. Try using the 64-bit version of UMFPACK.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments is missing.
+
+ UMFPACK_ERROR_internal_error
+
+ Something very serious went wrong. This is a bug.
+ Please contact the author (davis at cise.ufl.edu).
+
+ Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit,
+ for memory usage statistics below.
+
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]: the amount of memory (in Units)
+ required for umfpack_di_symbolic to complete. This count includes
+ the size of the Symbolic object itself, which is also reported in
+ Info [UMFPACK_SYMBOLIC_SIZE].
+
+ Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]: an estimate of the final size (in
+ Units) of the entire Numeric object (both fixed-size and variable-
+ sized parts), which holds the LU factorization (including the L, U,
+ P and Q matrices).
+
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE]: an estimate of the total amount of
+ memory (in Units) required by umfpack_di_symbolic and
+ umfpack_di_numeric to perform both the symbolic and numeric
+ factorization. This is the larger of the amount of memory needed
+ in umfpack_di_numeric itself, and the amount of memory needed in
+ umfpack_di_symbolic (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]). The
+ count includes the size of both the Symbolic and Numeric objects
+ themselves. It can be a very loose upper bound, particularly when
+ the symmetric or 2-by-2 strategies are used.
+
+ Info [UMFPACK_FLOPS_ESTIMATE]: an estimate of the total floating-point
+ operations required to factorize the matrix. This is a "true"
+ theoretical estimate of the number of flops that would be performed
+ by a flop-parsimonious sparse LU algorithm. It assumes that no
+ extra flops are performed except for what is strictly required to
+ compute the LU factorization. It ignores, for example, the flops
+ performed by umfpack_di_numeric to add contribution blocks of
+ frontal matrices together. If L and U are the upper bound on the
+ pattern of the factors, then this flop count estimate can be
+ represented in MATLAB (for real matrices, not complex) as:
+
+ Lnz = full (sum (spones (L))) - 1 ; % nz in each col of L
+ Unz = full (sum (spones (U')))' - 1 ; % nz in each row of U
+ flops = 2*Lnz*Unz + sum (Lnz) ;
+
+ The actual "true flop" count found by umfpack_di_numeric will be
+ less than this estimate.
+
+ Info [UMFPACK_LNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ L, including the diagonal. Since L is unit-diagonal, the diagonal
+ of L is not stored. This estimate is a strict upper bound on the
+ actual nonzeros in L to be computed by umfpack_di_numeric.
+
+ Info [UMFPACK_UNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ U, including the diagonal. This estimate is a strict upper bound on
+ the actual nonzeros in U to be computed by umfpack_di_numeric.
+
+ Info [UMFPACK_SYMBOLIC_TIME]: The CPU time taken, in seconds.
+
+ Info [UMFPACK_STRATEGY_USED]: The ordering strategy used:
+ UMFPACK_STRATEGY_SYMMETRIC, UMFPACK_STRATEGY_UNSYMMETRIC, or
+ UMFPACK_STRATEGY_2BY2.
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+\subsection{umfpack\_di\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+int umfpack_di_numeric
+(
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+Purpose:
+
+ Given a sparse matrix A in column-oriented form, and a symbolic analysis
+ computed by umfpack_di_symbolic, the umfpack_di_numeric routine performs the
+ numerical factorization, PAQ=LU, PRAQ=LU, or P(R\A)Q=LU, where P and Q are
+ permutation matrices (represented as permutation vectors), R is the row
+ scaling, L is unit-lower triangular, and U is upper triangular. This is
+ required before the system Ax=b (or other related linear systems) can be
+ solved. umfpack_di_numeric can be called multiple times for each call to
+ umfpack_di_symbolic, to factorize a sequence of matrices with identical
+ nonzero pattern. Simply compute the Symbolic object once, with
+ umfpack_di_symbolic, and reuse it for subsequent matrices.
+ umfpack_di_numeric safely detects if the pattern changes, and sets an
+ appropriate error code.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ int Ap [n_col+1] ; Input argument, not modified.
+
+ This must be identical to the Ap array passed to umfpack_di_symbolic.
+ The value of n_col is what was passed to umfpack_di_symbolic (this is
+ held in the Symbolic object).
+
+ int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ This must be identical to the Ai array passed to umfpack_di_symbolic.
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)].
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_di_symbolic. The Symbolic object is not modified by
+ umfpack_di_numeric.
+
+ void **Numeric ; Output argument.
+
+ **Numeric is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Numeric object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Only the primary parameters are listed below:
+
+ Control [UMFPACK_PIVOT_TOLERANCE]: relative pivot tolerance for
+ threshold partial pivoting with row interchanges. In any given
+ column, an entry is numerically acceptable if its absolute value is
+ greater than or equal to Control [UMFPACK_PIVOT_TOLERANCE] times
+ the largest absolute value in the column. A value of 1.0 gives true
+ partial pivoting. If less than or equal to zero, then any nonzero
+ entry is numerically acceptable as a pivot (this is changed from
+ Version 4.0). Default: 0.1.
+
+ Smaller values tend to lead to sparser LU factors, but the solution
+ to the linear system can become inaccurate. Larger values can lead
+ to a more accurate solution (but not always), and usually an
+ increase in the total work.
+
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE]: This parameter is new to V4.1.
+ If diagonal pivoting is attempted (the symmetric or symmetric-2by2
+ strategies are used) then this parameter is used to control when the
+ diagonal entry is selected in a given pivot column. The absolute
+ value of the entry must be >= Control [UMFPACK_SYM_PIVOT_TOLERANCE]
+ times the largest absolute value in the column. A value of zero
+ will ensure that no off-diagonal pivoting is performed, except that
+ zero diagonal entries are not selected if there are any off-diagonal
+ nonzero entries.
+
+ If an off-diagonal pivot is selected, an attempt is made to restore
+ symmetry later on. Suppose A (i,j) is selected, where i != j.
+ If column i has not yet been selected as a pivot column, then
+ the entry A (j,i) is redefined as a "diagonal" entry, except that
+ the tighter tolerance (Control [UMFPACK_PIVOT_TOLERANCE]) is
+ applied. This strategy has an effect similar to 2-by-2 pivoting
+ for symmetric indefinite matrices. If a 2-by-2 block pivot with
+ nonzero structure
+
+ i j
+ i: 0 x
+ j: x 0
+
+ is selected in a symmetric indefinite factorization method, the
+ 2-by-2 block is inverted and a rank-2 update is applied. In
+ UMFPACK, this 2-by-2 block would be reordered as
+
+ j i
+ i: x 0
+ j: 0 x
+
+ In both cases, the symmetry of the Schur complement is preserved.
+
+ Control [UMFPACK_SCALE]: This parameter is new to V4.1. Version 4.0
+ did not scale the matrix. Note that the user's input matrix is
+ never modified, only an internal copy is scaled.
+
+ There are three valid settings for this parameter. If any other
+ value is provided, the default is used.
+
+ UMFPACK_SCALE_NONE: no scaling is performed.
+
+ UMFPACK_SCALE_SUM: each row of the input matrix A is divided by
+ the sum of the absolute values of the entries in that row.
+ The scaled matrix has an infinity norm of 1.
+
+ UMFPACK_SCALE_MAX: each row of the input matrix A is divided by
+ the maximum the absolute values of the entries in that row.
+ In the scaled matrix the largest entry in each row has
+ a magnitude exactly equal to 1.
+
+ Scaling is very important for the "symmetric" strategy when
+ diagonal pivoting is attempted. It also improves the performance
+ of the "unsymmetric" strategy.
+
+ Default: UMFPACK_SCALE_SUM.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the numeric factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_di_numeric (only the primary statistics are listed):
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Numeric factorization was successful. umfpack_di_numeric
+ computed a valid numeric factorization.
+
+ UMFPACK_WARNING_singular_matrix
+
+ Numeric factorization was successful, but the matrix is
+ singular. umfpack_di_numeric computed a valid numeric
+ factorization, but you will get a divide by zero in
+ umfpack_di_solve. For the other cases below, no Numeric object
+ is created (*Numeric is (void *) NULL).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to complete the numeric factorization.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing.
+
+ UMFPACK_ERROR_invalid_Symbolic_object
+
+ Symbolic object provided as input is invalid.
+
+ UMFPACK_ERROR_different_pattern
+
+ The pattern (Ap and/or Ai) has changed since the call to
+ umfpack_di_symbolic which produced the Symbolic object.
+
+ Info [UMFPACK_NUMERIC_SIZE]: the actual final size (in Units) of the
+ entire Numeric object, including the final size of the variable
+ part of the object. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE],
+ an estimate, was computed by umfpack_di_symbolic. The estimate is
+ normally an upper bound on the actual final size, but this is not
+ guaranteed.
+
+ Info [UMFPACK_PEAK_MEMORY]: the actual peak memory usage (in Units) of
+ both umfpack_di_symbolic and umfpack_di_numeric. An estimate,
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE], was computed by
+ umfpack_di_symbolic. The estimate is normally an upper bound on the
+ actual peak usage, but this is not guaranteed. With testing on
+ hundreds of matrix arising in real applications, I have never
+ observed a matrix where this estimate or the Numeric size estimate
+ was less than the actual result, but this is theoretically possible.
+ Please send me one if you find such a matrix.
+
+ Info [UMFPACK_FLOPS]: the actual count of the (useful) floating-point
+ operations performed. An estimate, Info [UMFPACK_FLOPS_ESTIMATE],
+ was computed by umfpack_di_symbolic. The estimate is guaranteed to
+ be an upper bound on this flop count. The flop count excludes
+ "useless" flops on zero values, flops performed during the pivot
+ search (for tentative updates and assembly of candidate columns),
+ and flops performed to add frontal matrices together.
+
+ Info [UMFPACK_LNZ]: the actual nonzero entries in final factor L,
+ including the diagonal. This excludes any zero entries in L,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_LNZ_ESTIMATE],
+ an estimate, was computed by umfpack_di_symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_LNZ].
+
+ Info [UMFPACK_UNZ]: the actual nonzero entries in final factor U,
+ including the diagonal. This excludes any zero entries in U,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_UNZ_ESTIMATE],
+ an estimate, was computed by umfpack_di_symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_UNZ].
+
+ Info [UMFPACK_NUMERIC_TIME]: The CPU time taken, in seconds.
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\subsection{umfpack\_di\_solve}
+
+{\footnotesize
+\begin{verbatim}
+int umfpack_di_solve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+Purpose:
+
+ Given LU factors computed by umfpack_di_numeric (PAQ=LU, PRAQ=LU, or
+ P(R\A)Q=LU) and the right-hand-side, B, solve a linear system for the
+ solution X. Iterative refinement is optionally performed. Only square
+ systems are handled. Singular matrices result in a divide-by-zero for all
+ systems except those involving just the matrix L. Iterative refinement is
+ not performed for singular matrices.
+
+ In the discussion below, n is equal to n_row and n_col, because only
+ square systems are handled.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ int sys ; Input argument, not modified.
+
+ Defines which system to solve. (') is the linear algebraic transpose.
+
+ sys value system solved
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Pt_L P'Lx=b
+ UMFPACK_L Lx=b
+ UMFPACK_Lt_P L'Px=b
+ UMFPACK_Lt L'x=b
+ UMFPACK_U_Qt UQ'x=b
+ UMFPACK_U Ux=b
+ UMFPACK_Q_Ut QU'x=b
+ UMFPACK_Ut U'x=b
+
+ Iterative refinement can be optionally performed when sys is any of
+ the following:
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+
+ For the other values of the sys argument, iterative refinement is not
+ performed (Control [UMFPACK_IRSTEP], Ap, Ai, and Ax are ignored).
+
+ int Ap [n+1] ; Input argument, not modified.
+ int Ai [nz] ; Input argument, not modified.
+ double Ax [nz] ; Input argument, not modified.
+
+ If iterative refinement is requested (Control [UMFPACK_IRSTEP] >= 1,
+ Ax=b or A'x=b is being solved, and A is nonsingular), then
+ these arrays must be identical to the same ones passed to
+ umfpack_di_numeric. The umfpack_di_solve routine does not check the
+ contents of these arguments, so the results are undefined if Ap, Ai, Ax,
+ are modified between the calls the umfpack_di_numeric and
+ umfpack_di_solve. These three arrays do not need to be present (NULL
+ pointers can be passed) if Control [UMFPACK_IRSTEP] is zero, or if a
+ system other than Ax=b or A'x=b is being solved, or if A is
+ singular, since in each of these cases A is not accessed.
+
+ double X [n] ; Output argument.
+
+ The solution to the linear system, where n = n_row = n_col is the
+ dimension of the matrices A, L, and U.
+
+ double B [n] ; Input argument, not modified.
+
+ The right-hand side vector, b, stored as a conventional array of size n
+ (or two arrays of size n for complex versions). This routine does not
+ solve for multiple right-hand-sides, nor does it allow b to be stored in
+ a sparse-column form.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_di_numeric.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used.
+
+ Control [UMFPACK_IRSTEP]: The maximum number of iterative refinement
+ steps to attempt. A value less than zero is treated as zero. If
+ less than 1, or if Ax=b or A'x=b is not being solved, or
+ if A is singular, then the Ap, Ai, and Ax arguments are not
+ accessed. Default: 2.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the solution factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_di_solve (only the primary statistics are listed):
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ The linear system was successfully solved.
+
+ UMFPACK_WARNING_singular_matrix
+
+ A divide-by-zero occurred. Your solution will contain Inf's
+ and/or NaN's. Some parts of the solution may be valid. For
+ example, solving Ax=b with
+
+ A = [2 0] b = [ 1 ] returns x = [ 0.5 ]
+ [0 0] [ 0 ] [ Inf ]
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to solve the linear system.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing. The B and X
+ arguments are always required. Info and Control are not
+ required. Ap, Ai and Ax are required if Ax=b or
+ A'x=b is to be solved, the (default) iterative
+ refinement is requested, and the matrix A is nonsingular.
+
+ UMFPACK_ERROR_invalid_system
+
+ The sys argument is not valid, or the matrix A is not square.
+
+ UMFPACK_ERROR_invalid_Numeric_object
+
+ The Numeric object is not valid.
+
+ Info [UMFPACK_SOLVE_FLOPS]: the number of floating point operations
+ performed to solve the linear system. This includes the work
+ taken for all iterative refinement steps, including the backtrack
+ (if any).
+
+ Info [UMFPACK_SOLVE_TIME]: The time taken, in seconds.
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+
+\subsection{umfpack\_di\_free\_symbolic}
+{\footnotesize
+\begin{verbatim}
+void umfpack_di_free_symbolic
+(
+ void **Symbolic
+) ;
+
+Purpose:
+
+ Deallocates the Symbolic object and sets the Symbolic handle to NULL.
+
+Arguments:
+
+ void **Symbolic ; Input argument, deallocated and Symbolic is
+ set to (void *) NULL on output.
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{umfpack\_di\_free\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+void umfpack_di_free_numeric
+(
+ void **Numeric
+) ;
+
+Purpose:
+
+ Deallocates the Numeric object and sets the Numeric handle to NULL.
+
+Arguments:
+
+ void **Numeric ; Input argument, deallocated and Numeric is
+ set to (void *) NULL on output.
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{umfpack\_di\_defaults}
+
+{\footnotesize
+\begin{verbatim}
+void umfpack_di_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+Purpose:
+
+ Sets the default control parameter settings.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Output argument.
+
+ Control is set to the default control parameter settings.
+\end{verbatim}
+}
+\end{document}
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.bib b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.bib
new file mode 100644
index 0000000..540f12e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.bib
@@ -0,0 +1,322 @@
+ at string{TOMS = "ACM Trans. Math. Softw."}
+ at string{SIMAX = "SIAM J. Matrix Anal. Applic."}
+ at string{SINUM = "SIAM J. Numer. Anal."}
+ at string{SIAMJSC = "SIAM J. Sci. Comput."}
+ at string{SIAMJSSC = "SIAM J. Sci. Statist. Comput."}
+ at string{IJNME = "Internat. J. Numer. Methods Eng."}
+ at string{SIAMJADM = "SIAM J. Alg. Disc. Meth."}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886-905}}
+
+ at article{AmestoyDavisDuff03,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}}
+
+ at techreport{AmestoyDavisDuff03_user,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={{AMD} Version 1.0 User Guide},
+ institution={CISE Dept., Univ. of Florida},
+ year={2003}
+ ,number={TR-03-011}
+ ,address={Gainesville, FL}
+ ,note={www.cise.ufl.edu/tech-reports.}
+ }
+
+ at article{Davis03,
+ author={Davis, T. A.},
+ title={A column pre-ordering strategy for the unsymmetric-pattern multifrontal method},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={2}
+ ,pages={165-195}}
+
+ at article{Davis03_algo,
+ author={Davis, T. A.},
+ title={Algorithm 832: {UMFPACK}, an unsymmetric-pattern multifrontal method},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={2}
+ ,pages={196-199}}
+
+ at techreport{Davis03_umf,
+ author={Davis, T. A.},
+ title={{UMFPACK} User Guide},
+ institution={Univ. of Florida, CISE Dept.},
+ year={2005}
+ ,number={TR-04-003 (revised)}
+ ,address={Gainesville, FL}
+ ,note={(www.cise.ufl.edu/tech-reports)}
+ }
+
+ at techreport{Davis03_umfquick,
+ author={Davis, T. A.},
+ title={{UMFPACK} Quick Start Guide},
+ institution={Univ. of Florida, CISE Dept.},
+ year={2005}
+ ,number={TR-04-005 (revised)}
+ ,address={Gainesville, FL}
+ ,note={(www.cise.ufl.edu/tech-reports)}
+ }
+
+ at article{DavisDuff97,
+ author={Davis, T. A. and Duff, I. S.},
+ title={An unsymmetric-pattern multifrontal method for sparse {LU} factorization},
+ journal=SIMAX,
+ year={1997}
+ ,volume={18}
+ ,number={1}
+ ,pages={140-158}}
+
+ at article{DavisDuff99,
+ author={Davis, T. A. and Duff, I. S.},
+ title={A combined unifrontal/multifrontal method for unsymmetric sparse matrices},
+ journal=TOMS,
+ volume={25},
+ number={1},
+ pages={1-19},
+ year={1999}}
+
+ at article{SuperLU99,
+ author={Demmel, J. W. and Eisenstat, S. C. and Gilbert, J. R. and Li, X. S. and Liu, J. W. H.},
+ title={A supernodal approach to sparse partial pivoting},
+ journal=SIMAX,
+ year={1999}
+ ,volume={20}
+ ,number={3}
+ ,pages={720-755}
+ ,note={www.netlib.org}
+ }
+
+ at article{ACM679a,
+ author={Dongarra, J. J. and Du Croz, J. and Duff, I. S. and Hammarling, S.},
+ title={A set of level-3 basic linear algebra subprograms},
+ journal=TOMS,
+ year={1990}
+ ,volume={16}
+ ,number={1}
+ ,pages={1--17}}
+
+ at article{netlib,
+ author={Dongarra, J. J. and Grosse, E.},
+ title={Distribution of mathematical software via electronic mail},
+ journal={Comm. ACM},
+ year={1987}
+ ,volume={30}
+ ,pages={403-407}
+ ,note={www.netlib.org}
+ }
+
+ at article{Duff78b,
+ author={Duff, I. S. and Reid, J. K.},
+ year={1978},
+ title={Algorithm 529: Permutations to Block Triangular Form},
+ journal=TOMS,
+ volume={4},
+ annote={f},
+ number={2},
+ pages={189-192},
+ keywords={102 ordering block triangular form}}
+
+ at article{Duff81b,
+ author={Duff, I. S.},
+ year={1981},
+ title={Algorithm 575: Permutations for a Zero-Free Diagonal},
+ journal=TOMS,
+ annote={f},
+ volume={7},
+ pages={387-390},
+ keywords={ordering, zero-free diagonal}}
+
+ at techreport{GotoVandeGeijn02,
+ author = {Goto, K. and van de Geijn, R.},
+ title = {On Reducing {TLB} Misses in Matrix Multiplication, {FLAME} Working Note 9},
+ institution={The University of Texas at Austin, Department of Computer Sciences},
+ number={TR-2002-55},
+ month={Nov.},
+ year={2002}}
+
+ at article{GeorgeNg85,
+ author={George, A. and Ng, E. G.},
+ year={1985},
+ title={An Implementation of {G}aussian Elimination with
+ Partial Pivoting for Sparse Systems},
+ journal=SIAMJSSC,
+ volume={6},
+ number={2},
+ pages={390-409}}
+
+ at article{GeorgeNg87,
+ author={George, A. and Ng, E. G.},
+ year={1987},
+ title={Symbolic Factorization for Sparse {G}aussian Elimination
+ with Partial Pivoting},
+ journal={SIAM J. Sci. Statist. Comput.},
+ volume={8},
+ number={6},
+ pages={877-898}}
+
+ at article{GilbertMolerSchreiber,
+ author={Gilbert, J. R. and Moler, C. and Schreiber, R.},
+ title={Sparse matrices in {MATLAB}: design and implementation},
+ journal=SIMAX,
+ year={1992}
+ ,volume={13}
+ ,number={1}
+ ,pages={333-356}}
+
+ at article{GilbertPeierls88,
+ author={Gilbert, J. R. and Peierls, T.},
+ year={1988},
+ title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations},
+ journal={SIAM J. Sci. Statist. Comput.},
+ volume={9},
+ pages={862-874}}
+
+ at article{Gustavson78,
+ author={Gustavson, F. G.},
+ year={1978},
+ title={Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition},
+ journal=TOMS,
+ volume={4},
+ number={3},
+ pages={250-269}}
+
+ at techreport{Larimore98,
+ author={Larimore, S. I.},
+ title={An approximate minimum degree column ordering algorithm},
+ institution={Univ. of Florida, CISE Dept.},
+ year={1998}
+ ,number={TR-98-016}
+ ,address={Gainesville, FL}
+ ,note={www.cise.ufl.edu/tech-reports}}
+
+ at article{DavisGilbertLarimoreNg00,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={353-376}}
+
+ at article{DavisGilbertLarimoreNg00_algo,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={377-380}}
+
+ at INCOLLECTION{GilbertNg93,
+ author = {J. R. Gilbert and E. G. Ng},
+ editor = {A. George and J. R. Gilbert and J. W.H. Liu},
+ year = 1993,
+ title = {Predicting Structure in Nonsymmetric Sparse Matrix Factorizations},
+ booktitle = {Graph Theory and Sparse Matrix Computation},
+ series = {Volume 56 of the {IMA} Volumes in Mathematics and its Applications},
+ pages = {107-139},
+ publisher = {Springer-Verlag}
+}
+
+
+ at techreport{ATLAS,
+ author={Whaley, R. C and Petitet, A. and Dongarra, J. J.},
+ title={Automated Emperical Optimization of Software and the {ATLAS} Project},
+ institution={Computer Science Department, The University of Tennessee},
+ year={2000}
+ ,number={LAPACK Working Note 147}
+ ,month={September}
+ ,note={www.netlib.org/atlas}
+ }
+
+ at article{DaydeDuff99,
+ author = "M. J. Dayd\'{e} and I. S. Duff",
+ title = "The {RISC} {BLAS}: A Blocked Implementation of Level 3 {BLAS} for {RISC} Processors",
+ journal = TOMS,
+ volume = "25",
+ number = "3",
+ month = {Sept.},
+ year ="1999"
+ }
+
+
+ at article{ardd:89,
+ author = {M. Arioli and J. W. Demmel and I. S. Duff},
+ year = "1989",
+ title = {Solving sparse linear systems with sparse backward error},
+ journal = SIMAX,
+ volume = {10},
+ pages = {165-190}
+}
+
+
+ at article{DavisHager99,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Modifying a sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1999}
+ ,volume={20}
+ ,number={3}
+ ,pages={606-627}
+ }
+
+
+ at article{dusc:96,
+ author = {I. S. Duff and J. A. Scott},
+ title = {The design of a new frontal code for solving sparse unsymmetric systems},
+ journal = TOMS,
+ year = "1996",
+ volume = "22",
+ number = "1",
+ pages = "30-45"
+ }
+
+
+ at article{Duff78a,
+ author={Duff, I. S. and Reid, J. K.},
+ year={1978},
+ title={An Implementation of {T}arjan's Algorithm for the Block Triangularization of a Matrix},
+ journal=TOMS,
+ volume={4},
+ number={2},
+ pages={137-147}
+ }
+
+ at book{GeorgeLiu,
+ author={George, A. and Liu, J. W. H.},
+ year={1981},
+ title={Computer Solution of Large Sparse Positive Definite Systems},
+ publisher={Englewood Cliffs, New Jersey: Prentice-Hall}
+ }
+
+ at article{GilbertNgPeyton94,
+ author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.},
+ title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1994}
+ ,volume={15}
+ ,number={4}
+ ,pages={1075-1091}
+ }
+
+ at techreport{DuffGrimesLewis87b,
+ author={Duff, I. S. and Grimes, R. G. and Lewis, J. G.},
+ year={1987},
+ title={Users' Guide for the Harwell-Boeing Sparse Matrix Test Collection},
+ institution={AERE Harwell Laboratory, United Kingdom Atomic Energy Authority}}
+
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.pdf b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.pdf
new file mode 100644
index 0000000..a6087e1
Binary files /dev/null and b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.pdf differ
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed1 b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed1
new file mode 100644
index 0000000..c49e8c1
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed1
@@ -0,0 +1,33 @@
+/INCLUDE umfpack_col_to_triplet.h/r ../Include/umfpack_col_to_triplet.h
+/INCLUDE umfpack_defaults.h/r ../Include/umfpack_defaults.h
+/INCLUDE umfpack_free_numeric.h/r ../Include/umfpack_free_numeric.h
+/INCLUDE umfpack_free_symbolic.h/r ../Include/umfpack_free_symbolic.h
+/INCLUDE umfpack_get_lunz.h/r ../Include/umfpack_get_lunz.h
+/INCLUDE umfpack_get_numeric.h/r ../Include/umfpack_get_numeric.h
+/INCLUDE umfpack_get_symbolic.h/r ../Include/umfpack_get_symbolic.h
+/INCLUDE umfpack_get_scale.h/r ../Include/umfpack_get_scale.h
+/INCLUDE umfpack_numeric.h/r ../Include/umfpack_numeric.h
+/INCLUDE umfpack_qsymbolic.h/r ../Include/umfpack_qsymbolic.h
+/INCLUDE umfpack_report_control.h/r ../Include/umfpack_report_control.h
+/INCLUDE umfpack_report_info.h/r ../Include/umfpack_report_info.h
+/INCLUDE umfpack_report_matrix.h/r ../Include/umfpack_report_matrix.h
+/INCLUDE umfpack_report_numeric.h/r ../Include/umfpack_report_numeric.h
+/INCLUDE umfpack_report_perm.h/r ../Include/umfpack_report_perm.h
+/INCLUDE umfpack_report_status.h/r ../Include/umfpack_report_status.h
+/INCLUDE umfpack_report_symbolic.h/r ../Include/umfpack_report_symbolic.h
+/INCLUDE umfpack_report_triplet.h/r ../Include/umfpack_report_triplet.h
+/INCLUDE umfpack_report_vector.h/r ../Include/umfpack_report_vector.h
+/INCLUDE umfpack_simple.c/r ../Demo/umfpack_simple.c
+/INCLUDE umfpack_solve.h/r ../Include/umfpack_solve.h
+/INCLUDE umfpack_scale.h/r ../Include/umfpack_scale.h
+/INCLUDE umfpack_symbolic.h/r ../Include/umfpack_symbolic.h
+/INCLUDE umfpack_timer.h/r ../Include/umfpack_timer.h
+/INCLUDE umfpack_tictoc.h/r ../Include/umfpack_tictoc.h
+/INCLUDE umfpack_transpose.h/r ../Include/umfpack_transpose.h
+/INCLUDE umfpack_triplet_to_col.h/r ../Include/umfpack_triplet_to_col.h
+/INCLUDE umfpack_wsolve.h/r ../Include/umfpack_wsolve.h
+/INCLUDE umfpack_load_numeric.h/r ../Include/umfpack_load_numeric.h
+/INCLUDE umfpack_load_symbolic.h/r ../Include/umfpack_load_symbolic.h
+/INCLUDE umfpack_save_numeric.h/r ../Include/umfpack_save_numeric.h
+/INCLUDE umfpack_save_symbolic.h/r ../Include/umfpack_save_symbolic.h
+/INCLUDE umfpack_get_determinant.h/r ../Include/umfpack_get_determinant.h
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed2 b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed2
new file mode 100644
index 0000000..0df47d9
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.sed2
@@ -0,0 +1,3 @@
+/[/][*]/d
+/[*][/]/d
+/INCLUDE umfpack/d
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.stex b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.stex
new file mode 100644
index 0000000..601857d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/UserGuide.stex
@@ -0,0 +1,2695 @@
+%-------------------------------------------------------------------------------
+% The UserGuide.stex file. Processed into UserGuide.tex via sed.
+%-------------------------------------------------------------------------------
+
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+\newcommand{\he}{^{\sf H}} % complex conjugate transpose
+\newcommand{\implies}{\rightarrow}
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+\begin{document}
+
+\author{Timothy A. Davis \\
+Dept. of Computer and Information Science and Engineering \\
+Univ. of Florida, Gainesville, FL}
+\title{UMFPACK Version 5.0 User Guide}
+\date{May 5, 2006}
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+ UMFPACK is a set of routines for solving unsymmetric sparse linear
+ systems, $\m{Ax}=\m{b}$, using the Unsymmetric MultiFrontal method
+ and direct sparse LU factorization. It is written in ANSI/ISO C, with a
+ MATLAB interface. UMFPACK relies on the Level-3 Basic
+ Linear Algebra Subprograms (dense matrix multiply) for its performance.
+ This code works on Windows and many versions of Unix (Sun Solaris,
+ Red Hat Linux, IBM AIX, SGI IRIX, and Compaq Alpha).
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+Technical Report TR-04-003 (revised)
+
+UMFPACK Version 5.0, Copyright\copyright 1995-2006 by Timothy A. Davis.
+All Rights Reserved.
+UMFPACK is available under alternate licences; contact T. Davis for details.
+
+{\bf UMFPACK License:}
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+{\bf Availability:}
+ http://www.cise.ufl.edu/research/sparse/umfpack
+
+{\bf Acknowledgments:}
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+ The upgrade to Version 4.1 and the inclusion of the
+ symmetric and 2-by-2 pivoting strategies
+ were done while the author was on sabbatical at
+ Stanford University and Lawrence Berkeley National Laboratory.
+
+%-------------------------------------------------------------------------------
+\newpage
+%-------------------------------------------------------------------------------
+
+\tableofcontents
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Overview}
+%-------------------------------------------------------------------------------
+
+UMFPACK\footnote{Pronounced with two syllables: umph-pack}
+Version 5.0 is a set of routines for solving systems of linear
+equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and unsymmetric. It is based
+on the Unsymmetric-pattern MultiFrontal method \cite{DavisDuff97,DavisDuff99}.
+UMFPACK factorizes
+$\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$,
+where $\m{L}$ and $\m{U}$
+are lower and upper triangular, respectively, $\m{P}$ and $\m{Q}$ are
+permutation matrices, and $\m{R}$ is a diagonal matrix of row scaling factors
+(or $\m{R}=\m{I}$ if row-scaling is not used). Both $\m{P}$ and $\m{Q}$ are
+chosen to reduce fill-in (new nonzeros in $\m{L}$ and $\m{U}$ that are not
+present in $\m{A}$). The permutation $\m{P}$ has the dual role of reducing
+fill-in and maintaining numerical accuracy (via relaxed partial pivoting
+and row interchanges).
+
+The sparse matrix $\m{A}$ can be square or rectangular, singular
+or non-singular, and real or complex (or any combination). Only square
+matrices $\m{A}$ can be used to solve $\m{Ax}=\m{b}$ or related systems.
+Rectangular matrices can only be factorized.
+
+UMFPACK first finds a column pre-ordering that reduces fill-in, without regard
+to numerical values. It scales and analyzes the matrix, and then automatically
+selects one of three strategies for pre-ordering the rows and columns:
+{\em unsymmetric},
+{\em 2-by-2}, and
+{\em symmetric}. These strategies are described below.
+
+First, all pivots with zero Markowitz cost are eliminated and placed in the
+LU factors. The remaining submatrix $\m{S}$ is then analyzed.
+The following rules are applied, and the first one that matches defines
+the strategy.
+
+\begin{itemize}
+\item Rule 1: $\m{A}$ rectangular $\implies$ unsymmetric.
+\item Rule 2:
+ If the zero-Markowitz elimination results in a rectangular $\m{S}$,
+ or an $\m{S}$ whose diagonal has not been preserved, the
+ unsymmetric strategy is used.
+\item The symmetry $\sigma_1$ of $\m{S}$ is computed. It is defined as
+ the number of {\em matched} off-diagonal entries, divided by the
+ total number of off-diagonal entries. An entry $s_{ij}$ is matched
+ if $s_{ji}$ is also an entry. They need not be numerically equal.
+ An {\em entry} is a value in $\m{A}$ which is present
+ in the input data structure. All nonzeros are entries, but some entries
+ may be numerically zero.
+ Rule 3: $\sigma_1 < 0.1 \implies$ unsymmetric.
+ The matrix is very unsymmetric.
+\item Let $d$ be the number of nonzero entries on the diagonal of $\m{S}$.
+ Let $\m{S}$ be $\nu$-by-$\nu$.
+ Rule 4: $(\sigma_1 \ge 0.7) \:\wedge\: (d = \nu) \implies$ symmetric.
+ The matrix has a nearly symmetric nonzero pattern, and a zero-free
+ diagonal.
+\end{itemize}
+
+If the strategy has not yet been determined,
+the 2-by-2 strategy is attempted. A row permutation $\m{P}_2$
+is found which attempts to reduce the number of small
+diagonal entries of $\m{P}_2 \m{S}$.
+An entry $s_{ij}$ is determined to be small if
+$|s_{ij}| < 0.01 \max |s_{*j}|$, or large otherwise.
+If $s_{ii}$ is numerically small, the method attempts to swap
+two rows $i$ and $j$, such that both $s_{ij}$ and $s_{ji}$ are large.
+Once these rows are swapped,
+they remain in place. Let $\sigma_2$ be the symmetry of $\m{P}_2 \m{S}$,
+and let $d_2$ be the number of nonzero entries (either small or large)
+on the diagonal of $\m{P}_2 \m{S}$.
+
+\begin{itemize}
+\item Rule 5:
+ ($\sigma_2 > 1.1 \sigma_1) \:\wedge\: (d_2 > 0.9 \nu) \implies$ 2-by-2.
+ The 2-by-2 permutation has made the matrix significantly more symmetric.
+\item Rule 6: $\sigma_2 < 0.7 \sigma_1 \implies$ unsymmetric.
+ The 2-by-2 strategy has significantly deteriorated the symmetry,
+\item Rule 7: $\sigma_2 < 0.25 \implies$ unsymmetric.
+ The matrix is still very unsymmetric.
+\item Rule 8: $\sigma_2 \ge 0.51 \implies$ 2-by-2.
+ The matrix is roughly symmetric.
+\item Rule 9: $\sigma_2 \ge 0.999 \sigma_1 \implies$ 2-by-2.
+ The 2-by-2 permutation has preserved symmetry, or made it only
+ slightly worse.
+\item Rule 10: if no rule has yet triggered, use the unsymmetric strategy.
+\end{itemize}
+
+Each strategy is described below:
+\begin{itemize}
+\item {\em unsymmetric}:
+The column pre-ordering of $\m{S}$ is computed by a modified version of COLAMD
+\cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00,Larimore98}.
+The method finds a symmetric permutation $\m{Q}$ of the matrix $\m{S}\tr\m{S}$
+(without forming $\m{S}\tr\m{S}$ explicitly). This is a good choice for
+$\m{Q}$, since the Cholesky factors of $\m{(SQ)\tr(SQ)}$ are an upper bound (in
+terms of nonzero pattern) of the factor $\m{U}$ for the unsymmetric LU
+factorization ($\m{PSQ}=\m{LU}$) regardless of the choice of $\m{P}$
+\cite{GeorgeNg85,GeorgeNg87,GilbertNg93}. This modified version of
+COLAMD also computes the column elimination tree and post-orders the
+tree. It finds the upper bound on the number of nonzeros in L and U.
+It also has a different threshold for determining dense rows and columns.
+During factorization, the column pre-ordering can be modified.
+Columns within a single super-column can be reshuffled, to reduce fill-in.
+Threshold partial pivoting is used with no preference given to the diagonal
+entry. Within a given pivot column $j$, an entry $a_{ij}$ can be chosen if
+$|a_{ij}| \ge 0.1 \max |a_{*j}|$. Among those numerically acceptable
+entries, the sparsest row $i$ is chosen as the pivot row.
+
+\item {\em 2-by-2}:
+The symmetric strategy (see below) is applied to the matrix $\m{P}_2 \m{S}$,
+rather than $\m{S}$.
+
+\item {\em symmetric}:
+The column ordering is computed from AMD
+\cite{AmestoyDavisDuff96,AmestoyDavisDuff03},
+applied to the pattern of $\m{S}+\m{S}\tr$
+followed by a post-ordering of the supernodal elimination
+tree of $\m{S}+\m{S}\tr$.
+No modification of the column pre-ordering is made during numerical
+factorization. Threshold partial pivoting is used, with a strong
+preference given to the diagonal entry. The diagonal entry is chosen if
+$a_{jj} \ge 0.001 \max |a_{*j}|$. Otherwise, a sparse row is selected,
+using the same method used by the unsymmetric strategy.
+
+\end{itemize}
+
+The symmetric and 2-by-2 strategies, and their automatic selection,
+are new to Version 4.1. Version 4.0 only used the unsymmetric strategy.
+
+Once the strategy is selected,
+the factorization of the matrix $\m{A}$ is broken down into the factorization
+of a sequence of dense rectangular frontal matrices. The frontal matrices are
+related to each other by a supernodal column elimination tree, in which each
+node in the tree represents one frontal matrix. This analysis phase also
+determines upper bounds on the memory usage, the floating-point operation count,
+and the number of nonzeros in the LU factors.
+
+UMFPACK factorizes each {\em chain} of frontal matrices in a single working
+array, similar to how the unifrontal method \cite{dusc:96} factorizes the whole
+matrix. A chain of frontal matrices is a sequence of fronts where the parent
+of front $i$ is $i$+1 in the supernodal column elimination tree. For the
+nonsingular matrices factorized with the unsymmetric strategy, there are
+exactly the same number of chains as there are leaves in the supernodal
+column elimination tree. UMFPACK is an
+outer-product based, right-looking method. At the $k$-th step of Gaussian
+elimination, it represents the updated submatrix $\m{A}_k$ as an implicit
+summation of a set of dense sub-matrices (referred to as {\em elements},
+borrowing a phrase from finite-element methods) that arise when the frontal
+matrices are factorized and their pivot rows and columns eliminated.
+
+Each frontal matrix represents the elimination of one or more columns;
+each column of $\m{A}$ will be eliminated in a specific frontal matrix,
+and which frontal matrix will be used for which column is determined by
+the pre-analysis phase. The pre-analysis phase also determines the worst-case
+size of each frontal matrix so that they can hold any candidate pivot column
+and any candidate pivot row. From the perspective of the analysis phase, any
+candidate pivot column in the frontal matrix is identical (in terms of nonzero
+pattern), and so is any row. However, the numeric factorization phase has
+more information than the analysis phase. It uses this information to reorder
+the columns within each frontal matrix to reduce fill-in. Similarly, since
+the number of nonzeros in each row and column are maintained (more precisely,
+COLMMD-style approximate degrees \cite{GilbertMolerSchreiber}), a pivot row can
+be selected based on sparsity-preserving criteria (low degree) as well as
+numerical considerations (relaxed threshold partial pivoting).
+
+When the symmetric or 2-by-2 strategies are used,
+the column preordering is not refined during numeric factorization.
+Row pivoting for sparsity and numerical accuracy is performed if the
+diagonal entry is too small.
+
+More details of the method, including experimental results, are
+described in \cite{Davis03,Davis03_algo}, available at
+http://www.cise.ufl.edu/tech-reports.
+
+%-------------------------------------------------------------------------------
+\section{Availability}
+%-------------------------------------------------------------------------------
+
+In addition to appearing as a Collected Algorithm of the ACM,
+UMFPACK is available at http://www.cise.ufl.edu/research/sparse.
+It is included as a built-in routine in MATLAB.
+Version 4.0 (in MATLAB 6.5)
+does not have the symmetric or 2-by-2 strategies and it takes
+less advantage of the level-3
+BLAS \cite{DaydeDuff99,ACM679a,ATLAS,GotoVandeGeijn02}.
+Versions 5.0 through v4.1 tend to be much faster than Version 4.0,
+particularly on unsymmetric matrices with mostly symmetric
+nonzero pattern (such as finite element and circuit simulation matrices).
+Version 3.0 and following make
+use of a modified version of COLAMD V2.0 by Timothy A.~Davis, Stefan
+Larimore, John Gilbert, and Esmond Ng. The original COLAMD V2.1 is available in
+as a built-in routine in MATLAB V6.0 (or later), and at
+http://www.cise.ufl.edu/research/sparse.
+These codes are also available in Netlib \cite{netlib} at
+http://www.netlib.org.
+UMFPACK Versions 2.2.1 and earlier, co-authored with Iain Duff,
+are available at http://www.cise.ufl.edu/research/sparse and as
+MA38 (functionally equivalent to Version 2.2.1) in the Harwell
+Subroutine Library.
+
+%-------------------------------------------------------------------------------
+\section{Primary changes from prior versions}
+%-------------------------------------------------------------------------------
+
+A detailed list of changes is in the {\tt ChangeLog} file.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 5.0.3}
+%-------------------------------------------------------------------------------
+
+Renamed the MATLAB function to {\tt umfpack2}, so as not to confict with
+itself (the MATLAB built-in version of UMFPACK).
+
+%-------------------------------------------------------------------------------
+\subsection{Version 5.0}
+%-------------------------------------------------------------------------------
+
+Changed {\tt long} to {\tt UF\_long}, controlled by the {\tt UFconfig.h}
+file. A {\tt UF\_long} is normally just {\tt long}, except on the Windows 64
+(WIN64) platform. In that case, it becomes {\tt \_\_int64}.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.6}
+%-------------------------------------------------------------------------------
+
+Added additional options to {\tt umf\_solve.c}.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.5}
+%-------------------------------------------------------------------------------
+
+Added function pointers for malloc, calloc, realloc, free, printf, hypot,
+and complex divisiion, so that these functions can be redefined at run-time.
+Added a version number so you can determine the
+version of UMFPACK at run time or compile time. UMFPACK requires AMD v2.0
+or later.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.4}
+%-------------------------------------------------------------------------------
+
+Bug fix in strategy selection in {\tt umfpack\_*\_qsymbolic}.
+Added packed complex case for all complex input/output arguments.
+Added {\tt umfpack\_get\_determinant}.
+Added minimal support for Microsoft Visual Studio
+(the {\tt umf\_multicompile.c} file).
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.3.1}
+%-------------------------------------------------------------------------------
+
+Minor bug fix in the forward/backsolve. This bug had the effect of turning
+off iterative refinement when solving $\m{A}\tr\m{x}=\m{b}$ after factorizing
+$\m{A}$. UMFPACK mexFunction now factorizes $\m{A}\tr$ in its forward-slash
+operation.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.3}
+%-------------------------------------------------------------------------------
+
+No changes are visible to the C or MATLAB user, except the presence of
+one new control parameter in the {\tt Control} array,
+and three new statistics in the {\tt Info} array.
+The primary change is the addition of an (optional) drop tolerance.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.1}
+%-------------------------------------------------------------------------------
+
+The following is a summary of the main changes that are visible to the C
+or MATLAB user:
+
+\begin{enumerate}
+
+\item New ordering strategies added. No changes are required in user code
+ (either C or MATLAB) to use the new default strategy, which is an automatic
+ selection of the unsymmetric, symmetric, or 2-by-2 strategies.
+
+\item Row scaling added. This is only visible to the MATLAB caller when using
+ the form {\tt [L,U,P,Q,R] = umfpack (A)}, to retrieve the LU factors.
+ Likewise, it is only visible to the C caller when the LU factors are
+ retrieved, or when solving systems with just $\m{L}$ or $\m{U}$.
+ New C-callable and MATLAB-callable routines are included to get and to
+ apply the scale factors computed by UMFPACK. Row scaling is enabled by
+ default, but can be disabled. Row scaling usually leads to a better
+ factorization, particularly when the symmetric strategy is used.
+
+\item Error code {\tt UMFPACK\_ERROR\_problem\_to\_large} removed.
+ Version 4.0 would generate this error when the upper bound memory usage
+ exceeded 2GB (for the {\tt int} version), even when the actual memory
+ usage was less than this. The new version properly handles this case,
+ and can successfully factorize the matrix if sufficient memory is
+ available.
+
+\item New control parameters and statistics provided.
+
+\item The AMD symmetric approximate minimum degree ordering routine added
+ \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}.
+ It is used by UMFPACK, and can also be called independently from C or
+ MATLAB.
+
+\item The {\tt umfpack} mexFunction now returns permutation matrices, not
+ permutation vectors, when using the form {\tt [L,U,P,Q] = umfpack (A)}
+ or the new form {\tt [L,U,P,Q,R] = umfpack (A)}.
+
+\item New arguments added to the user-callable routines
+ {\tt umfpack\_*\_symbolic},
+ {\tt umfpack\_*\_qsymbolic},
+ {\tt umfpack\_*\_get\_numeric}, and
+ {\tt umfpack\_*\_get\_symbolic}.
+ The symbolic analysis now makes use of the numerical values of the matrix
+ $\m{A}$, to guide the 2-by-2 strategy. The subsequent matrix passed to
+ the numeric factorization step does not have to have the same numerical
+ values. All of the new arguments are optional. If you do not wish to
+ include them, simply pass {\tt NULL} pointers instead. The 2-by-2 strategy
+ will assume all entries are numerically large, for example.
+
+\item New routines added to save and load the {\tt Numeric} and {\tt Symbolic}
+ objects to and from a binary file.
+
+\item A Fortran interface added. It provides access to a subset of
+ UMFPACK's features.
+
+\item You can compute an incomplete LU factorization, by dropping small
+ entries from $\m{L}$ and $\m{U}$. By default, no nonzero entry is
+ dropped, no matter how small in absolute value. This feature is new
+ to Version 4.3.
+
+\end{enumerate}
+
+%-------------------------------------------------------------------------------
+\section{Using UMFPACK in MATLAB}
+%-------------------------------------------------------------------------------
+
+The easiest way to use UMFPACK is within MATLAB. Version 4.3 is a built-in
+routine in MATLAB 7.0.4, and is used in {\tt x = A}$\backslash${\tt b} when
+{\tt A} is sparse, square, unsymmetric (or symmetric but not positive definite),
+and with nonzero entries that are not confined in a narrow band.
+It is also used for the {\tt [L,U,P,Q] = lu (A)} usage of {\tt lu}.
+Type {\tt help lu} in MATLAB 6.5 or later for more details.
+
+To use the UMFPACK mexFunction, you must download and compile it,
+since the mexFunction itself is not part of MATLAB.
+The following discussion assumes that
+you have MATLAB Version 6.0 or later (which includes the BLAS, and the
+{\tt colamd} ordering routine). To compile both the UMFPACK and AMD
+mexFunctions, just type {\tt make} in the Unix system shell,
+while in the {\tt UMFPACK} directory.
+You can also type {\tt umfpack\_make} in MATLAB, if you are in the
+{\tt UMFPACK/MATLAB} directory, or if that directory is in your MATLAB path.
+This works on any system with MATLAB, including Windows.
+See Section~\ref{Install} for more details on how to install UMFPACK.
+Once installed, the UMFPACK mexFunction can analyze, factor, and solve linear
+systems. Table~\ref{matlab} summarizes some of the more common uses
+of the UMFPACK mexFunction within MATLAB.
+
+An optional input argument can be used to modify the control parameters for
+UMFPACK, and an optional output argument provides statistics on the
+factorization.
+
+Refer to the AMD User Guide for more details about the AMD mexFunction.
+
+\begin{table}
+\caption{Using UMFPACK's MATLAB interface}
+\label{matlab}
+\vspace{0.1in}
+{\footnotesize
+\begin{tabular}{l|l|l}
+\hline
+Function & Using UMFPACK & MATLAB 6.0 equivalent \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Solve $\m{Ax}=\m{b}$.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = umfpack (A,'\',b) ;
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = A \ b ;
+\end{verbatim}
+\end{minipage}
+ \\
+ & & \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Solve $\m{Ax}=\m{b}$ using a different row and column pre-ordering
+(symmetric ordering).
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+S = spones (A) ;
+Q = symamd (S+S') ;
+Control = umfpack ;
+Control (6) = 3 ;
+x = umfpack (A,Q,'\',b,Control) ;
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+spparms ('autommd',0) ;
+S = spones (A) ;
+Q = symamd (S+S') ;
+x = A (Q,Q) \ b (Q) ;
+x (Q) = x ;
+spparms ('autommd',1) ;
+\end{verbatim}
+\end{minipage}
+ \\
+ & & \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Solve $\m{A}\tr\m{x}\tr = \m{b}\tr$.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = umfpack (b,'/',A) ;
+\end{verbatim}
+Note: $\m{A}$ is factorized.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = b / A ;
+\end{verbatim}
+Note: $\m{A}\tr$ is factorized.
+\end{minipage}
+ \\
+ & & \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Scale and factorize $\m{A}$, then solve $\m{Ax}=\m{b}$.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+[L,U,P,Q,R] = umfpack (A) ;
+c = P * (R \ b) ;
+x = Q * (U \ (L \ c)) ;
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+[m n] = size (A) ;
+r = full (sum (abs (A), 2)) ;
+r (find (r == 0)) = 1 ;
+R = spdiags (r, 0, m, m) ;
+I = speye (n) ;
+Q = I (:, colamd (A)) ;
+[L,U,P] = lu ((R\A)*Q) ;
+c = P * (R \ b) ;
+x = Q * (U \ (L \ c)) ;
+\end{verbatim}
+\end{minipage}
+ \\
+ & & \\
+\hline
+\end{tabular}
+}
+\end{table}
+
+Note: in MATLAB 6.5 or later, use {\tt spparms ('autoamd',0)} in addition to
+{\tt spparms ('autommd',0)}, in Table~\ref{matlab}, to turn off MATLAB's
+default reordering.
+
+UMFPACK requires
+{\tt b} to be a dense vector (real or complex) of the appropriate dimension.
+This is more restrictive than what you can do with MATLAB's
+backslash or forward slash. See {\tt umfpack\_solve} for an M-file that
+removes this restriction.
+This restriction does not apply to the built-in backslash operator
+in MATLAB 6.5 or later, which uses UMFPACK to factorize the matrix.
+You can do this yourself in MATLAB:
+
+{\footnotesize
+\begin{verbatim}
+ [L,U,P,Q,R] = umfpack (A) ;
+ x = Q * (U \ (L \ (P * (R \ b)))) ;
+\end{verbatim}
+}
+
+or, with no row scaling:
+
+{\footnotesize
+\begin{verbatim}
+ [L,U,P,Q] = umfpack (A) ;
+ x = Q * (U \ (L \ (P * b))) ;
+\end{verbatim}
+}
+
+The above examples do not make use of the iterative refinement
+that is built into
+{\tt x = }{\tt umfpack (A,'}$\backslash${\tt ',b)}
+however.
+
+MATLAB's {\tt [L,U,P] = lu(A)} returns a lower triangular {\tt L}, an upper
+triangular {\tt U}, and a permutation matrix {\tt P} such that {\tt P*A} is
+equal to {\tt L*U}. UMFPACK behaves differently. By default, it scales
+the rows of {\tt A} and reorders the columns of {\tt A} prior to
+factorization, so that {\tt L*U} is equal to {\tt P*(R}$\backslash${\tt A)*Q},
+where {\tt R} is a diagonal sparse matrix of scale factors for the rows
+of {\tt A}. The scale factors {\tt R} are applied to {\tt A} via the MATLAB
+expression {\tt R}$\backslash${\tt A} to avoid multiplying by
+the reciprocal, which can be numerically inaccurate.
+
+There are more options; you can provide your own column pre-ordering (in which
+case UMFPACK does not call COLAMD or AMD), you can modify other control settings
+(similar to the {\tt spparms} in MATLAB), and you can get various statistics on
+the analysis, factorization, and solution of the linear system. Type
+{\tt umfpack\_details} and {\tt umfpack\_report} in MATLAB for more
+information. Two demo M-files are provided. Just type {\tt umfpack\_simple}
+and {\tt umfpack\_demo} to run them.
+The output of these two programs should be about the same
+as the files {\tt umfpack\_simple.m.out} and {\tt umfpack\_demo.m.out}
+that are provided.
+
+Factorizing {\tt A'} (or {\tt A.'}) and using the transposed factors can
+sometimes be faster than factorizing {\tt A}. It can also be preferable to
+factorize {\tt A'} if {\tt A} is rectangular. UMFPACK pre-orders the columns
+to maintain sparsity; the row ordering is not determined until the matrix
+is factorized. Thus, if {\tt A} is {\tt m} by {\tt n} with rank {\tt m}
+and {\tt m} $<$ {\tt n}, then {\tt umfpack} might not find a factor
+{\tt U} with a zero-free diagonal. Unless the matrix ill-conditioned or
+poorly scaled, factorizing {\tt A'} in this case will guarantee that both
+factors will have zero-free diagonals. Here's how you can factorize {\tt A'}
+and get the factors of {\tt A} instead:
+
+\begin{verbatim}
+ [l,u,p,q] = umfpack (A') ;
+ L = u' ;
+ U = l' ;
+ P = q ;
+ Q = p ;
+ clear l u p q
+\end{verbatim}
+
+This is an alternative to {\tt [L,U,P,Q]=umfpack(A)}.
+
+A simple M-file ({\tt umfpack\_btf}) is provided that first permutes the matrix
+to upper block triangular form, using MATLAB's {\tt dmperm} routine, and then
+solves each block. The LU factors are not returned. Its usage is simple:
+{\tt x = umfpack\_btf(A,b)}. Type {\tt help umfpack\_btf} for more options.
+An estimate of the 1-norm of {\tt L*U-P*A*Q} can be computed in MATLAB
+as {\tt lu\_normest(P*A*Q,L,U)}, using the {\tt lu\_normest.m} M-file
+by Hager and Davis \cite{DavisHager99} that is included with the
+UMFPACK distribution. With row scaling enabled, use
+{\tt lu\_normest(P*(R}$\backslash${\tt A)*Q,L,U)} instead.
+
+One issue you may encounter is how UMFPACK allocates its memory when being used
+in a mexFunction. One part of its working space is of variable size. The
+symbolic analysis phase determines an upper bound on the size of this memory,
+but not all of this memory will typically be used in the numerical
+factorization. UMFPACK tries to allocate a decent amount of working space.
+This is 70\% of the upper bound, by default, for the unsymmetric strategy.
+For the symmetric strategy, the fraction of the upper bound is computed
+automatically (assuming a best-case scenario with no numerical pivoting
+required during numeric factorization).
+If this initial allocation fails, it reduces its request
+and uses less memory. If the space is not large enough during factorization,
+it is increased via {\tt mxRealloc}.
+
+However, {\tt mxMalloc} and {\tt mxRealloc} abort the {\tt umfpack} mexFunction
+if they fail, so this strategy does not work in MATLAB.
+
+To compute the determinant with UMFPACK:
+
+\begin{verbatim}
+ d = umfpack (A, 'det') ;
+ [d e] = umfpack (A, 'det') ;
+\end{verbatim}
+
+The first case is identical to MATLAB's {\tt det}.
+The second case returns the determinant in the form
+$d \times 10^e$, which avoids overflow if $e$ is large.
+
+%-------------------------------------------------------------------------------
+\section{Using UMFPACK in a C program}
+\label{C}
+%-------------------------------------------------------------------------------
+
+The C-callable UMFPACK library consists of 32 user-callable routines and one
+include file. All but three of the routines come in four versions, with
+different sizes of integers and for real or complex floating-point numbers:
+\begin{enumerate}
+\item {\tt umfpack\_di\_*}: real double precision, {\tt int} integers.
+\item {\tt umfpack\_dl\_*}: real double precision, {\tt UF\_long} integers.
+\item {\tt umfpack\_zi\_*}: complex double precision, {\tt int} integers.
+\item {\tt umfpack\_zl\_*}: complex double precision, {\tt UF\_long} integers.
+\end{enumerate}
+where {\tt *} denotes the specific name of one of the routines.
+Routine names beginning with {\tt umf\_} are internal to the package,
+and should not be called by the user. The include file {\tt umfpack.h}
+must be included in any C program that uses UMFPACK.
+The other three routines are the same for all four versions.
+
+In addition, the C-callable AMD library distributed with UMFPACK
+includes 4 user-callable routines (in two versions with {\tt int} and
+{\tt UF\_long} integers) and one include file. Refer to the AMD documentation
+for more details.
+
+Use only one version for any one problem; do not attempt to use one version
+to analyze the matrix and another version to factorize the matrix, for example.
+
+The notation {\tt umfpack\_di\_*} refers to all user-callable routines
+for the real double precision and {\tt int} integer case. The notation
+{\tt umfpack\_*\_numeric}, for example, refers all four versions
+(real/complex, int/UF\_long) of a single operation
+(in this case numeric factorization).
+
+%-------------------------------------------------------------------------------
+\subsection{The size of an integer}
+%-------------------------------------------------------------------------------
+
+The {\tt umfpack\_di\_*} and {\tt umfpack\_zi\_*} routines use {\tt int} integer
+arguments; those starting with {\tt umfpack\_dl\_} or {\tt umfpack\_zl\_}
+use {\tt UF\_long} integer arguments. If you compile UMFPACK in the standard
+ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions
+are essentially identical. You will be able to solve problems using up to 2GB
+of memory. If you compile UMFPACK in the standard LP64 mode, the size of an
+{\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get
+promoted to 64-bits. In the LP64 mode, the {\tt umfpack\_dl\_*}
+and {\tt umfpack\_zl\_*} routines can solve huge
+problems (not limited to 2GB), limited of course by the amount of available
+memory. The only drawback to the 64-bit mode is that not all BLAS libraries
+support 64-bit integers. This limits the performance you will obtain.
+Those that do support 64-bit integers are specific to particular
+architectures, and are not portable. UMFPACK and AMD should be compiled
+in the same mode.
+If you compile UMFPACK and AMD in the LP64 mode,
+be sure to add {\tt -DLP64} to the compilation command. See the examples in
+the {\tt UFconfig/UFconfig.mk} file.
+
+%-------------------------------------------------------------------------------
+\subsection{Real and complex floating-point}
+%-------------------------------------------------------------------------------
+
+The {\tt umfpack\_di\_*} and {\tt umfpack\_dl\_*} routines take (real) double
+precision arguments, and return double precision arguments. In the
+{\tt umfpack\_zi\_*} and {\tt umfpack\_zl\_*} routines, these same arguments
+hold the real part of the matrices; and second double precision arrays hold
+the imaginary part of the input and output matrices. Internally, complex
+numbers are stored in arrays with their real and imaginary parts interleaved,
+as required by the BLAS (``packed'' complex form).
+
+New to Version 4.4 is the option of providing input/output arguments
+in packed complex form.
+
+%-------------------------------------------------------------------------------
+\subsection{Primary routines, and a simple example}
+%-------------------------------------------------------------------------------
+
+Five primary UMFPACK routines are required to factorize $\m{A}$ or
+solve $\m{Ax}=\m{b}$. They are fully described in Section~\ref{Primary}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_symbolic}:
+
+ Pre-orders the columns of $\m{A}$ to reduce fill-in.
+ Returns an opaque {\tt Symbolic} object as a {\tt void *}
+ pointer. The object contains the symbolic analysis and is needed for the
+ numeric factorization. This routine requires only $O(|\m{A}|)$ space,
+ where $|\m{A}|$ is the number of nonzero entries in the matrix. It computes
+ upper bounds on the nonzeros in $\m{L}$ and $\m{U}$, the floating-point
+ operations required, and the memory usage of {\tt umfpack\_*\_numeric}. The
+ {\tt Symbolic} object is small; it contains just the column pre-ordering,
+ the supernodal column elimination tree, and information about each frontal
+ matrix. It is no larger than about $13n$ integers if $\m{A}$ is
+ $n$-by-$n$.
+
+\item {\tt umfpack\_*\_numeric}:
+
+ Numerically scales and then factorizes a sparse matrix into
+ $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$,
+ where
+ $\m{P}$ and $\m{Q}$ are permutation matrices, $\m{R}$ is a diagonal
+ matrix of scale factors, $\m{L}$ is lower triangular with unit diagonal,
+ and $\m{U}$ is upper triangular. Requires the
+ symbolic ordering and analysis computed by {\tt umfpack\_*\_symbolic}
+ or {\tt umfpack\_*\_qsymbolic}.
+ Returns an opaque {\tt Numeric} object as a
+ {\tt void *} pointer. The object contains the numerical factorization and
+ is used by {\tt umfpack\_*\_solve}. You can factorize a new matrix with a
+ different values (but identical pattern) as the matrix analyzed by
+ {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic} by re-using the
+ {\tt Symbolic} object (this feature is available when using UMFPACK in a
+ C or Fortran program, but not in MATLAB).
+ The matrix
+ $\m{U}$ will have zeros on the diagonal if $\m{A}$ is singular; this
+ produces a warning, but the factorization is still valid.
+
+\item {\tt umfpack\_*\_solve}:
+
+ Solves a sparse linear system ($\m{Ax}=\m{b}$, $\m{A}\tr\m{x}=\m{b}$, or
+ systems involving just $\m{L}$ or $\m{U}$), using the numeric factorization
+ computed by {\tt umfpack\_*\_numeric}. Iterative refinement with sparse
+ backward error \cite{ardd:89} is used by default. The matrix $\m{A}$ must
+ be square. If it is singular, then a divide-by-zero will occur, and your
+ solution with contain IEEE Inf's or NaN's in the appropriate places.
+
+\item {\tt umfpack\_*\_free\_symbolic}:
+
+ Frees the {\tt Symbolic} object created by {\tt umfpack\_*\_symbolic}
+ or {\tt umfpack\_*\_qsymbolic}.
+
+\item {\tt umfpack\_*\_free\_numeric}:
+
+ Frees the {\tt Numeric} object created by {\tt umfpack\_*\_numeric}.
+
+\end{itemize}
+
+Be careful not to free a {\tt Symbolic} object with
+{\tt umfpack\_*\_free\_numeric}. Nor should you attempt to free a {\tt Numeric}
+object with {\tt umfpack\_*\_free\_symbolic}.
+Failure to free these objects will lead to memory leaks.
+
+The matrix $\m{A}$ is represented in compressed column form, which is
+identical to the sparse matrix representation used by MATLAB. It consists
+of three or four arrays, where the matrix is {\tt m}-by-{\tt n},
+with {\tt nz} entries. For the {\tt int} version of UMFPACK:
+
+{\footnotesize
+\begin{verbatim}
+ int Ap [n+1] ;
+ int Ai [nz] ;
+ double Ax [nz] ;
+\end{verbatim}
+}
+
+For the {\tt UF\_long} version of UMFPACK:
+
+{\footnotesize
+\begin{verbatim}
+ UF_long Ap [n+1] ;
+ UF_long Ai [nz] ;
+ double Ax [nz] ;
+\end{verbatim}
+}
+
+The complex versions add another array for the imaginary part:
+
+{\footnotesize
+\begin{verbatim}
+ double Az [nz] ;
+\end{verbatim}
+}
+
+Alternatively, if {\tt Az} is {\tt NULL},
+the real part of the $k$th entry is located in
+{\tt Ax[2*k]} and the imaginary part is located in
+{\tt Ax[2*k+1]}, and the {\tt Ax} array is of size {\tt 2*nz}.
+
+All nonzeros are entries, but an entry may be numerically zero. The row indices
+of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} \ldots {\tt Ap[j+1]-1]}.
+The corresponding numerical values are stored in
+ {\tt Ax[Ap[j]} \ldots {\tt Ap[j+1]-1]}.
+The imaginary part, for the complex versions, is stored in
+ {\tt Az[Ap[j]} \ldots {\tt Ap[j+1]-1]}
+ (see above for the packed complex case).
+
+No duplicate row indices may be present, and the row indices in any given
+column must be sorted in ascending order. The first entry {\tt Ap[0]} must be
+zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+Except for the fact that extra zero entries can be included, there is thus a
+unique compressed column representation of any given matrix $\m{A}$.
+For a more flexible method for providing an input matrix to UMFPACK,
+see Section~\ref{triplet}.
+
+Here is a simple main program, {\tt umfpack\_simple.c}, that illustrates the
+basic usage of UMFPACK. See Section~\ref{Synopsis} for a short description
+of each calling sequence, including a list of options for the first
+argument of {\tt umfpack\_di\_solve}.
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_simple.c via sed
+\end{verbatim}
+}
+
+The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 & -1 & -3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1 \\
+\end{array}
+\right].
+\]
+and the solution to $\m{Ax}=\m{b}$ is $\m{x} = [1 \, 2 \, 3 \, 4 \, 5]\tr$.
+The program uses default control settings and does not return any statistics
+about the ordering, factorization, or solution ({\tt Control} and {\tt Info}
+are both {\tt (double *) NULL}). It also ignores the status value returned by
+most user-callable UMFPACK routines.
+
+%-------------------------------------------------------------------------------
+\subsection{A note about zero-sized arrays}
+%-------------------------------------------------------------------------------
+
+UMFPACK uses many user-provided arrays of
+size {\tt m} or {\tt n} (the order of the matrix), and of size
+{\tt nz} (the number of nonzeros in a matrix). UMFPACK does not handle
+zero-dimensioned arrays;
+it returns an error code if {\tt m} or {\tt n}
+are zero. However, {\tt nz} can be zero, since all singular matrices are
+handled correctly. If you attempt to {\tt malloc} an array of size {\tt nz}
+= 0, however, {\tt malloc} will return a null pointer which UMFPACK will report
+as a missing argument. If you {\tt malloc} an array of
+size {\tt nz} to pass to UMFPACK, make sure that you handle the {\tt nz} = 0
+case correctly (use a size equal to the maximum of {\tt nz} and 1, or use a
+size of {\tt nz+1}).
+
+%-------------------------------------------------------------------------------
+\subsection{Alternative routines}
+%-------------------------------------------------------------------------------
+
+Three alternative routines are provided that modify UMFPACK's default
+behavior. They are fully described in Section~\ref{Alternative}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_defaults}:
+
+ Sets the default control parameters in the {\tt Control} array. These can
+ then be modified as desired before passing the array to the other UMFPACK
+ routines. Control parameters are summarized in Section~\ref{control_param}.
+ Three particular parameters deserve special notice.
+ UMFPACK uses relaxed partial pivoting, where a candidate pivot entry is
+ numerically acceptable if its magnitude is greater than or equal to a
+ tolerance parameter times the magnitude of the largest entry in the same
+ column. The parameter {\tt Control [UMFPACK\_PIVOT\_TOLERANCE]} has a
+ default value of 0.1, and is used for the unsymmetric strategy.
+ For complex matrices, a cheap approximation of the absolute value is
+ used for the threshold pivoting test
+ ($|a| \approx |a_{\mbox{real}}|+|a_{\mbox{imag}}|$).
+
+ For the symmetric strategy, a second tolerance is used for diagonal
+ entries: \newline {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]}, with
+ a default value of 0.001. The first parameter (with a default of 0.1)
+ is used for any off-diagonal candidate pivot entries.
+
+ These two parameters may be too small for some matrices, particularly for
+ ill-conditioned or poorly scaled ones. With the default pivot tolerances
+ and default iterative refinement,
+ {\tt x = umfpack (A,'}$\backslash${\tt ',b)}
+ is just as accurate as (or more accurate) than
+ {\tt x = A}$\backslash${\tt b}
+ in MATLAB 6.1 for nearly all matrices.
+
+ If {\tt Control [UMFPACK\_PIVOT\_TOLERANCE]} is zero, than any
+ nonzero entry is acceptable as a pivot (this is changed from Version 4.0,
+ which treated a value of 0.0 the same as 1.0). If the symmetric strategy is
+ used, and {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]} is zero, then any
+ nonzero entry on the diagonal is accepted as a pivot. Off-diagonal pivoting
+ will still occur if the diagonal entry is exactly zero. The
+ {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]} parameter is new to Version
+ 4.1. It is similar in function to the pivot tolerance for left-looking
+ methods (the MATLAB {\tt THRESH} option in {\tt [L,U,P] = lu (A, THRESH)},
+ and the pivot tolerance parameter in SuperLU).
+
+ The parameter {\tt Control [UMFPACK\_STRATEGY]} can be used to bypass
+ UMFPACK's automatic strategy selection. The automatic strategy nearly
+ always selects the best method. When it does not, the different methods
+ nearly always give about the same quality of results. There may be
+ cases where the automatic strategy fails to pick a good strategy. Also,
+ you can save some computing time if you know the right strategy for your
+ set of matrix problems.
+
+\item {\tt umfpack\_*\_qsymbolic}:
+
+ An alternative to {\tt umfpack\_*\_symbolic}. Allows the user to specify
+ his or her own column pre-ordering, rather than using the default COLAMD
+ or AMD pre-orderings. For example, a graph partitioning-based order
+ of $\m{A}\tr\m{A}$ would be suitable for UMFPACK's unsymmetric strategy.
+ A partitioning of $\m{A}+\m{A}\tr$ would be suitable for UMFPACK's
+ symmetric or 2-by-2 strategies.
+
+\item {\tt umfpack\_*\_wsolve}:
+
+ An alternative to {\tt umfpack\_*\_solve} which does not dynamically
+ allocate any memory. Requires the user to pass two additional work
+ arrays.
+
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{Matrix manipulation routines}
+\label{triplet}
+%-------------------------------------------------------------------------------
+
+The compressed column data structure is compact, and simplifies the UMFPACK
+routines that operate on the sparse matrix $\m{A}$. However, it can be
+inconvenient for the user to generate. Section~\ref{Manipulate} presents the
+details of routines for manipulating sparse matrices in {\em triplet} form,
+compressed column form, and compressed row form (the transpose of the
+compressed column form). The triplet form of a matrix consists of three or
+four arrays. For the {\tt int} version of UMFPACK:
+
+{\footnotesize
+\begin{verbatim}
+ int Ti [nz] ;
+ int Tj [nz] ;
+ double Tx [nz] ;
+\end{verbatim}
+}
+
+For the {\tt UF\_long} version:
+
+{\footnotesize
+\begin{verbatim}
+ UF_long Ti [nz] ;
+ UF_long Tj [nz] ;
+ double Tx [nz] ;
+\end{verbatim}
+}
+
+The complex versions use another array to hold the imaginary part:
+
+{\footnotesize
+\begin{verbatim}
+ double Tz [nz] ;
+\end{verbatim}
+}
+
+The {\tt k}-th triplet is $(i,j,a_{ij})$, where $i =$ {\tt Ti[k]},
+$j =$ {\tt Tj[k]}, and $a_{ij} =$ {\tt Tx[k]}. For the complex versions,
+{\tt Tx[k]} is the real part of $a_{ij}$ and
+{\tt Tz[k]} is the imaginary part.
+The triplets can be in any
+order in the {\tt Ti}, {\tt Tj}, and {\tt Tx} arrays (and {\tt Tz} for
+the complex versions), and duplicate entries may
+exist.
+If {\tt Tz} is NULL, then the array {\tt Tx} becomes of size {\tt 2*nz},
+and the real and imaginary parts of the
+{\tt k}-th triplet are located in {\tt Tx[2*k]} and {\tt Tx[2*k+1]},
+respectively.
+Any duplicate entries are summed when the triplet form is converted to
+compressed column form. This is a convenient way to create a matrix arising in
+finite-element methods, for example.
+
+Four routines are provided for manipulating sparse matrices:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_triplet\_to\_col}:
+
+ Converts a triplet form of a matrix to compressed column form (ready for
+ input to \newline
+ {\tt umfpack\_*\_symbolic}, {\tt umfpack\_*\_qsymbolic}, and
+ {\tt umfpack\_*\_numeric}). Identical to {\tt A = spconvert(i,j,x)} in
+ MATLAB, except that zero entries are not removed, so that the pattern of
+ entries in the compressed column form of $\m{A}$ are fully under user
+ control. This is important if you want to factorize a new matrix with the
+ {\tt Symbolic} object from a prior matrix with the same pattern as the new
+ one.
+
+\item {\tt umfpack\_*\_col\_to\_triplet}:
+
+ The opposite of {\tt umfpack\_*\_triplet\_to\_col}. Identical to
+ {\tt [i,j,x] = find(A)} in MATLAB, except that numerically zero entries
+ may be included.
+
+\item {\tt umfpack\_*\_transpose}:
+
+ Transposes and optionally permutes a column form matrix \cite{Gustavson78}.
+ Identical to
+ {\tt R = A(P,Q)'} (linear algebraic transpose, using the complex conjugate)
+ or {\tt R = A(P,Q).'} (the array transpose)
+ in MATLAB, except for the presence of numerically zero entries.
+
+ Factorizing $\m{A}\tr$ and then solving $\m{Ax}=\m{b}$ with the transposed
+ factors can sometimes be much faster or much slower than factorizing
+ $\m{A}$. It is highly dependent on your particular matrix.
+
+\item {\tt umfpack\_*\_scale}:
+
+ Applies the row scale factors to a user-provided vector. This is not
+ required to solve the sparse linear system $\m{Ax}=\m{b}$ or
+ $\m{A}\tr\m{x}=\m{b}$, since {\tt umfpack\_*\_solve} applies the scale
+ factors for those systems.
+
+\end{itemize}
+
+It is quite easy to add matrices in triplet form, subtract them, transpose
+them, permute them, construct a submatrix, and multiply a triplet-form matrix
+times a vector. UMFPACK does not provide code for these basic operations,
+however. Refer to the discussion of
+{\tt umfpack\_*\_triplet\_to\_col} in Section~\ref{Manipulate} for more details
+on how to compute these operations in your own code.
+The only primary matrix operation not provided by UMFPACK is the
+multiplication of two sparse matrices \cite{Gustavson78}.
+The CHOLMOD provides many of these matrix operations, which
+can then be used in conjunction with UMFPACK.
+See my web page for details.
+
+%-------------------------------------------------------------------------------
+\subsection{Getting the contents of opaque objects}
+%-------------------------------------------------------------------------------
+
+There are cases where you may wish to do more with the LU factorization
+of a matrix than solve a linear system. The opaque {\tt Symbolic} and
+{\tt Numeric} objects are just that - opaque. You cannot do anything with them
+except to pass them back to subsequent calls to UMFPACK. Three routines
+are provided for copying their contents into user-provided arrays using simpler
+data structures. Four routines are provided for saving and loading the
+{\tt Numeric} and {\tt Symbolic} objects to/from binary files.
+An additional routine is provided that computes the determinant.
+They are fully described in Section~\ref{Get}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_get\_lunz}:
+
+ Returns the number of nonzeros in $\m{L}$ and $\m{U}$.
+
+\item {\tt umfpack\_*\_get\_numeric}:
+
+ Copies $\m{L}$, $\m{U}$, $\m{P}$, $\m{Q}$, and $\m{R}$
+ from the {\tt Numeric} object
+ into arrays provided by the user. The matrix $\m{L}$ is returned in
+ compressed row form (with the column indices in each row sorted in ascending
+ order). The matrix $\m{U}$ is returned in compressed column form (with
+ sorted columns). There are no explicit zero entries in $\m{L}$ and $\m{U}$,
+ but such entries may exist in the {\tt Numeric} object. The permutations
+ $\m{P}$ and $\m{Q}$ are represented as permutation vectors, where
+ {\tt P[k] = i} means that row {\tt i} of the original matrix is the
+ the {\tt k}-th row of $\m{PAQ}$, and where
+ {\tt Q[k] = j} means that column {\tt j} of the original matrix is the
+ {\tt k}-th column of $\m{PAQ}$. This is identical to how MATLAB uses
+ permutation vectors (type {\tt help colamd} in MATLAB 6.1 or later).
+
+\item {\tt umfpack\_*\_get\_symbolic}:
+
+ Copies the contents of the {\tt Symbolic} object (the initial row and column
+ preordering, supernodal column elimination tree, and information
+ about each frontal matrix) into arrays provided by the user.
+
+\item {\tt umfpack\_*\_get\_determinant}:
+
+ Computes the determinant from the diagonal of $\m{U}$ and the permutations
+ $\m{P}$ and $\m{Q}$. This is mostly of theoretical interest.
+ It is not a good test to determine if your matrix is singular or not.
+
+\item {\tt umfpack\_*\_save\_numeric}:
+
+ Saves a copy of the {\tt Numeric} object to a file, in binary format.
+
+\item {\tt umfpack\_*\_load\_numeric}:
+
+ Creates a {\tt Numeric} object by loading it from a file created
+ by {\tt umfpack\_*\_save\_numeric}.
+
+\item {\tt umfpack\_*\_save\_symbolic}:
+
+ Saves a copy of the {\tt Symbolic} object to a file, in binary format.
+
+\item {\tt umfpack\_*\_load\_symbolic}:
+
+ Creates a {\tt Symbolic} object by loading it from a file created
+ by {\tt umfpack\_*\_save\_symbolic}.
+
+\end{itemize}
+
+UMFPACK itself does not make use of these routines;
+they are provided solely for returning the contents of the opaque
+{\tt Symbolic} and {\tt Numeric} objects to the user, and saving/loading
+them to/from a binary file. None of them do any computation, except for
+{\tt umfpack\_*\_get\_determinant}.
+
+%-------------------------------------------------------------------------------
+\subsection{Reporting routines}
+\label{Reporting}
+%-------------------------------------------------------------------------------
+
+None of the UMFPACK routines discussed so far prints anything, even when an
+error occurs. UMFPACK provides you with nine routines for printing the input
+and output arguments (including the {\tt Control} settings and {\tt Info}
+statistics) of UMFPACK routines discussed above. They are fully described in
+Section~\ref{Report}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_report\_status}:
+
+ Prints the status (return value) of other {\tt umfpack\_*} routines.
+
+\item {\tt umfpack\_*\_report\_info}:
+
+ Prints the statistics returned in the {\tt Info} array by
+ {\tt umfpack\_*\_*symbolic},
+ {\tt umfpack\_*\_numeric}, and {\tt umfpack\_*\_*solve}.
+
+\item {\tt umfpack\_*\_report\_control}:
+
+ Prints the {\tt Control} settings.
+
+\item {\tt umfpack\_*\_report\_matrix}:
+
+ Verifies and prints a compressed column-form or compressed row-form sparse
+ matrix.
+
+\item {\tt umfpack\_*\_report\_triplet}:
+
+ Verifies and prints a matrix in triplet form.
+
+\item {\tt umfpack\_*\_report\_symbolic}:
+
+ Verifies and prints a {\tt Symbolic} object.
+
+\item {\tt umfpack\_*\_report\_numeric}:
+
+ Verifies and prints a {\tt Numeric} object.
+
+\item {\tt umfpack\_*\_report\_perm}:
+
+ Verifies and prints a permutation vector.
+
+\item {\tt umfpack\_*\_report\_vector}:
+
+ Verifies and prints a real or complex vector.
+
+\end{itemize}
+
+The {\tt umfpack\_*\_report\_*} routines behave slightly differently when
+compiled
+into the C-callable UMFPACK library than when used in the MATLAB mexFunction.
+MATLAB stores its sparse matrices using the same compressed column data
+structure discussed above, where row and column indices of an $m$-by-$n$
+matrix are in the range 0 to $m-1$ or $n-1$, respectively\footnote{Complex
+matrices in MATLAB use the split array form, with one {\tt double} array
+for the real part and another array for the imaginary part. UMFPACK
+supports that format, as well as the packed complex format (new to Version 4.4).}
+It prints them as if they are in the range 1 to $m$ or $n$.
+The UMFPACK mexFunction behaves the same way.
+
+You can control how much the {\tt umfpack\_*\_report\_*} routines print by
+modifying the {\tt Control [UMFPACK\_PRL]} parameter. Its default value is 1.
+Here is a summary of how the routines use this print level parameter:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_report\_status}:
+
+ No output if the print level is 0 or less, even when an error occurs.
+ If 1, then error messages are printed, and nothing is printed if
+ the status is {\tt UMFPACK\_OK}. A warning message is printed if
+ the matrix is singular. If 2 or more, then the status is always
+ printed. If 4 or more, then the UMFPACK Copyright is printed.
+ If 6 or more, then the UMFPACK License is printed. See also the first page
+ of this User Guide for the Copyright and License.
+
+\item {\tt umfpack\_*\_report\_control}:
+
+ No output if the print level is 1 or less. If 2 or more, all of
+ {\tt Control} is printed.
+
+\item {\tt umfpack\_*\_report\_info}:
+
+ No output if the print level is 1 or less. If 2 or more, all of
+ {\tt Info} is printed.
+
+\item all other {\tt umfpack\_*\_report\_*} routines:
+
+ If the print level is 2 or less, then these routines return silently without
+ checking their inputs. If 3 or more, the inputs are fully verified and a
+ short status summary is printed. If 4, then the first few entries of the
+ input arguments are printed. If 5, then all of the input arguments are
+ printed.
+
+\end{itemize}
+
+This print level parameter has an additional effect on the MATLAB mexFunction.
+If zero, then no warnings of singular or nearly singular matrices are
+printed (similar to the MATLAB commands
+{\tt warning off MATLAB:singularMatrix} and
+{\tt warning off MATLAB:nearlySingularMatrix}).
+
+%-------------------------------------------------------------------------------
+\subsection{Utility routines}
+%-------------------------------------------------------------------------------
+
+UMFPACK v4.0 included a routine that returns the time used by the process,
+{\tt umfpack\_timer}. The routine uses either {\tt getrusage} (which is
+preferred), or the ANSI C {\tt clock} routine if that is not available.
+It is fully described in Section~\ref{Utility}. It is still available in
+UMFPACK v4.1 and following, but not used internally.
+Two new timing routines are provided in UMFPACK Version 4.1 and following,
+{\tt umfpack\_tic} and {\tt umfpack\_toc}. They use POSIX-compliant
+{\tt sysconf} and {\tt times} routines to find both the CPU time
+and wallclock time.
+These three routines are the only user-callable
+routine that is identical in all four {\tt int}/{\tt UF\_long}, real/complex
+versions (there is no {\tt umfpack\_di\_timer} routine, for example).
+
+%-------------------------------------------------------------------------------
+\subsection{Control parameters}
+\label{control_param}
+%-------------------------------------------------------------------------------
+
+UMFPACK uses an optional {\tt double} array (currently of size 20)
+to modify its control parameters. If you pass {\tt (double *) NULL} instead
+of a {\tt Control} array, then defaults are used. These defaults provide
+nearly optimal performance (both speed, memory usage, and numerical accuracy)
+for a wide range of matrices from real applications.
+
+This array will almost certainly grow in size in future releases,
+so be sure to dimension your {\tt Control} array to be of size
+{\tt UMFPACK\_CONTROL}. That constant is currently defined to be 20,
+but may increase in future versions, since all 20 entries are in use.
+
+The contents of this array may be modified by the user
+(see {\tt umfpack\_*\_defaults}). Each
+user-callable routine includes a complete description of how each control
+setting modifies its behavior. Table~\ref{control} summarizes the entire
+contents of the {\tt Control} array.
+Note that ANSI C uses 0-based indexing, while MATLAB uses 1-based
+indexing. Thus, {\tt Control(1)} in MATLAB is the same as
+{\tt Control[0]} or {\tt Control[UMFPACK\_PRL]} in ANSI C.
+
+\begin{table}
+\caption{UMFPACK Control parameters}
+\label{control}
+{\footnotesize
+\begin{tabular}{llll}
+\hline
+
+MATLAB & ANSI C & default & description \\
+\hline
+{\tt Control(1)} & {\tt Control[UMFPACK\_PRL]} & 1 & printing level \\
+{\tt Control(2)} & {\tt Control[UMFPACK\_DENSE\_ROW]} & 0.2 & dense row parameter \\
+{\tt Control(3)} & {\tt Control[UMFPACK\_DENSE\_COL]} & 0.2 & dense column parameter \\
+{\tt Control(4)} & {\tt Control[UMFPACK\_PIVOT\_TOLERANCE]} & 0.1 & partial pivoting tolerance \\
+{\tt Control(5)} & {\tt Control[UMFPACK\_BLOCK\_SIZE]} & 32 & BLAS block size \\
+{\tt Control(6)} & {\tt Control[UMFPACK\_STRATEGY]} & 0 (auto) & select strategy \\
+{\tt Control(7)} & {\tt Control[UMFPACK\_ALLOC\_INIT]} & 0.7 & initial memory allocation \\
+{\tt Control(8)} & {\tt Control[UMFPACK\_IRSTEP]} & 2 & max iter. refinement steps \\
+{\tt Control(13)} & {\tt Control[UMFPACK\_2BY2\_TOLERANCE]} & 0.01 & defines ``large'' entries \\
+{\tt Control(14)} & {\tt Control[UMFPACK\_FIXQ]} & 0 (auto) & fix or modify Q \\
+{\tt Control(15)} & {\tt Control[UMFPACK\_AMD\_DENSE]} & 10 & AMD dense row/column parameter \\
+{\tt Control(16)} & {\tt Control[UMFPACK\_SYM\_PIVOT\_TOLERANCE]} & 0.001 & for diagonal entries \\
+{\tt Control(17)} & {\tt Control[UMFPACK\_SCALE]} & 1 (sum) & row scaling (none, sum, or max) \\
+{\tt Control(18)} & {\tt Control[UMFPACK\_FRONT\_ALLOC\_INIT]} & 0.5 & frontal matrix allocation ratio \\
+{\tt Control(19)} & {\tt Control[UMFPACK\_DROPTOL]} & 0 & drop tolerance \\
+{\tt Control(20)} & {\tt Control[UMFPACK\_AGGRESSIVE]} & 1 (yes) & aggressive absorption \\
+ & & & in AMD and COLAMD \\
+%
+\hline
+\multicolumn{4}{l}{Can only be changed at compile time:} \\
+{\tt Control(9)} & {\tt Control[UMFPACK\_COMPILED\_WITH\_BLAS]} & - & true if BLAS is used \\
+{\tt Control(10)} & {\tt Control[UMFPACK\_COMPILED\_FOR\_MATLAB]} & - & true for mexFunction \\
+{\tt Control(11)} & {\tt Control[UMFPACK\_COMPILED\_WITH\_GETRUSAGE]} & - & 1 if {\tt getrusage} used \\
+{\tt Control(12)} & {\tt Control[UMFPACK\_COMPILED\_IN\_DEBUG\_MODE]} & - & true if debug mode enabled \\
+\hline
+\end{tabular}
+}
+\end{table}
+
+Let $\alpha_r = ${\tt Control [UMFPACK\_DENSE\_ROW]},
+ $\alpha_c = ${\tt Control [UMFPACK\_DENSE\_COL]}, and
+ $\alpha = ${\tt Control [UMFPACK\_AMD\_DENSE]}.
+Suppose the submatrix $\m{S}$, obtained after eliminating pivots with
+zero Markowitz cost, is $m$-by-$n$.
+Then a row is considered ``dense'' if it has more than
+$\max (16, 16 \alpha_r \sqrt{n})$ entries.
+A column is considered ``dense'' if it has more than
+$\max (16, 16 \alpha_c \sqrt{m})$ entries.
+These rows and columns are treated different in COLAMD and during numerical
+factorization. In COLAMD, dense columns are placed last in their natural
+order, and dense rows are ignored. During numerical factorization, dense
+rows are stored differently.
+In AMD, a row/column of the square matrix $\m{S}+\m{S}\tr$ is
+considered ``dense'' if it has more than $\max (16, \alpha \sqrt{n})$ entries.
+These rows/columns are placed last in AMD's output ordering.
+For more details on the control parameters, refer to the documentation of
+{\tt umfpack\_*\_qsymbolic}, {\tt umfpack\_*\_numeric}, {\tt umfpack\_*\_solve},
+and the {\tt umfpack\_*\_report\_*} routines,
+in Sections~\ref{Primary}~through~\ref{Report}, below.
+
+%-------------------------------------------------------------------------------
+\subsection{Error codes}
+\label{error_codes}
+%-------------------------------------------------------------------------------
+
+Many of the routines return a {\tt status} value.
+This is also returned as the first entry in the {\tt Info} array, for
+those routines with that argument. The following list summarizes
+all of the error codes in UMFPACK. Each error code is given a
+specific name in the {\tt umfpack.h} include file, so you can use
+those constants instead of hard-coded values in your program.
+Future versions may report additional error codes.
+
+A value of zero means everything was successful, and the matrix is
+non-singular. A value greater than zero means the routine was successful,
+but a warning occurred.
+A negative value means the routine was not successful.
+In this case, no {\tt Symbolic} or {\tt Numeric} object was created.
+
+\begin{itemize}
+\item {\tt UMFPACK\_OK}, (0): UMFPACK was successful.
+
+\item {\tt UMFPACK\_WARNING\_singular\_matrix}, (1): Matrix is singular.
+ There are exact zeros on the diagonal of $\m{U}$.
+
+\item {\tt UMFPACK\_WARNING\_determinant\_underflow}, (2):
+ The determinant is nonzero, but smaller in magnitude than
+ the smallest positive floating-point number.
+
+\item {\tt UMFPACK\_WARNING\_determinant\_overflow}, (3):
+ The determinant is larger in magnitude than
+ the largest positive floating-point number (IEEE Inf).
+
+\item {\tt UMFPACK\_ERROR\_out\_of\_memory}, (-1): Not enough memory.
+ The ANSI C {\tt malloc} or {\tt realloc} routine failed.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_Numeric\_object}, (-3):
+ Routines that take a {\tt Numeric} object as input (or load it
+ from a file) check this object and return this error code if it is
+ invalid. This can be caused by a memory leak or overrun in your
+ program, which can overwrite part of the Numeric object. It can also
+ be caused by passing a Symbolic object by mistake, or some other pointer.
+ If you try to factorize a matrix using one version of UMFPACK and
+ then use the factors in another version, this error code will trigger as
+ well. You cannot factor your matrix using
+ version 4.0 and then solve with version 4.1, for example.\footnote{
+ Exception: v4.3, v4.3.1, and v4.4 use identical data structures
+ for the {\tt Numeric} and {\tt Symbolic} objects}.
+ You cannot use different precisions of the same version
+ (real and complex, for example).
+ It is possible for the {\tt Numeric} object to be corrupted by your
+ program in subtle ways that are not detectable by this quick check.
+ In this case, you may see an
+ {\tt UMFPACK\_ERROR\_different\_pattern} error code, or even an
+ {\tt UMFPACK\_ERROR\_internal\_error}.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_Symbolic\_object}, (-4):
+ Routines that take a {\tt Symbolic} object as input (or load it
+ from a file) check this object and return this error code if it is
+ invalid. The causes of this error are analogous to the
+ {\tt UMFPACK\_ERROR\_invalid\_Numeric\_object} error described above.
+
+\item {\tt UMFPACK\_ERROR\_argument\_missing}, (-5):
+ Some arguments of some are optional (you can pass a {\tt NULL} pointer
+ instead of an array). This error code occurs if you pass a {\tt NULL}
+ pointer when that argument is required to be present.
+
+\item {\tt UMFPACK\_ERROR\_n\_nonpositive} (-6):
+ The number of rows or columns of the matrix must be greater than zero.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_matrix} (-8):
+ The matrix is invalid. For the column-oriented input, this error
+ code will occur if the contents of {\tt Ap} and/or {\tt Ai} are invalid.
+
+ {\tt Ap} is an integer array of size {\tt n\_col+1}.
+ On input, it holds the
+ ``pointers'' for the column form of the sparse matrix $\m{A}$.
+ Column {\tt j} of
+ the matrix A is held in {\tt Ai [(Ap [j])} \ldots {\tt (Ap [j+1]-1)]}.
+ The first entry, {\tt Ap [0]}, must be zero,
+ and {\tt Ap [j]} $\le$ {\tt Ap [j+1]} must hold for all
+ {\tt j} in the range 0 to {\tt n\_col-1}.
+ The value {\tt nz = Ap [n\_col]} is thus the
+ total number of entries in the pattern of the matrix A.
+ {\tt nz} must be greater than or equal to zero.
+
+ The nonzero pattern (row indices) for column {\tt j} is stored in
+ {\tt Ai [(Ap [j])} \ldots {\tt (Ap [j+1]-1)]}. The row indices in a given
+ column {\tt j}
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to {\tt n\_row-1}
+ (the matrix is 0-based).
+
+ Some routines take a triplet-form input, with arguments
+ {\tt nz}, {\tt Ti}, and {\tt Tj}. This error code is returned
+ if {\tt nz} is less than zero,
+ if any row index in {\tt Ti} is outside the range 0 to {\tt n\_col-1}, or
+ if any column index in {\tt Tj} is outside the range 0 to {\tt n\_row-1}.
+
+\item {\tt UMFPACK\_ERROR\_different\_pattern}, (-11):
+ The most common cause of this error is that the pattern of the
+ matrix has changed between the symbolic and numeric factorization.
+ It can also occur if the {\tt Numeric} or {\tt Symbolic} object has
+ been subtly corrupted by your program.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_system}, (-13):
+ The {\tt sys} argument provided to one of the solve routines is invalid.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_permutation}, (-15):
+ The permutation vector provided as input is invalid.
+
+\item {\tt UMFPACK\_ERROR\_file\_IO}, (-17):
+ This error code is returned by the routines that save and load
+ the {\tt Numeric} or {\tt Symbolic} objects to/from a file, if a
+ file I/O error has occurred. The file may not exist or may not be readable,
+ you may be trying to create a file that you don't have permission to create,
+ or you may be out of disk space. The file you are trying to read might
+ be the wrong one, and an earlier end-of-file condition would then result
+ in this error.
+
+\item {\tt UMFPACK\_ERROR\_internal\_error}, (-911):
+ An internal error has occurred, of unknown cause. This is either a bug
+ in UMFPACK, or the result of a memory overrun from your program.
+ Try modifying the file {\tt AMD/Source/amd\_internal.h} and adding
+ the statement {\tt \#undef NDEBUG}, to enable the debugging mode.
+ Recompile UMFPACK and rerun your program.
+ A failed assertion might occur which
+ can give you a better indication as to what is going wrong. Be aware that
+ UMFPACK will be extraordinarily slow when running in debug mode.
+ If all else fails, contact the developer (davis at cise.ufl.edu) with
+ as many details as possible.
+
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{Larger examples}
+%-------------------------------------------------------------------------------
+
+Full examples of all user-callable UMFPACK routines
+are available in four stand-alone C main programs, {\tt umfpack\_*\_demo.c}.
+Another example is
+the UMFPACK mexFunction, {\tt umfpackmex.c}. The mexFunction accesses only the
+user-callable C interface to UMFPACK. The only features that it does not use
+are the support for the triplet form (MATLAB's sparse arrays are already in the
+compressed column form) and the ability to reuse the {\tt Symbolic} object to
+numerically factorize a matrix whose pattern is the same as a prior matrix
+analyzed by {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic}. The
+latter is an important feature, but the mexFunction does not return its opaque
+{\tt Symbolic} and {\tt Numeric} objects to MATLAB. Instead, it gets the
+contents of these objects after extracting them via the {\tt umfpack\_*\_get\_*}
+routines, and returns them as MATLAB sparse matrices.
+
+The {\tt umf4.c} program for reading matrices in Harwell/Boeing format
+\cite{DuffGrimesLewis87b} is provided. It requires three Fortran 77 programs
+({\tt readhb.f}, {\tt readhb\_nozeros.f}, and {\tt readhb\_size.f})
+for reading in the sample Harwell/Boeing files in the {\tt UMFPACK/Demo/HB}
+directory. More matrices are available at
+http://www.cise.ufl.edu/research/sparse/matrices.
+Type {\tt make hb} in the {\tt UMFPACK/Demo/HB} directory
+to compile and run this demo. This program was used for the experimental
+results in \cite{Davis03}.
+
+%-------------------------------------------------------------------------------
+\section{Synopsis of C-callable routines}
+\label{Synopsis}
+%-------------------------------------------------------------------------------
+
+Each subsection, below, summarizes the input variables, output variables, return
+values, and calling sequences of the routines in one category. Variables with
+the same name as those already listed in a prior category have the same size
+and type.
+
+The real, {\tt UF\_long} integer {\tt umfpack\_dl\_*} routines are
+identical to the real, {\tt int} routines, except that {\tt \_di\_} is replaced
+with {\tt \_dl\_} in the name, and all {\tt int} arguments become
+{\tt UF\_long}.
+Similarly, the complex, {\tt UF\_long} integer {\tt umfpack\_zl\_*} routines are
+identical to the complex, {\tt int} routines, except that {\tt \_zi\_} is
+replaced
+with {\tt \_zl\_} in the name, and all {\tt int} arguments become
+{\tt UF\_long}.
+Only the real and complex {\tt int} versions are listed in the synopsis below.
+
+The matrix $\m{A}$ is {\tt m}-by-{\tt n} with {\tt nz} entries.
+
+The {\tt sys} argument of {\tt umfpack\_*\_solve}
+is an integer in the range 0 to 14 which defines which linear system is
+to be solved.
+\footnote{Integer values for {\tt sys} are used instead of strings (as in LINPACK
+and LAPACK) to avoid C-to-Fortran portability issues.}
+Valid values are listed in Table~\ref{sys}.
+The notation $\m{A}\he$ refers to the matrix transpose, which is the
+complex conjugate transpose for complex matrices ({\tt A'} in MATLAB).
+The array transpose is $\m{A}\tr$, which is {\tt A.'} in MATLAB.
+
+\begin{table}
+\begin{center}
+\caption{UMFPACK {\tt sys} parameter}
+\label{sys}
+{\footnotesize
+\begin{tabular}{ll|l}
+\hline
+Value & & system \\
+\hline
+& & \\
+{\tt UMFPACK\_A} & (0) & $\m{Ax}=\m{b}$ \\
+{\tt UMFPACK\_At} & (1) & $\m{A}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Aat} & (2) & $\m{A}\tr\m{x}=\m{b}$ \\
+& & \\
+\hline
+& & \\
+{\tt UMFPACK\_Pt\_L} & (3) & $\m{P}\tr\m{Lx}=\m{b}$ \\
+{\tt UMFPACK\_L} & (4) & $\m{Lx}=\m{b}$ \\
+{\tt UMFPACK\_Lt\_P} & (5) & $\m{L}\he\m{Px}=\m{b}$ \\
+{\tt UMFPACK\_Lat\_P} & (6) & $\m{L}\tr\m{Px}=\m{b}$ \\
+{\tt UMFPACK\_Lt} & (7) & $\m{L}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Lat} & (8) & $\m{L}\tr\m{x}=\m{b}$ \\
+& & \\
+\hline
+& & \\
+{\tt UMFPACK\_U\_Qt} & (9) & $\m{UQ}\tr\m{x}=\m{b}$ \\
+{\tt UMFPACK\_U} & (10) & $\m{Ux}=\m{b}$ \\
+{\tt UMFPACK\_Q\_Ut} & (11) & $\m{QU}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Q\_Uat} & (12) & $\m{QU}\tr\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Ut} & (13) & $\m{U}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Uat} & (14) & $\m{U}\tr\m{x}=\m{b}$ \\
+& & \\
+\hline
+\end{tabular}
+}
+\end{center}
+\end{table}
+
+%-------------------------------------------------------------------------------
+\subsection{Primary routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+#include "umfpack.h"
+int status, sys, n, m, nz, Ap [n+1], Ai [nz] ;
+double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], Ax [nz], X [n], B [n] ;
+void *Symbolic, *Numeric ;
+
+status = umfpack_di_symbolic (m, n, Ap, Ai, Ax, &Symbolic, Control, Info) ;
+status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ;
+status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+umfpack_di_free_symbolic (&Symbolic) ;
+umfpack_di_free_numeric (&Numeric) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Alternative routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+int Qinit [n], Wi [n] ;
+double W [5*n] ;
+
+umfpack_di_defaults (Control) ;
+status = umfpack_di_qsymbolic (m, n, Ap, Ai, Ax, Qinit, &Symbolic, Control, Info) ;
+status = umfpack_di_wsolve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info, Wi, W) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Matrix manipulation routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+int Ti [nz], Tj [nz], P [m], Q [n], Rp [m+1], Ri [nz], Map [nz] ;
+double Tx [nz], Rx [nz], Y [m], Z [m] ;
+
+status = umfpack_di_col_to_triplet (n, Ap, Tj) ;
+status = umfpack_di_triplet_to_col (m, n, nz, Ti, Tj, Tx, Ap, Ai, Ax, Map) ;
+status = umfpack_di_transpose (m, n, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ;
+status = umfpack_di_scale (Y, Z, Numeric) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Getting the contents of opaque objects: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+The {\tt filename} string should be large enough to hold the name of a file.
+
+{\footnotesize
+\begin{verbatim}
+int lnz, unz, Lp [m+1], Lj [lnz], Up [n+1], Ui [unz], do_recip ;
+double Lx [lnz], Ux [unz], D [min (m,n)], Rs [m], Mx [1], Ex [1] ;
+int nfr, nchains, P1 [m], Q1 [n], Front_npivcol [n+1], Front_parent [n+1], Front_1strow [n+1],
+ Front_leftmostdesc [n+1], Chain_start [n+1], Chain_maxrows [n+1], Chain_maxcols [n+1] ;
+char filename [100] ;
+
+status = umfpack_di_get_lunz (&lnz, &unz, &m, &n, &nz_udiag, Numeric) ;
+status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, D,
+ &do_recip, Rs, Numeric) ;
+status = umfpack_di_get_symbolic (&m, &n, &n1, &nz, &nfr, &nchains, P1, Q1,
+ Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+status = umfpack_di_load_numeric (&Numeric, filename) ;
+status = umfpack_di_save_numeric (Numeric, filename) ;
+status = umfpack_di_load_symbolic (&Symbolic, filename) ;
+status = umfpack_di_save_symbolic (Symbolic, filename) ;
+status = umfapck_di_get_determinant (Mx, Ex, Numeric, Info) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Reporting routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+
+umfpack_di_report_status (Control, status) ;
+umfpack_di_report_control (Control) ;
+umfpack_di_report_info (Control, Info) ;
+status = umfpack_di_report_matrix (m, n, Ap, Ai, Ax, 1, Control) ;
+status = umfpack_di_report_matrix (m, n, Rp, Ri, Rx, 0, Control) ;
+status = umfpack_di_report_numeric (Numeric, Control) ;
+status = umfpack_di_report_perm (m, P, Control) ;
+status = umfpack_di_report_perm (n, Q, Control) ;
+status = umfpack_di_report_symbolic (Symbolic, Control) ;
+status = umfpack_di_report_triplet (m, n, nz, Ti, Tj, Tx, Control) ;
+status = umfpack_di_report_vector (n, X, Control) ;
+\end{verbatim}
+}
+
+
+
+
+
+
+%-------------------------------------------------------------------------------
+\subsection{Primary routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Az [nz], Xx [n], Xz [n], Bx [n], Bz [n] ;
+
+status = umfpack_zi_symbolic (m, n, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ;
+status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ;
+status = umfpack_zi_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info) ;
+umfpack_zi_free_symbolic (&Symbolic) ;
+umfpack_zi_free_numeric (&Numeric) ;
+\end{verbatim}
+}
+
+The arrays {\tt Ax}, {\tt Bx}, and {\tt Xx} double in size if
+any imaginary argument ({\tt Az}, {\tt Xz}, or {\tt Bz}) is {\tt NULL}.
+
+%-------------------------------------------------------------------------------
+\subsection{Alternative routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Wz [10*n] ;
+
+umfpack_zi_defaults (Control) ;
+status = umfpack_zi_qsymbolic (m, n, Ap, Ai, Ax, Az, Qinit, &Symbolic, Control, Info) ;
+status = umfpack_zi_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info, Wi, Wz) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Matrix manipulation routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Tz [nz], Rz [nz], Yx [m], Yz [m], Zx [m], Zz [m] ;
+
+status = umfpack_zi_col_to_triplet (n, Ap, Tj) ;
+status = umfpack_zi_triplet_to_col (m, n, nz, Ti, Tj, Tx, Tz, Ap, Ai, Ax, Az, Map) ;
+status = umfpack_zi_transpose (m, n, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, 1) ;
+status = umfpack_zi_transpose (m, n, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, 0) ;
+status = umfpack_zi_scale (Yx, Yz, Zx, Zz, Numeric) ;
+\end{verbatim}
+}
+
+The arrays {\tt Tx}, {\tt Rx}, {\tt Yx}, and {\tt Zx} double in size if
+any imaginary argument ({\tt Tz}, {\tt Rz}, {\tt Yz}, or {\tt Zz}) is {\tt NULL}.
+
+%-------------------------------------------------------------------------------
+\subsection{Getting the contents of opaque objects: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Lz [lnz], Uz [unz], Dx [min (m,n)], Dz [min (m,n)], Mz [1] ;
+
+status = umfpack_zi_get_lunz (&lnz, &unz, &m, &n, &nz_udiag, Numeric) ;
+status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz,
+ &do_recip, Rs, Numeric) ;
+status = umfpack_zi_get_symbolic (&m, &n, &n1, &nz, &nfr, &nchains, P1, Q1,
+ Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+status = umfpack_zi_load_numeric (&Numeric, filename) ;
+status = umfpack_zi_save_numeric (Numeric, filename) ;
+status = umfpack_zi_load_symbolic (&Symbolic, filename) ;
+status = umfpack_zi_save_symbolic (Symbolic, filename) ;
+status = umfapck_zi_get_determinant (Mx, Mz, Ex, Numeric, Info) ;
+\end{verbatim}
+}
+
+The arrays {\tt Lx}, {\tt Ux}, {\tt Dx}, and {\tt Mx} double in size if
+any imaginary argument ({\tt Lz}, {\tt Uz}, {\tt Dz}, or {\tt Mz}) is {\tt NULL}.
+
+%-------------------------------------------------------------------------------
+\subsection{Reporting routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+
+umfpack_zi_report_status (Control, status) ;
+umfpack_zi_report_control (Control) ;
+umfpack_zi_report_info (Control, Info) ;
+status = umfpack_zi_report_matrix (m, n, Ap, Ai, Ax, Az, 1, Control) ;
+status = umfpack_zi_report_matrix (m, n, Rp, Ri, Rx, Rz, 0, Control) ;
+status = umfpack_zi_report_numeric (Numeric, Control) ;
+status = umfpack_zi_report_perm (m, P, Control) ;
+status = umfpack_zi_report_perm (n, Q, Control) ;
+status = umfpack_zi_report_symbolic (Symbolic, Control) ;
+status = umfpack_zi_report_triplet (m, n, nz, Ti, Tj, Tx, Tz, Control) ;
+status = umfpack_zi_report_vector (n, Xx, Xz, Control) ;
+\end{verbatim}
+}
+
+The arrays {\tt Ax}, {\tt Rx}, {\tt Tx}, and {\tt Xx} double in size if
+any imaginary argument ({\tt Az}, {\tt Rz}, {\tt Tz}, or {\tt Xz}) is {\tt NULL}.
+
+
+
+
+%-------------------------------------------------------------------------------
+\subsection{Utility routines}
+%-------------------------------------------------------------------------------
+
+These routines are the same in all four versions of UMFPACK.
+
+{\footnotesize
+\begin{verbatim}
+double t, s [2] ;
+
+t = umfpack_timer ( ) ;
+umfpack_tic (s) ;
+umfpack_toc (s) ;
+
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{AMD ordering routines}
+%-------------------------------------------------------------------------------
+
+UMFPACK makes use of the AMD ordering package for its symmetric ordering
+strategy. You may also use these four user-callable routines in your own C
+programs. You need to include the {\tt amd.h} file only if you make direct
+calls to the AMD routines themselves. The {\tt int} versions are summarized
+below; {\tt UF\_long} versions are also available. Refer to the AMD User Guide
+for more information, or to the file {\tt amd.h} which documents these routines.
+
+{\footnotesize
+\begin{verbatim}
+#include "amd.h"
+double amd_control [AMD_CONTROL], amd_info [AMD_INFO] ;
+
+amd_defaults (amd_control) ;
+status = amd_order (n, Ap, Ai, P, amd_control, amd_info) ;
+amd_control (amd_control) ;
+amd_info (amd_info) ;
+
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\section{Using UMFPACK in a Fortran program}
+%-------------------------------------------------------------------------------
+
+UMFPACK includes a basic Fortran 77 interface to some of the C-callable
+UMFPACK routines.
+Since interfacing C and Fortran programs is not portable, this interface might
+not work with all C and Fortran compilers. Refer to Section~\ref{Install} for
+more details. The following Fortran routines are provided.
+The list includes the C-callable routines that the Fortran interface
+routine calls. Refer to the corresponding C routines in Section~\ref{C} for
+more details on what the Fortran routine does.
+
+\begin{itemize}
+\item {\tt umf4def}: sets the default control parameters
+ ({\tt umfpack\_di\_defaults}).
+
+\item {\tt umf4sym}: pre-ordering and symbolic factorization
+ ({\tt umfpack\_di\_symbolic}).
+
+\item {\tt umf4num}: numeric factorization
+ ({\tt umfpack\_di\_numeric}).
+
+\item {\tt umf4solr}: solve a linear system with iterative refinement
+ ({\tt umfpack\_di\_solve}).
+
+\item {\tt umf4sol}: solve a linear system without iterative refinement
+ ({\tt umfpack\_di\_solve}). Sets {\tt Control [UMFPACK\_IRSTEP]}
+ to zero, and does not require the matrix $\m{A}$.
+
+\item {\tt umf4scal}: scales a vector using UMFPACK's scale factors
+ ({\tt umfpack\_di\_scale}).
+
+\item {\tt umf4fnum}: free the {\tt Numeric} object
+ ({\tt umfpack\_di\_free\_numeric}).
+
+\item {\tt umf4fsym}: free the {\tt Symbolic} object
+ ({\tt umfpack\_di\_free\_symbolic}).
+
+\item {\tt umf4pcon}: prints the control parameters
+ ({\tt umfpack\_di\_report\_control}).
+
+\item {\tt umf4pinf}: print statistics
+ ({\tt umfpack\_di\_report\_info}).
+
+\item {\tt umf4snum}: save the {\tt Numeric} object to a file
+ ({\tt umfpack\_di\_save\_numeric}).
+
+\item {\tt umf4ssym}: save the {\tt Symbolic} object to a file
+ ({\tt umfpack\_di\_save\_symbolic}).
+
+\item {\tt umf4lnum}: load the {\tt Numeric} object from a file
+ ({\tt umfpack\_di\_load\_numeric}).
+
+\item {\tt umf4lsym}: load the {\tt Symbolic} object from a file
+ ({\tt umfpack\_di\_load\_symbolic}).
+\end{itemize}
+
+The matrix $\m{A}$ is passed to UMFPACK in compressed column form, with 0-based
+indices. In Fortran, for an {\tt m}-by-{\tt n} matrix $\m{A}$ with {\tt nz}
+entries, the row indices of the first column (column 1) are in
+{\tt Ai (Ap(1)+1} \ldots {\tt Ap(2))}, with values in
+{\tt Ax (Ap(1)+1} \ldots {\tt Ap(2))}. The last column (column {\tt n}) is in
+{\tt Ai (Ap(n)+1} \ldots {\tt Ap(n+1))} and
+{\tt Ax (Ap(n)+1} \ldots {\tt Ap(n+1))}.
+The number of entries in the matrix is thus {\tt nz = Ap (n+1)}.
+The row indices in {\tt Ai} are in the range 0 to {\tt m}-1. They must be
+sorted, with no duplicate entries allowed. None of the UMFPACK routines
+modify the input matrix $\m{A}$.
+The following definitions apply for the Fortran routines:
+
+{\footnotesize
+\begin{verbatim}
+ integer m, n, Ap (n+1), Ai (nz), symbolic, numeric, filenum, status
+ double precision Ax (nz), control (20), info (90), x (n), b (n)
+\end{verbatim}
+}
+
+UMFPACK's status is returned in either a {\tt status} argument, or in
+{\tt info (1)}.
+It is zero if UMFPACK was successful, 1 if the matrix is singular (this is a
+warning, not an error), and negative if an error occurred.
+Section~\ref{error_codes} summarizes the possible values of {\tt status}
+and {\tt info (1)}.
+See Table~\ref{sys} for a list of the values of the {\tt sys} argument.
+See Table~\ref{control} for a list of the control parameters (the
+Fortran usage is the same as the MATLAB usage for this array).
+
+For the {\tt Numeric} and {\tt Symbolic} handles, it is probably safe to
+assume that a Fortran {\tt integer} is sufficient to store a C pointer. If
+that does not work, try defining {\tt numeric} and {\tt symbolic} in your
+Fortran program as integer arrays of size 2. You will need to define them
+as {\tt integer*8} if you compile UMFPACK in the 64-bit mode.
+
+To avoid passing strings between C and Fortran in the load/save routines,
+a file number is passed instead, and the C interface constructs a file name
+(if {\tt filenum} is 42, the {\tt Numeric} file name is {\tt n42.umf}, and
+the {\tt Symbolic} file name is {\tt s42.umf}).
+
+The following is a summary of the calling sequence of each Fortran
+interface routine. An example of their use is in the {\tt Demo/umf4hb.f}
+file. That routine also includes an example of how to convert a 1-based
+sparse matrix into 0-based form. For more details on the arguments of each
+routine, refer to the arguments of the same name in the corresponding
+C-callable routine, in Sections~\ref{Primary}~through~\ref{Utility}.
+The only exception is the {\tt control} argument of {\tt umf4sol},
+which sets {\tt control (8)} to zero to disable iterative refinement.
+Note that the solve routines do not overwrite {\tt b} with the solution,
+but return their solution in a different array, {\tt x}.
+
+{\footnotesize
+\begin{verbatim}
+ call umf4def (control)
+ call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info)
+ call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info)
+ call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info)
+ call umf4sol (sys, x, b, numeric, control, info)
+ call umf4scal (x, b, numeric, status)
+ call umf4fnum (numeric)
+ call umf4fsym (symbolic)
+ call umf4pcon (control)
+ call umf4pinf (control)
+ call umf4snum (numeric, filenum, status)
+ call umf4ssym (symbolic, filenum, status)
+ call umf4lnum (numeric, filenum, status)
+ call umf4lsym (symbolic, filenum, status)
+\end{verbatim}
+}
+
+Access to the complex routines in UMFPACK is provided by the interface
+routines in {\tt umf4\_f77zwrapper.c}. The following is a synopsis
+of each routine. All the arguments are the same as the real versions,
+except {\tt Az}, {\tt xz}, and {\tt bz} are the imaginary parts of
+the matrix, solution, and right-hand side, respectively. The
+{\tt Ax}, {\tt x}, and {\tt b} are the real parts.
+
+{\footnotesize
+\begin{verbatim}
+ call umf4zdef (control)
+ call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info)
+ call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
+ call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info)
+ call umf4zsol (sys, x, xz, b, bz, numeric, control, info)
+ call umf4zscal (x, xz, b, bz, numeric, status)
+ call umf4zfnum (numeric)
+ call umf4zfsym (symbolic)
+ call umf4zpcon (control)
+ call umf4zpinf (control)
+ call umf4zsnum (numeric, filenum, status)
+ call umf4zssym (symbolic, filenum, status)
+ call umf4zlnum (numeric, filenum, status)
+ call umf4zlsym (symbolic, filenum, status)
+\end{verbatim}
+}
+
+The Fortran interface does not support the packed complex case.
+
+%-------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%-------------------------------------------------------------------------------
+
+%-------------------------------------------------------------------------------
+\subsection{Installing the C library}
+%-------------------------------------------------------------------------------
+
+The following discussion assumes you have the {\tt make} program, either in
+Unix, or in Windows with Cygwin\footnote{www.cygwin.com}.
+You can skip this section and go to next one if all you want to use is
+the UMFPACK and AMD mexFunctions in MATLAB.
+
+You will need to install both UMFPACK v5.0 and AMD v2.0 to use UMFPACK.
+The {\tt UMFPACK} and {\tt AMD} subdirectories must be placed side-by-side
+within the same directory. AMD is a stand-alone package that
+is required by UMFPACK. UMFPACK can be compiled without the
+BLAS \cite{DaydeDuff99,ACM679a,ATLAS,GotoVandeGeijn02},
+but your performance will be much less than what it should be.
+
+System-dependent configurations are in the {\tt UFconfig/UFconfig.mk}
+file. The default
+settings will work on most systems, except that UMFPACK will be compiled so
+that it does not use the BLAS. Sample configurations are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install both packages,
+go to the {\tt UMFPACK} directory and type {\tt make}. This will compile the
+libraries ({\tt AMD/Lib/libamd.a} and {\tt UMFPACK/Lib/libumfpack.a}).
+A demo of the AMD ordering routine will be compiled and tested in
+the {\tt AMD/Demo} directory, and five demo programs will then be
+compiled and tested in the {\tt UMFPACK/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution. Expect to see a few differences, such as
+residual norms, compile-time control settings, and perhaps memory usage
+differences. The AMD and UMFPACK mexFunctions for
+use in MATLAB will also be compiled. If you do not have MATLAB 6.0 or
+later, type {\tt make lib} instead.
+
+If you have the GNU version of {\tt make}, the {\tt Source/GNUmakefile} and
+{\tt MATLAB/GNUmakefile} files are used. These are much more concise than
+what the ``old'' version of {\tt make} can handle. If you do not have
+GNU {\tt make}, the {\tt Source/Makefile} and {\tt MATLAB/Makefile} files
+are used instead. Each UMFPACK source file is compiled into four
+versions ({\tt double} / complex, and {\tt int} / {\tt UF\_long}). A proper
+old-style {\tt Makefile} is cumbersome in this case, so these two
+{\tt Makefile}'s have been constructed by brute force. They ignore
+dependencies, and simply compile everything. I highly recommend using GNU
+{\tt make} if you wish to modify UMFPACK.
+
+If you compile UMFPACK and AMD and then later change the
+{\tt UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+Here are the various parameters that you can control in your
+{\tt UFconfig/UFconfig.mk} file:
+
+\begin{itemize}
+\item {\tt CC = } your C compiler, such as {\tt cc}.
+\item {\tt RANLIB = } your system's {\tt ranlib} program, if needed.
+\item {\tt CFLAGS = } optimization flags, such as {\tt -O}.
+\item {\tt UMFPACK\_CONFIG = } configuration settings for the BLAS,
+ memory allocation routines, and timing routines.
+\item {\tt LIB = } your libraries, such as {\tt -lm} or {\tt -lblas}.
+\item {\tt RM =} the command to delete a file.
+\item {\tt MV =} the command to rename a file.
+\item {\tt MEX =} the command to compile a MATLAB mexFunction.
+ If you are using MATLAB 5, you need to add {\tt -DNBLAS} and
+ {\tt -DNUTIL} to this command.
+\item {\tt F77 =} the command to compile a Fortran program (optional).
+\item {\tt F77FLAGS =} the Fortran compiler flags (optional).
+\item {\tt F77LIB =} the Fortran libraries (optional).
+\end{itemize}
+
+The {\tt UMFPACK\_CONFIG} string can include combinations of the following;
+most deal with how the BLAS are called:
+\begin{itemize}
+\item {\tt -DNBLAS} if you do not have any BLAS at all.
+\item {\tt -DNSUNPERF} if you are on Solaris but do not have the Sun
+ Performance Library (for the BLAS).
+\item {\tt -DLONGBLAS} if your BLAS takes non-{\tt int} integer arguments.
+\item {\tt -DBLAS\_INT = } the integer used by the BLAS.
+
+\item {\tt -DBLAS\_NO\_UNDERSCORE}
+ for controlling how C calls the Fortran BLAS.
+ This is set automatically for Windows,
+ Sun Solaris, SGI Irix, Red Hat Linux, Compaq Alpha, and
+ AIX (the IBM RS 6000).
+
+\item {\tt -DGETRUSAGE} if you have the {\tt getrusage} function.
+\item {\tt -DNPOSIX} if you do not have the POSIX-compliant
+ {\tt sysconf} and {\tt times} routines used by
+ {\tt umfpack\_tic} and {\tt umfpack\_toc}.
+\item {\tt -DNRECIPROCAL} controls a trade-off between speed and accuracy.
+ If defined (or if the pivot value itself is less than $10^{-12}$),
+ then the pivot column is divided by the pivot value during numeric
+ factorization. Otherwise, it is multiplied by the reciprocal of the
+ pivot, which is faster but can be less accurate. The default is
+ to multiply by the reciprocal unless the pivot value is small.
+ This option also modifies how the rows of the matrix $\m{A}$ are
+ scaled. If {\tt -DNRECIPROCAL} is defined (or if any scale factor is
+ less than $10^{-12}$), entries in the rows of $\m{A}$ are divided
+ by the scale factors. Otherwise, they are multiplied by the reciprocal.
+ When compiling the complex routines with the GNU {\tt gcc} compiler, the
+ pivot column is always divided by the pivot entry, because of a
+ numerical accuracy issue encountered with {\tt gcc} version 3.2 with a
+ few complex matrices on a Pentium 4M (running Linux). You can still
+ use {\tt -DNRECIPROCAL} to control how the scale factors
+ for the rows of $\m{A}$ are applied.
+\item {\tt -DNO\_DIVIDE\_BY\_ZERO} controls how UMFPACK treats zeros
+ on the diagonal of $\m{U}$, for a singular matrix $\m{A}$.
+ If defined, then no division by
+ zero is performed (a zero entry on the diagonal of $\m{U}$ is
+ treated as if it were equal to one). By default,
+ UMFPACK will divide by zero.
+\item {\tt -DNO\_TIMER} controls whether or not timing routines
+ are to be called. If defined, no timers are used.
+ Timers are included by default.
+\end{itemize}
+
+If a Fortran BLAS package is used you may see compiler warnings. The BLAS
+routines
+{\tt dgemm}, {\tt dgemv}, {\tt dger}, {\tt dtrsm}, {\tt dtrsv}, {\tt dscal}
+and their corresponding complex versions are used.
+Header files are not provided for the Fortran
+BLAS. You may safely ignore all of these warnings.
+
+I highly recommend the recent BLAS by Goto and van de Geijn
+\cite{GotoVandeGeijn02}. Using this BLAS increased the performance
+of UMFPACK by up to 50\% on a Dell Latitude C840 laptop (2GHz Pentium 4M,
+512K L2 cache, 1GB main memory). The peak performance of
+{\tt umfpack\_di\_numeric} with Goto and van de Geijn's BLAS is 1.6 Gflops
+on this computer. In MATLAB, the peak performance of UMFPACK on
+a dense matrix (stored in sparse format) is 900 Mflops, as compared to
+1 Gflop for {\tt x = A}$\backslash${\tt b}
+when {\tt A} is stored as a regular full matrix.
+
+When you compile your program that uses the C-callable UMFPACK library,
+you need to link your program with both libraries
+({\tt UMFPACK/Lib/libumfpack.a} and {\tt AMD/Lib/libamd.a})
+and you need to tell your compiler to look in the
+directories {\tt UMFPACK/Include} and {\tt AMD/Include} for include
+files. See {\tt UMFPACK/Demo/Makefile} for an example.
+You do not need to directly include any AMD include files in your
+program, unless you directly call AMD routines. You only need the
+\begin{verbatim}
+#include "umfpack.h"
+\end{verbatim}
+statement, as described in Section~\ref{Synopsis}.
+
+If you would like to compile both 32-bit and 64-bit versions of the libraries,
+you will need to do it in two steps. Modify your {\tt UFconfig/UFconfig.mk}
+file, and select the 32-bit option. Type {\tt make} in the {\tt UMFPACK}
+directory, which creates the {\tt UMFPACK/Lib/libumfpack.a} and
+{\tt AMD/Lib/libamd.a} libraries. Rename those two files. Edit your
+{\tt UFconfig/UFconfig.mk} file and select the 64-bit option.
+Type {\tt make purge},
+and then {\tt make}, and you will create the 64-bit libraries.
+You can use the same {\tt umfpack.h} include file for both 32-bit and
+64-bit versions. Simply link your program with the appropriate 32-bit
+or 64-bit compiled version of the UMFPACK and AMD libraries.
+
+Type {\tt make hb} in the {\tt UMFPACK/Demo/HB} directory
+to compile and run a C program that reads in and factorizes
+Harwell/Boeing matrices. Note that this uses a stand-alone Fortran
+program to read in the Fortran-formatted Harwell/Boeing matrices and
+write them to a file which can be read by a C program.
+
+The {\tt umf\_multicompile.c} file has been added to assist in the
+compilation of UMFPACK in Microsoft Visual Studio, for Windows.
+
+%-------------------------------------------------------------------------------
+\subsection{Installing the MATLAB interface}
+%-------------------------------------------------------------------------------
+
+If all you want to do is use the UMFPACK mexFunction in MATLAB, you can skip
+the use of the {\tt make} command described above. Simply type
+{\tt umfpack\_make} in MATLAB while in the {\tt UMFPACK/MATLAB} directory.
+You can also type {\tt amd\_make} in the {\tt AMD/MATLAB} directory
+to compile the stand-alone AMD mexFunction (this is not required to
+compile the UMFPACK mexFunction). This works on any computer with MATLAB,
+including Windows.
+
+You will be prompted to select several configuration options, including
+whether or not to use the BLAS.
+MATLAB 5.3 (or earlier) does not include the BLAS, so you either have to
+compile UMFPACK without the BLAS (UMFPACK will be slow), or modify your
+{\tt <matlab>/bin/mexopts.sh} by adding your BLAS library
+to the {\tt CLIBS} string,
+where {\tt <matlab>} is the directory in which MATLAB is installed.
+
+If you are using Windows and the {\tt lcc} compiler bundled with
+MATLAB 6.1, then you may need to copy the
+{\tt UMFPACK}$\backslash${\tt MATLAB}$\backslash${\tt lcc\_lib}$\backslash${\tt libmwlapack.lib}
+file into the
+{\tt <matlab>}$\backslash${\tt extern}$\backslash${\tt lib}$\backslash${\tt win32}$\backslash${\tt lcc}$\backslash$
+directory.
+Next, type {\tt mex -setup}
+at the MATLAB prompt, and ask MATLAB to select the {\tt lcc} compiler.
+MATLAB 6.1 has built-in BLAS, but in that version of MATLAB the BLAS
+cannot be accessed by a mexFunction compiled by {\tt lcc} without first copying
+this file to the location listed above.
+If you have MATLAB 6.5 or later, you can probably skip this step.
+
+%-------------------------------------------------------------------------------
+\subsection{Installing the Fortran interface}
+%-------------------------------------------------------------------------------
+
+Once the 32-bit C-callable UMFPACK library is compiled, you can also compile
+the Fortran interface, by typing {\tt make fortran}. This will create
+the {\tt umf4hb} program, test it, and compare the output with the
+file {\tt umf4hb.out} in the distribution.
+If you compiled UMFPACK in 64-bit mode, you need to use {\tt make fortran64}
+instead, which compiles the {\tt umf4hb64} program and compares its output
+with the file {\tt umf4hb64.out}.
+Refer to the comments in the {\tt Demo/umf4\_f77wrapper.c} file
+for more details.
+
+This interface is {\bf highly} non-portable, since it depends
+on how C and Fortran are interfaced.
+Because of this issue, the interface is included in the {\tt Demo} directory,
+and not as a primary part of the UMFPACK library. The interface routines are
+not included in the compiled {\tt UMFPACK/Lib/libumfpack.a} library, but left
+as stand-alone compiled files ({\tt umf4\_f77wrapper.o} and
+{\tt umf4\_f77wrapper64.o} in the {\tt Demo} directory).
+You may need to modify the interface routines in the file
+{\tt umf4\_f77wrapper.c} if you are using compilers for which this interface
+has not been tested.
+
+%-------------------------------------------------------------------------------
+\subsection{Known Issues}
+%-------------------------------------------------------------------------------
+
+The Microsoft C or C++ compilers on a Pentium badly break the IEEE 754 standard,
+and do not treat NaN's properly. According to IEEE 754, the expression
+{\tt (x != x)} is supposed to be true if and only if {\tt x} is NaN. For
+non-compliant compilers in Windows that expression is always false, and another
+test must be used: {\tt (x < x)} is true if and only if {\tt x}
+is NaN. For compliant compilers, {\tt (x < x)} is always false, for any
+value of {\tt x} (including NaN).
+To cover both cases, UMFPACK when running under Microsoft Windows
+defines the following macro, which is true if and only if {\tt x} is NaN,
+regardless of whether your compiler is compliant or not:
+
+\begin{verbatim}
+#define SCALAR_IS_NAN(x) (((x) != (x)) || ((x) < (x)))
+\end{verbatim}
+
+If your compiler breaks this test, then UMFPACK will fail catastrophically
+if it encounters a NaN. You will not just see NaN's in your output; UMFPACK
+will probably crash with a segmentation fault. In that case, you might try to
+see if the common (but non-ANSI C) routine {\tt isnan} is available, and modify
+the macro {\tt SCALAR\_IS\_NAN} in {\tt umf\_version.h} accordingly. The
+simpler (and IEEE 754-compliant) test {\tt (x != x)} is always true with Linux
+on a PC, and on every Unix compiler I have tested.
+
+Some compilers will complain about the Fortran BLAS being defined implicitly.
+C prototypes for the BLAS are not used, except the C-BLAS. Some compilers
+will complain about unrecognized {\tt \#pragma}'s. You may safely ignore
+all of these warnings.
+
+%-------------------------------------------------------------------------------
+\section{Future work}
+\label{Future}
+%-------------------------------------------------------------------------------
+
+Here are a few features that are not in the current version of UMFPACK,
+in no particular
+order. They may appear in a future release of UMFPACK. If you are interested,
+let me know and I could consider including them:
+
+\begin{enumerate}
+
+\item Remove the restriction that the column-oriented form be given with
+ sorted columns. This has already been done in AMD Version 2.0.
+
+\item Future versions may have different default {\tt Control} parameters.
+ Future versions may return more statistics in the {\tt Info} array, and
+ they may use more entries in the {\tt Control} array.
+ These two arrays will probably become larger, since there are very few
+ unused entries. If they change in size, the constants
+ {\tt UMFPACK\_CONTROL} and {\tt UMFPACK\_INFO} defined in {\tt umfpack.h}
+ will be changed to reflect their new size. Your C program should use
+ these constants when declaring the size of these two arrays. Do not
+ define them as {\tt Control [20]} and {\tt Info [90]}.
+
+\item Forward/back solvers for the conventional row or column-form data
+ structure for $\m{L}$ and $\m{U}$ (the output of
+ {\tt umfpack\_*\_di\_get\_numeric}). This would enable a separate
+ solver that could be used to write a MATLAB mexFunction
+ {\tt x = lu\_refine (A, b, L, U, P, Q, R)} that gives MATLAB access
+ to the iterative refinement algorithm with sparse backward error
+ analysis. It would also be easier to handle sparse right-hand sides
+ in this data structure, and end up with good asymptotic run-time
+ in this case
+ (particularly for $\m{Lx}=\m{b}$; see \cite{GilbertPeierls88}).
+ See also CSparse and
+ CXSparse for software for handling sparse right-hand sides.
+
+\item Complex absolute value computations could be
+ based on FDLIBM (see \newline
+ http://www.netlib.org/fdlibm),
+ using the {\tt hypot(x,y)} routine.
+
+\item When using iterative refinement, the residual $\m{Ax}-\m{b}$ could be
+ returned by {\tt umfpack\_solve}.
+
+\item The solve routines could handle multiple right-hand sides, and sparse
+ right-hand sides. See {\tt umfpack\_solve} for the MATLAB version
+ of this feature.
+ See also CSparse and
+ CXSparse for software for handling sparse right-hand sides.
+
+\item An option to redirect the error and diagnostic output.
+
+\item Permutation to block-triangular-form \cite{Duff78a} for the C-callable
+ interface. There are two routines in the ACM Collected
+ Algorithms (529 and 575) \cite{Duff81b,Duff78b}
+ that could be translated from Fortran
+ to C and included in UMFPACK. This would result in better performance
+ for matrices from circuit simulation and
+ chemical process engineering. See {\tt umfpack\_btf.m} for the MATLAB
+ version of this feature. KLU includes this feature.
+ See also {\tt cs\_dmperm} in CSparse and CXSparse.
+
+\item The ability to use user-provided work arrays, so that {\tt malloc},
+ {\tt free}, and {\tt realloc} realloc are not called. The
+ {\tt umfpack\_*\_wsolve} routine is one example.
+
+\item A method that takes time proportional to the number of nonzeros in
+ $\m{A}$ to compute the symbolic factorization \cite{GilbertNgPeyton94}.
+ This would improve the performance of the symmetric and 2-by-2 strategies,
+ and the unsymmetric strategy when dense rows are present.
+ The current method takes
+ time proportional to the number of nonzeros in the upper bound of $\m{U}$.
+ The method used in UMFPACK exploits super-columns, however, so this
+ bound is rarely reached.
+ See {\tt cs\_counts} in CSparse and CXSparse,
+ and {\tt cholmod\_analyze} in CHOLMOD.
+
+\item Other basic sparse matrix operations, such as sparse matrix
+ multiplication, could be included.
+
+\item A more complete Fortran interface.
+
+\item A C++ interface.
+
+\item A parallel version using MPI. This would require a large amount
+ of effort.
+
+\end{enumerate}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{The primary UMFPACK routines}
+\label{Primary}
+%-------------------------------------------------------------------------------
+
+The include files are the same for all four versions of
+UMFPACK. The generic integer type is {\tt Int}, which is an {\tt int} or
+{\tt UF\_long}, depending on which version of UMFPACK you are using.
+
+\subsection{umfpack\_*\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_solve}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_solve.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_free\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_free_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_free\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_free_numeric.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Alternative routines}
+\label{Alternative}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_defaults}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_defaults.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_qsymbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_qsymbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_wsolve}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_wsolve.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Matrix manipulation routines}
+\label{Manipulate}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_col\_to\_triplet}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_col_to_triplet.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_triplet\_to\_col}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_triplet_to_col.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_transpose}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_transpose.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_scale}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_scale.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Getting the contents of opaque objects}
+\label{Get}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_get\_lunz}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_lunz.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_get\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_get\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_save\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_save_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_load\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_load_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_save\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_save_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_load\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_load_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_get\_determinant}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_determinant.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Reporting routines}
+\label{Report}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_report\_status}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_status.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_control}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_control.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_info}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_info.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_matrix}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_matrix.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_perm}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_perm.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_triplet}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_triplet.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_vector}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_vector.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Utility routines}
+\label{Utility}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_timer}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_timer.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_tic and umfpack\_toc}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_tictoc.h via sed
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+% References
+%-------------------------------------------------------------------------------
+
+\bibliographystyle{plain}
+\bibliography{UserGuide}
+
+\end{document}
diff --git a/src/C/SuiteSparse/UMFPACK/Doc/lesser.txt b/src/C/SuiteSparse/UMFPACK/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Doc/lesser.txt
@@ -0,0 +1,504 @@
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+
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack.h
new file mode 100644
index 0000000..f128f43
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack.h
@@ -0,0 +1,438 @@
+/* ========================================================================== */
+/* === umfpack.h ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This is the umfpack.h include file, and should be included in all user code
+ that uses UMFPACK. Do not include any of the umf_* header files in user
+ code. All routines in UMFPACK starting with "umfpack_" are user-callable.
+ All other routines are prefixed "umf_XY_", (where X is d or z, and Y is
+ i or l) and are not user-callable.
+*/
+
+#ifndef UMFPACK_H
+#define UMFPACK_H
+
+/* -------------------------------------------------------------------------- */
+/* Make it easy for C++ programs to include UMFPACK */
+/* -------------------------------------------------------------------------- */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* define UF_long */
+#include "UFconfig.h"
+
+/* -------------------------------------------------------------------------- */
+/* size of Info and Control arrays */
+/* -------------------------------------------------------------------------- */
+
+/* These might be larger in future versions, since there are only 3 unused
+ * entries in Info, and no unused entries in Control. */
+
+#define UMFPACK_INFO 90
+#define UMFPACK_CONTROL 20
+
+/* -------------------------------------------------------------------------- */
+/* User-callable routines */
+/* -------------------------------------------------------------------------- */
+
+/* Primary routines: */
+#include "umfpack_symbolic.h"
+#include "umfpack_numeric.h"
+#include "umfpack_solve.h"
+#include "umfpack_free_symbolic.h"
+#include "umfpack_free_numeric.h"
+
+/* Alternative routines: */
+#include "umfpack_defaults.h"
+#include "umfpack_qsymbolic.h"
+#include "umfpack_wsolve.h"
+
+/* Matrix manipulation routines: */
+#include "umfpack_triplet_to_col.h"
+#include "umfpack_col_to_triplet.h"
+#include "umfpack_transpose.h"
+#include "umfpack_scale.h"
+
+/* Getting the contents of the Symbolic and Numeric opaque objects: */
+#include "umfpack_get_lunz.h"
+#include "umfpack_get_numeric.h"
+#include "umfpack_get_symbolic.h"
+#include "umfpack_save_numeric.h"
+#include "umfpack_load_numeric.h"
+#include "umfpack_save_symbolic.h"
+#include "umfpack_load_symbolic.h"
+#include "umfpack_get_determinant.h"
+
+/* Reporting routines (the above 14 routines print nothing): */
+#include "umfpack_report_status.h"
+#include "umfpack_report_info.h"
+#include "umfpack_report_control.h"
+#include "umfpack_report_matrix.h"
+#include "umfpack_report_triplet.h"
+#include "umfpack_report_vector.h"
+#include "umfpack_report_symbolic.h"
+#include "umfpack_report_numeric.h"
+#include "umfpack_report_perm.h"
+
+/* Utility routines: */
+#include "umfpack_timer.h"
+#include "umfpack_tictoc.h"
+
+/* AMD */
+#include "amd.h"
+
+/* global function pointers */
+#include "umfpack_global.h"
+
+/* -------------------------------------------------------------------------- */
+/* Version, copyright, and license */
+/* -------------------------------------------------------------------------- */
+
+#define UMFPACK_VERSION "UMFPACK V5.0.3 (Dec 12, 2006)"
+
+#define UMFPACK_COPYRIGHT \
+"UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.\n"
+
+#define UMFPACK_LICENSE_PART1 \
+"\nUMFPACK License:\n" \
+"\n" \
+" UMFPACK is available under alternate licenses,\n" \
+" contact T. Davis for details.\n" \
+"\n" \
+" Your use or distribution of UMFPACK or any modified version of\n" \
+" UMFPACK implies that you agree to this License.\n" \
+"\n" \
+" This library is free software; you can redistribute it and/or\n" \
+" modify it under the terms of the GNU Lesser General Public\n" \
+" License as published by the Free Software Foundation; either\n" \
+" version 2.1 of the License, or (at your option) any later version.\n" \
+"\n" \
+" This library is distributed in the hope that it will be useful,\n" \
+" but WITHOUT ANY WARRANTY; without even the implied warranty of\n" \
+" MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU\n" \
+" Lesser General Public License for more details.\n" \
+"\n" \
+" You should have received a copy of the GNU Lesser General Public\n" \
+" License along with this library; if not, write to the Free Software\n" \
+" Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301\n" \
+" USA\n" \
+
+#define UMFPACK_LICENSE_PART2 \
+"\n" \
+" Permission is hereby granted to use or copy this program under the\n" \
+" terms of the GNU LGPL, provided that the Copyright, this License,\n" \
+" and the Availability of the original version is retained on all copies.\n" \
+" User documentation of any code that uses this code or any modified\n" \
+" version of this code must cite the Copyright, this License, the\n" \
+" Availability note, and \"Used by permission.\" Permission to modify\n" \
+" the code and to distribute modified code is granted, provided the\n" \
+" Copyright, this License, and the Availability note are retained,\n" \
+" and a notice that the code was modified is included.\n"
+
+#define UMFPACK_LICENSE_PART3 \
+"\n" \
+"Availability: http://www.cise.ufl.edu/research/sparse/umfpack\n" \
+"\n"
+
+/* UMFPACK Version 4.5 and later will include the following definitions.
+ * As an example, to test if the version you are using is 4.5 or later:
+ *
+ * #ifdef UMFPACK_VER
+ * if (UMFPACK_VER >= UMFPACK_VER_CODE (4,5)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(UMFPACK_VER) && (UMFPACK >= UMFPACK_VER_CODE (4,5))
+ * printf ("This is version 4.5 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 4.4 and earlier of UMFPACK do not include a #define'd version
+ * number, although they do include the UMFPACK_VERSION string, defined
+ * above.
+ */
+
+#define UMFPACK_DATE "Dec 12, 2006"
+#define UMFPACK_VER_CODE(main,sub) ((main) * 1000 + (sub))
+#define UMFPACK_MAIN_VERSION 5
+#define UMFPACK_SUB_VERSION 0
+#define UMFPACK_SUBSUB_VERSION 3
+#define UMFPACK_VER UMFPACK_VER_CODE(UMFPACK_MAIN_VERSION,UMFPACK_SUB_VERSION)
+
+/* -------------------------------------------------------------------------- */
+/* contents of Info */
+/* -------------------------------------------------------------------------- */
+
+/* Note that umfpack_report.m must coincide with these definitions. S is
+ * the submatrix of A after removing row/col singletons and empty rows/cols. */
+
+/* returned by all routines that use Info: */
+#define UMFPACK_STATUS 0 /* UMFPACK_OK, or other result */
+#define UMFPACK_NROW 1 /* n_row input value */
+#define UMFPACK_NCOL 16 /* n_col input value */
+#define UMFPACK_NZ 2 /* # of entries in A */
+
+/* computed in UMFPACK_*symbolic and UMFPACK_numeric: */
+#define UMFPACK_SIZE_OF_UNIT 3 /* sizeof (Unit) */
+
+/* computed in UMFPACK_*symbolic: */
+#define UMFPACK_SIZE_OF_INT 4 /* sizeof (int) */
+#define UMFPACK_SIZE_OF_LONG 5 /* sizeof (UF_long) */
+#define UMFPACK_SIZE_OF_POINTER 6 /* sizeof (void *) */
+#define UMFPACK_SIZE_OF_ENTRY 7 /* sizeof (Entry), real or complex */
+#define UMFPACK_NDENSE_ROW 8 /* number of dense rows */
+#define UMFPACK_NEMPTY_ROW 9 /* number of empty rows */
+#define UMFPACK_NDENSE_COL 10 /* number of dense rows */
+#define UMFPACK_NEMPTY_COL 11 /* number of empty rows */
+#define UMFPACK_SYMBOLIC_DEFRAG 12 /* # of memory compactions */
+#define UMFPACK_SYMBOLIC_PEAK_MEMORY 13 /* memory used by symbolic analysis */
+#define UMFPACK_SYMBOLIC_SIZE 14 /* size of Symbolic object, in Units */
+#define UMFPACK_SYMBOLIC_TIME 15 /* time (sec.) for symbolic analysis */
+#define UMFPACK_SYMBOLIC_WALLTIME 17 /* wall clock time for sym. analysis */
+#define UMFPACK_STRATEGY_USED 18 /* strategy used: sym, unsym, 2by2 */
+#define UMFPACK_ORDERING_USED 19 /* ordering used: colamd, amd, given */
+#define UMFPACK_QFIXED 31 /* whether Q is fixed or refined */
+#define UMFPACK_DIAG_PREFERRED 32 /* whether diagonal pivoting attempted*/
+#define UMFPACK_PATTERN_SYMMETRY 33 /* symmetry of pattern of S */
+#define UMFPACK_NZ_A_PLUS_AT 34 /* nnz (S+S'), excl. diagonal */
+#define UMFPACK_NZDIAG 35 /* nnz (diag (S)) */
+
+/* AMD statistics, computed in UMFPACK_*symbolic: */
+#define UMFPACK_SYMMETRIC_LUNZ 36 /* nz in L+U, if AMD ordering used */
+#define UMFPACK_SYMMETRIC_FLOPS 37 /* flops for LU, if AMD ordering used */
+#define UMFPACK_SYMMETRIC_NDENSE 38 /* # of "dense" rows/cols in S+S' */
+#define UMFPACK_SYMMETRIC_DMAX 39 /* max nz in cols of L, for AMD */
+
+/* statistics for 2-by-2 strategy */
+#define UMFPACK_2BY2_NWEAK 51 /* number of weak diagonal entries*/
+#define UMFPACK_2BY2_UNMATCHED 52 /* # of weak diagonals not matched*/
+#define UMFPACK_2BY2_PATTERN_SYMMETRY 53 /* symmetry of pattern of P*S */
+#define UMFPACK_2BY2_NZ_PA_PLUS_PAT 54 /* nz in PS+(PS)' */
+#define UMFPACK_2BY2_NZDIAG 55 /* nz on diagonal of PS+(PS)' */
+
+/* statistcs for singleton pruning */
+#define UMFPACK_COL_SINGLETONS 56 /* # of column singletons */
+#define UMFPACK_ROW_SINGLETONS 57 /* # of row singletons */
+#define UMFPACK_N2 58 /* size of S */
+#define UMFPACK_S_SYMMETRIC 59 /* 1 if S square and symmetricly perm.*/
+
+/* estimates computed in UMFPACK_*symbolic: */
+#define UMFPACK_NUMERIC_SIZE_ESTIMATE 20 /* final size of Numeric->Memory */
+#define UMFPACK_PEAK_MEMORY_ESTIMATE 21 /* for symbolic & numeric */
+#define UMFPACK_FLOPS_ESTIMATE 22 /* flop count */
+#define UMFPACK_LNZ_ESTIMATE 23 /* nz in L, incl. diagonal */
+#define UMFPACK_UNZ_ESTIMATE 24 /* nz in U, incl. diagonal */
+#define UMFPACK_VARIABLE_INIT_ESTIMATE 25 /* initial size of Numeric->Memory*/
+#define UMFPACK_VARIABLE_PEAK_ESTIMATE 26 /* peak size of Numeric->Memory */
+#define UMFPACK_VARIABLE_FINAL_ESTIMATE 27 /* final size of Numeric->Memory */
+#define UMFPACK_MAX_FRONT_SIZE_ESTIMATE 28 /* max frontal matrix size */
+#define UMFPACK_MAX_FRONT_NROWS_ESTIMATE 29 /* max # rows in any front */
+#define UMFPACK_MAX_FRONT_NCOLS_ESTIMATE 30 /* max # columns in any front */
+
+/* exact values, (estimates shown above) computed in UMFPACK_numeric: */
+#define UMFPACK_NUMERIC_SIZE 40 /* final size of Numeric->Memory */
+#define UMFPACK_PEAK_MEMORY 41 /* for symbolic & numeric */
+#define UMFPACK_FLOPS 42 /* flop count */
+#define UMFPACK_LNZ 43 /* nz in L, incl. diagonal */
+#define UMFPACK_UNZ 44 /* nz in U, incl. diagonal */
+#define UMFPACK_VARIABLE_INIT 45 /* initial size of Numeric->Memory*/
+#define UMFPACK_VARIABLE_PEAK 46 /* peak size of Numeric->Memory */
+#define UMFPACK_VARIABLE_FINAL 47 /* final size of Numeric->Memory */
+#define UMFPACK_MAX_FRONT_SIZE 48 /* max frontal matrix size */
+#define UMFPACK_MAX_FRONT_NROWS 49 /* max # rows in any front */
+#define UMFPACK_MAX_FRONT_NCOLS 50 /* max # columns in any front */
+
+/* computed in UMFPACK_numeric: */
+#define UMFPACK_NUMERIC_DEFRAG 60 /* # of garbage collections */
+#define UMFPACK_NUMERIC_REALLOC 61 /* # of memory reallocations */
+#define UMFPACK_NUMERIC_COSTLY_REALLOC 62 /* # of costlly memory realloc's */
+#define UMFPACK_COMPRESSED_PATTERN 63 /* # of integers in LU pattern */
+#define UMFPACK_LU_ENTRIES 64 /* # of reals in LU factors */
+#define UMFPACK_NUMERIC_TIME 65 /* numeric factorization time */
+#define UMFPACK_UDIAG_NZ 66 /* nz on diagonal of U */
+#define UMFPACK_RCOND 67 /* est. reciprocal condition # */
+#define UMFPACK_WAS_SCALED 68 /* none, max row, or sum row */
+#define UMFPACK_RSMIN 69 /* min (max row) or min (sum row) */
+#define UMFPACK_RSMAX 70 /* max (max row) or max (sum row) */
+#define UMFPACK_UMIN 71 /* min abs diagonal entry of U */
+#define UMFPACK_UMAX 72 /* max abs diagonal entry of U */
+#define UMFPACK_ALLOC_INIT_USED 73 /* alloc_init parameter used */
+#define UMFPACK_FORCED_UPDATES 74 /* # of forced updates */
+#define UMFPACK_NUMERIC_WALLTIME 75 /* numeric wall clock time */
+#define UMFPACK_NOFF_DIAG 76 /* number of off-diagonal pivots */
+
+#define UMFPACK_ALL_LNZ 77 /* nz in L, if no dropped entries */
+#define UMFPACK_ALL_UNZ 78 /* nz in U, if no dropped entries */
+#define UMFPACK_NZDROPPED 79 /* # of dropped small entries */
+
+/* computed in UMFPACK_solve: */
+#define UMFPACK_IR_TAKEN 80 /* # of iterative refinement steps taken */
+#define UMFPACK_IR_ATTEMPTED 81 /* # of iter. refinement steps attempted */
+#define UMFPACK_OMEGA1 82 /* omega1, sparse backward error estimate */
+#define UMFPACK_OMEGA2 83 /* omega2, sparse backward error estimate */
+#define UMFPACK_SOLVE_FLOPS 84 /* flop count for solve */
+#define UMFPACK_SOLVE_TIME 85 /* solve time (seconds) */
+#define UMFPACK_SOLVE_WALLTIME 86 /* solve time (wall clock, seconds) */
+
+/* Info [87, 88, 89] unused */
+
+/* Unused parts of Info may be used in future versions of UMFPACK. */
+
+/* -------------------------------------------------------------------------- */
+
+/* Info [UMFPACK_ORDERING_USED] is one of the following: */
+#define UMFPACK_ORDERING_COLAMD 0 /* COLAMD(A) */
+#define UMFPACK_ORDERING_AMD 1 /* AMD(A+A') */
+#define UMFPACK_ORDERING_GIVEN 2 /* Q is provided on input */
+
+/* -------------------------------------------------------------------------- */
+/* contents of Control */
+/* -------------------------------------------------------------------------- */
+
+/* used in all UMFPACK_report_* routines: */
+#define UMFPACK_PRL 0 /* print level */
+
+/* used in UMFPACK_*symbolic only: */
+#define UMFPACK_DENSE_ROW 1 /* dense row parameter */
+#define UMFPACK_DENSE_COL 2 /* dense col parameter */
+#define UMFPACK_BLOCK_SIZE 4 /* BLAS-3 block size */
+#define UMFPACK_STRATEGY 5 /* auto, symmetric, unsym., or 2by2 */
+#define UMFPACK_2BY2_TOLERANCE 12 /* 2-by-2 pivot tolerance */
+#define UMFPACK_FIXQ 13 /* -1: no fixQ, 0: default, 1: fixQ */
+#define UMFPACK_AMD_DENSE 14 /* for AMD ordering */
+#define UMFPACK_AGGRESSIVE 19 /* whether or not to use aggressive
+ * absorption in AMD and COLAMD */
+
+/* used in UMFPACK_numeric only: */
+#define UMFPACK_PIVOT_TOLERANCE 3 /* threshold partial pivoting setting */
+#define UMFPACK_ALLOC_INIT 6 /* initial allocation ratio */
+#define UMFPACK_SYM_PIVOT_TOLERANCE 15 /* threshold, only for diag. entries */
+#define UMFPACK_SCALE 16 /* what row scaling to do */
+#define UMFPACK_FRONT_ALLOC_INIT 17 /* frontal matrix allocation ratio */
+#define UMFPACK_DROPTOL 18 /* drop tolerance for entries in L,U */
+
+/* used in UMFPACK_*solve only: */
+#define UMFPACK_IRSTEP 7 /* max # of iterative refinements */
+
+/* compile-time settings - Control [8..11] cannot be changed at run time: */
+#define UMFPACK_COMPILED_WITH_BLAS 8 /* uses the BLAS */
+#define UMFPACK_COMPILED_FOR_MATLAB 9 /* 1 if MATLAB mexFunction, etc. */
+#define UMFPACK_COMPILED_WITH_GETRUSAGE 10 /* uses getrusage timer, or not */
+#define UMFPACK_COMPILED_IN_DEBUG_MODE 11 /* debugging enabled (very slow!) */
+
+/* -------------------------------------------------------------------------- */
+
+/* Control [UMFPACK_STRATEGY] is one of the following: */
+#define UMFPACK_STRATEGY_AUTO 0 /* use sym. or unsym. strategy */
+#define UMFPACK_STRATEGY_UNSYMMETRIC 1 /* COLAMD(A), coletree postorder,
+ not prefer diag*/
+#define UMFPACK_STRATEGY_2BY2 2 /* AMD(PA+PA'), no coletree postorder,
+ prefer diag(PA) where P is pseudo
+ max transversal */
+#define UMFPACK_STRATEGY_SYMMETRIC 3 /* AMD(A+A'), no coletree postorder,
+ prefer diagonal */
+
+/* Control [UMFPACK_SCALE] is one of the following: */
+#define UMFPACK_SCALE_NONE 0 /* no scaling */
+#define UMFPACK_SCALE_SUM 1 /* default: divide each row by sum (abs (row))*/
+#define UMFPACK_SCALE_MAX 2 /* divide each row by max (abs (row)) */
+
+/* -------------------------------------------------------------------------- */
+/* default values of Control: */
+/* -------------------------------------------------------------------------- */
+
+#define UMFPACK_DEFAULT_PRL 1
+#define UMFPACK_DEFAULT_DENSE_ROW 0.2
+#define UMFPACK_DEFAULT_DENSE_COL 0.2
+#define UMFPACK_DEFAULT_PIVOT_TOLERANCE 0.1
+#define UMFPACK_DEFAULT_2BY2_TOLERANCE 0.01
+#define UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE 0.001
+#define UMFPACK_DEFAULT_BLOCK_SIZE 32
+#define UMFPACK_DEFAULT_ALLOC_INIT 0.7
+#define UMFPACK_DEFAULT_FRONT_ALLOC_INIT 0.5
+#define UMFPACK_DEFAULT_IRSTEP 2
+#define UMFPACK_DEFAULT_SCALE UMFPACK_SCALE_SUM
+#define UMFPACK_DEFAULT_STRATEGY UMFPACK_STRATEGY_AUTO
+#define UMFPACK_DEFAULT_AMD_DENSE AMD_DEFAULT_DENSE
+#define UMFPACK_DEFAULT_FIXQ 0
+#define UMFPACK_DEFAULT_AGGRESSIVE 1
+#define UMFPACK_DEFAULT_DROPTOL 0
+
+/* default values of Control may change in future versions of UMFPACK. */
+
+/* -------------------------------------------------------------------------- */
+/* status codes */
+/* -------------------------------------------------------------------------- */
+
+#define UMFPACK_OK (0)
+
+/* status > 0 means a warning, but the method was successful anyway. */
+/* A Symbolic or Numeric object was still created. */
+#define UMFPACK_WARNING_singular_matrix (1)
+
+/* The following warnings were added in umfpack_*_get_determinant */
+#define UMFPACK_WARNING_determinant_underflow (2)
+#define UMFPACK_WARNING_determinant_overflow (3)
+
+/* status < 0 means an error, and the method was not successful. */
+/* No Symbolic of Numeric object was created. */
+#define UMFPACK_ERROR_out_of_memory (-1)
+#define UMFPACK_ERROR_invalid_Numeric_object (-3)
+#define UMFPACK_ERROR_invalid_Symbolic_object (-4)
+#define UMFPACK_ERROR_argument_missing (-5)
+#define UMFPACK_ERROR_n_nonpositive (-6)
+#define UMFPACK_ERROR_invalid_matrix (-8)
+#define UMFPACK_ERROR_different_pattern (-11)
+#define UMFPACK_ERROR_invalid_system (-13)
+#define UMFPACK_ERROR_invalid_permutation (-15)
+#define UMFPACK_ERROR_internal_error (-911) /* yes, call me if you get this! */
+#define UMFPACK_ERROR_file_IO (-17)
+
+/* -------------------------------------------------------------------------- */
+/* solve codes */
+/* -------------------------------------------------------------------------- */
+
+/* Solve the system ( )x=b, where ( ) is defined below. "t" refers to the */
+/* linear algebraic transpose (complex conjugate if A is complex), or the (') */
+/* operator in MATLAB. "at" refers to the array transpose, or the (.') */
+/* operator in MATLAB. */
+
+#define UMFPACK_A (0) /* Ax=b */
+#define UMFPACK_At (1) /* A'x=b */
+#define UMFPACK_Aat (2) /* A.'x=b */
+
+#define UMFPACK_Pt_L (3) /* P'Lx=b */
+#define UMFPACK_L (4) /* Lx=b */
+#define UMFPACK_Lt_P (5) /* L'Px=b */
+#define UMFPACK_Lat_P (6) /* L.'Px=b */
+#define UMFPACK_Lt (7) /* L'x=b */
+#define UMFPACK_Lat (8) /* L.'x=b */
+
+#define UMFPACK_U_Qt (9) /* UQ'x=b */
+#define UMFPACK_U (10) /* Ux=b */
+#define UMFPACK_Q_Ut (11) /* QU'x=b */
+#define UMFPACK_Q_Uat (12) /* QU.'x=b */
+#define UMFPACK_Ut (13) /* U'x=b */
+#define UMFPACK_Uat (14) /* U.'x=b */
+
+/* -------------------------------------------------------------------------- */
+
+/* Integer constants are used for status and solve codes instead of enum */
+/* to make it easier for a Fortran code to call UMFPACK. */
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* UMFPACK_H */
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_col_to_triplet.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_col_to_triplet.h
new file mode 100644
index 0000000..427571e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_col_to_triplet.h
@@ -0,0 +1,110 @@
+/* ========================================================================== */
+/* === umfpack_col_to_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_col_to_triplet
+(
+ int n_col,
+ const int Ap [ ],
+ int Tj [ ]
+) ;
+
+UF_long umfpack_dl_col_to_triplet
+(
+ UF_long n_col,
+ const UF_long Ap [ ],
+ UF_long Tj [ ]
+) ;
+
+int umfpack_zi_col_to_triplet
+(
+ int n_col,
+ const int Ap [ ],
+ int Tj [ ]
+) ;
+
+UF_long umfpack_zl_col_to_triplet
+(
+ UF_long n_col,
+ const UF_long Ap [ ],
+ UF_long Tj [ ]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_col, *Tj, *Ap, status ;
+ status = umfpack_di_col_to_triplet (n_col, Ap, Tj) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_col, *Tj, *Ap, status ;
+ status = umfpack_dl_col_to_triplet (n_col, Ap, Tj) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_col, *Tj, *Ap, status ;
+ status = umfpack_zi_col_to_triplet (n_col, Ap, Tj) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_col, *Tj, *Ap, status ;
+ status = umfpack_zl_col_to_triplet (n_col, Ap, Tj) ;
+
+Purpose:
+
+ Converts a column-oriented matrix to a triplet form. Only the column
+ pointers, Ap, are required, and only the column indices of the triplet form
+ are constructed. This routine is the opposite of umfpack_*_triplet_to_col.
+ The matrix may be singular and/or rectangular. Analogous to [i, Tj, x] =
+ find (A) in MATLAB, except that zero entries present in the column-form of
+ A are present in the output, and i and x are not created (those are just Ai
+ and Ax+Az*1i, respectively, for a column-form matrix A).
+
+Returns:
+
+ UMFPACK_OK if successful
+ UMFPACK_ERROR_argument_missing if Ap or Tj is missing
+ UMFPACK_ERROR_n_nonpositive if n_col <= 0
+ UMFPACK_ERROR_invalid_matrix if Ap [n_col] < 0, Ap [0] != 0, or
+ Ap [j] > Ap [j+1] for any j in the range 0 to n-1.
+ Unsorted columns and duplicate entries do not cause an error (these would
+ only be evident by examining Ai). Empty rows and columns are OK.
+
+Arguments:
+
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_col > 0.
+ (n_row is not required)
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ The column pointers of the column-oriented form of the matrix. See
+ umfpack_*_*symbolic for a description. The number of entries in
+ the matrix is nz = Ap [n_col]. Restrictions on Ap are the same as those
+ for umfpack_*_transpose. Ap [0] must be zero, nz must be >= 0, and
+ Ap [j] <= Ap [j+1] and Ap [j] <= Ap [n_col] must be true for all j in
+ the range 0 to n_col-1. Empty columns are OK (that is, Ap [j] may equal
+ Ap [j+1] for any j in the range 0 to n_col-1).
+
+ Int Tj [nz] ; Output argument.
+
+ Tj is an integer array of size nz on input, where nz = Ap [n_col].
+ Suppose the column-form of the matrix is held in Ap, Ai, Ax, and Az
+ (see umfpack_*_*symbolic for a description). Then on output, the
+ triplet form of the same matrix is held in Ai (row indices), Tj (column
+ indices), and Ax (numerical values). Note, however, that this routine
+ does not require Ai and Ax (or Az for the complex version) in order to
+ do the conversion.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_defaults.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_defaults.h
new file mode 100644
index 0000000..bc40313
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_defaults.h
@@ -0,0 +1,69 @@
+/* ========================================================================== */
+/* === umfpack_defaults ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_dl_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zi_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zl_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_di_defaults (Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_dl_defaults (Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zi_defaults (Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zl_defaults (Control) ;
+
+Purpose:
+
+ Sets the default control parameter settings.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Output argument.
+
+ Control is set to the default control parameter settings. You can
+ then modify individual settings by changing specific entries in the
+ Control array. If Control is a (double *) NULL pointer, then
+ umfpack_*_defaults returns silently (no error is generated, since
+ passing a NULL pointer for Control to any UMFPACK routine is valid).
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_free_numeric.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_free_numeric.h
new file mode 100644
index 0000000..94bbf98
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_free_numeric.h
@@ -0,0 +1,67 @@
+/* ========================================================================== */
+/* === umfpack_free_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_free_numeric
+(
+ void **Numeric
+) ;
+
+void umfpack_dl_free_numeric
+(
+ void **Numeric
+) ;
+
+void umfpack_zi_free_numeric
+(
+ void **Numeric
+) ;
+
+void umfpack_zl_free_numeric
+(
+ void **Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_di_free_numeric (&Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_dl_free_numeric (&Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_zi_free_numeric (&Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_zl_free_numeric (&Numeric) ;
+
+Purpose:
+
+ Deallocates the Numeric object and sets the Numeric handle to NULL. This
+ routine is the only valid way of destroying the Numeric object.
+
+Arguments:
+
+ void **Numeric ; Input argument, set to (void *) NULL on output.
+
+ Numeric points to a valid Numeric object, computed by umfpack_*_numeric.
+ No action is taken if Numeric is a (void *) NULL pointer.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_free_symbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_free_symbolic.h
new file mode 100644
index 0000000..cf9262e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_free_symbolic.h
@@ -0,0 +1,67 @@
+/* ========================================================================== */
+/* === umfpack_free_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_free_symbolic
+(
+ void **Symbolic
+) ;
+
+void umfpack_dl_free_symbolic
+(
+ void **Symbolic
+) ;
+
+void umfpack_zi_free_symbolic
+(
+ void **Symbolic
+) ;
+
+void umfpack_zl_free_symbolic
+(
+ void **Symbolic
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_dl_free_symbolic (&Symbolic) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_zi_free_symbolic (&Symbolic) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_zl_free_symbolic (&Symbolic) ;
+
+Purpose:
+
+ Deallocates the Symbolic object and sets the Symbolic handle to NULL. This
+ routine is the only valid way of destroying the Symbolic object.
+
+Arguments:
+
+ void **Symbolic ; Input argument, set to (void *) NULL on output.
+
+ Points to a valid Symbolic object computed by umfpack_*_symbolic.
+ No action is taken if Symbolic is a (void *) NULL pointer.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_determinant.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_determinant.h
new file mode 100644
index 0000000..71b4158
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_determinant.h
@@ -0,0 +1,196 @@
+/* ========================================================================== */
+/* === UMFPACK_get_determinant ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_determinant
+(
+ double *Mx,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_get_determinant
+(
+ double *Mx,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_get_determinant
+(
+ double *Mx,
+ double *Mz,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_get_determinant
+(
+ double *Mx,
+ double *Mz,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status ;
+ double Mx, Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_di_get_determinant (&Mx, &Ex, Numeric, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status ;
+ double Mx, Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_dl_get_determinant (&Mx, &Ex, Numeric, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status ;
+ double Mx, Mz, Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_zi_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status ;
+ double *Mx, *Mz, *Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_zl_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
+
+packed complex int Syntax:
+
+ Same as above, except Mz is NULL.
+
+Author: Contributed by David Bateman, Motorola, Paris
+
+Purpose:
+
+ Using the LU factors and the permutation vectors contained in the Numeric
+ object, calculate the determinant of the matrix A.
+
+ The value of the determinant can be returned in two forms, depending on
+ whether Ex is NULL or not. If Ex is NULL then the value of the determinant
+ is returned on Mx and Mz for the real and imaginary parts. However, to
+ avoid over- or underflows, the determinant can be split into a mantissa
+ and exponent, and the parts returned separately, in which case Ex is not
+ NULL. The actual determinant is then given by
+
+ double det ;
+ det = Mx * pow (10.0, Ex) ;
+
+ for the double case, or
+
+ double det [2] ;
+ det [0] = Mx * pow (10.0, Ex) ; // real part
+ det [1] = Mz * pow (10.0, Ex) ; // imaginary part
+
+ for the complex case. Information on if the determinant will or has
+ over or under-flowed is given by Info [UMFPACK_STATUS].
+
+ In the "packed complex" syntax, Mx [0] holds the real part and Mx [1]
+ holds the imaginary part. Mz is not used (it is NULL).
+
+Returns:
+
+ Returns UMFPACK_OK if sucessful. Returns UMFPACK_ERROR_out_of_memory if
+ insufficient memory is available for the n_row integer workspace that
+ umfpack_*_get_determinant allocates to construct pivots from the
+ permutation vectors. Returns UMFPACK_ERROR_invalid_Numeric_object if the
+ Numeric object provided as input is invalid. Returns
+ UMFPACK_WARNING_singular_matrix if the determinant is zero. Returns
+ UMFPACK_WARNING_determinant_underflow or
+ UMFPACK_WARNING_determinant_overflow if the determinant has underflowed
+ overflowed (for the case when Ex is NULL), or will overflow if Ex is not
+ NULL and det is computed (see above) in the user program.
+
+Arguments:
+
+ double *Mx ; Output argument (array of size 1, or size 2 if Mz is NULL)
+ double *Mz ; Output argument (optional)
+ double *Ex ; Output argument (optional)
+
+ The determinant returned in mantissa/exponent form, as discussed above.
+ If Mz is NULL, then both the original and imaginary parts will be
+ returned in Mx. If Ex is NULL then the determinant is returned directly
+ in Mx and Mz (or Mx [0] and Mx [1] if Mz is NULL), rather than in
+ mantissa/exponent form.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains information about the calculation of the determinant. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_*_determinant:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ The determinant was successfully found.
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to solve the linear system.
+
+ UMFPACK_ERROR_argument_missing
+
+ Mx is missing (NULL).
+
+ UMFPACK_ERROR_invalid_Numeric_object
+
+ The Numeric object is not valid.
+
+ UMFPACK_ERROR_invalid_system
+
+ The matrix is rectangular. Only square systems can be
+ handled.
+
+ UMFPACK_WARNING_singluar_matrix
+
+ The determinant is zero or NaN. The matrix is singular.
+
+ UMFPACK_WARNING_determinant_underflow
+
+ When passing from mantissa/exponent form to the determinant
+ an underflow has or will occur. If the mantissa/exponent from
+ of obtaining the determinant is used, the underflow will occur
+ in the user program. If the single argument method of
+ obtaining the determinant is used, the underflow has already
+ occurred.
+
+ UMFPACK_WARNING_determinant_overflow
+
+ When passing from mantissa/exponent form to the determinant
+ an overflow has or will occur. If the mantissa/exponent from
+ of obtaining the determinant is used, the overflow will occur
+ in the user program. If the single argument method of
+ obtaining the determinant is used, the overflow has already
+ occurred.
+
+
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_lunz.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_lunz.h
new file mode 100644
index 0000000..8e53520
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_lunz.h
@@ -0,0 +1,137 @@
+/* ========================================================================== */
+/* === umfpack_get_lunz ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_lunz
+(
+ int *lnz,
+ int *unz,
+ int *n_row,
+ int *n_col,
+ int *nz_udiag,
+ void *Numeric
+) ;
+
+UF_long umfpack_dl_get_lunz
+(
+ UF_long *lnz,
+ UF_long *unz,
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *nz_udiag,
+ void *Numeric
+) ;
+
+int umfpack_zi_get_lunz
+(
+ int *lnz,
+ int *unz,
+ int *n_row,
+ int *n_col,
+ int *nz_udiag,
+ void *Numeric
+) ;
+
+UF_long umfpack_zl_get_lunz
+(
+ UF_long *lnz,
+ UF_long *unz,
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *nz_udiag,
+ void *Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_di_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_dl_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_zi_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_zl_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+Purpose:
+
+ Determines the size and number of nonzeros in the LU factors held by the
+ Numeric object. These are also the sizes of the output arrays required
+ by umfpack_*_get_numeric.
+
+ The matrix L is n_row -by- min(n_row,n_col), with lnz nonzeros, including
+ the entries on the unit diagonal of L.
+
+ The matrix U is min(n_row,n_col) -by- n_col, with unz nonzeros, including
+ nonzeros on the diagonal of U.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_invalid_Numeric_object if Numeric is not a valid object.
+ UMFPACK_ERROR_argument_missing if any other argument is (Int *) NULL.
+
+Arguments:
+
+ Int *lnz ; Output argument.
+
+ The number of nonzeros in L, including the diagonal (which is all
+ one's). This value is the required size of the Lj and Lx arrays as
+ computed by umfpack_*_get_numeric. The value of lnz is identical to
+ Info [UMFPACK_LNZ], if that value was returned by umfpack_*_numeric.
+
+ Int *unz ; Output argument.
+
+ The number of nonzeros in U, including the diagonal. This value is the
+ required size of the Ui and Ux arrays as computed by
+ umfpack_*_get_numeric. The value of unz is identical to
+ Info [UMFPACK_UNZ], if that value was returned by umfpack_*_numeric.
+
+ Int *n_row ; Output argument.
+ Int *n_col ; Output argument.
+
+ The order of the L and U matrices. L is n_row -by- min(n_row,n_col)
+ and U is min(n_row,n_col) -by- n_col.
+
+ Int *nz_udiag ; Output argument.
+
+ The number of numerically nonzero values on the diagonal of U. The
+ matrix is singular if nz_diag < min(n_row,n_col). A divide-by-zero
+ will occur if nz_diag < n_row == n_col when solving a sparse system
+ involving the matrix U in umfpack_*_*solve. The value of nz_udiag is
+ identical to Info [UMFPACK_UDIAG_NZ] if that value was returned by
+ umfpack_*_numeric.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_numeric.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_numeric.h
new file mode 100644
index 0000000..07c8252
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_numeric.h
@@ -0,0 +1,254 @@
+/* ========================================================================== */
+/* === umfpack_get_numeric ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_numeric
+(
+ int Lp [ ],
+ int Lj [ ],
+ double Lx [ ],
+ int Up [ ],
+ int Ui [ ],
+ double Ux [ ],
+ int P [ ],
+ int Q [ ],
+ double Dx [ ],
+ int *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_dl_get_numeric
+(
+ UF_long Lp [ ],
+ UF_long Lj [ ],
+ double Lx [ ],
+ UF_long Up [ ],
+ UF_long Ui [ ],
+ double Ux [ ],
+ UF_long P [ ],
+ UF_long Q [ ],
+ double Dx [ ],
+ UF_long *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+int umfpack_zi_get_numeric
+(
+ int Lp [ ],
+ int Lj [ ],
+ double Lx [ ], double Lz [ ],
+ int Up [ ],
+ int Ui [ ],
+ double Ux [ ], double Uz [ ],
+ int P [ ],
+ int Q [ ],
+ double Dx [ ], double Dz [ ],
+ int *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_zl_get_numeric
+(
+ UF_long Lp [ ],
+ UF_long Lj [ ],
+ double Lx [ ], double Lz [ ],
+ UF_long Up [ ],
+ UF_long Ui [ ],
+ double Ux [ ], double Uz [ ],
+ UF_long P [ ],
+ UF_long Q [ ],
+ double Dx [ ], double Dz [ ],
+ UF_long *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Ux, *Dx, *Rs ;
+ status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx,
+ &do_recip, Rs, Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Ux, *Dx, *Rs ;
+ status = umfpack_dl_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx,
+ &do_recip, Rs, Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Lz, *Ux, *Uz, *Dx, *Dz, *Rs ;
+ status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q,
+ Dx, Dz, &do_recip, Rs, Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Lz, *Ux, *Uz, *Dx, *Dz, *Rs ;
+ status = umfpack_zl_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q,
+ Dx, Dz, &do_recip, Rs, Numeric) ;
+
+packed complex int/UF_long Syntax:
+
+ Same as above, except Lz, Uz, and Dz are all NULL.
+
+Purpose:
+
+ This routine copies the LU factors and permutation vectors from the Numeric
+ object into user-accessible arrays. This routine is not needed to solve a
+ linear system. Note that the output arrays Lp, Lj, Lx, Up, Ui, Ux, P, Q,
+ Dx, and Rs are not allocated by umfpack_*_get_numeric; they must exist on
+ input.
+
+ All output arguments are optional. If any of them are NULL
+ on input, then that part of the LU factorization is not copied. You can
+ use this routine to extract just the parts of the LU factorization that
+ you want. For example, to retrieve just the column permutation Q, use:
+
+ #define noD (double *) NULL
+ #define noI (int *) NULL
+ status = umfpack_di_get_numeric (noI, noI, noD, noI, noI, noD, noI,
+ Q, noD, noI, noD, Numeric) ;
+
+Returns:
+
+ Returns UMFPACK_OK if successful. Returns UMFPACK_ERROR_out_of_memory
+ if insufficient memory is available for the 2*max(n_row,n_col) integer
+ workspace that umfpack_*_get_numeric allocates to construct L and/or U.
+ Returns UMFPACK_ERROR_invalid_Numeric_object if the Numeric object provided
+ as input is invalid.
+
+Arguments:
+
+ Int Lp [n_row+1] ; Output argument.
+ Int Lj [lnz] ; Output argument.
+ double Lx [lnz] ; Output argument. Size 2*lnz for packed complex case.
+ double Lz [lnz] ; Output argument for complex versions.
+
+ The n_row-by-min(n_row,n_col) matrix L is returned in compressed-row
+ form. The column indices of row i and corresponding numerical values
+ are in:
+
+ Lj [Lp [i] ... Lp [i+1]-1]
+ Lx [Lp [i] ... Lp [i+1]-1] real part
+ Lz [Lp [i] ... Lp [i+1]-1] imaginary part (complex versions)
+
+ respectively. Each row is stored in sorted order, from low column
+ indices to higher. The last entry in each row is the diagonal, which
+ is numerically equal to one. The sizes of Lp, Lj, Lx, and Lz are
+ returned by umfpack_*_get_lunz. If Lp, Lj, or Lx are not present,
+ then the matrix L is not returned. This is not an error condition.
+ The L matrix can be printed if n_row, Lp, Lj, Lx (and Lz for the split
+ complex case) are passed to umfpack_*_report_matrix (using the
+ "row" form).
+
+ If Lx is present and Lz is NULL, then both real
+ and imaginary parts are returned in Lx[0..2*lnz-1], with Lx[2*k]
+ and Lx[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int Up [n_col+1] ; Output argument.
+ Int Ui [unz] ; Output argument.
+ double Ux [unz] ; Output argument. Size 2*unz for packed complex case.
+ double Uz [unz] ; Output argument for complex versions.
+
+ The min(n_row,n_col)-by-n_col matrix U is returned in compressed-column
+ form. The row indices of column j and corresponding numerical values
+ are in
+
+ Ui [Up [j] ... Up [j+1]-1]
+ Ux [Up [j] ... Up [j+1]-1] real part
+ Uz [Up [j] ... Up [j+1]-1] imaginary part (complex versions)
+
+ respectively. Each column is stored in sorted order, from low row
+ indices to higher. The last entry in each column is the diagonal
+ (assuming that it is nonzero). The sizes of Up, Ui, Ux, and Uz are
+ returned by umfpack_*_get_lunz. If Up, Ui, or Ux are not present,
+ then the matrix U is not returned. This is not an error condition.
+ The U matrix can be printed if n_col, Up, Ui, Ux (and Uz for the
+ split complex case) are passed to umfpack_*_report_matrix (using the
+ "column" form).
+
+ If Ux is present and Uz is NULL, then both real
+ and imaginary parts are returned in Ux[0..2*unz-1], with Ux[2*k]
+ and Ux[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int P [n_row] ; Output argument.
+
+ The permutation vector P is defined as P [k] = i, where the original
+ row i of A is the kth pivot row in PAQ. If you do not want the P vector
+ to be returned, simply pass (Int *) NULL for P. This is not an error
+ condition. You can print P and Q with umfpack_*_report_perm.
+
+ Int Q [n_col] ; Output argument.
+
+ The permutation vector Q is defined as Q [k] = j, where the original
+ column j of A is the kth pivot column in PAQ. If you not want the Q
+ vector to be returned, simply pass (Int *) NULL for Q. This is not
+ an error condition. Note that Q is not necessarily identical to
+ Qtree, the column pre-ordering held in the Symbolic object. Refer to
+ the description of Qtree and Front_npivcol in umfpack_*_get_symbolic for
+ details.
+
+ double Dx [min(n_row,n_col)] ; Output argument. Size 2*n for
+ the packed complex case.
+ double Dz [min(n_row,n_col)] ; Output argument for complex versions.
+
+ The diagonal of U is also returned in Dx and Dz. You can extract the
+ diagonal of U without getting all of U by passing a non-NULL Dx (and
+ Dz for the complex version) and passing Up, Ui, and Ux as NULL. Dx is
+ the real part of the diagonal, and Dz is the imaginary part.
+
+ If Dx is present and Dz is NULL, then both real
+ and imaginary parts are returned in Dx[0..2*min(n_row,n_col)-1],
+ with Dx[2*k] and Dx[2*k+1] being the real and imaginary part of the kth
+ entry.
+
+ Int *do_recip ; Output argument.
+
+ This argument defines how the scale factors Rs are to be interpretted.
+
+ If do_recip is TRUE (one), then the scale factors Rs [i] are to be used
+ by multiplying row i by Rs [i]. Otherwise, the entries in row i are to
+ be divided by Rs [i].
+
+ If UMFPACK has been compiled with gcc, or for MATLAB as either a
+ built-in routine or as a mexFunction, then the NRECIPROCAL flag is
+ set, and do_recip will always be FALSE (zero).
+
+ double Rs [n_row] ; Output argument.
+
+ The row scale factors are returned in Rs [0..n_row-1]. Row i of A is
+ scaled by dividing or multiplying its values by Rs [i]. If default
+ scaling is in use, Rs [i] is the sum of the absolute values of row i
+ (or its reciprocal). If max row scaling is in use, then Rs [i] is the
+ maximum absolute value in row i (or its reciprocal).
+ Otherwise, Rs [i] = 1. If row i is all zero, Rs [i] = 1 as well. For
+ the complex version, an approximate absolute value is used
+ (|x_real|+|x_imag|).
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_symbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_symbolic.h
new file mode 100644
index 0000000..545825e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_get_symbolic.h
@@ -0,0 +1,339 @@
+/* ========================================================================== */
+/* === umfpack_get_symbolic ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_symbolic
+(
+ int *n_row,
+ int *n_col,
+ int *n1,
+ int *nz,
+ int *nfr,
+ int *nchains,
+ int P [ ],
+ int Q [ ],
+ int Front_npivcol [ ],
+ int Front_parent [ ],
+ int Front_1strow [ ],
+ int Front_leftmostdesc [ ],
+ int Chain_start [ ],
+ int Chain_maxrows [ ],
+ int Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+UF_long umfpack_dl_get_symbolic
+(
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *n1,
+ UF_long *nz,
+ UF_long *nfr,
+ UF_long *nchains,
+ UF_long P [ ],
+ UF_long Q [ ],
+ UF_long Front_npivcol [ ],
+ UF_long Front_parent [ ],
+ UF_long Front_1strow [ ],
+ UF_long Front_leftmostdesc [ ],
+ UF_long Chain_start [ ],
+ UF_long Chain_maxrows [ ],
+ UF_long Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+int umfpack_zi_get_symbolic
+(
+ int *n_row,
+ int *n_col,
+ int *n1,
+ int *nz,
+ int *nfr,
+ int *nchains,
+ int P [ ],
+ int Q [ ],
+ int Front_npivcol [ ],
+ int Front_parent [ ],
+ int Front_1strow [ ],
+ int Front_leftmostdesc [ ],
+ int Chain_start [ ],
+ int Chain_maxrows [ ],
+ int Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+UF_long umfpack_zl_get_symbolic
+(
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *n1,
+ UF_long *nz,
+ UF_long *nfr,
+ UF_long *nchains,
+ UF_long P [ ],
+ UF_long Q [ ],
+ UF_long Front_npivcol [ ],
+ UF_long Front_parent [ ],
+ UF_long Front_1strow [ ],
+ UF_long Front_leftmostdesc [ ],
+ UF_long Chain_start [ ],
+ UF_long Chain_maxrows [ ],
+ UF_long Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+/*
+
+double int Syntax:
+
+ #include "umfpack.h"
+ int status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_di_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_dl_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_zi_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_zl_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+Purpose:
+
+ Copies the contents of the Symbolic object into simple integer arrays
+ accessible to the user. This routine is not needed to factorize and/or
+ solve a sparse linear system using UMFPACK. Note that the output arrays
+ P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, and Chain_maxcols are not allocated by
+ umfpack_*_get_symbolic; they must exist on input.
+
+ All output arguments are optional. If any of them are NULL
+ on input, then that part of the symbolic analysis is not copied. You can
+ use this routine to extract just the parts of the symbolic analysis that
+ you want. For example, to retrieve just the column permutation Q, use:
+
+ #define noI (int *) NULL
+ status = umfpack_di_get_symbolic (noI, noI, noI, noI, noI, noI, noI,
+ Q, noI, noI, noI, noI, noI, noI, noI, Symbolic) ;
+
+ The only required argument the last one, the pointer to the Symbolic object.
+
+ The Symbolic object is small. Its size for an n-by-n square matrix varies
+ from 4*n to 13*n, depending on the matrix. The object holds the initial
+ column permutation, the supernodal column elimination tree, and information
+ about each frontal matrix. You can print it with umfpack_*_report_symbolic.
+
+Returns:
+
+ Returns UMFPACK_OK if successful, UMFPACK_ERROR_invalid_Symbolic_object
+ if Symbolic is an invalid object.
+
+Arguments:
+
+ Int *n_row ; Output argument.
+ Int *n_col ; Output argument.
+
+ The dimensions of the matrix A analyzed by the call to
+ umfpack_*_symbolic that generated the Symbolic object.
+
+ Int *n1 ; Output argument.
+
+ The number of pivots with zero Markowitz cost (they have just one entry
+ in the pivot row, or the pivot column, or both). These appear first in
+ the output permutations P and Q.
+
+ Int *nz ; Output argument.
+
+ The number of nonzeros in A.
+
+ Int *nfr ; Output argument.
+
+ The number of frontal matrices that will be used by umfpack_*_numeric
+ to factorize the matrix A. It is in the range 0 to n_col.
+
+ Int *nchains ; Output argument.
+
+ The frontal matrices are related to one another by the supernodal
+ column elimination tree. Each node in this tree is one frontal matrix.
+ The tree is partitioned into a set of disjoint paths, and a frontal
+ matrix chain is one path in this tree. Each chain is factorized using
+ a unifrontal technique, with a single working array that holds each
+ frontal matrix in the chain, one at a time. nchains is in the range
+ 0 to nfr.
+
+ Int P [n_row] ; Output argument.
+
+ The initial row permutation. If P [k] = i, then this means that
+ row i is the kth row in the pre-ordered matrix. In general, this P is
+ not the same as the final row permutation computed by umfpack_*_numeric.
+
+ For the unsymmetric strategy, P defines the row-merge order. Let j be
+ the column index of the leftmost nonzero entry in row i of A*Q. Then
+ P defines a sort of the rows according to this value. A row can appear
+ earlier in this ordering if it is aggressively absorbed before it can
+ become a pivot row. If P [k] = i, row i typically will not be the kth
+ pivot row.
+
+ For the symmetric strategy, P = Q. For the 2-by-2 strategy, P is the
+ row permutation that places large entries on the diagonal of P*A*Q.
+ If no pivoting occurs during numerical factorization, P [k] = i also
+ defines the final permutation of umfpack_*_numeric, for either the
+ symmetric or 2-by-2 strategies.
+
+ Int Q [n_col] ; Output argument.
+
+ The initial column permutation. If Q [k] = j, then this means that
+ column j is the kth pivot column in the pre-ordered matrix. Q is
+ not necessarily the same as the final column permutation Q, computed by
+ umfpack_*_numeric. The numeric factorization may reorder the pivot
+ columns within each frontal matrix to reduce fill-in. If the matrix is
+ structurally singular, and if the symmetric or 2-by-2 strategies or
+ used (or if Control [UMFPACK_FIXQ] > 0), then this Q will be the same
+ as the final column permutation computed in umfpack_*_numeric.
+
+ Int Front_npivcol [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ The kth frontal matrix holds Front_npivcol [k] pivot columns. Thus, the
+ first frontal matrix, front 0, is used to factorize the first
+ Front_npivcol [0] columns; these correspond to the original columns
+ Q [0] through Q [Front_npivcol [0]-1]. The next frontal matrix
+ is used to factorize the next Front_npivcol [1] columns, which are thus
+ the original columns Q [Front_npivcol [0]] through
+ Q [Front_npivcol [0] + Front_npivcol [1] - 1], and so on. Columns
+ with no entries at all are put in a placeholder "front",
+ Front_npivcol [nfr]. The sum of Front_npivcol [0..nfr] is equal to
+ n_col.
+
+ Any modifications that umfpack_*_numeric makes to the initial column
+ permutation are constrained to within each frontal matrix. Thus, for
+ the first frontal matrix, Q [0] through Q [Front_npivcol [0]-1] is some
+ permutation of the columns Q [0] through
+ Q [Front_npivcol [0]-1]. For second frontal matrix,
+ Q [Front_npivcol [0]] through Q [Front_npivcol [0] + Front_npivcol[1]-1]
+ is some permutation of the same portion of Q, and so on. All pivot
+ columns are numerically factorized within the frontal matrix originally
+ determined by the symbolic factorization; there is no delayed pivoting
+ across frontal matrices.
+
+ Int Front_parent [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ Front_parent [0..nfr] holds the supernodal column elimination tree
+ (including the placeholder front nfr, which may be empty). Each node in
+ the tree corresponds to a single frontal matrix. The parent of node f
+ is Front_parent [f].
+
+ Int Front_1strow [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ Front_1strow [k] is the row index of the first row in A (P,Q)
+ whose leftmost entry is in a pivot column for the kth front. This is
+ necessary only to properly factorize singular matrices. Rows in the
+ range Front_1strow [k] to Front_1strow [k+1]-1 first become pivot row
+ candidates at the kth front. Any rows not eliminated in the kth front
+ may be selected as pivot rows in the parent of k (Front_parent [k])
+ and so on up the tree.
+
+ Int Front_leftmostdesc [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ Front_leftmostdesc [k] is the leftmost descendant of front k, or k
+ if the front has no children in the tree. Since the rows and columns
+ (P and Q) have been post-ordered via a depth-first-search of
+ the tree, rows in the range Front_1strow [Front_leftmostdesc [k]] to
+ Front_1strow [k+1]-1 form the entire set of candidate pivot rows for
+ the kth front (some of these will typically have already been selected
+ by fronts in the range Front_leftmostdesc [k] to front k-1, before
+ the factorization reaches front k).
+
+ Chain_start [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first
+ nchains+1 entries are used, however.
+
+ The kth frontal matrix chain consists of frontal matrices Chain_start[k]
+ through Chain_start [k+1]-1. Thus, Chain_start [0] is always 0, and
+ Chain_start [nchains] is the total number of frontal matrices, nfr. For
+ two adjacent fronts f and f+1 within a single chain, f+1 is always the
+ parent of f (that is, Front_parent [f] = f+1).
+
+ Int Chain_maxrows [n_col+1] ; Output argument.
+ Int Chain_maxcols [n_col+1] ; Output argument.
+
+ These arrays should be of size at least n_col+1, in order to guarantee
+ that they will be large enough to hold the output. Only the first
+ nchains entries are used, however.
+
+ The kth frontal matrix chain requires a single working array of
+ dimension Chain_maxrows [k] by Chain_maxcols [k], for the unifrontal
+ technique that factorizes the frontal matrix chain. Since the symbolic
+ factorization only provides an upper bound on the size of each frontal
+ matrix, not all of the working array is necessarily used during the
+ numerical factorization.
+
+ Note that the upper bound on the number of rows and columns of each
+ frontal matrix is computed by umfpack_*_symbolic, but all that is
+ required by umfpack_*_numeric is the maximum of these two sets of
+ values for each frontal matrix chain. Thus, the size of each
+ individual frontal matrix is not preserved in the Symbolic object.
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_*_symbolic. The Symbolic object is not modified by
+ umfpack_*_get_symbolic.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_global.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_global.h
new file mode 100644
index 0000000..c2c946b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_global.h
@@ -0,0 +1,22 @@
+/* ========================================================================== */
+/* === umfpack_global ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* prototypes for global variables, and basic operators for complex values */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN double (*umfpack_hypot) (double, double) ;
+EXTERN int (*umfpack_divcomplex) (double, double, double, double, double *, double *) ;
+
+double umf_hypot (double x, double y) ;
+int umf_divcomplex (double, double, double, double, double *, double *) ;
+
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_load_numeric.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_load_numeric.h
new file mode 100644
index 0000000..4473821
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_load_numeric.h
@@ -0,0 +1,95 @@
+/* ========================================================================== */
+/* === umfpack_load_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_dl_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+int umfpack_zi_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_zl_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_di_load_numeric (&Numeric, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_dl_load_numeric (&Numeric, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zi_load_numeric (&Numeric, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zl_load_numeric (&Numeric, filename) ;
+
+Purpose:
+
+ Loads a Numeric object from a file created by umfpack_*_save_numeric. The
+ Numeric handle passed to this routine is overwritten with the new object.
+ If that object exists prior to calling this routine, a memory leak will
+ occur. The contents of Numeric are ignored on input.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_out_of_memory if not enough memory is available.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void **Numeric ; Output argument.
+
+ **Numeric is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Numeric object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename from which to read the Numeric
+ object.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_load_symbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_load_symbolic.h
new file mode 100644
index 0000000..8952445
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_load_symbolic.h
@@ -0,0 +1,95 @@
+/* ========================================================================== */
+/* === umfpack_load_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_dl_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+int umfpack_zi_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_zl_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_di_load_symbolic (&Symbolic, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_dl_load_symbolic (&Symbolic, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zi_load_symbolic (&Symbolic, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zl_load_symbolic (&Symbolic, filename) ;
+
+Purpose:
+
+ Loads a Symbolic object from a file created by umfpack_*_save_symbolic. The
+ Symbolic handle passed to this routine is overwritten with the new object.
+ If that object exists prior to calling this routine, a memory leak will
+ occur. The contents of Symbolic are ignored on input.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_out_of_memory if not enough memory is available.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void **Symbolic ; Output argument.
+
+ **Symbolic is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Symbolic object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename from which to read the Symbolic
+ object.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_numeric.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_numeric.h
new file mode 100644
index 0000000..0f437b9
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_numeric.h
@@ -0,0 +1,543 @@
+/* ========================================================================== */
+/* === umfpack_numeric ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_numeric
+(
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_numeric
+(
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_numeric
+(
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_numeric
+(
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ int *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info);
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ UF_long *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info);
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ int *Ap, *Ai, status ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ UF_long *Ap, *Ai, status ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, except that Az is NULL.
+
+Purpose:
+
+ Given a sparse matrix A in column-oriented form, and a symbolic analysis
+ computed by umfpack_*_*symbolic, the umfpack_*_numeric routine performs the
+ numerical factorization, PAQ=LU, PRAQ=LU, or P(R\A)Q=LU, where P and Q are
+ permutation matrices (represented as permutation vectors), R is the row
+ scaling, L is unit-lower triangular, and U is upper triangular. This is
+ required before the system Ax=b (or other related linear systems) can be
+ solved. umfpack_*_numeric can be called multiple times for each call to
+ umfpack_*_*symbolic, to factorize a sequence of matrices with identical
+ nonzero pattern. Simply compute the Symbolic object once, with
+ umfpack_*_*symbolic, and reuse it for subsequent matrices. This routine
+ safely detects if the pattern changes, and sets an appropriate error code.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ This must be identical to the Ap array passed to umfpack_*_*symbolic.
+ The value of n_col is what was passed to umfpack_*_*symbolic (this is
+ held in the Symbolic object).
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ This must be identical to the Ai array passed to umfpack_*_*symbolic.
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+ Size 2*nz for packed complex case.
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)].
+
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ For the complex versions, this holds the imaginary part of A. The
+ imaginary part of column j is held in Az [(Ap [j]) ... (Ap [j+1]-1)].
+
+ If Az is NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_*_*symbolic. The Symbolic object is not modified by
+ umfpack_*_numeric.
+
+ void **Numeric ; Output argument.
+
+ **Numeric is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Numeric object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PIVOT_TOLERANCE]: relative pivot tolerance for
+ threshold partial pivoting with row interchanges. In any given
+ column, an entry is numerically acceptable if its absolute value is
+ greater than or equal to Control [UMFPACK_PIVOT_TOLERANCE] times
+ the largest absolute value in the column. A value of 1.0 gives true
+ partial pivoting. If less than or equal to zero, then any nonzero
+ entry is numerically acceptable as a pivot. Default: 0.1.
+
+ Smaller values tend to lead to sparser LU factors, but the solution
+ to the linear system can become inaccurate. Larger values can lead
+ to a more accurate solution (but not always), and usually an
+ increase in the total work.
+
+ For complex matrices, a cheap approximate of the absolute value
+ is used for the threshold partial pivoting test (|a_real| + |a_imag|
+ instead of the more expensive-to-compute exact absolute value
+ sqrt (a_real^2 + a_imag^2)).
+
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE]:
+ If diagonal pivoting is attempted (the symmetric or symmetric-2by2
+ strategies are used) then this parameter is used to control when the
+ diagonal entry is selected in a given pivot column. The absolute
+ value of the entry must be >= Control [UMFPACK_SYM_PIVOT_TOLERANCE]
+ times the largest absolute value in the column. A value of zero
+ will ensure that no off-diagonal pivoting is performed, except that
+ zero diagonal entries are not selected if there are any off-diagonal
+ nonzero entries.
+
+ If an off-diagonal pivot is selected, an attempt is made to restore
+ symmetry later on. Suppose A (i,j) is selected, where i != j.
+ If column i has not yet been selected as a pivot column, then
+ the entry A (j,i) is redefined as a "diagonal" entry, except that
+ the tighter tolerance (Control [UMFPACK_PIVOT_TOLERANCE]) is
+ applied. This strategy has an effect similar to 2-by-2 pivoting
+ for symmetric indefinite matrices. If a 2-by-2 block pivot with
+ nonzero structure
+
+ i j
+ i: 0 x
+ j: x 0
+
+ is selected in a symmetric indefinite factorization method, the
+ 2-by-2 block is inverted and a rank-2 update is applied. In
+ UMFPACK, this 2-by-2 block would be reordered as
+
+ j i
+ i: x 0
+ j: 0 x
+
+ In both cases, the symmetry of the Schur complement is preserved.
+
+ Control [UMFPACK_SCALE]: Note that the user's input matrix is
+ never modified, only an internal copy is scaled.
+
+ There are three valid settings for this parameter. If any other
+ value is provided, the default is used.
+
+ UMFPACK_SCALE_NONE: no scaling is performed.
+
+ UMFPACK_SCALE_SUM: each row of the input matrix A is divided by
+ the sum of the absolute values of the entries in that row.
+ The scaled matrix has an infinity norm of 1.
+
+ UMFPACK_SCALE_MAX: each row of the input matrix A is divided by
+ the maximum the absolute values of the entries in that row.
+ In the scaled matrix the largest entry in each row has
+ a magnitude exactly equal to 1.
+
+ Note that for complex matrices, a cheap approximate absolute value
+ is used, |a_real| + |a_imag|, instead of the exact absolute value
+ sqrt ((a_real)^2 + (a_imag)^2).
+
+ Scaling is very important for the "symmetric" strategy when
+ diagonal pivoting is attempted. It also improves the performance
+ of the "unsymmetric" strategy.
+
+ Default: UMFPACK_SCALE_SUM.
+
+ Control [UMFPACK_ALLOC_INIT]:
+
+ When umfpack_*_numeric starts, it allocates memory for the Numeric
+ object. Part of this is of fixed size (approximately n double's +
+ 12*n integers). The remainder is of variable size, which grows to
+ hold the LU factors and the frontal matrices created during
+ factorization. A estimate of the upper bound is computed by
+ umfpack_*_*symbolic, and returned by umfpack_*_*symbolic in
+ Info [UMFPACK_VARIABLE_PEAK_ESTIMATE] (in Units).
+
+ If Control [UMFPACK_ALLOC_INIT] is >= 0, umfpack_*_numeric initially
+ allocates space for the variable-sized part equal to this estimate
+ times Control [UMFPACK_ALLOC_INIT]. Typically, for matrices for
+ which the "unsymmetric" strategy applies, umfpack_*_numeric needs
+ only about half the estimated memory space, so a setting of 0.5 or
+ 0.6 often provides enough memory for umfpack_*_numeric to factorize
+ the matrix with no subsequent increases in the size of this block.
+
+ If the matrix is ordered via AMD, then this non-negative parameter
+ is ignored. The initial allocation ratio computed automatically,
+ as 1.2 * (nz + Info [UMFPACK_SYMMETRIC_LUNZ]) /
+ (Info [UMFPACK_LNZ_ESTIMATE] + Info [UMFPACK_UNZ_ESTIMATE] -
+ min (n_row, n_col)).
+
+ If Control [UMFPACK_ALLOC_INIT] is negative, then umfpack_*_numeric
+ allocates a space with initial size (in Units) equal to
+ (-Control [UMFPACK_ALLOC_INIT]).
+
+ Regardless of the value of this parameter, a space equal to or
+ greater than the the bare minimum amount of memory needed to start
+ the factorization is always initially allocated. The bare initial
+ memory required is returned by umfpack_*_*symbolic in
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE] (an exact value, not an
+ estimate).
+
+ If the variable-size part of the Numeric object is found to be too
+ small sometime after numerical factorization has started, the memory
+ is increased in size by a factor of 1.2. If this fails, the
+ request is reduced by a factor of 0.95 until it succeeds, or until
+ it determines that no increase in size is possible. Garbage
+ collection then occurs.
+
+ The strategy of attempting to "malloc" a working space, and
+ re-trying with a smaller space, may not work when UMFPACK is used
+ as a mexFunction MATLAB, since mxMalloc aborts the mexFunction if it
+ fails. This issue does not affect the use of UMFPACK as a part of
+ the built-in x=A\b in MATLAB 6.5 and later.
+
+ If you are using the umfpack mexFunction, decrease the magnitude of
+ Control [UMFPACK_ALLOC_INIT] if you run out of memory in MATLAB.
+
+ Default initial allocation size: 0.7. Thus, with the default
+ control settings and the "unsymmetric" strategy, the upper-bound is
+ reached after two reallocations (0.7 * 1.2 * 1.2 = 1.008).
+
+ Changing this parameter has little effect on fill-in or operation
+ count. It has a small impact on run-time (the extra time required
+ to do the garbage collection and memory reallocation).
+
+ Control [UMFPACK_FRONT_ALLOC_INIT]:
+
+ When UMFPACK starts the factorization of each "chain" of frontal
+ matrices, it allocates a working array to hold the frontal matrices
+ as they are factorized. The symbolic factorization computes the
+ size of the largest possible frontal matrix that could occur during
+ the factorization of each chain.
+
+ If Control [UMFPACK_FRONT_ALLOC_INIT] is >= 0, the following
+ strategy is used. If the AMD ordering was used, this non-negative
+ parameter is ignored. A front of size (d+2)*(d+2) is allocated,
+ where d = Info [UMFPACK_SYMMETRIC_DMAX]. Otherwise, a front of
+ size Control [UMFPACK_FRONT_ALLOC_INIT] times the largest front
+ possible for this chain is allocated.
+
+ If Control [UMFPACK_FRONT_ALLOC_INIT] is negative, then a front of
+ size (-Control [UMFPACK_FRONT_ALLOC_INIT]) is allocated (where the
+ size is in terms of the number of numerical entries). This is done
+ regardless of the ordering method or ordering strategy used.
+
+ Default: 0.5.
+
+ Control [UMFPACK_DROPTOL]:
+
+ Entries in L and U with absolute value less than or equal to the
+ drop tolerance are removed from the data structures (unless leaving
+ them there reduces memory usage by reducing the space required
+ for the nonzero pattern of L and U).
+
+ Default: 0.0.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the numeric factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_*_numeric:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Numeric factorization was successful. umfpack_*_numeric
+ computed a valid numeric factorization.
+
+ UMFPACK_WARNING_singular_matrix
+
+ Numeric factorization was successful, but the matrix is
+ singular. umfpack_*_numeric computed a valid numeric
+ factorization, but you will get a divide by zero in
+ umfpack_*_*solve. For the other cases below, no Numeric object
+ is created (*Numeric is (void *) NULL).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to complete the numeric factorization.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing.
+
+ UMFPACK_ERROR_invalid_Symbolic_object
+
+ Symbolic object provided as input is invalid.
+
+ UMFPACK_ERROR_different_pattern
+
+ The pattern (Ap and/or Ai) has changed since the call to
+ umfpack_*_*symbolic which produced the Symbolic object.
+
+ Info [UMFPACK_NROW]: the value of n_row stored in the Symbolic object.
+
+ Info [UMFPACK_NCOL]: the value of n_col stored in the Symbolic object.
+
+ Info [UMFPACK_NZ]: the number of entries in the input matrix.
+ This value is obtained from the Symbolic object.
+
+ Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit, for memory
+ usage statistics below.
+
+ Info [UMFPACK_VARIABLE_INIT]: the initial size (in Units) of the
+ variable-sized part of the Numeric object. If this differs from
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE], then the pattern (Ap and/or
+ Ai) has changed since the last call to umfpack_*_*symbolic, which is
+ an error condition.
+
+ Info [UMFPACK_VARIABLE_PEAK]: the peak size (in Units) of the
+ variable-sized part of the Numeric object. This size is the amount
+ of space actually used inside the block of memory, not the space
+ allocated via UMF_malloc. You can reduce UMFPACK's memory
+ requirements by setting Control [UMFPACK_ALLOC_INIT] to the ratio
+ Info [UMFPACK_VARIABLE_PEAK] / Info[UMFPACK_VARIABLE_PEAK_ESTIMATE].
+ This will ensure that no memory reallocations occur (you may want to
+ add 0.001 to make sure that integer roundoff does not lead to a
+ memory size that is 1 Unit too small; otherwise, garbage collection
+ and reallocation will occur).
+
+ Info [UMFPACK_VARIABLE_FINAL]: the final size (in Units) of the
+ variable-sized part of the Numeric object. It holds just the
+ sparse LU factors.
+
+ Info [UMFPACK_NUMERIC_SIZE]: the actual final size (in Units) of the
+ entire Numeric object, including the final size of the variable
+ part of the object. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE],
+ an estimate, was computed by umfpack_*_*symbolic. The estimate is
+ normally an upper bound on the actual final size, but this is not
+ guaranteed.
+
+ Info [UMFPACK_PEAK_MEMORY]: the actual peak memory usage (in Units) of
+ both umfpack_*_*symbolic and umfpack_*_numeric. An estimate,
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE], was computed by
+ umfpack_*_*symbolic. The estimate is normally an upper bound on the
+ actual peak usage, but this is not guaranteed. With testing on
+ hundreds of matrix arising in real applications, I have never
+ observed a matrix where this estimate or the Numeric size estimate
+ was less than the actual result, but this is theoretically possible.
+ Please send me one if you find such a matrix.
+
+ Info [UMFPACK_FLOPS]: the actual count of the (useful) floating-point
+ operations performed. An estimate, Info [UMFPACK_FLOPS_ESTIMATE],
+ was computed by umfpack_*_*symbolic. The estimate is guaranteed to
+ be an upper bound on this flop count. The flop count excludes
+ "useless" flops on zero values, flops performed during the pivot
+ search (for tentative updates and assembly of candidate columns),
+ and flops performed to add frontal matrices together.
+
+ For the real version, only (+ - * /) are counted. For the complex
+ version, the following counts are used:
+
+ operation flops
+ c = 1/b 6
+ c = a*b 6
+ c -= a*b 8
+
+ Info [UMFPACK_LNZ]: the actual nonzero entries in final factor L,
+ including the diagonal. This excludes any zero entries in L,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_LNZ_ESTIMATE],
+ an estimate, was computed by umfpack_*_*symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_LNZ].
+
+ Info [UMFPACK_UNZ]: the actual nonzero entries in final factor U,
+ including the diagonal. This excludes any zero entries in U,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_UNZ_ESTIMATE],
+ an estimate, was computed by umfpack_*_*symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_UNZ].
+
+ Info [UMFPACK_NUMERIC_DEFRAG]: The number of garbage collections
+ performed during umfpack_*_numeric, to compact the contents of the
+ variable-sized workspace used by umfpack_*_numeric. No estimate was
+ computed by umfpack_*_*symbolic. In the current version of UMFPACK,
+ garbage collection is performed and then the memory is reallocated,
+ so this statistic is the same as Info [UMFPACK_NUMERIC_REALLOC],
+ below. It may differ in future releases.
+
+ Info [UMFPACK_NUMERIC_REALLOC]: The number of times that the Numeric
+ object was increased in size from its initial size. A rough upper
+ bound on the peak size of the Numeric object was computed by
+ umfpack_*_*symbolic, so reallocations should be rare. However, if
+ umfpack_*_numeric is unable to allocate that much storage, it
+ reduces its request until either the allocation succeeds, or until
+ it gets too small to do anything with. If the memory that it
+ finally got was small, but usable, then the reallocation count
+ could be high. No estimate of this count was computed by
+ umfpack_*_*symbolic.
+
+ Info [UMFPACK_NUMERIC_COSTLY_REALLOC]: The number of times that the
+ system realloc library routine (or mxRealloc for the mexFunction)
+ had to move the workspace. Realloc can sometimes increase the size
+ of a block of memory without moving it, which is much faster. This
+ statistic will always be <= Info [UMFPACK_NUMERIC_REALLOC]. If your
+ memory space is fragmented, then the number of "costly" realloc's
+ will be equal to Info [UMFPACK_NUMERIC_REALLOC].
+
+ Info [UMFPACK_COMPRESSED_PATTERN]: The number of integers used to
+ represent the pattern of L and U.
+
+ Info [UMFPACK_LU_ENTRIES]: The total number of numerical values that
+ are stored for the LU factors. Some of the values may be explicitly
+ zero in order to save space (allowing for a smaller compressed
+ pattern).
+
+ Info [UMFPACK_NUMERIC_TIME]: The CPU time taken, in seconds.
+
+ Info [UMFPACK_RCOND]: A rough estimate of the condition number, equal
+ to min (abs (diag (U))) / max (abs (diag (U))), or zero if the
+ diagonal of U is all zero.
+
+ Info [UMFPACK_UDIAG_NZ]: The number of numerically nonzero values on
+ the diagonal of U.
+
+ Info [UMFPACK_UMIN]: the smallest absolute value on the diagonal of U.
+
+ Info [UMFPACK_UMAX]: the smallest absolute value on the diagonal of U.
+
+ Info [UMFPACK_MAX_FRONT_SIZE]: the size of the
+ largest frontal matrix (number of entries).
+
+ Info [UMFPACK_NUMERIC_WALLTIME]: The wallclock time taken, in seconds.
+
+ Info [UMFPACK_MAX_FRONT_NROWS]: the max number of
+ rows in any frontal matrix.
+
+ Info [UMFPACK_MAX_FRONT_NCOLS]: the max number of
+ columns in any frontal matrix.
+
+ Info [UMFPACK_WAS_SCALED]: the scaling used, either UMFPACK_SCALE_NONE,
+ UMFPACK_SCALE_SUM, or UMFPACK_SCALE_MAX.
+
+ Info [UMFPACK_RSMIN]: if scaling is performed, the smallest scale factor
+ for any row (either the smallest sum of absolute entries, or the
+ smallest maximum of absolute entries).
+
+ Info [UMFPACK_RSMAX]: if scaling is performed, the largest scale factor
+ for any row (either the largest sum of absolute entries, or the
+ largest maximum of absolute entries).
+
+ Info [UMFPACK_ALLOC_INIT_USED]: the initial allocation parameter used.
+
+ Info [UMFPACK_FORCED_UPDATES]: the number of BLAS-3 updates to the
+ frontal matrices that were required because the frontal matrix
+ grew larger than its current working array.
+
+ Info [UMFPACK_NOFF_DIAG]: number of off-diagonal pivots selected, if the
+ symmetric or 2-by-2 strategies are used.
+
+ Info [UMFPACK_NZDROPPED]: the number of entries smaller in absolute
+ value than Control [UMFPACK_DROPTOL] that were dropped from L and U.
+ Note that entries on the diagonal of U are never dropped.
+
+ Info [UMFPACK_ALL_LNZ]: the number of entries in L, including the
+ diagonal, if no small entries are dropped.
+
+ Info [UMFPACK_ALL_UNZ]: the number of entries in U, including the
+ diagonal, if no small entries are dropped.
+
+ Only the above listed Info [...] entries are accessed. The remaining
+ entries of Info are not accessed or modified by umfpack_*_numeric.
+ Future versions might modify different parts of Info.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_qsymbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_qsymbolic.h
new file mode 100644
index 0000000..28362f2
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_qsymbolic.h
@@ -0,0 +1,150 @@
+/* ========================================================================== */
+/* === umfpack_qsymbolic ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_qsymbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ const int Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_qsymbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ const UF_long Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_qsymbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const int Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_qsymbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const UF_long Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_di_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit,
+ &Symbolic, Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_dl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit,
+ &Symbolic, Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zi_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit,
+ &Symbolic, Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit,
+ &Symbolic, Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, except Az is NULL.
+
+Purpose:
+
+ Given the nonzero pattern of a sparse matrix A in column-oriented form, and
+ a sparsity preserving column pre-ordering Qinit, umfpack_*_qsymbolic
+ performs the symbolic factorization of A*Qinit (or A (:,Qinit) in MATLAB
+ notation). This is identical to umfpack_*_symbolic, except that neither
+ COLAMD nor AMD are called and the user input column order Qinit is used
+ instead. Note that in general, the Qinit passed to umfpack_*_qsymbolic
+ can differ from the final Q found in umfpack_*_numeric. The unsymmetric
+ strategy will perform a column etree postordering done in
+ umfpack_*_qsymbolic and sparsity-preserving modifications are made within
+ each frontal matrix during umfpack_*_numeric. The symmetric and 2-by-2
+ strategies will preserve Qinit, unless the matrix is structurally singular.
+
+ See umfpack_*_symbolic for more information.
+
+ *** WARNING *** A poor choice of Qinit can easily cause umfpack_*_numeric
+ to use a huge amount of memory and do a lot of work. The "default" symbolic
+ analysis method is umfpack_*_symbolic, not this routine. If you use this
+ routine, the performance of UMFPACK is your responsibility; UMFPACK will
+ not try to second-guess a poor choice of Qinit.
+
+Returns:
+
+ The value of Info [UMFPACK_STATUS]; see umfpack_*_symbolic.
+ Also returns UMFPACK_ERROR_invalid_permuation if Qinit is not a valid
+ permutation vector.
+
+Arguments:
+
+ All arguments are the same as umfpack_*_symbolic, except for the following:
+
+ Int Qinit [n_col] ; Input argument, not modified.
+
+ The user's fill-reducing initial column pre-ordering. This must be a
+ permutation of 0..n_col-1. If Qinit [k] = j, then column j is the kth
+ column of the matrix A (:,Qinit) to be factorized. If Qinit is an
+ (Int *) NULL pointer, then COLAMD or AMD are called instead.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If Qinit is not NULL, then only two strategies are recognized:
+ the unsymmetric strategy and the symmetric strategy.
+ If Control [UMFPACK_STRATEGY] is UMFPACK_STRATEGY_SYMMETRIC,
+ then the symmetric strategy is used. Otherwise the unsymmetric
+ strategy is used.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_control.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_control.h
new file mode 100644
index 0000000..2084409
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_control.h
@@ -0,0 +1,76 @@
+/* ========================================================================== */
+/* === umfpack_report_control =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_dl_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zi_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zl_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_di_report_control (Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_dl_report_control (Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zi_report_control (Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zl_report_control (Control) ;
+
+Purpose:
+
+ Prints the current control settings. Note that with the default print
+ level, nothing is printed. Does nothing if Control is (double *) NULL.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 1 or less: no output
+ 2 or more: print all of Control
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_info.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_info.h
new file mode 100644
index 0000000..e78ae44
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_info.h
@@ -0,0 +1,86 @@
+/* ========================================================================== */
+/* === umfpack_report_info ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+void umfpack_dl_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+void umfpack_zi_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+void umfpack_zl_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_di_report_info (Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_dl_report_info (Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_zi_report_info (Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_zl_report_info (Control, Info) ;
+
+Purpose:
+
+ Reports statistics from the umfpack_*_*symbolic, umfpack_*_numeric, and
+ umfpack_*_*solve routines.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 0 or less: no output, even when an error occurs
+ 1: error messages only
+ 2 or more: error messages, and print all of Info
+ Default: 1
+
+ double Info [UMFPACK_INFO] ; Input argument, not modified.
+
+ Info is an output argument of several UMFPACK routines.
+ The contents of Info are printed on standard output.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_matrix.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_matrix.h
new file mode 100644
index 0000000..7148896
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_matrix.h
@@ -0,0 +1,203 @@
+/* ========================================================================== */
+/* === umfpack_report_matrix ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_matrix
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ int col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_matrix
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ UF_long col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_matrix
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ int col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_matrix
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ UF_long col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ;
+or:
+ status = umfpack_di_report_matrix (n_row, n_col, Ap, Ai, Ax, 0, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ;
+or:
+ status = umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 0, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1,
+ Control) ;
+or:
+ status = umfpack_zi_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 0,
+ Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1,
+ Control) ;
+or:
+ status = umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 0,
+ Control) ;
+
+packed complex Syntax:
+
+ Same as above, except Az is NULL.
+
+Purpose:
+
+ Verifies and prints a row or column-oriented sparse matrix.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise (where n is n_col for the column form and n_row for row
+ and let ni be n_row for the column form and n_col for row):
+
+ UMFPACK_OK if the matrix is valid.
+
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0.
+ UMFPACK_ERROR_argument_missing if Ap and/or Ai are missing.
+ UMFPACK_ERROR_invalid_matrix if Ap [n] < 0, if Ap [0] is not zero,
+ if Ap [j+1] < Ap [j] for any j in the range 0 to n-1,
+ if any row index in Ai is not in the range 0 to ni-1, or
+ if the row indices in any column are not in
+ ascending order, or contain duplicates.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_row matrix. Restriction: n_row > 0 and n_col > 0.
+
+ Int Ap [n+1] ; Input argument, not modified.
+
+ n is n_row for a row-form matrix, and n_col for a column-form matrix.
+
+ Ap is an integer array of size n+1. If col_form is true (nonzero),
+ then on input, it holds the "pointers" for the column form of the
+ sparse matrix A. The row indices of column j of the matrix A are held
+ in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Otherwise, Ap holds the
+ row pointers, and the column indices of row j of the matrix are held
+ in Ai [(Ap [j]) ... (Ap [j+1]-1)].
+
+ The first entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold
+ for all j in the range 0 to n-1. The value nz = Ap [n] is thus the
+ total number of entries in the pattern of the matrix A.
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n].
+
+ If col_form is true (nonzero), then the nonzero pattern (row indices)
+ for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Row indices
+ must be in the range 0 to n_row-1 (the matrix is 0-based).
+
+ Otherwise, the nonzero pattern (column indices) for row j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. Column indices must be in the range 0
+ to n_col-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n].
+ Size 2*nz for packed complex case.
+
+ The numerical values of the sparse matrix A.
+
+ If col_form is true (nonzero), then the nonzero pattern (row indices)
+ for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the
+ corresponding (real) numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in
+ Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions
+ (see below if Az is NULL).
+
+ Otherwise, the nonzero pattern (column indices) for row j
+ is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding
+ (real) numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)].
+ The imaginary parts are stored in Az [(Ap [j]) ... (Ap [j+1]-1)],
+ for the complex versions (see below if Az is NULL).
+
+ No numerical values are printed if Ax is NULL.
+
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ The imaginary values of the sparse matrix A. See the description
+ of Ax, above.
+
+ If Az is NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int col_form ; Input argument, not modified.
+
+ The matrix is in row-oriented form if form is col_form is false (0).
+ Otherwise, the matrix is in column-oriented form.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_numeric.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_numeric.h
new file mode 100644
index 0000000..635f8cd
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_numeric.h
@@ -0,0 +1,112 @@
+/* ========================================================================== */
+/* === umfpack_report_numeric =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_di_report_numeric (Numeric, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_dl_report_numeric (Numeric, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_zi_report_numeric (Numeric, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_zl_report_numeric (Numeric, Control) ;
+
+Purpose:
+
+ Verifies and prints a Numeric object (the LU factorization, both its pattern
+ numerical values, and permutation vectors P and Q). This routine checks the
+ object more carefully than the computational routines. Normally, this check
+ is not required, since umfpack_*_numeric either returns (void *) NULL, or a
+ valid Numeric object. However, if you suspect that your own code has
+ corrupted the Numeric object (by overruning memory bounds, for example),
+ then this routine might be able to detect a corrupted Numeric object. Since
+ this is a complex object, not all such user-generated errors are guaranteed
+ to be caught by this routine.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the Numeric object is valid.
+ UMFPACK_ERROR_invalid_Numeric_object if the Numeric object is invalid.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+
+Arguments:
+
+ void *Numeric ; Input argument, not modified.
+
+ The Numeric object, which holds the numeric factorization computed by
+ umfpack_*_numeric.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_perm.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_perm.h
new file mode 100644
index 0000000..0bf0865
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_perm.h
@@ -0,0 +1,112 @@
+/* ========================================================================== */
+/* === umfpack_report_perm ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_perm
+(
+ int np,
+ const int Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_perm
+(
+ UF_long np,
+ const UF_long Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_perm
+(
+ int np,
+ const int Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_perm
+(
+ UF_long np,
+ const UF_long Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_perm (np, Perm, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_perm (np, Perm, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_perm (np, Perm, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_perm (np, Perm, Control) ;
+
+Purpose:
+
+ Verifies and prints a permutation vector.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+ UMFPACK_OK if the permutation vector is valid (this includes that case
+ when Perm is (Int *) NULL, which is not an error condition).
+ UMFPACK_ERROR_n_nonpositive if np <= 0.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+ UMFPACK_ERROR_invalid_permutation if Perm is not a valid permutation vector.
+
+Arguments:
+
+ Int np ; Input argument, not modified.
+
+ Perm is an integer vector of size np. Restriction: np > 0.
+
+ Int Perm [np] ; Input argument, not modified.
+
+ A permutation vector of size np. If Perm is not present (an (Int *)
+ NULL pointer), then it is assumed to be the identity permutation. This
+ is consistent with its use as an input argument to umfpack_*_qsymbolic,
+ and is not an error condition. If Perm is present, the entries in Perm
+ must range between 0 and np-1, and no duplicates may exist.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_status.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_status.h
new file mode 100644
index 0000000..5acf73c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_status.h
@@ -0,0 +1,90 @@
+/* ========================================================================== */
+/* === umfpack_report_status ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ int status
+) ;
+
+void umfpack_dl_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ UF_long status
+) ;
+
+void umfpack_zi_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ int status
+) ;
+
+void umfpack_zl_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ UF_long status
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ umfpack_di_report_status (Control, status) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ umfpack_dl_report_status (Control, status) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ umfpack_zi_report_status (Control, status) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ umfpack_zl_report_status (Control, status) ;
+
+Purpose:
+
+ Prints the status (return value) of other umfpack_* routines.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 0 or less: no output, even when an error occurs
+ 1: error messages only
+ 2 or more: print status, whether or not an error occurred
+ 4 or more: also print the UMFPACK Copyright
+ 6 or more: also print the UMFPACK License
+ Default: 1
+
+ Int status ; Input argument, not modified.
+
+ The return value from another umfpack_* routine.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_symbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_symbolic.h
new file mode 100644
index 0000000..a3a9413
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_symbolic.h
@@ -0,0 +1,111 @@
+/* ========================================================================== */
+/* === umfpack_report_symbolic ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_di_report_symbolic (Symbolic, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_dl_report_symbolic (Symbolic, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_zi_report_symbolic (Symbolic, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_zl_report_symbolic (Symbolic, Control) ;
+
+Purpose:
+
+ Verifies and prints a Symbolic object. This routine checks the object more
+ carefully than the computational routines. Normally, this check is not
+ required, since umfpack_*_*symbolic either returns (void *) NULL, or a valid
+ Symbolic object. However, if you suspect that your own code has corrupted
+ the Symbolic object (by overruning memory bounds, for example), then this
+ routine might be able to detect a corrupted Symbolic object. Since this is
+ a complex object, not all such user-generated errors are guaranteed to be
+ caught by this routine.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] is <= 2 (no inputs are checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the Symbolic object is valid.
+ UMFPACK_ERROR_invalid_Symbolic_object if the Symbolic object is invalid.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+
+Arguments:
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_*_*symbolic.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_triplet.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_triplet.h
new file mode 100644
index 0000000..0f4f60a
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_triplet.h
@@ -0,0 +1,153 @@
+/* ========================================================================== */
+/* === umfpack_report_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_triplet
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_triplet
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_triplet
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_triplet
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, *Tz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, *Tz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Control) ;
+
+packed complex Syntax:
+
+ Same as above, except Tz is NULL.
+
+Purpose:
+
+ Verifies and prints a matrix in triplet form.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the Triplet matrix is OK.
+ UMFPACK_ERROR_argument_missing if Ti and/or Tj are missing.
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0.
+ UMFPACK_ERROR_invalid_matrix if nz < 0, or
+ if any row or column index in Ti and/or Tj
+ is not in the range 0 to n_row-1 or 0 to n_col-1, respectively.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix.
+
+ Int nz ; Input argument, not modified.
+
+ The number of entries in the triplet form of the matrix.
+
+ Int Ti [nz] ; Input argument, not modified.
+ Int Tj [nz] ; Input argument, not modified.
+ double Tx [nz] ; Input argument, not modified.
+ Size 2*nz for packed complex case.
+ double Tz [nz] ; Input argument, not modified, for complex versions.
+
+ Ti, Tj, Tx (and Tz for complex versions) hold the "triplet" form of a
+ sparse matrix. The kth nonzero entry is in row i = Ti [k], column
+ j = Tj [k], the real numerical value of a_ij is Tx [k], and the
+ imaginary part of a_ij is Tz [k] (for complex versions). The row and
+ column indices i and j must be in the range 0 to n_row-1 or 0 to
+ n_col-1, respectively. Duplicate entries may be present. The
+ "triplets" may be in any order. Tx and Tz are optional; if Tx is
+ not present ((double *) NULL), then the numerical values are
+ not printed.
+
+ If Tx is present and Tz is NULL, then both real
+ and imaginary parts are contained in Tx[0..2*nz-1], with Tx[2*k]
+ and Tx[2*k+1] being the real and imaginary part of the kth entry.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_vector.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_vector.h
new file mode 100644
index 0000000..d930b1e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_report_vector.h
@@ -0,0 +1,133 @@
+/* ========================================================================== */
+/* === umfpack_report_vector ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_vector
+(
+ int n,
+ const double X [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_vector
+(
+ UF_long n,
+ const double X [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_vector
+(
+ int n,
+ const double Xx [ ], const double Xz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_vector
+(
+ UF_long n,
+ const double Xx [ ], const double Xz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n, status ;
+ double *X, Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_vector (n, X, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n, status ;
+ double *X, Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_vector (n, X, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n, status ;
+ double *Xx, *Xz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_vector (n, Xx, Xz, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n, status ;
+ double *Xx, *Xz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_vector (n, Xx, Xz, Control) ;
+
+Purpose:
+
+ Verifies and prints a dense vector.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the vector is valid.
+ UMFPACK_ERROR_argument_missing if X or Xx is missing.
+ UMFPACK_ERROR_n_nonpositive if n <= 0.
+
+Arguments:
+
+ Int n ; Input argument, not modified.
+
+ X is a real or complex vector of size n. Restriction: n > 0.
+
+ double X [n] ; Input argument, not modified. For real versions.
+
+ A real vector of size n. X must not be (double *) NULL.
+
+ double Xx [n or 2*n] ; Input argument, not modified. For complex versions.
+ double Xz [n or 0] ; Input argument, not modified. For complex versions.
+
+ A complex vector of size n, in one of two storage formats.
+ Xx must not be (double *) NULL.
+
+ If Xz is not (double *) NULL, then Xx [i] is the real part of X (i) and
+ Xz [i] is the imaginary part of X (i). Both vectors are of length n.
+ This is the "split" form of the complex vector X.
+
+ If Xz is (double *) NULL, then Xx holds both real and imaginary parts,
+ where Xx [2*i] is the real part of X (i) and Xx [2*i+1] is the imaginary
+ part of X (i). Xx is of length 2*n doubles. If you have an ANSI C99
+ compiler with the intrinsic double _Complex type, then Xx can be of
+ type double _Complex in the calling routine and typecast to (double *)
+ when passed to umfpack_*_report_vector (this is untested, however).
+ This is the "merged" form of the complex vector X.
+
+ Note that all complex routines in UMFPACK V4.4 and later use this same
+ strategy for their complex arguments. The split format is useful for
+ MATLAB, which holds its real and imaginary parts in seperate arrays.
+ The packed format is compatible with the intrinsic double _Complex
+ type in ANSI C99, and is also compatible with SuperLU's method of
+ storing complex matrices. In Version 4.3, this routine was the only
+ one that allowed for packed complex arguments.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_save_numeric.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_save_numeric.h
new file mode 100644
index 0000000..72eb3b1
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_save_numeric.h
@@ -0,0 +1,90 @@
+/* ========================================================================== */
+/* === umfpack_save_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_dl_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+int umfpack_zi_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_zl_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_di_save_numeric (Numeric, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_dl_save_numeric (Numeric, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zi_save_numeric (Numeric, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zl_save_numeric (Numeric, filename) ;
+
+Purpose:
+
+ Saves a Numeric object to a file, which can later be read by
+ umfpack_*_load_numeric. The Numeric object is not modified.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_invalid_Numeric_object if Numeric is not valid.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric or loaded by umfpack_*_load_numeric.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename to which the Numeric
+ object is written.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_save_symbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_save_symbolic.h
new file mode 100644
index 0000000..3e64a26
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_save_symbolic.h
@@ -0,0 +1,90 @@
+/* ========================================================================== */
+/* === umfpack_save_symbolic================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_dl_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+int umfpack_zi_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_zl_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_di_save_symbolic (Symbolic, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_dl_save_symbolic (Symbolic, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zi_save_symbolic (Symbolic, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zl_save_symbolic (Symbolic, filename) ;
+
+Purpose:
+
+ Saves a Symbolic object to a file, which can later be read by
+ umfpack_*_load_symbolic. The Symbolic object is not modified.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_invalid_Symbolic_object if Symbolic is not valid.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void *Symbolic ; Input argument, not modified.
+
+ Symbolic must point to a valid Symbolic object, computed by
+ umfpack_*_symbolic or loaded by umfpack_*_load_symbolic.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename to which the Symbolic
+ object is written.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_scale.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_scale.h
new file mode 100644
index 0000000..6f698b1
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_scale.h
@@ -0,0 +1,112 @@
+/* ========================================================================== */
+/* === umfpack_scale ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_scale
+(
+ double X [ ],
+ const double B [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_dl_scale
+(
+ double X [ ],
+ const double B [ ],
+ void *Numeric
+) ;
+
+int umfpack_zi_scale
+(
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_zl_scale
+(
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *B, *X ;
+ status = umfpack_di_scale (X, B, Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *B, *X ;
+ status = umfpack_dl_scale (X, B, Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *Bx, *Bz, *Xx, *Xz ;
+ status = umfpack_zi_scale (Xx, Xz, Bx, Bz, Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *Bx, *Bz, *Xx, *Xz ;
+ status = umfpack_zl_scale (Xx, Xz, Bx, Bz, Numeric) ;
+
+packed complex Syntax:
+
+ Same as above, except both Xz and Bz are NULL.
+
+Purpose:
+
+ Given LU factors computed by umfpack_*_numeric (PAQ=LU, PRAQ=LU, or
+ P(R\A)Q=LU), and a vector B, this routine computes X = B, X = R*B, or
+ X = R\B, as appropriate. X and B must be vectors equal in length to the
+ number of rows of A.
+
+Returns:
+
+ The status code is returned. UMFPACK_OK is returned if successful.
+ UMFPACK_ERROR_invalid_Numeric_object is returned in the Numeric
+ object is invalid. UMFPACK_ERROR_argument_missing is returned if
+ any of the input vectors are missing (X and B for the real version,
+ and Xx and Bx for the complex version).
+
+Arguments:
+
+ double X [n_row] ; Output argument.
+ or:
+ double Xx [n_row] ; Output argument, real part.
+ Size 2*n_row for packed complex case.
+ double Xz [n_row] ; Output argument, imaginary part.
+
+ The output vector X. If either Xz or Bz are NULL, the vector
+ X is in packed complex form, with the kth entry in Xx [2*k] and
+ Xx [2*k+1], and likewise for B.
+
+ double B [n_row] ; Input argument, not modified.
+ or:
+ double Bx [n_row] ; Input argument, not modified, real part.
+ Size 2*n_row for packed complex case.
+ double Bz [n_row] ; Input argument, not modified, imaginary part.
+
+ The input vector B. See above if either Xz or Bz are NULL.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_solve.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_solve.h
new file mode 100644
index 0000000..a4b984b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_solve.h
@@ -0,0 +1,301 @@
+/* ========================================================================== */
+/* === umfpack_solve ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_solve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_solve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_solve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_solve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, sys ;
+ double *B, *X, *Ax, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, sys ;
+ double *B, *X, *Ax, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, Info [UMFPACK_INFO],
+ Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, Info [UMFPACK_INFO],
+ Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, Xz, Bz, and Az are NULL.
+
+Purpose:
+
+ Given LU factors computed by umfpack_*_numeric (PAQ=LU, PRAQ=LU, or
+ P(R\A)Q=LU) and the right-hand-side, B, solve a linear system for the
+ solution X. Iterative refinement is optionally performed. Only square
+ systems are handled. Singular matrices result in a divide-by-zero for all
+ systems except those involving just the matrix L. Iterative refinement is
+ not performed for singular matrices. In the discussion below, n is equal
+ to n_row and n_col, because only square systems are handled.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int sys ; Input argument, not modified.
+
+ Defines which system to solve. (') is the linear algebraic transpose
+ (complex conjugate if A is complex), and (.') is the array transpose.
+
+ sys value system solved
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Aat A.'x=b
+ UMFPACK_Pt_L P'Lx=b
+ UMFPACK_L Lx=b
+ UMFPACK_Lt_P L'Px=b
+ UMFPACK_Lat_P L.'Px=b
+ UMFPACK_Lt L'x=b
+ UMFPACK_U_Qt UQ'x=b
+ UMFPACK_U Ux=b
+ UMFPACK_Q_Ut QU'x=b
+ UMFPACK_Q_Uat QU.'x=b
+ UMFPACK_Ut U'x=b
+ UMFPACK_Uat U.'x=b
+
+ Iterative refinement can be optionally performed when sys is any of
+ the following:
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Aat A.'x=b
+
+ For the other values of the sys argument, iterative refinement is not
+ performed (Control [UMFPACK_IRSTEP], Ap, Ai, Ax, and Az are ignored).
+
+ Int Ap [n+1] ; Input argument, not modified.
+ Int Ai [nz] ; Input argument, not modified.
+ double Ax [nz] ; Input argument, not modified.
+ Size 2*nz for packed complex case.
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ If iterative refinement is requested (Control [UMFPACK_IRSTEP] >= 1,
+ Ax=b, A'x=b, or A.'x=b is being solved, and A is nonsingular), then
+ these arrays must be identical to the same ones passed to
+ umfpack_*_numeric. The umfpack_*_solve routine does not check the
+ contents of these arguments, so the results are undefined if Ap, Ai, Ax,
+ and/or Az are modified between the calls the umfpack_*_numeric and
+ umfpack_*_solve. These three arrays do not need to be present (NULL
+ pointers can be passed) if Control [UMFPACK_IRSTEP] is zero, or if a
+ system other than Ax=b, A'x=b, or A.'x=b is being solved, or if A is
+ singular, since in each of these cases A is not accessed.
+
+ If Az, Xz, or Bz are NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ double X [n] ; Output argument.
+ or:
+ double Xx [n] ; Output argument, real part
+ Size 2*n for packed complex case.
+ double Xz [n] ; Output argument, imaginary part.
+
+ The solution to the linear system, where n = n_row = n_col is the
+ dimension of the matrices A, L, and U.
+
+ If Az, Xz, or Bz are NULL, then both real
+ and imaginary parts are returned in Xx[0..2*n-1], with Xx[2*k] and
+ Xx[2*k+1] being the real and imaginary part of the kth entry.
+
+ double B [n] ; Input argument, not modified.
+ or:
+ double Bx [n] ; Input argument, not modified, real part.
+ Size 2*n for packed complex case.
+ double Bz [n] ; Input argument, not modified, imaginary part.
+
+ The right-hand side vector, b, stored as a conventional array of size n
+ (or two arrays of size n for complex versions). This routine does not
+ solve for multiple right-hand-sides, nor does it allow b to be stored in
+ a sparse-column form.
+
+ If Az, Xz, or Bz are NULL, then both real
+ and imaginary parts are contained in Bx[0..2*n-1], with Bx[2*k]
+ and Bx[2*k+1] being the real and imaginary part of the kth entry.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_IRSTEP]: The maximum number of iterative refinement
+ steps to attempt. A value less than zero is treated as zero. If
+ less than 1, or if Ax=b, A'x=b, or A.'x=b is not being solved, or
+ if A is singular, then the Ap, Ai, Ax, and Az arguments are not
+ accessed. Default: 2.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the solution factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_*_solve:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ The linear system was successfully solved.
+
+ UMFPACK_WARNING_singular_matrix
+
+ A divide-by-zero occurred. Your solution will contain Inf's
+ and/or NaN's. Some parts of the solution may be valid. For
+ example, solving Ax=b with
+
+ A = [2 0] b = [ 1 ] returns x = [ 0.5 ]
+ [0 0] [ 0 ] [ Inf ]
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to solve the linear system.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing. The B, X, (or
+ Bx and Xx for the complex versions) arguments
+ are always required. Info and Control are not required. Ap,
+ Ai, Ax are required if Ax=b,
+ A'x=b, A.'x=b is to be solved, the (default) iterative
+ refinement is requested, and the matrix A is nonsingular.
+
+ UMFPACK_ERROR_invalid_system
+
+ The sys argument is not valid, or the matrix A is not square.
+
+ UMFPACK_ERROR_invalid_Numeric_object
+
+ The Numeric object is not valid.
+
+ Info [UMFPACK_NROW], Info [UMFPACK_NCOL]:
+ The dimensions of the matrix A (L is n_row-by-n_inner and
+ U is n_inner-by-n_col, with n_inner = min(n_row,n_col)).
+
+ Info [UMFPACK_NZ]: the number of entries in the input matrix, Ap [n],
+ if iterative refinement is requested (Ax=b, A'x=b, or A.'x=b is
+ being solved, Control [UMFPACK_IRSTEP] >= 1, and A is nonsingular).
+
+ Info [UMFPACK_IR_TAKEN]: The number of iterative refinement steps
+ effectively taken. The number of steps attempted may be one more
+ than this; the refinement algorithm backtracks if the last
+ refinement step worsens the solution.
+
+ Info [UMFPACK_IR_ATTEMPTED]: The number of iterative refinement steps
+ attempted. The number of times a linear system was solved is one
+ more than this (once for the initial Ax=b, and once for each Ay=r
+ solved for each iterative refinement step attempted).
+
+ Info [UMFPACK_OMEGA1]: sparse backward error estimate, omega1, if
+ iterative refinement was performed, or -1 if iterative refinement
+ not performed.
+
+ Info [UMFPACK_OMEGA2]: sparse backward error estimate, omega2, if
+ iterative refinement was performed, or -1 if iterative refinement
+ not performed.
+
+ Info [UMFPACK_SOLVE_FLOPS]: the number of floating point operations
+ performed to solve the linear system. This includes the work
+ taken for all iterative refinement steps, including the backtrack
+ (if any).
+
+ Info [UMFPACK_SOLVE_TIME]: The time taken, in seconds.
+
+ Info [UMFPACK_SOLVE_WALLTIME]: The wallclock time taken, in seconds.
+
+ Only the above listed Info [...] entries are accessed. The remaining
+ entries of Info are not accessed or modified by umfpack_*_solve.
+ Future versions might modify different parts of Info.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_symbolic.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_symbolic.h
new file mode 100644
index 0000000..52ed167
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_symbolic.h
@@ -0,0 +1,536 @@
+/* ========================================================================== */
+/* === umfpack_symbolic ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_symbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_symbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_symbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_symbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_di_symbolic (n_row, n_col, Ap, Ai, Ax,
+ &Symbolic, Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_dl_symbolic (n_row, n_col, Ap, Ai, Ax,
+ &Symbolic, Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zi_symbolic (n_row, n_col, Ap, Ai, Ax, Az,
+ &Symbolic, Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zl_symbolic (n_row, n_col, Ap, Ai, Ax, Az,
+ &Symbolic, Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, except Az is NULL.
+
+Purpose:
+
+ Given nonzero pattern of a sparse matrix A in column-oriented form,
+ umfpack_*_symbolic performs a column pre-ordering to reduce fill-in
+ (using COLAMD or AMD) and a symbolic factorization. This is required
+ before the matrix can be numerically factorized with umfpack_*_numeric.
+ If you wish to bypass the COLAMD or AMD pre-ordering and provide your own
+ ordering, use umfpack_*_qsymbolic instead.
+
+ Since umfpack_*_symbolic and umfpack_*_qsymbolic are very similar, options
+ for both routines are discussed below.
+
+ For the following discussion, let S be the submatrix of A obtained after
+ eliminating all pivots of zero Markowitz cost. S has dimension
+ (n_row-n1-nempty_row) -by- (n_col-n1-nempty_col), where
+ n1 = Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS],
+ nempty_row = Info [UMFPACK_NEMPTY_ROW] and
+ nempty_col = Info [UMFPACK_NEMPTY_COL].
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ Ap is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the sparse matrix A. Column j of
+ the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first
+ entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all
+ j in the range 0 to n_col-1. The value nz = Ap [n_col] is thus the
+ total number of entries in the pattern of the matrix A. nz must be
+ greater than or equal to zero.
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to n_row-1 (the matrix is 0-based).
+ See umfpack_*_triplet_to_col for how to sort the columns of a matrix
+ and sum up the duplicate entries. See umfpack_*_report_matrix for how
+ to print the matrix A.
+
+ double Ax [nz] ; Optional input argument, not modified.
+ Size 2*nz for packed complex case.
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. Used only by the 2-by-2 strategy to
+ determine whether entries are "large" or "small". You do not have to
+ pass the same numerical values to umfpack_*_numeric. If Ax is not
+ present (a (double *) NULL pointer), then any entry in A is assumed to
+ be "large".
+
+ double Az [nz] ; Optional input argument, not modified, for complex
+ versions.
+
+ For the complex versions, this holds the imaginary part of A. The
+ imaginary part of column j is held in Az [(Ap [j]) ... (Ap [j+1]-1)].
+
+ If Az is NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ Used by the 2-by-2 strategy only. See the description of Ax, above.
+
+ void **Symbolic ; Output argument.
+
+ **Symbolic is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Symbolic object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used (the defaults are suitable for all matrices,
+ ranging from those with highly unsymmetric nonzero pattern, to
+ symmetric matrices). Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_STRATEGY]: This is the most important control
+ parameter. It determines what kind of ordering and pivoting
+ strategy that UMFPACK should use. There are 4 options:
+
+ UMFPACK_STRATEGY_AUTO: This is the default. The input matrix is
+ analyzed to determine how symmetric the nonzero pattern is, and
+ how many entries there are on the diagonal. It then selects one
+ of the following strategies. Refer to the User Guide for a
+ description of how the strategy is automatically selected.
+
+ UMFPACK_STRATEGY_UNSYMMETRIC: Use the unsymmetric strategy. COLAMD
+ is used to order the columns of A, followed by a postorder of
+ the column elimination tree. No attempt is made to perform
+ diagonal pivoting. The column ordering is refined during
+ factorization.
+
+ In the numerical factorization, the
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE] parameter is ignored. A
+ pivot is selected if its magnitude is >=
+ Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the
+ largest entry in its column.
+
+ UMFPACK_STRATEGY_SYMMETRIC: Use the symmetric strategy
+ In this method, the approximate minimum degree
+ ordering (AMD) is applied to A+A', followed by a postorder of
+ the elimination tree of A+A'. UMFPACK attempts to perform
+ diagonal pivoting during numerical factorization. No refinement
+ of the column pre-ordering is performed during factorization.
+
+ In the numerical factorization, a nonzero entry on the diagonal
+ is selected as the pivot if its magnitude is >= Control
+ [UMFPACK_SYM_PIVOT_TOLERANCE] (default 0.001) times the largest
+ entry in its column. If this is not acceptable, then an
+ off-diagonal pivot is selected with magnitude >= Control
+ [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry
+ in its column.
+
+ UMFPACK_STRATEGY_2BY2: a row permutation P2 is found that places
+ large entries on the diagonal. The matrix P2*A is then
+ factorized using the symmetric strategy, described above.
+ Refer to the User Guide for more information.
+
+ Control [UMFPACK_DENSE_COL]:
+ If COLAMD is used, columns with more than
+ max (16, Control [UMFPACK_DENSE_COL] * 16 * sqrt (n_row)) entries
+ are placed placed last in the column pre-ordering. Default: 0.2.
+
+ Control [UMFPACK_DENSE_ROW]:
+ Rows with more than max (16, Control [UMFPACK_DENSE_ROW] * 16 *
+ sqrt (n_col)) entries are treated differently in the COLAMD
+ pre-ordering, and in the internal data structures during the
+ subsequent numeric factorization. Default: 0.2.
+
+ Control [UMFPACK_AMD_DENSE]: rows/columns in A+A' with more than
+ max (16, Control [UMFPACK_AMD_DENSE] * sqrt (n)) entries
+ (where n = n_row = n_col) are ignored in the AMD pre-ordering.
+ Default: 10.
+
+ Control [UMFPACK_BLOCK_SIZE]: the block size to use for Level-3 BLAS
+ in the subsequent numerical factorization (umfpack_*_numeric).
+ A value less than 1 is treated as 1. Default: 32. Modifying this
+ parameter affects when updates are applied to the working frontal
+ matrix, and can indirectly affect fill-in and operation count.
+ Assuming the block size is large enough (8 or so), this parameter
+ has a modest effect on performance.
+
+ Control [UMFPACK_2BY2_TOLERANCE]: a diagonal entry S (k,k) is
+ considered "small" if it is < tol * max (abs (S (:,k))), where S a
+ submatrix of the scaled input matrix, with pivots of zero Markowitz
+ cost removed.
+
+ Control [UMFPACK_SCALE]: See umfpack_numeric.h for a description.
+ Only affects the 2-by-2 strategy. Default: UMFPACK_SCALE_SUM.
+
+ Control [UMFPACK_FIXQ]: If > 0, then the pre-ordering Q is not modified
+ during numeric factorization. If < 0, then Q may be modified. If
+ zero, then this is controlled automatically (the unsymmetric
+ strategy modifies Q, the others do not). Default: 0.
+
+ Control [UMFPACK_AGGRESSIVE]: If nonzero, aggressive absorption is used
+ in COLAMD and AMD. Default: 1.
+
+ double Info [UMFPACK_INFO] ; Output argument, not defined on input.
+
+ Contains statistics about the symbolic analysis. If a (double *) NULL
+ pointer is passed, then no statistics are returned in Info (this is not
+ an error condition). The entire Info array is cleared (all entries set
+ to -1) and then the following statistics are computed:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Each column of the input matrix contained row indices
+ in increasing order, with no duplicates. Only in this case
+ does umfpack_*_symbolic compute a valid symbolic factorization.
+ For the other cases below, no Symbolic object is created
+ (*Symbolic is (void *) NULL).
+
+ UMFPACK_ERROR_n_nonpositive
+
+ n is less than or equal to zero.
+
+ UMFPACK_ERROR_invalid_matrix
+
+ Number of entries in the matrix is negative, Ap [0] is nonzero,
+ a column has a negative number of entries, a row index is out of
+ bounds, or the columns of input matrix were jumbled (unsorted
+ columns or duplicate entries).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to perform the symbolic analysis. If the
+ analysis requires more than 2GB of memory and you are using
+ the 32-bit ("int") version of UMFPACK, then you are guaranteed
+ to run out of memory. Try using the 64-bit version of UMFPACK.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments is missing.
+
+ UMFPACK_ERROR_internal_error
+
+ Something very serious went wrong. This is a bug.
+ Please contact the author (davis at cise.ufl.edu).
+
+ Info [UMFPACK_NROW]: the value of the input argument n_row.
+
+ Info [UMFPACK_NCOL]: the value of the input argument n_col.
+
+ Info [UMFPACK_NZ]: the number of entries in the input matrix
+ (Ap [n_col]).
+
+ Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit,
+ for memory usage statistics below.
+
+ Info [UMFPACK_SIZE_OF_INT]: the number of bytes in an int.
+
+ Info [UMFPACK_SIZE_OF_LONG]: the number of bytes in a UF_long.
+
+ Info [UMFPACK_SIZE_OF_POINTER]: the number of bytes in a void *
+ pointer.
+
+ Info [UMFPACK_SIZE_OF_ENTRY]: the number of bytes in a numerical entry.
+
+ Info [UMFPACK_NDENSE_ROW]: number of "dense" rows in A. These rows are
+ ignored when the column pre-ordering is computed in COLAMD. They
+ are also treated differently during numeric factorization. If > 0,
+ then the matrix had to be re-analyzed by UMF_analyze, which does
+ not ignore these rows.
+
+ Info [UMFPACK_NEMPTY_ROW]: number of "empty" rows in A, as determined
+ These are rows that either have no entries, or whose entries are
+ all in pivot columns of zero-Markowitz-cost pivots.
+
+ Info [UMFPACK_NDENSE_COL]: number of "dense" columns in A. COLAMD
+ orders these columns are ordered last in the factorization, but
+ before "empty" columns.
+
+ Info [UMFPACK_NEMPTY_COL]: number of "empty" columns in A. These are
+ columns that either have no entries, or whose entries are all in
+ pivot rows of zero-Markowitz-cost pivots. These columns are
+ ordered last in the factorization, to the right of "dense" columns.
+
+ Info [UMFPACK_SYMBOLIC_DEFRAG]: number of garbage collections
+ performed during ordering and symbolic pre-analysis.
+
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]: the amount of memory (in Units)
+ required for umfpack_*_symbolic to complete. This count includes
+ the size of the Symbolic object itself, which is also reported in
+ Info [UMFPACK_SYMBOLIC_SIZE].
+
+ Info [UMFPACK_SYMBOLIC_SIZE]: the final size of the Symbolic object (in
+ Units). This is fairly small, roughly 2*n to 13*n integers,
+ depending on the matrix.
+
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE]: the Numeric object contains two
+ parts. The first is fixed in size (O (n_row+n_col)). The
+ second part holds the sparse LU factors and the contribution blocks
+ from factorized frontal matrices. This part changes in size during
+ factorization. Info [UMFPACK_VARIABLE_INIT_ESTIMATE] is the exact
+ size (in Units) required for this second variable-sized part in
+ order for the numerical factorization to start.
+
+ Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]: the estimated peak size (in
+ Units) of the variable-sized part of the Numeric object. This is
+ usually an upper bound, but that is not guaranteed.
+
+ Info [UMFPACK_VARIABLE_FINAL_ESTIMATE]: the estimated final size (in
+ Units) of the variable-sized part of the Numeric object. This is
+ usually an upper bound, but that is not guaranteed. It holds just
+ the sparse LU factors.
+
+ Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]: an estimate of the final size (in
+ Units) of the entire Numeric object (both fixed-size and variable-
+ sized parts), which holds the LU factorization (including the L, U,
+ P and Q matrices).
+
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE]: an estimate of the total amount of
+ memory (in Units) required by umfpack_*_symbolic and
+ umfpack_*_numeric to perform both the symbolic and numeric
+ factorization. This is the larger of the amount of memory needed
+ in umfpack_*_numeric itself, and the amount of memory needed in
+ umfpack_*_symbolic (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]). The
+ count includes the size of both the Symbolic and Numeric objects
+ themselves. It can be a very loose upper bound, particularly when
+ the symmetric or 2-by-2 strategies are used.
+
+ Info [UMFPACK_FLOPS_ESTIMATE]: an estimate of the total floating-point
+ operations required to factorize the matrix. This is a "true"
+ theoretical estimate of the number of flops that would be performed
+ by a flop-parsimonious sparse LU algorithm. It assumes that no
+ extra flops are performed except for what is strictly required to
+ compute the LU factorization. It ignores, for example, the flops
+ performed by umfpack_di_numeric to add contribution blocks of
+ frontal matrices together. If L and U are the upper bound on the
+ pattern of the factors, then this flop count estimate can be
+ represented in MATLAB (for real matrices, not complex) as:
+
+ Lnz = full (sum (spones (L))) - 1 ; % nz in each col of L
+ Unz = full (sum (spones (U')))' - 1 ; % nz in each row of U
+ flops = 2*Lnz*Unz + sum (Lnz) ;
+
+ The actual "true flop" count found by umfpack_*_numeric will be
+ less than this estimate.
+
+ For the real version, only (+ - * /) are counted. For the complex
+ version, the following counts are used:
+
+ operation flops
+ c = 1/b 6
+ c = a*b 6
+ c -= a*b 8
+
+ Info [UMFPACK_LNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ L, including the diagonal. Since L is unit-diagonal, the diagonal
+ of L is not stored. This estimate is a strict upper bound on the
+ actual nonzeros in L to be computed by umfpack_*_numeric.
+
+ Info [UMFPACK_UNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ U, including the diagonal. This estimate is a strict upper bound on
+ the actual nonzeros in U to be computed by umfpack_*_numeric.
+
+ Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE]: estimate of the size of the
+ largest frontal matrix (# of entries), for arbitrary partial
+ pivoting during numerical factorization.
+
+ Info [UMFPACK_SYMBOLIC_TIME]: The CPU time taken, in seconds.
+
+ Info [UMFPACK_SYMBOLIC_WALLTIME]: The wallclock time taken, in seconds.
+
+ Info [UMFPACK_STRATEGY_USED]: The ordering strategy used:
+ UMFPACK_STRATEGY_SYMMETRIC, UMFPACK_STRATEGY_UNSYMMETRIC, or
+ UMFPACK_STRATEGY_2BY2.
+
+ Info [UMFPACK_ORDERING_USED]: The ordering method used:
+ UMFPACK_ORDERING_COLAMD or UMFPACK_ORDERING_AMD. It can be
+ UMFPACK_ORDERING_GIVEN for umfpack_*_qsymbolic.
+
+ Info [UMFPACK_QFIXED]: 1 if the column pre-ordering will be refined
+ during numerical factorization, 0 if not.
+
+ Info [UMFPACK_DIAG_PREFERED]: 1 if diagonal pivoting will be attempted,
+ 0 if not.
+
+ Info [UMFPACK_COL_SINGLETONS]: the matrix A is analyzed by first
+ eliminating all pivots with zero Markowitz cost. This count is the
+ number of these pivots with exactly one nonzero in their pivot
+ column.
+
+ Info [UMFPACK_ROW_SINGLETONS]: the number of zero-Markowitz-cost
+ pivots with exactly one nonzero in their pivot row.
+
+ Info [UMFPACK_PATTERN_SYMMETRY]: the symmetry of the pattern of S.
+
+ Info [UMFPACK_NZ_A_PLUS_AT]: the number of off-diagonal entries in S+S'.
+
+ Info [UMFPACK_NZDIAG]: the number of entries on the diagonal of S.
+
+ Info [UMFPACK_N2]: if S is square, and nempty_row = nempty_col, this
+ is equal to n_row - n1 - nempty_row.
+
+ Info [UMFPACK_S_SYMMETRIC]: 1 if S is square and its diagonal has been
+ preserved, 0 otherwise.
+
+
+ Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE]: estimate of the max number of
+ rows in any frontal matrix, for arbitrary partial pivoting.
+
+ Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE]: estimate of the max number of
+ columns in any frontal matrix, for arbitrary partial pivoting.
+
+ ------------------------------------------------------------------------
+ The next four statistics are computed only if AMD is used:
+ ------------------------------------------------------------------------
+
+ Info [UMFPACK_SYMMETRIC_LUNZ]: The number of nonzeros in L and U,
+ assuming no pivoting during numerical factorization, and assuming a
+ zero-free diagonal of U. Excludes the entries on the diagonal of
+ L. If the matrix has a purely symmetric nonzero pattern, this is
+ often a lower bound on the nonzeros in the actual L and U computed
+ in the numerical factorization, for matrices that fit the criteria
+ for the "symmetric" strategy.
+
+ Info [UMFPACK_SYMMETRIC_FLOPS]: The floating-point operation count in
+ the numerical factorization phase, assuming no pivoting. If the
+ pattern of the matrix is symmetric, this is normally a lower bound
+ on the floating-point operation count in the actual numerical
+ factorization, for matrices that fit the criteria for the symmetric
+ or 2-by-2 strategies
+
+ Info [UMFPACK_SYMMETRIC_NDENSE]: The number of "dense" rows/columns of
+ S+S' that were ignored during the AMD ordering. These are placed
+ last in the output order. If > 0, then the
+ Info [UMFPACK_SYMMETRIC_*] statistics, above are rough upper bounds.
+
+ Info [UMFPACK_SYMMETRIC_DMAX]: The maximum number of nonzeros in any
+ column of L, if no pivoting is performed during numerical
+ factorization. Excludes the part of the LU factorization for
+ pivots with zero Markowitz cost.
+
+ ------------------------------------------------------------------------
+ The following statistics are computed only if the 2-by-2 strategy is
+ used or attempted:
+ ------------------------------------------------------------------------
+
+ Info [UMFPACK_2BY2_NWEAK]: the number of small diagonal entries in S.
+
+ Info [UMFPACK_2BY2_UNMATCHED]: the number of small diagonal entries
+ in P2*S.
+
+ Info [UMFPACK_2BY2_PATTERN_SYMMETRY]: the symmetry of P2*S.
+
+ Info [UMFPACK_2BY2_NZ_PA_PLUS_AT]: the number of off-diagonal entries
+ in (P2*S)+(P2*S)'.
+
+ Info [UMFPACK_2BY2_NZDIAG]: the number of nonzero entries on the
+ diagonal of P2*S.
+
+
+ At the start of umfpack_*_symbolic, all of Info is set of -1, and then
+ after that only the above listed Info [...] entries are accessed.
+ Future versions might modify different parts of Info.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_tictoc.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_tictoc.h
new file mode 100644
index 0000000..c2d7e57
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_tictoc.h
@@ -0,0 +1,60 @@
+/* ========================================================================== */
+/* === umfpack_tictoc ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_tic (double stats [2]) ;
+
+void umfpack_toc (double stats [2]) ;
+
+
+/*
+Syntax (for all versions: di, dl, zi, and zl):
+
+ #include "umfpack.h"
+ double stats [2] ;
+ umfpack_tic (stats) ;
+ ...
+ umfpack_toc (stats) ;
+
+Purpose:
+
+ umfpack_tic returns the CPU time and wall clock time used by the process.
+ The CPU time includes both "user" and "system" time (the latter is time
+ spent by the system on behalf of the process, and is thus charged to the
+ process). umfpack_toc returns the CPU time and wall clock time since the
+ last call to umfpack_tic with the same stats array.
+
+ Typical usage:
+
+ umfpack_tic (stats) ;
+ ... do some work ...
+ umfpack_toc (stats) ;
+
+ then stats [1] contains the time in seconds used by the code between
+ umfpack_tic and umfpack_toc, and stats [0] contains the wall clock time
+ elapsed between the umfpack_tic and umfpack_toc. These two routines act
+ just like tic and toc in MATLAB, except that the both process time and
+ wall clock time are returned.
+
+ This routine normally uses the sysconf and times routines in the POSIX
+ standard. If -DNPOSIX is defined at compile time, then the ANSI C clock
+ routine is used instead, and only the CPU time is returned (stats [0]
+ is set to zero).
+
+ umfpack_tic and umfpack_toc are the routines used internally in UMFPACK
+ to time the symbolic analysis, numerical factorization, and the forward/
+ backward solve.
+
+Arguments:
+
+ double stats [2]:
+
+ stats [0]: wall clock time, in seconds
+ stats [1]: CPU time, in seconds
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_timer.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_timer.h
new file mode 100644
index 0000000..7284a08
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_timer.h
@@ -0,0 +1,39 @@
+/* ========================================================================== */
+/* === umfpack_timer ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+double umfpack_timer ( void ) ;
+
+/*
+Syntax (for all versions: di, dl, zi, and zl):
+
+ #include "umfpack.h"
+ double t ;
+ t = umfpack_timer ( ) ;
+
+Purpose:
+
+ Returns the CPU time used by the process. Includes both "user" and "system"
+ time (the latter is time spent by the system on behalf of the process, and
+ is thus charged to the process). It does not return the wall clock time.
+ See umfpack_tic and umfpack_toc (the file umfpack_tictoc.h) for the timer
+ used internally by UMFPACK.
+
+ This routine uses the Unix getrusage routine, if available. It is less
+ subject to overflow than the ANSI C clock routine. If getrusage is not
+ available, the portable ANSI C clock routine is used instead.
+ Unfortunately, clock ( ) overflows if the CPU time exceeds 2147 seconds
+ (about 36 minutes) when sizeof (clock_t) is 4 bytes. If you have getrusage,
+ be sure to compile UMFPACK with the -DGETRUSAGE flag set; see umf_config.h
+ and the User Guide for details. Even the getrusage routine can overlow.
+
+Arguments:
+
+ None.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_transpose.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_transpose.h
new file mode 100644
index 0000000..15aa60d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_transpose.h
@@ -0,0 +1,216 @@
+/* ========================================================================== */
+/* === umfpack_transpose ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_transpose
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ const int P [ ],
+ const int Q [ ],
+ int Rp [ ],
+ int Ri [ ],
+ double Rx [ ]
+) ;
+
+UF_long umfpack_dl_transpose
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ const UF_long P [ ],
+ const UF_long Q [ ],
+ UF_long Rp [ ],
+ UF_long Ri [ ],
+ double Rx [ ]
+) ;
+
+int umfpack_zi_transpose
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const int P [ ],
+ const int Q [ ],
+ int Rp [ ],
+ int Ri [ ],
+ double Rx [ ], double Rz [ ],
+ int do_conjugate
+) ;
+
+UF_long umfpack_zl_transpose
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const UF_long P [ ],
+ const UF_long Q [ ],
+ UF_long Rp [ ],
+ UF_long Ri [ ],
+ double Rx [ ], double Rz [ ],
+ UF_long do_conjugate
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri ;
+ double *Ax, *Rx ;
+ status = umfpack_di_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri ;
+ double *Ax, *Rx ;
+ status = umfpack_dl_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri, do_conjugate ;
+ double *Ax, *Az, *Rx, *Rz ;
+ status = umfpack_zi_transpose (n_row, n_col, Ap, Ai, Ax, Az, P, Q,
+ Rp, Ri, Rx, Rz, do_conjugate) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri, do_conjugate ;
+ double *Ax, *Az, *Rx, *Rz ;
+ status = umfpack_zl_transpose (n_row, n_col, Ap, Ai, Ax, Az, P, Q,
+ Rp, Ri, Rx, Rz, do_conjugate) ;
+
+packed complex Syntax:
+
+ Same as above, except Az are Rz are NULL.
+
+Purpose:
+
+ Transposes and optionally permutes a sparse matrix in row or column-form,
+ R = (PAQ)'. In MATLAB notation, R = (A (P,Q))' or R = (A (P,Q)).' doing
+ either the linear algebraic transpose or the array transpose. Alternatively,
+ this routine can be viewed as converting A (P,Q) from column-form to
+ row-form, or visa versa (for the array transpose). Empty rows and columns
+ may exist. The matrix A may be singular and/or rectangular.
+
+ umfpack_*_transpose is useful if you want to factorize A' or A.' instead of
+ A. Factorizing A' or A.' instead of A can be much better, particularly if
+ AA' is much sparser than A'A. You can still solve Ax=b if you factorize
+ A' or A.', by solving with the sys argument UMFPACK_At or UMFPACK_Aat,
+ respectively, in umfpack_*_*solve.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_out_of_memory if umfpack_*_transpose fails to allocate a
+ size-max (n_row,n_col) workspace.
+ UMFPACK_ERROR_argument_missing if Ai, Ap, Ri, and/or Rp are missing.
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0
+ UMFPACK_ERROR_invalid_permutation if P and/or Q are invalid.
+ UMFPACK_ERROR_invalid_matrix if Ap [n_col] < 0, if Ap [0] != 0,
+ if Ap [j] > Ap [j+1] for any j in the range 0 to n_col-1,
+ if any row index i is < 0 or >= n_row, or if the row indices
+ in any column are not in ascending order.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ The column pointers of the column-oriented form of the matrix A. See
+ umfpack_*_symbolic for a description. The number of entries in
+ the matrix is nz = Ap [n_col]. Ap [0] must be zero, Ap [n_col] must be
+ => 0, and Ap [j] <= Ap [j+1] and Ap [j] <= Ap [n_col] must be true for
+ all j in the range 0 to n_col-1. Empty columns are OK (that is, Ap [j]
+ may equal Ap [j+1] for any j in the range 0 to n_col-1).
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to n_row-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+ Size 2*nz if Az or Rz are NULL.
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ If present, these are the numerical values of the sparse matrix A.
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding real numerical
+ values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary
+ values are stored in Az [(Ap [j]) ... (Ap [j+1]-1)]. The values are
+ transposed only if Ax and Rx are present.
+ This is not an error conditions; you are able to transpose
+ and permute just the pattern of a matrix.
+
+ If Az or Rz are NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int P [n_row] ; Input argument, not modified.
+
+ The permutation vector P is defined as P [k] = i, where the original
+ row i of A is the kth row of PAQ. If you want to use the identity
+ permutation for P, simply pass (Int *) NULL for P. This is not an error
+ condition. P is a complete permutation of all the rows of A; this
+ routine does not support the creation of a transposed submatrix of A
+ (R = A (1:3,:)' where A has more than 3 rows, for example, cannot be
+ done; a future version might support this operation).
+
+ Int Q [n_col] ; Input argument, not modified.
+
+ The permutation vector Q is defined as Q [k] = j, where the original
+ column j of A is the kth column of PAQ. If you want to use the identity
+ permutation for Q, simply pass (Int *) NULL for Q. This is not an error
+ condition. Q is a complete permutation of all the columns of A; this
+ routine does not support the creation of a transposed submatrix of A.
+
+ Int Rp [n_row+1] ; Output argument.
+
+ The column pointers of the matrix R = (A (P,Q))' or (A (P,Q)).', in the
+ same form as the column pointers Ap for the matrix A.
+
+ Int Ri [nz] ; Output argument.
+
+ The row indices of the matrix R = (A (P,Q))' or (A (P,Q)).' , in the
+ same form as the row indices Ai for the matrix A.
+
+ double Rx [nz] ; Output argument.
+ Size 2*nz if Az or Rz are NULL.
+ double Rz [nz] ; Output argument, imaginary part for complex versions.
+
+ If present, these are the numerical values of the sparse matrix R,
+ in the same form as the values Ax and Az of the matrix A.
+
+ If Az or Rz are NULL, then both real
+ and imaginary parts are contained in Rx[0..2*nz-1], with Rx[2*k]
+ and Rx[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int do_conjugate ; Input argument for complex versions only.
+
+ If true, and if Ax and Rx are present, then the linear
+ algebraic transpose is computed (complex conjugate). If false, the
+ array transpose is computed instead.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_triplet_to_col.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_triplet_to_col.h
new file mode 100644
index 0000000..b519d86
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_triplet_to_col.h
@@ -0,0 +1,263 @@
+/* ========================================================================== */
+/* === umfpack_triplet_to_col =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_triplet_to_col
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ],
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ],
+ int Map [ ]
+) ;
+
+UF_long umfpack_dl_triplet_to_col
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ],
+ UF_long Ap [ ],
+ UF_long Ai [ ],
+ double Ax [ ],
+ UF_long Map [ ]
+) ;
+
+int umfpack_zi_triplet_to_col
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ], double Az [ ],
+ int Map [ ]
+) ;
+
+UF_long umfpack_zl_triplet_to_col
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ UF_long Ap [ ],
+ UF_long Ai [ ],
+ double Ax [ ], double Az [ ],
+ UF_long Map [ ]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Ax ;
+ status = umfpack_di_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx,
+ Ap, Ai, Ax, Map) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Ax ;
+ status = umfpack_dl_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx,
+ Ap, Ai, Ax, Map) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Tz, *Ax, *Az ;
+ status = umfpack_zi_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Ap, Ai, Ax, Az, Map) ;
+
+UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Tz, *Ax, *Az ;
+ status = umfpack_zl_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Ap, Ai, Ax, Az, Map) ;
+
+packed complex Syntax:
+
+ Same as above, except Tz and Az are NULL.
+
+Purpose:
+
+ Converts a sparse matrix from "triplet" form to compressed-column form.
+ Analogous to A = spconvert (Ti, Tj, Tx + Tz*1i) in MATLAB, except that
+ zero entries present in the triplet form are present in A.
+
+ The triplet form of a matrix is a very simple data structure for basic
+ sparse matrix operations. For example, suppose you wish to factorize a
+ matrix A coming from a finite element method, in which A is a sum of
+ dense submatrices, A = E1 + E2 + E3 + ... . The entries in each element
+ matrix Ei can be concatenated together in the three triplet arrays, and
+ any overlap between the elements will be correctly summed by
+ umfpack_*_triplet_to_col.
+
+ Transposing a matrix in triplet form is simple; just interchange the
+ use of Ti and Tj. You can construct the complex conjugate transpose by
+ negating Tz, for the complex versions.
+
+ Permuting a matrix in triplet form is also simple. If you want the matrix
+ PAQ, or A (P,Q) in MATLAB notation, where P [k] = i means that row i of
+ A is the kth row of PAQ and Q [k] = j means that column j of A is the kth
+ column of PAQ, then do the following. First, create inverse permutations
+ Pinv and Qinv such that Pinv [i] = k if P [k] = i and Qinv [j] = k if
+ Q [k] = j. Next, for the mth triplet (Ti [m], Tj [m], Tx [m], Tz [m]),
+ replace Ti [m] with Pinv [Ti [m]] and replace Tj [m] with Qinv [Tj [m]].
+
+ If you have a column-form matrix with duplicate entries or unsorted
+ columns, you can sort it and sum up the duplicates by first converting it
+ to triplet form with umfpack_*_col_to_triplet, and then converting it back
+ with umfpack_*_triplet_to_col.
+
+ Constructing a submatrix is also easy. Just scan the triplets and remove
+ those entries outside the desired subset of 0...n_row-1 and 0...n_col-1,
+ and renumber the indices according to their position in the subset.
+
+ You can do all these operations on a column-form matrix by first
+ converting it to triplet form with umfpack_*_col_to_triplet, doing the
+ operation on the triplet form, and then converting it back with
+ umfpack_*_triplet_to_col.
+
+ The only operation not supported easily in the triplet form is the
+ multiplication of two sparse matrices (UMFPACK does not provide this
+ operation).
+
+ You can print the input triplet form with umfpack_*_report_triplet, and
+ the output matrix with umfpack_*_report_matrix.
+
+ The matrix may be singular (nz can be zero, and empty rows and/or columns
+ may exist). It may also be rectangular and/or complex.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_argument_missing if Ap, Ai, Ti, and/or Tj are missing.
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0.
+ UMFPACK_ERROR_invalid_matrix if nz < 0, or if for any k, Ti [k] and/or
+ Tj [k] are not in the range 0 to n_row-1 or 0 to n_col-1, respectively.
+ UMFPACK_ERROR_out_of_memory if unable to allocate sufficient workspace.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+ All row and column indices in the triplet form must be in the range
+ 0 to n_row-1 and 0 to n_col-1, respectively.
+
+ Int nz ; Input argument, not modified.
+
+ The number of entries in the triplet form of the matrix. Restriction:
+ nz >= 0.
+
+ Int Ti [nz] ; Input argument, not modified.
+ Int Tj [nz] ; Input argument, not modified.
+ double Tx [nz] ; Input argument, not modified.
+ Size 2*nz if Tz or Az are NULL.
+ double Tz [nz] ; Input argument, not modified, for complex versions.
+
+ Ti, Tj, Tx, and Tz hold the "triplet" form of a sparse matrix. The kth
+ nonzero entry is in row i = Ti [k], column j = Tj [k], and the real part
+ of a_ij is Tx [k]. The imaginary part of a_ij is Tz [k], for complex
+ versions. The row and column indices i and j must be in the range 0 to
+ n_row-1 and 0 to n_col-1, respectively. Duplicate entries may be
+ present; they are summed in the output matrix. This is not an error
+ condition. The "triplets" may be in any order. Tx, Tz, Ax, and Az
+ are optional. Ax is computed only if both Ax and Tx are present
+ (not (double *) NULL). This is not error condition; the routine can
+ create just the pattern of the output matrix from the pattern of the
+ triplets.
+
+ If Az or Tz are NULL, then both real
+ and imaginary parts are contained in Tx[0..2*nz-1], with Tx[2*k]
+ and Tx[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int Ap [n_col+1] ; Output argument.
+
+ Ap is an integer array of size n_col+1 on input. On output, Ap holds
+ the "pointers" for the column form of the sparse matrix A. Column j of
+ the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first
+ entry, Ap [0], is zero, and Ap [j] <= Ap [j+1] holds for all j in the
+ range 0 to n_col-1. The value nz2 = Ap [n_col] is thus the total
+ number of entries in the pattern of the matrix A. Equivalently, the
+ number of duplicate triplets is nz - Ap [n_col].
+
+ Int Ai [nz] ; Output argument.
+
+ Ai is an integer array of size nz on input. Note that only the first
+ Ap [n_col] entries are used.
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ are in ascending order, and no duplicate row indices are present.
+ Row indices are in the range 0 to n_col-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Output argument. Size 2*nz if Tz or Az are NULL.
+ double Az [nz] ; Output argument for complex versions.
+
+ Ax and Az (for the complex versions) are double arrays of size nz on
+ input. Note that only the first Ap [n_col] entries are used
+ in both arrays.
+
+ Ax is optional; if Tx and/or Ax are not present (a (double *) NULL
+ pointer), then Ax is not computed. If present, Ax holds the
+ numerical values of the the real part of the sparse matrix A and Az
+ holds the imaginary parts. The nonzero pattern (row indices) for
+ column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the
+ corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in
+ Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions.
+
+ If Az or Tz are NULL, then both real
+ and imaginary parts are returned in Ax[0..2*nz2-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ int Map [nz] ; Optional output argument.
+
+ If Map is present (a non-NULL pointer to an Int array of size nz), then
+ on output it holds the position of the triplets in the column-form
+ matrix. That is, suppose p = Map [k], and the k-th triplet is i=Ti[k],
+ j=Tj[k], and aij=Tx[k]. Then i=Ai[p], and aij will have been summed
+ into Ax[p] (or simply aij=Ax[p] if there were no duplicate entries also
+ in row i and column j). Also, Ap[j] <= p < Ap[j+1]. The Map array is
+ not computed if it is (Int *) NULL. The Map array is useful for
+ converting a subsequent triplet form matrix with the same pattern as the
+ first one, without calling this routine. If Ti and Tj do not change,
+ then Ap, and Ai can be reused from the prior call to
+ umfpack_*_triplet_to_col. You only need to recompute Ax (and Az for the
+ split complex version). This code excerpt properly sums up all
+ duplicate values (for the real version):
+
+ for (p = 0 ; p < Ap [n_col] ; p++) Ax [p] = 0 ;
+ for (k = 0 ; k < nz ; k++) Ax [Map [k]] += Tx [k] ;
+
+ This feature is useful (along with the reuse of the Symbolic object) if
+ you need to factorize a sequence of triplet matrices with identical
+ nonzero pattern (the order of the triplets in the Ti,Tj,Tx arrays must
+ also remain unchanged). It is faster than calling this routine for
+ each matrix, and requires no workspace.
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Include/umfpack_wsolve.h b/src/C/SuiteSparse/UMFPACK/Include/umfpack_wsolve.h
new file mode 100644
index 0000000..c2ed033
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Include/umfpack_wsolve.h
@@ -0,0 +1,172 @@
+/* ========================================================================== */
+/* === umfpack_wsolve ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_wsolve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ int Wi [ ],
+ double W [ ]
+) ;
+
+UF_long umfpack_dl_wsolve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ UF_long Wi [ ],
+ double W [ ]
+) ;
+
+int umfpack_zi_wsolve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ int Wi [ ],
+ double W [ ]
+) ;
+
+UF_long umfpack_zl_wsolve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ UF_long Wi [ ],
+ double W [ ]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, *Wi, sys ;
+ double *B, *X, *Ax, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_wsolve (sys, Ap, Ai, Ax, X, B, Numeric,
+ Control, Info, Wi, W) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, *Wi, sys ;
+ double *B, *X, *Ax, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_wsolve (sys, Ap, Ai, Ax, X, B, Numeric,
+ Control, Info, Wi, W) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, *Wi, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, *W,
+ Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info, Wi, W) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, *Wi, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, *W,
+ Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info, Wi, W) ;
+
+packed complex Syntax:
+
+ Same as above, except Az, Xz, and Bz are NULL.
+
+Purpose:
+
+ Given LU factors computed by umfpack_*_numeric (PAQ=LU) and the
+ right-hand-side, B, solve a linear system for the solution X. Iterative
+ refinement is optionally performed. This routine is identical to
+ umfpack_*_solve, except that it does not dynamically allocate any workspace.
+ When you have many linear systems to solve, this routine is faster than
+ umfpack_*_solve, since the workspace (Wi, W) needs to be allocated only
+ once, prior to calling umfpack_*_wsolve.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int sys ; Input argument, not modified.
+ Int Ap [n+1] ; Input argument, not modified.
+ Int Ai [nz] ; Input argument, not modified.
+ double Ax [nz] ; Input argument, not modified.
+ Size 2*nz in packed complex case.
+ double X [n] ; Output argument.
+ double B [n] ; Input argument, not modified.
+ void *Numeric ; Input argument, not modified.
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ for complex versions:
+ double Az [nz] ; Input argument, not modified, imaginary part
+ double Xx [n] ; Output argument, real part.
+ Size 2*n in packed complex case.
+ double Xz [n] ; Output argument, imaginary part
+ double Bx [n] ; Input argument, not modified, real part.
+ Size 2*n in packed complex case.
+ double Bz [n] ; Input argument, not modified, imaginary part
+
+ The above arguments are identical to umfpack_*_solve, except that the
+ error code UMFPACK_ERROR_out_of_memory will not be returned in
+ Info [UMFPACK_STATUS], since umfpack_*_wsolve does not allocate any
+ memory.
+
+ Int Wi [n] ; Workspace.
+ double W [c*n] ; Workspace, where c is defined below.
+
+ The Wi and W arguments are workspace used by umfpack_*_wsolve. They
+ need not be initialized on input, and their contents are undefined on
+ output. The size of W depends on whether or not iterative refinement is
+ used, and which version (real or complex) is called. Iterative
+ refinement is performed if Ax=b, A'x=b, or A.'x=b is being solved,
+ Control [UMFPACK_IRSTEP] > 0, and A is nonsingular. The size of W is
+ given below:
+
+ no iter. with iter.
+ refinement refinement
+ umfpack_di_wsolve n 5*n
+ umfpack_dl_wsolve n 5*n
+ umfpack_zi_wsolve 4*n 10*n
+ umfpack_zl_wsolve 4*n 10*n
+*/
diff --git a/src/C/SuiteSparse/UMFPACK/Lib/libumfpack.def b/src/C/SuiteSparse/UMFPACK/Lib/libumfpack.def
new file mode 100644
index 0000000..72e6991
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Lib/libumfpack.def
@@ -0,0 +1,105 @@
+LIBRARY libumfpack.dll
+EXPORTS
+umfpack_di_col_to_triplet
+umfpack_di_defaults
+umfpack_di_free_numeric
+umfpack_di_free_symbolic
+umfpack_di_get_numeric
+umfpack_di_get_lunz
+umfpack_di_get_symbolic
+umfpack_di_get_determinant
+umfpack_di_numeric
+umfpack_di_qsymbolic
+umfpack_di_report_control
+umfpack_di_report_info
+umfpack_di_report_matrix
+umfpack_di_report_numeric
+umfpack_di_report_perm
+umfpack_di_report_status
+umfpack_di_report_symbolic
+umfpack_di_report_triplet
+umfpack_di_report_vector
+umfpack_di_solve
+umfpack_di_wsolve
+umfpack_di_symbolic
+umfpack_di_transpose
+umfpack_di_triplet_to_col
+umfpack_di_scale
+umfpack_dl_col_to_triplet
+umfpack_dl_defaults
+umfpack_dl_free_numeric
+umfpack_dl_free_symbolic
+umfpack_dl_get_numeric
+umfpack_dl_get_lunz
+umfpack_dl_get_symbolic
+umfpack_dl_get_determinant
+umfpack_dl_numeric
+umfpack_dl_qsymbolic
+umfpack_dl_report_control
+umfpack_dl_report_info
+umfpack_dl_report_matrix
+umfpack_dl_report_numeric
+umfpack_dl_report_perm
+umfpack_dl_report_status
+umfpack_dl_report_symbolic
+umfpack_dl_report_triplet
+umfpack_dl_report_vector
+umfpack_dl_solve
+umfpack_dl_wsolve
+umfpack_dl_symbolic
+umfpack_dl_transpose
+umfpack_dl_triplet_to_col
+umfpack_dl_scale
+umfpack_zi_col_to_triplet
+umfpack_zi_defaults
+umfpack_zi_free_numeric
+umfpack_zi_free_symbolic
+umfpack_zi_get_numeric
+umfpack_zi_get_lunz
+umfpack_zi_get_symbolic
+umfpack_zi_get_determinant
+umfpack_zi_numeric
+umfpack_zi_qsymbolic
+umfpack_zi_report_control
+umfpack_zi_report_info
+umfpack_zi_report_matrix
+umfpack_zi_report_numeric
+umfpack_zi_report_perm
+umfpack_zi_report_status
+umfpack_zi_report_symbolic
+umfpack_zi_report_triplet
+umfpack_zi_report_vector
+umfpack_zi_solve
+umfpack_zi_wsolve
+umfpack_zi_symbolic
+umfpack_zi_transpose
+umfpack_zi_triplet_to_col
+umfpack_zi_scale
+umfpack_zl_col_to_triplet
+umfpack_zl_defaults
+umfpack_zl_free_numeric
+umfpack_zl_free_symbolic
+umfpack_zl_get_numeric
+umfpack_zl_get_lunz
+umfpack_zl_get_symbolic
+umfpack_zl_get_determinant
+umfpack_zl_numeric
+umfpack_zl_qsymbolic
+umfpack_zl_report_control
+umfpack_zl_report_info
+umfpack_zl_report_matrix
+umfpack_zl_report_numeric
+umfpack_zl_report_perm
+umfpack_zl_report_status
+umfpack_zl_report_symbolic
+umfpack_zl_report_triplet
+umfpack_zl_report_vector
+umfpack_zl_solve
+umfpack_zl_wsolve
+umfpack_zl_symbolic
+umfpack_zl_transpose
+umfpack_zl_triplet_to_col
+umfpack_zl_scale
+umfpack_timer
+umfpack_tic
+umfpack_toc
diff --git a/src/C/SuiteSparse/UMFPACK/Makefile b/src/C/SuiteSparse/UMFPACK/Makefile
new file mode 100644
index 0000000..07afd04
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Makefile
@@ -0,0 +1,74 @@
+#-------------------------------------------------------------------------------
+# UMFPACK makefile (for GNU make or original make)
+#-------------------------------------------------------------------------------
+
+# UMFPACK requires the AMD package to be in ../AMD
+
+default: library
+
+include ../UFconfig/UFconfig.mk
+
+# compile all C code (except hb, fortran, and fortran64), including AMD and the
+# MATLAB mexFunctions
+all:
+ ( cd ../AMD ; $(MAKE) )
+ ( cd ../AMD/MATLAB ; $(MAKE) )
+ ( cd Source ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+ - cat Doc/License
+
+# compile just the C-callable libraries and demo programs (not mexFunctions)
+library:
+ ( cd ../AMD ; $(MAKE) )
+ ( cd Source ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ - cat Doc/License
+
+# compile the FORTRAN interface and demo program
+fortran:
+ ( cd Demo ; $(MAKE) fortran )
+
+# compile the 64-bit FORTRAN interface and demo program
+fortran64:
+ ( cd Demo ; $(MAKE) fortran64 )
+
+# compile the Harwell/Boeing demo program
+hb:
+ ( cd Demo ; $(MAKE) hb )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd ../AMD ; $(MAKE) clean )
+ ( cd Source ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Doc ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd ../AMD ; $(MAKE) purge )
+ ( cd Source ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+# create PDF documents for the original distribution
+doc:
+ ( cd ../AMD ; $(MAKE) doc )
+ ( cd Doc ; $(MAKE) )
+
+# get ready for distribution
+dist: purge
+ ( cd ../AMD ; $(MAKE) dist )
+ ( cd Demo ; $(MAKE) dist )
+ ( cd Doc ; $(MAKE) )
+
+distclean: purge
+
+ccode: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd ../AMD/MATLAB ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
diff --git a/src/C/SuiteSparse/UMFPACK/README.txt b/src/C/SuiteSparse/UMFPACK/README.txt
new file mode 100644
index 0000000..61ed73c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/README.txt
@@ -0,0 +1,409 @@
+UMFPACK Version 5.0.2: a set of routines solving sparse linear systems via LU
+ factorization. Requires three other packages: the BLAS (dense matrix
+ operations), AMD (sparse matrix minimum degree ordering), and UFconfig.
+ Includes a C-callable and MATLAB interface, and a basic FORTRAN 77
+ interface to a subset of the C-callable routines. Requires AMD Version
+ 2.0 or later.
+
+The AMD, UFconfig, and UMFPACK directories must all reside in the same parent
+directory.
+
+Quick start (Unix, or Windows with Cygwin):
+
+ To compile, test, and install both UMFPACK and AMD, the UMFPACK and AMD
+ directories must be in the same parent directory. To configure, edit
+ the UFconfig/UFconfig.mk file (otherwise, you may get warnings that the
+ BLAS (dgemm, etc) are not found). You may use UMFPACK_CONFIG = -DNBLAS in
+ the UFconfig/UFconfig.mk file, to avoid using the BLAS, but UMFPACK will be
+ slow. Next, cd to this directory (UMFPACK) and type "make". To compile
+ and run a FORTRAN demo program for Harwell/Boeing matrices, type "make hb".
+ To compile a FORTRAN main program that calls the 32-bit C-callable UMFPACK
+ library, type "make fortran". When done, type "make clean" to remove
+ unused *.o files (keeps the compiled libraries and demo programs). See
+ the User Guide (Doc/UserGuide.pdf), or ../UFconfig/UFconfig.mk for more
+ details (including options for compiling in 64-bit mode).
+
+Quick start (for MATLAB users):
+
+ To compile, test, and install the UMFPACK mexFunction, cd to the
+ UMFPACK/MATLAB directory and type umfpack_make at the MATLAB prompt.
+
+ NOTE: DO NOT ATTEMPT TO USE THIS CODE IN 64-BIT MATLAB (v7.3).
+ It is not yet ported to that version of MATLAB.
+
+--------------------------------------------------------------------------------
+
+UMFPACK, Copyright (c) 1995-2006 by Timothy A. Davis. All Rights Reserved.
+UMFPACK is available under alternate licences; contact T. Davis for details.
+
+UMFPACK License:
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/umfpack
+
+ UMFPACK (including versions 2.2.1 and earlier, in FORTRAN) is available at
+ http://www.cise.ufl.edu/research/sparse. MA38 is available in the Harwell
+ Subroutine Library. This version of UMFPACK includes a modified form of
+ COLAMD Version 2.0, originally released on Jan. 31, 2000, also available at
+ http://www.cise.ufl.edu/research/sparse. COLAMD V2.0 is also incorporated
+ as a built-in function in MATLAB version 6.1, by The MathWorks, Inc.
+ (http://www.mathworks.com). COLAMD V1.0 appears as a column-preordering
+ in SuperLU (SuperLU is available at http://www.netlib.org).
+ UMFPACK v4.0 is a built-in routine in MATLAB 6.5.
+ UMFPACK v4.3 is a built-in routine in MATLAB 7.1.
+
+--------------------------------------------------------------------------------
+
+Refer to ../AMD/README for the License for AMD, which is a separate
+package for ordering sparse matrices that is required by UMFPACK.
+UMFPACK v4.5 cannot use AMD v1.1 or earlier. UMFPACK 5.0
+requires AMD v2.0 or later.
+
+--------------------------------------------------------------------------------
+
+This is the UMFPACK README.txt file. It is a terse overview of UMFPACK.
+Refer to the User Guide (Doc/UserGuide.pdf) for how to install and use UMFPACK,
+or to the Quick Start Guide, QuickStart.pdf.
+
+Description:
+
+ UMFPACK is a set of routines for solving unsymmetric sparse linear systems,
+ Ax=b, using the Unsymmetric MultiFrontal method. Written in ANSI/ISO C,
+ with a MATLAB (Version 6.0 or later) interface.
+
+ For best performance, UMFPACK requires an optimized BLAS library. It can
+ also be compiled without any BLAS at all. UMFPACK requires AMD Version 2.0.
+
+Authors:
+
+ Timothy A. Davis (davis at cise.ufl.edu), University of Florida.
+
+ Includes a modified version of COLAMD V2.0, by Stefan I. Larimore and
+ Timothy A. Davis, University of Florida. The COLAMD algorithm was developed
+ in collaboration with John Gilbert, Xerox Palo Alto Research Center, and
+ Esmond Ng, Lawrence Berkeley National Laboratory.
+
+ Includes AMD, by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff.
+
+ UMFPACK Version 2.2.1 (MA38 in the Harwell Subroutine Library) is
+ co-authored with Iain S. Duff, Rutherford Appleton Laboratory.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+ Portions of this work were done while on sabbatical at Stanford University
+ and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+ program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+ for making this sabbatical possible.
+
+ I would also like to thank the many researchers who provided sparse
+ matrices from a wide range of domains and used earlier versions of UMFPACK/
+ MA38 in their applications, and thus assisted in the practical development
+ of the algorithm (see http://www.cise.ufl.edu/research/sparse, future
+ contributions of matrices are always welcome).
+
+ The MathWorks, Inc., provided a pre-release of MATLAB V6 which allowed me
+ to release the first umfpack mexFunction (v3.0) about 6 months earlier than
+ I had originally planned. They also supported the extension of UMFPACK to
+ complex, singular, and rectangular matrices (UMFPACK v4.0).
+
+ Penny Anderson (The MathWorks, Inc.), Anshul Gupta (IBM), and Friedrich
+ Grund (WAIS) assisted in porting UMFPACK to different platforms. Penny
+ Anderson also incorporated UMFPACK v4.0 into MATLAB, for lu, backslash (\),
+ and forward slash (/).
+
+ David Bateman (Motorola) wrote the initial version of the packed complex
+ input option, and umfpack_get_determinant.
+
+--------------------------------------------------------------------------------
+Files and directories in the UMFPACK distribution:
+--------------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ Subdirectories of the UMFPACK directory:
+ ----------------------------------------------------------------------------
+
+ Doc documentation
+ Source primary source code
+ Include include files for use in your code that calls UMFPACK
+ Demo demo programs. also serves as test of the UMFPACK installation.
+ MATLAB UMFPACK mexFunction for MATLAB, and supporting m-files
+ Lib where the compiled C-callable UMFPACK library is placed.
+
+ ----------------------------------------------------------------------------
+ Files in the UMFPACK directory:
+ ----------------------------------------------------------------------------
+
+ Makefile top-level Makefile for GNU make or original make.
+ Windows users would require Cygwin to use "make"
+
+ README.txt this file
+
+ ----------------------------------------------------------------------------
+ Doc directory: documentation
+ ----------------------------------------------------------------------------
+
+ ChangeLog change log
+ License the UMFPACK License
+ Makefile for creating the documentation
+ QuickStart.tex Quick Start guide (source)
+ QuickStart.pdf Quick Start guide (PDF)
+ UserGuide.bib User Guide (references)
+ UserGuide.sed1 sed script for processing UserGuide.stex
+ UserGuide.sed2 sed script for processing UserGuide.stex
+ UserGuide.stex User Guide (LaTeX)
+ UserGuide.pdf User Guide (PDF)
+
+ ----------------------------------------------------------------------------
+ Source directory:
+ ----------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ cholmod_blas.h an exact copy of CHOLMOD/Include/cholmod_blas.h
+
+ umfpack_col_to_triplet.c convert col form to triplet
+ umfpack_defaults.c set Control defaults
+ umfpack_free_numeric.c free Numeric object
+ umfpack_free_symbolic.c free Symbolic object
+ umfpack_get_determinant.c compute determinant from Numeric object
+ umfpack_get_lunz.c get nz's in L and U
+ umfpack_get_numeric.c get Numeric object
+ umfpack_get_symbolic.c get Symbolic object
+ umfpack_load_numeric.c load Numeric object from file
+ umfpack_load_symbolic.c load Symbolic object from file
+ umfpack_numeric.c numeric factorization
+ umfpack_qsymbolic.c symbolic factorization, user Q
+ umfpack_report_control.c print Control settings
+ umfpack_report_info.c print Info statistics
+ umfpack_report_matrix.c print col or row-form sparse matrix
+ umfpack_report_numeric.c print Numeric object
+ umfpack_report_perm.c print permutation
+ umfpack_report_status.c print return status
+ umfpack_report_symbolic.c print Symbolic object
+ umfpack_report_triplet.c print triplet matrix
+ umfpack_report_vector.c print dense vector
+ umfpack_save_numeric.c save Numeric object to file
+ umfpack_save_symbolic.c save Symbolic object to file
+ umfpack_scale.c scale a vector
+ umfpack_solve.c solve a linear system
+ umfpack_symbolic.c symbolic factorization
+ umfpack_tictoc.c timer
+ umfpack_timer.c timer
+ umfpack_transpose.c transpose a matrix
+ umfpack_triplet_to_col.c convert triplet to col form
+
+ umf_config.h configuration file (BLAS, memory, timer)
+ umf_internal.h definitions internal to UMFPACK
+ umf_version.h version definitions (int/UF_long, real/complex)
+
+ umf_2by2.[ch]
+ umf_analyze.[ch] symbolic factorization of A'*A
+ umf_apply_order.[ch] apply column etree postorder
+ umf_assemble.[ch] assemble elements into current front
+ umf_blas3_update.[ch] rank-k update. Uses level-3 BLAS
+ umf_build_tuples.[ch] construct tuples for elements
+ umf_colamd.[ch] COLAMD pre-ordering, modified for UMFPACK
+ umf_create_element.[ch] create a new element
+ umf_dump.[ch] debugging routines, not normally active
+ umf_extend_front.[ch] extend the current frontal matrix
+ umf_free.[ch] free memory
+ umf_fsize.[ch] determine largest front in each subtree
+ umf_garbage_collection.[ch] compact Numeric->Memory
+ umf_get_memory.[ch] make Numeric->Memory bigger
+ umf_grow_front.[ch] make current frontal matrix bigger
+ umf_init_front.[ch] initialize a new frontal matrix
+ umf_is_permutation.[ch] checks the validity of a permutation vector
+ umf_kernel.[ch] the main numeric factorization kernel
+ umf_kernel_init.[ch] initializations for umf_kernel
+ umf_kernel_wrapup.[ch] wrapup for umf_kernel
+ umf_local_search.[ch] local row and column pivot search
+ umf_lsolve.[ch] solve Lx=b
+ umf_ltsolve.[ch] solve L'x=b and L.'x=b
+ umf_malloc.[ch] malloc some memory
+ umf_mem_alloc_element.[ch] allocate element in Numeric->Memory
+ umf_mem_alloc_head_block.[ch] alloc. block at head of Numeric->Memory
+ umf_mem_alloc_tail_block.[ch] alloc. block at tail of Numeric->Memory
+ umf_mem_free_tail_block.[ch] free block at tail of Numeric->Memory
+ umf_mem_init_memoryspace.[ch] initialize Numeric->Memory
+ umf_realloc.[ch] realloc memory
+ umf_report_perm.[ch] print a permutation vector
+ umf_report_vector.[ch] print a double vector
+ umf_row_search.[ch] look for a pivot row
+ umf_scale.[ch] scale the pivot column
+ umf_scale_column.[ch] move pivot row & column into place, log P and Q
+ umf_set_stats.[ch] set statistics (final or estimates)
+ umf_singletons.[ch] find all zero-cost pivots
+ umf_solve.[ch] solve a linear system
+ umf_start_front.[ch] start a new frontal matrix for one frontal chain
+ umf_store_lu.[ch] store LU factors of current front
+ umf_symbolic_usage.[ch] determine memory usage for Symbolic object
+ umf_transpose.[ch] transpose a matrix in row or col form
+ umf_triplet.[ch] convert triplet to column form
+ umf_tuple_lengths.[ch] determine the tuple list lengths
+ umf_usolve.[ch] solve Ux=b
+ umf_utsolve.[ch] solve U'x=b and U.'x=b
+ umf_valid_numeric.[ch] checks the validity of a Numeric object
+ umf_valid_symbolic.[ch] check the validity of a Symbolic object
+
+ ----------------------------------------------------------------------------
+ Include directory:
+ ----------------------------------------------------------------------------
+
+ umfpack.h include file for user programs. Includes all of
+ the following files. This serves are source-
+ code level documenation. These files are also
+ used to construct the User Guide.
+
+ umfpack_col_to_triplet.h
+ umfpack_defaults.h
+ umfpack_free_numeric.h
+ umfpack_free_symbolic.h
+ umfpack_get_determinant.h
+ umfpack_get_lunz.h
+ umfpack_get_numeric.h
+ umfpack_get_symbolic.h
+ umfpack_load_numeric.h
+ umfpack_load_symbolic.h
+ umfpack_numeric.h
+ umfpack_qsymbolic.h
+ umfpack_report_control.h
+ umfpack_report_info.h
+ umfpack_report_matrix.h
+ umfpack_report_numeric.h
+ umfpack_report_perm.h
+ umfpack_report_status.h
+ umfpack_report_symbolic.h
+ umfpack_report_triplet.h
+ umfpack_report_vector.h
+ umfpack_save_numeric.h
+ umfpack_save_symbolic.h
+ umfpack_scale.h
+ umfpack_solve.h
+ umfpack_symbolic.h
+ umfpack_tictoc.h
+ umfpack_timer.h
+ umfpack_transpose.h
+ umfpack_triplet_to_col.h
+
+ umfpack_wsolve.h note that there is no umfpack_wsolve.c. The
+ umfpack_*_wsolve routines are created from the
+ umfpack_solve.c file.
+
+ ----------------------------------------------------------------------------
+ Demo directory:
+ ----------------------------------------------------------------------------
+
+ Makefile for GNU make or original make
+
+ umfpack_simple.c a simple demo
+ umpack_xx_demo.c template to create the demo codes below
+
+ umfpack_di_demo.sed for creating umfpack_di_demo.c
+ umfpack_dl_demo.sed for creating umfpack_dl_demo.c
+ umfpack_zi_demo.sed for creating umfpack_zi_demo.c
+ umfpack_zl_demo.sed for creating umfpack_zl_demo.c
+
+ umfpack_di_demo.c a full demo (real/int version)
+ umfpack_dl_demo.c a full demo (real/UF_long version)
+ umfpack_zi_demo.c a full demo (complex/int version)
+ umfpack_zl_demo.c a full demo (complex/UF_long version)
+
+ umfpack_di_demo.out umfpack_di_demo output
+ umfpack_dl_demo.out umfpack_dl_demo output
+ umfpack_zi_demo.out umfpack_zi_demo output
+ umfpack_zl_demo.out umfpack_zl_demo output
+
+ umf4.c a demo (real/int) for Harwell/Boeing matrices
+ umf4.out output of "make hb"
+ HB directory of sample Harwell/Boeing matrices
+ readhb.f reads HB matrices, keeps zero entries
+ readhb_nozeros.f reads HB matrices, removes zero entries
+ readhb_size.f reads HB matrix dimension, nnz
+ tmp empty directory for umf4.c demo
+
+ umf4_f77wrapper.c a simple FORTRAN interface for UMFPACK.
+ compile with "make fortran"
+ umf4hb.f a demo of the FORTRAN interface
+ umf4hb.out output of "make fortran"
+
+ umf4_f77zwrapper.c a simple FORTRAN interface for the complex
+ UMFPACK routines. compile with "make fortran"
+ umf4zhb.f a demo of the FORTRAN interface (complex)
+ umf4zhb.out output of umf4zhb with HB/qc324.cua
+
+ umf4hb64.f 64-bit version of umf4hb.f
+
+ simple_compile a single command that compiles the double/int
+ version of UMFPACK (useful prototype for
+ Microsoft Visual Studio project)
+
+ Opteron64/ demo output files on an AMD Opteron
+
+ ----------------------------------------------------------------------------
+ MATLAB directory:
+ ----------------------------------------------------------------------------
+
+ Contents.m for "help umfpack" listing of toolbox contents
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ lu_normest.m 1-norm estimate of A-L*U (by Hager & Davis).
+ luflop.m for "help luflop"
+ luflopmex.c luflop mexFunction, for computing LU flop count
+ umfpack.m for "help umfpack"
+ umfpack_btf.m solve Ax=b using umfpack and dmperm
+ umfpack_demo.m a full umfpack demo
+ umfpack_details.m the details of how to use umfpack
+ umfpack_make.m compile the umfpack mexFunction within MATLAB
+ umfpack_report.m report statistics
+ umfpack_simple.m a simple umfpack demo
+ umfpack_solve.m x=A\b or b/A for arbitrary b
+ umfpack_test.m extensive test, requires UF sparse matrices
+ umfpackmex.c the umfpack mexFunction
+ west0067.mat sparse matrix for umfpack_demo.m
+
+ umfpack_demo.m.out output of umfpack_demo.m
+ umfpack_demo.m.out_verbose ditto, but with print level 2, on AMD Opteron
+ umfpack_simple.m.out output of umfpack_simple
+
+ lcc_lib/lapacksyms.def LAPACK definitions for lcc compiler (Windows)
+ lcc_lib/libmwlapack.lib LAPACK definitions for lcc compiler (Windows)
+
+ ----------------------------------------------------------------------------
+ Lib directory: libumfpack.a library placed here
+ ----------------------------------------------------------------------------
+
+ libumfpack.def UMPFACK definitions for Windows
diff --git a/src/C/SuiteSparse/UMFPACK/Source/GNUmakefile b/src/C/SuiteSparse/UMFPACK/Source/GNUmakefile
new file mode 100644
index 0000000..1326653
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/GNUmakefile
@@ -0,0 +1,257 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for compiling on Unix systems (for GNU Make)
+#-------------------------------------------------------------------------------
+
+default: ../Lib/libumfpack.a
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) \
+ -I../Include -I../../AMD/Include -I../../UFconfig
+
+#-------------------------------------------------------------------------------
+# source files
+#-------------------------------------------------------------------------------
+
+# non-user-callable umf_*.[ch] files:
+UMFCH = umf_assemble umf_blas3_update umf_build_tuples umf_create_element \
+ umf_dump umf_extend_front umf_garbage_collection umf_get_memory \
+ umf_init_front umf_kernel umf_kernel_init umf_kernel_wrapup \
+ umf_local_search umf_lsolve umf_ltsolve umf_mem_alloc_element \
+ umf_mem_alloc_head_block umf_mem_alloc_tail_block \
+ umf_mem_free_tail_block umf_mem_init_memoryspace \
+ umf_report_vector umf_row_search umf_scale_column \
+ umf_set_stats umf_solve umf_symbolic_usage umf_transpose \
+ umf_tuple_lengths umf_usolve umf_utsolve umf_valid_numeric \
+ umf_valid_symbolic umf_grow_front umf_start_front umf_2by2 \
+ umf_store_lu umf_scale
+
+# non-user-callable umf_*.[ch] files, int/UF_long versions only (no real/complex):
+UMFINT = umf_analyze umf_apply_order umf_colamd umf_free umf_fsize \
+ umf_is_permutation umf_malloc umf_realloc umf_report_perm \
+ umf_singletons
+
+# non-user-callable, created from umf_ltsolve.c, umf_utsolve.c,
+# umf_triplet.c, and umf_assemble.c , with int/UF_long and real/complex versions:
+UMF_CREATED = umf_lhsolve umf_uhsolve umf_triplet_map_nox \
+ umf_triplet_nomap_x umf_triplet_nomap_nox umf_triplet_map_x \
+ umf_assemble_fixq umf_store_lu_drop
+
+# non-user-callable, int/UF_long and real/complex versions:
+UMF = $(UMF_CREATED) $(UMFCH)
+
+# user-callable umfpack_*.[ch] files (int/UF_long and real/complex):
+UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \
+ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \
+ umfpack_get_symbolic umfpack_get_determinant umfpack_numeric \
+ umfpack_qsymbolic umfpack_report_control umfpack_report_info \
+ umfpack_report_matrix umfpack_report_numeric umfpack_report_perm \
+ umfpack_report_status umfpack_report_symbolic umfpack_report_triplet \
+ umfpack_report_vector umfpack_solve umfpack_symbolic \
+ umfpack_transpose umfpack_triplet_to_col umfpack_scale \
+ umfpack_load_numeric umfpack_save_numeric \
+ umfpack_load_symbolic umfpack_save_symbolic
+
+# user-callable, created from umfpack_solve.c (umfpack_wsolve.h exists, though):
+# with int/UF_long and real/complex versions:
+UMFPACKW = umfpack_wsolve
+
+USER = $(UMFPACKW) $(UMFPACK)
+
+# user-callable, only one version for int/UF_long, real/complex, *.[ch] files:
+GENERIC = umfpack_timer umfpack_tictoc umfpack_global
+
+#-------------------------------------------------------------------------------
+# include files:
+#-------------------------------------------------------------------------------
+
+INC = ../Include/umfpack.h ../../UFconfig/UFconfig.h \
+ umf_config.h umf_version.h umf_internal.h umf_triplet.h \
+ $(addsuffix .h,$(UMFCH)) \
+ $(addsuffix .h,$(UMFINT)) \
+ $(addprefix ../Include/, $(addsuffix .h,$(USER))) \
+ $(addprefix ../Include/, $(addsuffix .h,$(GENERIC))) \
+ ../../AMD/Include/amd_internal.h ../../AMD/Include/amd.h
+
+#-------------------------------------------------------------------------------
+# object files for each version
+#-------------------------------------------------------------------------------
+
+DI = $(addsuffix .o, $(subst umf_,umf_di_,$(UMF)) $(subst umfpack_,umfpack_di_,$(USER)))
+DL = $(addsuffix .o, $(subst umf_,umf_dl_,$(UMF)) $(subst umfpack_,umfpack_dl_,$(USER)))
+ZI = $(addsuffix .o, $(subst umf_,umf_zi_,$(UMF)) $(subst umfpack_,umfpack_zi_,$(USER)))
+ZL = $(addsuffix .o, $(subst umf_,umf_zl_,$(UMF)) $(subst umfpack_,umfpack_zl_,$(USER)))
+II = $(addsuffix .o, $(subst umf_,umf_i_,$(UMFINT)))
+LL = $(addsuffix .o, $(subst umf_,umf_l_,$(UMFINT)))
+GN = $(addsuffix .o, $(subst umfpack_,umfpack_gn_,$(GENERIC)))
+
+#-------------------------------------------------------------------------------
+# compile each int and UF_long routine (with no real/complex version)
+#-------------------------------------------------------------------------------
+
+umf_i_%.o: umf_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+umf_l_%.o: umf_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the DI version
+#-------------------------------------------------------------------------------
+
+umf_di_%.o: umf_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+umf_di_%hsolve.o: umf_%tsolve.c $(INC)
+ $(C) -DDINT -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_di_triplet_map_x.o: umf_triplet.c $(INC)
+ $(C) -DDINT -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_di_triplet_map_nox.o: umf_triplet.c $(INC)
+ $(C) -DDINT -DDO_MAP -c $< -o $@
+
+umf_di_triplet_nomap_x.o: umf_triplet.c $(INC)
+ $(C) -DDINT -DDO_VALUES -c $< -o $@
+
+umf_di_triplet_nomap_nox.o: umf_triplet.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+umf_di_assemble_fixq.o: umf_assemble.c $(INC)
+ $(C) -DDINT -DFIXQ -c $< -o $@
+
+umf_di_store_lu_drop.o: umf_store_lu.c $(INC)
+ $(C) -DDINT -DDROP -c $< -o $@
+
+umfpack_di_wsolve.o: umfpack_solve.c $(INC)
+ $(C) -DDINT -DWSOLVE -c $< -o $@
+
+umfpack_di_%.o: umfpack_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the DL version
+#-------------------------------------------------------------------------------
+
+umf_dl_%.o: umf_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+umf_dl_%hsolve.o: umf_%tsolve.c $(INC)
+ $(C) -DDLONG -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_dl_triplet_map_x.o: umf_triplet.c $(INC)
+ $(C) -DDLONG -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_dl_triplet_map_nox.o: umf_triplet.c $(INC)
+ $(C) -DDLONG -DDO_MAP -c $< -o $@
+
+umf_dl_triplet_nomap_x.o: umf_triplet.c $(INC)
+ $(C) -DDLONG -DDO_VALUES -c $< -o $@
+
+umf_dl_triplet_nomap_nox.o: umf_triplet.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+umf_dl_assemble_fixq.o: umf_assemble.c $(INC)
+ $(C) -DDLONG -DFIXQ -c $< -o $@
+
+umf_dl_store_lu_drop.o: umf_store_lu.c $(INC)
+ $(C) -DDLONG -DDROP -c $< -o $@
+
+umfpack_dl_wsolve.o: umfpack_solve.c $(INC)
+ $(C) -DDLONG -DWSOLVE -c $< -o $@
+
+umfpack_dl_%.o: umfpack_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the ZI version
+#-------------------------------------------------------------------------------
+
+umf_zi_%.o: umf_%.c $(INC)
+ $(C) -DZINT -c $< -o $@
+
+umf_zi_%hsolve.o: umf_%tsolve.c $(INC)
+ $(C) -DZINT -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_zi_triplet_map_x.o: umf_triplet.c $(INC)
+ $(C) -DZINT -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_zi_triplet_map_nox.o: umf_triplet.c $(INC)
+ $(C) -DZINT -DDO_MAP -c $< -o $@
+
+umf_zi_triplet_nomap_x.o: umf_triplet.c $(INC)
+ $(C) -DZINT -DDO_VALUES -c $< -o $@
+
+umf_zi_triplet_nomap_nox.o: umf_triplet.c $(INC)
+ $(C) -DZINT -c $< -o $@
+
+umf_zi_assemble_fixq.o: umf_assemble.c $(INC)
+ $(C) -DZINT -DFIXQ -c $< -o $@
+
+umf_zi_store_lu_drop.o: umf_store_lu.c $(INC)
+ $(C) -DZINT -DDROP -c $< -o $@
+
+umfpack_zi_wsolve.o: umfpack_solve.c $(INC)
+ $(C) -DZINT -DWSOLVE -c $< -o $@
+
+umfpack_zi_%.o: umfpack_%.c $(INC)
+ $(C) -DZINT -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the ZL version
+#-------------------------------------------------------------------------------
+
+umf_zl_%.o: umf_%.c $(INC)
+ $(C) -DZLONG -c $< -o $@
+
+umf_zl_%hsolve.o: umf_%tsolve.c $(INC)
+ $(C) -DZLONG -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_zl_triplet_map_x.o: umf_triplet.c $(INC)
+ $(C) -DZLONG -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_zl_triplet_map_nox.o: umf_triplet.c $(INC)
+ $(C) -DZLONG -DDO_MAP -c $< -o $@
+
+umf_zl_triplet_nomap_x.o: umf_triplet.c $(INC)
+ $(C) -DZLONG -DDO_VALUES -c $< -o $@
+
+umf_zl_triplet_nomap_nox.o: umf_triplet.c $(INC)
+ $(C) -DZLONG -c $< -o $@
+
+umf_zl_assemble_fixq.o: umf_assemble.c $(INC)
+ $(C) -DZLONG -DFIXQ -c $< -o $@
+
+umf_zl_store_lu_drop.o: umf_store_lu.c $(INC)
+ $(C) -DZLONG -DDROP -c $< -o $@
+
+umfpack_zl_wsolve.o: umfpack_solve.c $(INC)
+ $(C) -DZLONG -DWSOLVE -c $< -o $@
+
+umfpack_zl_%.o: umfpack_%.c $(INC)
+ $(C) -DZLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the generic routines (GN) using a generic rule
+#-------------------------------------------------------------------------------
+
+umfpack_gn_%.o: umfpack_%.c $(INC)
+ $(C) -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the libumfpack.a library
+#-------------------------------------------------------------------------------
+
+../Lib/libumfpack.a: $(II) $(LL) $(GN) $(DI) $(DL) $(ZI) $(ZL)
+ $(AR) ../Lib/libumfpack.a $^
+ - $(RANLIB) ../Lib/libumfpack.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) ../Lib/libumfpack.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/src/C/SuiteSparse/UMFPACK/Source/Makefile b/src/C/SuiteSparse/UMFPACK/Source/Makefile
new file mode 100644
index 0000000..56ab48b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/Makefile
@@ -0,0 +1,482 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for compiling on Unix systems (for original make only)
+#-------------------------------------------------------------------------------
+
+# This is a very ugly Makefile, and is only provided for those who do not
+# have GNU make. Note that it is not used if you have GNU make. It ignores
+# dependency checking and just compiles everything.
+
+default: everything
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include
+
+everything:
+ $(C) -c umfpack_global.c -o umfpack_gn_global.o
+ $(C) -DDINT -c umf_analyze.c -o umf_i_analyze.o
+ $(C) -DDINT -c umf_apply_order.c -o umf_i_apply_order.o
+ $(C) -DDINT -c umf_colamd.c -o umf_i_colamd.o
+ $(C) -DDINT -c umf_free.c -o umf_i_free.o
+ $(C) -DDINT -c umf_fsize.c -o umf_i_fsize.o
+ $(C) -DDINT -c umf_is_permutation.c -o umf_i_is_permutation.o
+ $(C) -DDINT -c umf_malloc.c -o umf_i_malloc.o
+ $(C) -DDINT -c umf_realloc.c -o umf_i_realloc.o
+ $(C) -DDINT -c umf_report_perm.c -o umf_i_report_perm.o
+ $(C) -DDINT -c umf_singletons.c -o umf_i_singletons.o
+ $(C) -DDLONG -c umf_analyze.c -o umf_l_analyze.o
+ $(C) -DDLONG -c umf_apply_order.c -o umf_l_apply_order.o
+ $(C) -DDLONG -c umf_colamd.c -o umf_l_colamd.o
+ $(C) -DDLONG -c umf_free.c -o umf_l_free.o
+ $(C) -DDLONG -c umf_fsize.c -o umf_l_fsize.o
+ $(C) -DDLONG -c umf_is_permutation.c -o umf_l_is_permutation.o
+ $(C) -DDLONG -c umf_malloc.c -o umf_l_malloc.o
+ $(C) -DDLONG -c umf_realloc.c -o umf_l_realloc.o
+ $(C) -DDLONG -c umf_report_perm.c -o umf_l_report_perm.o
+ $(C) -DDLONG -c umf_singletons.c -o umf_l_singletons.o
+ $(C) -c umfpack_timer.c -o umfpack_gn_timer.o
+ $(C) -c umfpack_tictoc.c -o umfpack_gn_tictoc.o
+ $(C) -DDINT -DCONJUGATE_SOLVE -c umf_ltsolve.c -o umf_di_lhsolve.o
+ $(C) -DDINT -DCONJUGATE_SOLVE -c umf_utsolve.c -o umf_di_uhsolve.o
+ $(C) -DDINT -DDO_MAP -c umf_triplet.c -o umf_di_triplet_map_nox.o
+ $(C) -DDINT -DDO_VALUES -c umf_triplet.c -o umf_di_triplet_nomap_x.o
+ $(C) -DDINT -c umf_triplet.c -o umf_di_triplet_nomap_nox.o
+ $(C) -DDINT -DDO_MAP -DDO_VALUES -c umf_triplet.c -o umf_di_triplet_map_x.o
+ $(C) -DDINT -DFIXQ -c umf_assemble.c -o umf_di_assemble_fixq.o
+ $(C) -DDINT -DDROP -c umf_store_lu.c -o umf_di_store_lu_drop.o
+ $(C) -DDINT -c umf_assemble.c -o umf_di_assemble.o
+ $(C) -DDINT -c umf_blas3_update.c -o umf_di_blas3_update.o
+ $(C) -DDINT -c umf_build_tuples.c -o umf_di_build_tuples.o
+ $(C) -DDINT -c umf_create_element.c -o umf_di_create_element.o
+ $(C) -DDINT -c umf_dump.c -o umf_di_dump.o
+ $(C) -DDINT -c umf_extend_front.c -o umf_di_extend_front.o
+ $(C) -DDINT -c umf_garbage_collection.c -o umf_di_garbage_collection.o
+ $(C) -DDINT -c umf_get_memory.c -o umf_di_get_memory.o
+ $(C) -DDINT -c umf_init_front.c -o umf_di_init_front.o
+ $(C) -DDINT -c umf_kernel.c -o umf_di_kernel.o
+ $(C) -DDINT -c umf_kernel_init.c -o umf_di_kernel_init.o
+ $(C) -DDINT -c umf_kernel_wrapup.c -o umf_di_kernel_wrapup.o
+ $(C) -DDINT -c umf_local_search.c -o umf_di_local_search.o
+ $(C) -DDINT -c umf_lsolve.c -o umf_di_lsolve.o
+ $(C) -DDINT -c umf_ltsolve.c -o umf_di_ltsolve.o
+ $(C) -DDINT -c umf_mem_alloc_element.c -o umf_di_mem_alloc_element.o
+ $(C) -DDINT -c umf_mem_alloc_head_block.c -o umf_di_mem_alloc_head_block.o
+ $(C) -DDINT -c umf_mem_alloc_tail_block.c -o umf_di_mem_alloc_tail_block.o
+ $(C) -DDINT -c umf_mem_free_tail_block.c -o umf_di_mem_free_tail_block.o
+ $(C) -DDINT -c umf_mem_init_memoryspace.c -o umf_di_mem_init_memoryspace.o
+ $(C) -DDINT -c umf_report_vector.c -o umf_di_report_vector.o
+ $(C) -DDINT -c umf_row_search.c -o umf_di_row_search.o
+ $(C) -DDINT -c umf_scale_column.c -o umf_di_scale_column.o
+ $(C) -DDINT -c umf_set_stats.c -o umf_di_set_stats.o
+ $(C) -DDINT -c umf_solve.c -o umf_di_solve.o
+ $(C) -DDINT -c umf_symbolic_usage.c -o umf_di_symbolic_usage.o
+ $(C) -DDINT -c umf_transpose.c -o umf_di_transpose.o
+ $(C) -DDINT -c umf_tuple_lengths.c -o umf_di_tuple_lengths.o
+ $(C) -DDINT -c umf_usolve.c -o umf_di_usolve.o
+ $(C) -DDINT -c umf_utsolve.c -o umf_di_utsolve.o
+ $(C) -DDINT -c umf_valid_numeric.c -o umf_di_valid_numeric.o
+ $(C) -DDINT -c umf_valid_symbolic.c -o umf_di_valid_symbolic.o
+ $(C) -DDINT -c umf_grow_front.c -o umf_di_grow_front.o
+ $(C) -DDINT -c umf_start_front.c -o umf_di_start_front.o
+ $(C) -DDINT -c umf_2by2.c -o umf_di_2by2.o
+ $(C) -DDINT -c umf_store_lu.c -o umf_di_store_lu.o
+ $(C) -DDINT -c umf_scale.c -o umf_di_scale.o
+ $(C) -DDINT -DWSOLVE -c umfpack_solve.c -o umfpack_di_wsolve.o
+ $(C) -DDINT -c umfpack_col_to_triplet.c -o umfpack_di_col_to_triplet.o
+ $(C) -DDINT -c umfpack_defaults.c -o umfpack_di_defaults.o
+ $(C) -DDINT -c umfpack_free_numeric.c -o umfpack_di_free_numeric.o
+ $(C) -DDINT -c umfpack_free_symbolic.c -o umfpack_di_free_symbolic.o
+ $(C) -DDINT -c umfpack_get_numeric.c -o umfpack_di_get_numeric.o
+ $(C) -DDINT -c umfpack_get_lunz.c -o umfpack_di_get_lunz.o
+ $(C) -DDINT -c umfpack_get_symbolic.c -o umfpack_di_get_symbolic.o
+ $(C) -DDINT -c umfpack_get_determinant.c -o umfpack_di_get_determinant.o
+ $(C) -DDINT -c umfpack_numeric.c -o umfpack_di_numeric.o
+ $(C) -DDINT -c umfpack_qsymbolic.c -o umfpack_di_qsymbolic.o
+ $(C) -DDINT -c umfpack_report_control.c -o umfpack_di_report_control.o
+ $(C) -DDINT -c umfpack_report_info.c -o umfpack_di_report_info.o
+ $(C) -DDINT -c umfpack_report_matrix.c -o umfpack_di_report_matrix.o
+ $(C) -DDINT -c umfpack_report_numeric.c -o umfpack_di_report_numeric.o
+ $(C) -DDINT -c umfpack_report_perm.c -o umfpack_di_report_perm.o
+ $(C) -DDINT -c umfpack_report_status.c -o umfpack_di_report_status.o
+ $(C) -DDINT -c umfpack_report_symbolic.c -o umfpack_di_report_symbolic.o
+ $(C) -DDINT -c umfpack_report_triplet.c -o umfpack_di_report_triplet.o
+ $(C) -DDINT -c umfpack_report_vector.c -o umfpack_di_report_vector.o
+ $(C) -DDINT -c umfpack_solve.c -o umfpack_di_solve.o
+ $(C) -DDINT -c umfpack_symbolic.c -o umfpack_di_symbolic.o
+ $(C) -DDINT -c umfpack_transpose.c -o umfpack_di_transpose.o
+ $(C) -DDINT -c umfpack_triplet_to_col.c -o umfpack_di_triplet_to_col.o
+ $(C) -DDINT -c umfpack_scale.c -o umfpack_di_scale.o
+ $(C) -DDINT -c umfpack_load_numeric.c -o umfpack_di_load_numeric.o
+ $(C) -DDINT -c umfpack_save_numeric.c -o umfpack_di_save_numeric.o
+ $(C) -DDINT -c umfpack_load_symbolic.c -o umfpack_di_load_symbolic.o
+ $(C) -DDINT -c umfpack_save_symbolic.c -o umfpack_di_save_symbolic.o
+ $(C) -DDLONG -DCONJUGATE_SOLVE -c umf_ltsolve.c -o umf_dl_lhsolve.o
+ $(C) -DDLONG -DCONJUGATE_SOLVE -c umf_utsolve.c -o umf_dl_uhsolve.o
+ $(C) -DDLONG -DDO_MAP -c umf_triplet.c -o umf_dl_triplet_map_nox.o
+ $(C) -DDLONG -DDO_VALUES -c umf_triplet.c -o umf_dl_triplet_nomap_x.o
+ $(C) -DDLONG -c umf_triplet.c -o umf_dl_triplet_nomap_nox.o
+ $(C) -DDLONG -DDO_MAP -DDO_VALUES -c umf_triplet.c -o umf_dl_triplet_map_x.o
+ $(C) -DDLONG -DFIXQ -c umf_assemble.c -o umf_dl_assemble_fixq.o
+ $(C) -DDLONG -DDROP -c umf_store_lu.c -o umf_dl_store_lu_drop.o
+ $(C) -DDLONG -c umf_assemble.c -o umf_dl_assemble.o
+ $(C) -DDLONG -c umf_blas3_update.c -o umf_dl_blas3_update.o
+ $(C) -DDLONG -c umf_build_tuples.c -o umf_dl_build_tuples.o
+ $(C) -DDLONG -c umf_create_element.c -o umf_dl_create_element.o
+ $(C) -DDLONG -c umf_dump.c -o umf_dl_dump.o
+ $(C) -DDLONG -c umf_extend_front.c -o umf_dl_extend_front.o
+ $(C) -DDLONG -c umf_garbage_collection.c -o umf_dl_garbage_collection.o
+ $(C) -DDLONG -c umf_get_memory.c -o umf_dl_get_memory.o
+ $(C) -DDLONG -c umf_init_front.c -o umf_dl_init_front.o
+ $(C) -DDLONG -c umf_kernel.c -o umf_dl_kernel.o
+ $(C) -DDLONG -c umf_kernel_init.c -o umf_dl_kernel_init.o
+ $(C) -DDLONG -c umf_kernel_wrapup.c -o umf_dl_kernel_wrapup.o
+ $(C) -DDLONG -c umf_local_search.c -o umf_dl_local_search.o
+ $(C) -DDLONG -c umf_lsolve.c -o umf_dl_lsolve.o
+ $(C) -DDLONG -c umf_ltsolve.c -o umf_dl_ltsolve.o
+ $(C) -DDLONG -c umf_mem_alloc_element.c -o umf_dl_mem_alloc_element.o
+ $(C) -DDLONG -c umf_mem_alloc_head_block.c -o umf_dl_mem_alloc_head_block.o
+ $(C) -DDLONG -c umf_mem_alloc_tail_block.c -o umf_dl_mem_alloc_tail_block.o
+ $(C) -DDLONG -c umf_mem_free_tail_block.c -o umf_dl_mem_free_tail_block.o
+ $(C) -DDLONG -c umf_mem_init_memoryspace.c -o umf_dl_mem_init_memoryspace.o
+ $(C) -DDLONG -c umf_report_vector.c -o umf_dl_report_vector.o
+ $(C) -DDLONG -c umf_row_search.c -o umf_dl_row_search.o
+ $(C) -DDLONG -c umf_scale_column.c -o umf_dl_scale_column.o
+ $(C) -DDLONG -c umf_set_stats.c -o umf_dl_set_stats.o
+ $(C) -DDLONG -c umf_solve.c -o umf_dl_solve.o
+ $(C) -DDLONG -c umf_symbolic_usage.c -o umf_dl_symbolic_usage.o
+ $(C) -DDLONG -c umf_transpose.c -o umf_dl_transpose.o
+ $(C) -DDLONG -c umf_tuple_lengths.c -o umf_dl_tuple_lengths.o
+ $(C) -DDLONG -c umf_usolve.c -o umf_dl_usolve.o
+ $(C) -DDLONG -c umf_utsolve.c -o umf_dl_utsolve.o
+ $(C) -DDLONG -c umf_valid_numeric.c -o umf_dl_valid_numeric.o
+ $(C) -DDLONG -c umf_valid_symbolic.c -o umf_dl_valid_symbolic.o
+ $(C) -DDLONG -c umf_grow_front.c -o umf_dl_grow_front.o
+ $(C) -DDLONG -c umf_start_front.c -o umf_dl_start_front.o
+ $(C) -DDLONG -c umf_2by2.c -o umf_dl_2by2.o
+ $(C) -DDLONG -c umf_store_lu.c -o umf_dl_store_lu.o
+ $(C) -DDLONG -c umf_scale.c -o umf_dl_scale.o
+ $(C) -DDLONG -DWSOLVE -c umfpack_solve.c -o umfpack_dl_wsolve.o
+ $(C) -DDLONG -c umfpack_col_to_triplet.c -o umfpack_dl_col_to_triplet.o
+ $(C) -DDLONG -c umfpack_defaults.c -o umfpack_dl_defaults.o
+ $(C) -DDLONG -c umfpack_free_numeric.c -o umfpack_dl_free_numeric.o
+ $(C) -DDLONG -c umfpack_free_symbolic.c -o umfpack_dl_free_symbolic.o
+ $(C) -DDLONG -c umfpack_get_numeric.c -o umfpack_dl_get_numeric.o
+ $(C) -DDLONG -c umfpack_get_lunz.c -o umfpack_dl_get_lunz.o
+ $(C) -DDLONG -c umfpack_get_symbolic.c -o umfpack_dl_get_symbolic.o
+ $(C) -DDLONG -c umfpack_get_determinant.c -o umfpack_dl_get_determinant.o
+ $(C) -DDLONG -c umfpack_numeric.c -o umfpack_dl_numeric.o
+ $(C) -DDLONG -c umfpack_qsymbolic.c -o umfpack_dl_qsymbolic.o
+ $(C) -DDLONG -c umfpack_report_control.c -o umfpack_dl_report_control.o
+ $(C) -DDLONG -c umfpack_report_info.c -o umfpack_dl_report_info.o
+ $(C) -DDLONG -c umfpack_report_matrix.c -o umfpack_dl_report_matrix.o
+ $(C) -DDLONG -c umfpack_report_numeric.c -o umfpack_dl_report_numeric.o
+ $(C) -DDLONG -c umfpack_report_perm.c -o umfpack_dl_report_perm.o
+ $(C) -DDLONG -c umfpack_report_status.c -o umfpack_dl_report_status.o
+ $(C) -DDLONG -c umfpack_report_symbolic.c -o umfpack_dl_report_symbolic.o
+ $(C) -DDLONG -c umfpack_report_triplet.c -o umfpack_dl_report_triplet.o
+ $(C) -DDLONG -c umfpack_report_vector.c -o umfpack_dl_report_vector.o
+ $(C) -DDLONG -c umfpack_solve.c -o umfpack_dl_solve.o
+ $(C) -DDLONG -c umfpack_symbolic.c -o umfpack_dl_symbolic.o
+ $(C) -DDLONG -c umfpack_transpose.c -o umfpack_dl_transpose.o
+ $(C) -DDLONG -c umfpack_triplet_to_col.c -o umfpack_dl_triplet_to_col.o
+ $(C) -DDLONG -c umfpack_scale.c -o umfpack_dl_scale.o
+ $(C) -DDLONG -c umfpack_load_numeric.c -o umfpack_dl_load_numeric.o
+ $(C) -DDLONG -c umfpack_save_numeric.c -o umfpack_dl_save_numeric.o
+ $(C) -DDLONG -c umfpack_load_symbolic.c -o umfpack_dl_load_symbolic.o
+ $(C) -DDLONG -c umfpack_save_symbolic.c -o umfpack_dl_save_symbolic.o
+ $(C) -DZINT -DCONJUGATE_SOLVE -c umf_ltsolve.c -o umf_zi_lhsolve.o
+ $(C) -DZINT -DCONJUGATE_SOLVE -c umf_utsolve.c -o umf_zi_uhsolve.o
+ $(C) -DZINT -DDO_MAP -c umf_triplet.c -o umf_zi_triplet_map_nox.o
+ $(C) -DZINT -DDO_VALUES -c umf_triplet.c -o umf_zi_triplet_nomap_x.o
+ $(C) -DZINT -c umf_triplet.c -o umf_zi_triplet_nomap_nox.o
+ $(C) -DZINT -DDO_MAP -DDO_VALUES -c umf_triplet.c -o umf_zi_triplet_map_x.o
+ $(C) -DZINT -DFIXQ -c umf_assemble.c -o umf_zi_assemble_fixq.o
+ $(C) -DZINT -DDROP -c umf_store_lu.c -o umf_zi_store_lu_drop.o
+ $(C) -DZINT -c umf_assemble.c -o umf_zi_assemble.o
+ $(C) -DZINT -c umf_blas3_update.c -o umf_zi_blas3_update.o
+ $(C) -DZINT -c umf_build_tuples.c -o umf_zi_build_tuples.o
+ $(C) -DZINT -c umf_create_element.c -o umf_zi_create_element.o
+ $(C) -DZINT -c umf_dump.c -o umf_zi_dump.o
+ $(C) -DZINT -c umf_extend_front.c -o umf_zi_extend_front.o
+ $(C) -DZINT -c umf_garbage_collection.c -o umf_zi_garbage_collection.o
+ $(C) -DZINT -c umf_get_memory.c -o umf_zi_get_memory.o
+ $(C) -DZINT -c umf_init_front.c -o umf_zi_init_front.o
+ $(C) -DZINT -c umf_kernel.c -o umf_zi_kernel.o
+ $(C) -DZINT -c umf_kernel_init.c -o umf_zi_kernel_init.o
+ $(C) -DZINT -c umf_kernel_wrapup.c -o umf_zi_kernel_wrapup.o
+ $(C) -DZINT -c umf_local_search.c -o umf_zi_local_search.o
+ $(C) -DZINT -c umf_lsolve.c -o umf_zi_lsolve.o
+ $(C) -DZINT -c umf_ltsolve.c -o umf_zi_ltsolve.o
+ $(C) -DZINT -c umf_mem_alloc_element.c -o umf_zi_mem_alloc_element.o
+ $(C) -DZINT -c umf_mem_alloc_head_block.c -o umf_zi_mem_alloc_head_block.o
+ $(C) -DZINT -c umf_mem_alloc_tail_block.c -o umf_zi_mem_alloc_tail_block.o
+ $(C) -DZINT -c umf_mem_free_tail_block.c -o umf_zi_mem_free_tail_block.o
+ $(C) -DZINT -c umf_mem_init_memoryspace.c -o umf_zi_mem_init_memoryspace.o
+ $(C) -DZINT -c umf_report_vector.c -o umf_zi_report_vector.o
+ $(C) -DZINT -c umf_row_search.c -o umf_zi_row_search.o
+ $(C) -DZINT -c umf_scale_column.c -o umf_zi_scale_column.o
+ $(C) -DZINT -c umf_set_stats.c -o umf_zi_set_stats.o
+ $(C) -DZINT -c umf_solve.c -o umf_zi_solve.o
+ $(C) -DZINT -c umf_symbolic_usage.c -o umf_zi_symbolic_usage.o
+ $(C) -DZINT -c umf_transpose.c -o umf_zi_transpose.o
+ $(C) -DZINT -c umf_tuple_lengths.c -o umf_zi_tuple_lengths.o
+ $(C) -DZINT -c umf_usolve.c -o umf_zi_usolve.o
+ $(C) -DZINT -c umf_utsolve.c -o umf_zi_utsolve.o
+ $(C) -DZINT -c umf_valid_numeric.c -o umf_zi_valid_numeric.o
+ $(C) -DZINT -c umf_valid_symbolic.c -o umf_zi_valid_symbolic.o
+ $(C) -DZINT -c umf_grow_front.c -o umf_zi_grow_front.o
+ $(C) -DZINT -c umf_start_front.c -o umf_zi_start_front.o
+ $(C) -DZINT -c umf_2by2.c -o umf_zi_2by2.o
+ $(C) -DZINT -c umf_store_lu.c -o umf_zi_store_lu.o
+ $(C) -DZINT -c umf_scale.c -o umf_zi_scale.o
+ $(C) -DZINT -DWSOLVE -c umfpack_solve.c -o umfpack_zi_wsolve.o
+ $(C) -DZINT -c umfpack_col_to_triplet.c -o umfpack_zi_col_to_triplet.o
+ $(C) -DZINT -c umfpack_defaults.c -o umfpack_zi_defaults.o
+ $(C) -DZINT -c umfpack_free_numeric.c -o umfpack_zi_free_numeric.o
+ $(C) -DZINT -c umfpack_free_symbolic.c -o umfpack_zi_free_symbolic.o
+ $(C) -DZINT -c umfpack_get_numeric.c -o umfpack_zi_get_numeric.o
+ $(C) -DZINT -c umfpack_get_lunz.c -o umfpack_zi_get_lunz.o
+ $(C) -DZINT -c umfpack_get_symbolic.c -o umfpack_zi_get_symbolic.o
+ $(C) -DZINT -c umfpack_get_determinant.c -o umfpack_zi_get_determinant.o
+ $(C) -DZINT -c umfpack_numeric.c -o umfpack_zi_numeric.o
+ $(C) -DZINT -c umfpack_qsymbolic.c -o umfpack_zi_qsymbolic.o
+ $(C) -DZINT -c umfpack_report_control.c -o umfpack_zi_report_control.o
+ $(C) -DZINT -c umfpack_report_info.c -o umfpack_zi_report_info.o
+ $(C) -DZINT -c umfpack_report_matrix.c -o umfpack_zi_report_matrix.o
+ $(C) -DZINT -c umfpack_report_numeric.c -o umfpack_zi_report_numeric.o
+ $(C) -DZINT -c umfpack_report_perm.c -o umfpack_zi_report_perm.o
+ $(C) -DZINT -c umfpack_report_status.c -o umfpack_zi_report_status.o
+ $(C) -DZINT -c umfpack_report_symbolic.c -o umfpack_zi_report_symbolic.o
+ $(C) -DZINT -c umfpack_report_triplet.c -o umfpack_zi_report_triplet.o
+ $(C) -DZINT -c umfpack_report_vector.c -o umfpack_zi_report_vector.o
+ $(C) -DZINT -c umfpack_solve.c -o umfpack_zi_solve.o
+ $(C) -DZINT -c umfpack_symbolic.c -o umfpack_zi_symbolic.o
+ $(C) -DZINT -c umfpack_transpose.c -o umfpack_zi_transpose.o
+ $(C) -DZINT -c umfpack_triplet_to_col.c -o umfpack_zi_triplet_to_col.o
+ $(C) -DZINT -c umfpack_scale.c -o umfpack_zi_scale.o
+ $(C) -DZINT -c umfpack_load_numeric.c -o umfpack_zi_load_numeric.o
+ $(C) -DZINT -c umfpack_save_numeric.c -o umfpack_zi_save_numeric.o
+ $(C) -DZINT -c umfpack_load_symbolic.c -o umfpack_zi_load_symbolic.o
+ $(C) -DZINT -c umfpack_save_symbolic.c -o umfpack_zi_save_symbolic.o
+ $(C) -DZLONG -DCONJUGATE_SOLVE -c umf_ltsolve.c -o umf_zl_lhsolve.o
+ $(C) -DZLONG -DCONJUGATE_SOLVE -c umf_utsolve.c -o umf_zl_uhsolve.o
+ $(C) -DZLONG -DDO_MAP -c umf_triplet.c -o umf_zl_triplet_map_nox.o
+ $(C) -DZLONG -DDO_VALUES -c umf_triplet.c -o umf_zl_triplet_nomap_x.o
+ $(C) -DZLONG -c umf_triplet.c -o umf_zl_triplet_nomap_nox.o
+ $(C) -DZLONG -DDO_MAP -DDO_VALUES -c umf_triplet.c -o umf_zl_triplet_map_x.o
+ $(C) -DZLONG -DFIXQ -c umf_assemble.c -o umf_zl_assemble_fixq.o
+ $(C) -DZLONG -DDROP -c umf_store_lu.c -o umf_zl_store_lu_drop.o
+ $(C) -DZLONG -c umf_assemble.c -o umf_zl_assemble.o
+ $(C) -DZLONG -c umf_blas3_update.c -o umf_zl_blas3_update.o
+ $(C) -DZLONG -c umf_build_tuples.c -o umf_zl_build_tuples.o
+ $(C) -DZLONG -c umf_create_element.c -o umf_zl_create_element.o
+ $(C) -DZLONG -c umf_dump.c -o umf_zl_dump.o
+ $(C) -DZLONG -c umf_extend_front.c -o umf_zl_extend_front.o
+ $(C) -DZLONG -c umf_garbage_collection.c -o umf_zl_garbage_collection.o
+ $(C) -DZLONG -c umf_get_memory.c -o umf_zl_get_memory.o
+ $(C) -DZLONG -c umf_init_front.c -o umf_zl_init_front.o
+ $(C) -DZLONG -c umf_kernel.c -o umf_zl_kernel.o
+ $(C) -DZLONG -c umf_kernel_init.c -o umf_zl_kernel_init.o
+ $(C) -DZLONG -c umf_kernel_wrapup.c -o umf_zl_kernel_wrapup.o
+ $(C) -DZLONG -c umf_local_search.c -o umf_zl_local_search.o
+ $(C) -DZLONG -c umf_lsolve.c -o umf_zl_lsolve.o
+ $(C) -DZLONG -c umf_ltsolve.c -o umf_zl_ltsolve.o
+ $(C) -DZLONG -c umf_mem_alloc_element.c -o umf_zl_mem_alloc_element.o
+ $(C) -DZLONG -c umf_mem_alloc_head_block.c -o umf_zl_mem_alloc_head_block.o
+ $(C) -DZLONG -c umf_mem_alloc_tail_block.c -o umf_zl_mem_alloc_tail_block.o
+ $(C) -DZLONG -c umf_mem_free_tail_block.c -o umf_zl_mem_free_tail_block.o
+ $(C) -DZLONG -c umf_mem_init_memoryspace.c -o umf_zl_mem_init_memoryspace.o
+ $(C) -DZLONG -c umf_report_vector.c -o umf_zl_report_vector.o
+ $(C) -DZLONG -c umf_row_search.c -o umf_zl_row_search.o
+ $(C) -DZLONG -c umf_scale_column.c -o umf_zl_scale_column.o
+ $(C) -DZLONG -c umf_set_stats.c -o umf_zl_set_stats.o
+ $(C) -DZLONG -c umf_solve.c -o umf_zl_solve.o
+ $(C) -DZLONG -c umf_symbolic_usage.c -o umf_zl_symbolic_usage.o
+ $(C) -DZLONG -c umf_transpose.c -o umf_zl_transpose.o
+ $(C) -DZLONG -c umf_tuple_lengths.c -o umf_zl_tuple_lengths.o
+ $(C) -DZLONG -c umf_usolve.c -o umf_zl_usolve.o
+ $(C) -DZLONG -c umf_utsolve.c -o umf_zl_utsolve.o
+ $(C) -DZLONG -c umf_valid_numeric.c -o umf_zl_valid_numeric.o
+ $(C) -DZLONG -c umf_valid_symbolic.c -o umf_zl_valid_symbolic.o
+ $(C) -DZLONG -c umf_grow_front.c -o umf_zl_grow_front.o
+ $(C) -DZLONG -c umf_start_front.c -o umf_zl_start_front.o
+ $(C) -DZLONG -c umf_2by2.c -o umf_zl_2by2.o
+ $(C) -DZLONG -c umf_store_lu.c -o umf_zl_store_lu.o
+ $(C) -DZLONG -c umf_scale.c -o umf_zl_scale.o
+ $(C) -DZLONG -DWSOLVE -c umfpack_solve.c -o umfpack_zl_wsolve.o
+ $(C) -DZLONG -c umfpack_col_to_triplet.c -o umfpack_zl_col_to_triplet.o
+ $(C) -DZLONG -c umfpack_defaults.c -o umfpack_zl_defaults.o
+ $(C) -DZLONG -c umfpack_free_numeric.c -o umfpack_zl_free_numeric.o
+ $(C) -DZLONG -c umfpack_free_symbolic.c -o umfpack_zl_free_symbolic.o
+ $(C) -DZLONG -c umfpack_get_numeric.c -o umfpack_zl_get_numeric.o
+ $(C) -DZLONG -c umfpack_get_lunz.c -o umfpack_zl_get_lunz.o
+ $(C) -DZLONG -c umfpack_get_symbolic.c -o umfpack_zl_get_symbolic.o
+ $(C) -DZLONG -c umfpack_get_determinant.c -o umfpack_zl_get_determinant.o
+ $(C) -DZLONG -c umfpack_numeric.c -o umfpack_zl_numeric.o
+ $(C) -DZLONG -c umfpack_qsymbolic.c -o umfpack_zl_qsymbolic.o
+ $(C) -DZLONG -c umfpack_report_control.c -o umfpack_zl_report_control.o
+ $(C) -DZLONG -c umfpack_report_info.c -o umfpack_zl_report_info.o
+ $(C) -DZLONG -c umfpack_report_matrix.c -o umfpack_zl_report_matrix.o
+ $(C) -DZLONG -c umfpack_report_numeric.c -o umfpack_zl_report_numeric.o
+ $(C) -DZLONG -c umfpack_report_perm.c -o umfpack_zl_report_perm.o
+ $(C) -DZLONG -c umfpack_report_status.c -o umfpack_zl_report_status.o
+ $(C) -DZLONG -c umfpack_report_symbolic.c -o umfpack_zl_report_symbolic.o
+ $(C) -DZLONG -c umfpack_report_triplet.c -o umfpack_zl_report_triplet.o
+ $(C) -DZLONG -c umfpack_report_vector.c -o umfpack_zl_report_vector.o
+ $(C) -DZLONG -c umfpack_solve.c -o umfpack_zl_solve.o
+ $(C) -DZLONG -c umfpack_symbolic.c -o umfpack_zl_symbolic.o
+ $(C) -DZLONG -c umfpack_transpose.c -o umfpack_zl_transpose.o
+ $(C) -DZLONG -c umfpack_triplet_to_col.c -o umfpack_zl_triplet_to_col.o
+ $(C) -DZLONG -c umfpack_scale.c -o umfpack_zl_scale.o
+ $(C) -DZLONG -c umfpack_load_numeric.c -o umfpack_zl_load_numeric.o
+ $(C) -DZLONG -c umfpack_save_numeric.c -o umfpack_zl_save_numeric.o
+ $(C) -DZLONG -c umfpack_load_symbolic.c -o umfpack_zl_load_symbolic.o
+ $(C) -DZLONG -c umfpack_save_symbolic.c -o umfpack_zl_save_symbolic.o
+ $(AR) ../Lib/libumfpack.a \
+ umfpack_gn_global.o \
+ umf_i_analyze.o umf_i_apply_order.o umf_i_colamd.o umf_i_free.o \
+ umf_i_fsize.o umf_i_is_permutation.o umf_i_malloc.o umf_i_realloc.o \
+ umf_i_report_perm.o umf_i_singletons.o \
+ umf_l_analyze.o umf_l_apply_order.o umf_l_colamd.o umf_l_free.o \
+ umf_l_fsize.o umf_l_is_permutation.o umf_l_malloc.o umf_l_realloc.o \
+ umf_l_report_perm.o umf_l_singletons.o \
+ umfpack_gn_timer.o umfpack_gn_tictoc.o \
+ umf_di_lhsolve.o \
+ umf_di_uhsolve.o umf_di_triplet_map_nox.o umf_di_triplet_nomap_x.o \
+ umf_di_triplet_nomap_nox.o umf_di_triplet_map_x.o \
+ umf_di_assemble_fixq.o umf_di_store_lu_drop.o umf_di_assemble.o \
+ umf_di_blas3_update.o umf_di_build_tuples.o \
+ umf_di_create_element.o umf_di_dump.o umf_di_extend_front.o \
+ umf_di_garbage_collection.o umf_di_get_memory.o \
+ umf_di_init_front.o umf_di_kernel.o umf_di_kernel_init.o \
+ umf_di_kernel_wrapup.o umf_di_local_search.o umf_di_lsolve.o \
+ umf_di_ltsolve.o umf_di_mem_alloc_element.o \
+ umf_di_mem_alloc_head_block.o umf_di_mem_alloc_tail_block.o \
+ umf_di_mem_free_tail_block.o umf_di_mem_init_memoryspace.o \
+ umf_di_report_vector.o umf_di_row_search.o umf_di_scale_column.o \
+ umf_di_set_stats.o umf_di_solve.o umf_di_symbolic_usage.o \
+ umf_di_transpose.o umf_di_tuple_lengths.o umf_di_usolve.o \
+ umf_di_utsolve.o umf_di_valid_numeric.o umf_di_valid_symbolic.o \
+ umf_di_grow_front.o umf_di_start_front.o umf_di_2by2.o \
+ umf_di_store_lu.o umf_di_scale.o umfpack_di_wsolve.o \
+ umfpack_di_col_to_triplet.o umfpack_di_defaults.o \
+ umfpack_di_free_numeric.o umfpack_di_free_symbolic.o \
+ umfpack_di_get_numeric.o umfpack_di_get_lunz.o \
+ umfpack_di_get_symbolic.o umfpack_di_get_determinant.o \
+ umfpack_di_numeric.o \
+ umfpack_di_qsymbolic.o umfpack_di_report_control.o \
+ umfpack_di_report_info.o umfpack_di_report_matrix.o \
+ umfpack_di_report_numeric.o umfpack_di_report_perm.o \
+ umfpack_di_report_status.o umfpack_di_report_symbolic.o \
+ umfpack_di_report_triplet.o umfpack_di_report_vector.o \
+ umfpack_di_solve.o umfpack_di_symbolic.o umfpack_di_transpose.o \
+ umfpack_di_triplet_to_col.o umfpack_di_scale.o \
+ umfpack_di_load_numeric.o umfpack_di_save_numeric.o \
+ umfpack_di_load_symbolic.o umfpack_di_save_symbolic.o \
+ umf_dl_lhsolve.o \
+ umf_dl_uhsolve.o umf_dl_triplet_map_nox.o umf_dl_triplet_nomap_x.o \
+ umf_dl_triplet_nomap_nox.o umf_dl_triplet_map_x.o \
+ umf_dl_assemble_fixq.o umf_dl_store_lu_drop.o umf_dl_assemble.o \
+ umf_dl_blas3_update.o umf_dl_build_tuples.o \
+ umf_dl_create_element.o umf_dl_dump.o umf_dl_extend_front.o \
+ umf_dl_garbage_collection.o umf_dl_get_memory.o \
+ umf_dl_init_front.o umf_dl_kernel.o umf_dl_kernel_init.o \
+ umf_dl_kernel_wrapup.o umf_dl_local_search.o umf_dl_lsolve.o \
+ umf_dl_ltsolve.o umf_dl_mem_alloc_element.o \
+ umf_dl_mem_alloc_head_block.o umf_dl_mem_alloc_tail_block.o \
+ umf_dl_mem_free_tail_block.o umf_dl_mem_init_memoryspace.o \
+ umf_dl_report_vector.o umf_dl_row_search.o umf_dl_scale_column.o \
+ umf_dl_set_stats.o umf_dl_solve.o umf_dl_symbolic_usage.o \
+ umf_dl_transpose.o umf_dl_tuple_lengths.o umf_dl_usolve.o \
+ umf_dl_utsolve.o umf_dl_valid_numeric.o umf_dl_valid_symbolic.o \
+ umf_dl_grow_front.o umf_dl_start_front.o umf_dl_2by2.o \
+ umf_dl_store_lu.o umf_dl_scale.o umfpack_dl_wsolve.o \
+ umfpack_dl_col_to_triplet.o umfpack_dl_defaults.o \
+ umfpack_dl_free_numeric.o umfpack_dl_free_symbolic.o \
+ umfpack_dl_get_numeric.o umfpack_dl_get_lunz.o \
+ umfpack_dl_get_symbolic.o umfpack_dl_get_determinant.o \
+ umfpack_dl_numeric.o \
+ umfpack_dl_qsymbolic.o umfpack_dl_report_control.o \
+ umfpack_dl_report_info.o umfpack_dl_report_matrix.o \
+ umfpack_dl_report_numeric.o umfpack_dl_report_perm.o \
+ umfpack_dl_report_status.o umfpack_dl_report_symbolic.o \
+ umfpack_dl_report_triplet.o umfpack_dl_report_vector.o \
+ umfpack_dl_solve.o umfpack_dl_symbolic.o umfpack_dl_transpose.o \
+ umfpack_dl_triplet_to_col.o umfpack_dl_scale.o \
+ umfpack_dl_load_numeric.o umfpack_dl_save_numeric.o \
+ umfpack_dl_load_symbolic.o umfpack_dl_save_symbolic.o \
+ umf_zi_lhsolve.o \
+ umf_zi_uhsolve.o umf_zi_triplet_map_nox.o umf_zi_triplet_nomap_x.o \
+ umf_zi_triplet_nomap_nox.o umf_zi_triplet_map_x.o \
+ umf_zi_assemble_fixq.o umf_zi_store_lu_drop.o umf_zi_assemble.o \
+ umf_zi_blas3_update.o umf_zi_build_tuples.o \
+ umf_zi_create_element.o umf_zi_dump.o umf_zi_extend_front.o \
+ umf_zi_garbage_collection.o umf_zi_get_memory.o \
+ umf_zi_init_front.o umf_zi_kernel.o umf_zi_kernel_init.o \
+ umf_zi_kernel_wrapup.o umf_zi_local_search.o umf_zi_lsolve.o \
+ umf_zi_ltsolve.o umf_zi_mem_alloc_element.o \
+ umf_zi_mem_alloc_head_block.o umf_zi_mem_alloc_tail_block.o \
+ umf_zi_mem_free_tail_block.o umf_zi_mem_init_memoryspace.o \
+ umf_zi_report_vector.o umf_zi_row_search.o umf_zi_scale_column.o \
+ umf_zi_set_stats.o umf_zi_solve.o umf_zi_symbolic_usage.o \
+ umf_zi_transpose.o umf_zi_tuple_lengths.o umf_zi_usolve.o \
+ umf_zi_utsolve.o umf_zi_valid_numeric.o umf_zi_valid_symbolic.o \
+ umf_zi_grow_front.o umf_zi_start_front.o umf_zi_2by2.o \
+ umf_zi_store_lu.o umf_zi_scale.o umfpack_zi_wsolve.o \
+ umfpack_zi_col_to_triplet.o umfpack_zi_defaults.o \
+ umfpack_zi_free_numeric.o umfpack_zi_free_symbolic.o \
+ umfpack_zi_get_numeric.o umfpack_zi_get_lunz.o \
+ umfpack_zi_get_symbolic.o umfpack_zi_get_determinant.o \
+ umfpack_zi_numeric.o \
+ umfpack_zi_qsymbolic.o umfpack_zi_report_control.o \
+ umfpack_zi_report_info.o umfpack_zi_report_matrix.o \
+ umfpack_zi_report_numeric.o umfpack_zi_report_perm.o \
+ umfpack_zi_report_status.o umfpack_zi_report_symbolic.o \
+ umfpack_zi_report_triplet.o umfpack_zi_report_vector.o \
+ umfpack_zi_solve.o umfpack_zi_symbolic.o umfpack_zi_transpose.o \
+ umfpack_zi_triplet_to_col.o umfpack_zi_scale.o \
+ umfpack_zi_load_numeric.o umfpack_zi_save_numeric.o \
+ umfpack_zi_load_symbolic.o umfpack_zi_save_symbolic.o \
+ umf_zl_lhsolve.o \
+ umf_zl_uhsolve.o umf_zl_triplet_map_nox.o umf_zl_triplet_nomap_x.o \
+ umf_zl_triplet_nomap_nox.o umf_zl_triplet_map_x.o \
+ umf_zl_assemble_fixq.o umf_zl_store_lu_drop.o umf_zl_assemble.o \
+ umf_zl_blas3_update.o umf_zl_build_tuples.o \
+ umf_zl_create_element.o umf_zl_dump.o umf_zl_extend_front.o \
+ umf_zl_garbage_collection.o umf_zl_get_memory.o \
+ umf_zl_init_front.o umf_zl_kernel.o umf_zl_kernel_init.o \
+ umf_zl_kernel_wrapup.o umf_zl_local_search.o umf_zl_lsolve.o \
+ umf_zl_ltsolve.o umf_zl_mem_alloc_element.o \
+ umf_zl_mem_alloc_head_block.o umf_zl_mem_alloc_tail_block.o \
+ umf_zl_mem_free_tail_block.o umf_zl_mem_init_memoryspace.o \
+ umf_zl_report_vector.o umf_zl_row_search.o umf_zl_scale_column.o \
+ umf_zl_set_stats.o umf_zl_solve.o umf_zl_symbolic_usage.o \
+ umf_zl_transpose.o umf_zl_tuple_lengths.o umf_zl_usolve.o \
+ umf_zl_utsolve.o umf_zl_valid_numeric.o umf_zl_valid_symbolic.o \
+ umf_zl_grow_front.o umf_zl_start_front.o umf_zl_2by2.o \
+ umf_zl_store_lu.o umf_zl_scale.o umfpack_zl_wsolve.o \
+ umfpack_zl_col_to_triplet.o umfpack_zl_defaults.o \
+ umfpack_zl_free_numeric.o umfpack_zl_free_symbolic.o \
+ umfpack_zl_get_numeric.o umfpack_zl_get_lunz.o \
+ umfpack_zl_get_symbolic.o umfpack_zl_get_determinant.o \
+ umfpack_zl_numeric.o \
+ umfpack_zl_qsymbolic.o umfpack_zl_report_control.o \
+ umfpack_zl_report_info.o umfpack_zl_report_matrix.o \
+ umfpack_zl_report_numeric.o umfpack_zl_report_perm.o \
+ umfpack_zl_report_status.o umfpack_zl_report_symbolic.o \
+ umfpack_zl_report_triplet.o umfpack_zl_report_vector.o \
+ umfpack_zl_solve.o umfpack_zl_symbolic.o umfpack_zl_transpose.o \
+ umfpack_zl_triplet_to_col.o umfpack_zl_scale.o \
+ umfpack_zl_load_numeric.o umfpack_zl_save_numeric.o \
+ umfpack_zl_load_symbolic.o umfpack_zl_save_symbolic.o
+ - $(RANLIB) ../Lib/libumfpack.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) ../Lib/libumfpack.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/src/C/SuiteSparse/UMFPACK/Source/cholmod_blas.h b/src/C/SuiteSparse/UMFPACK/Source/cholmod_blas.h
new file mode 100644
index 0000000..9619804
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/cholmod_blas.h
@@ -0,0 +1,451 @@
+/* ========================================================================== */
+/* === Include/cholmod_blas.h =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_blas.h. Version 1.2.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* This does not need to be included in the user's program. */
+
+#ifndef CHOLMOD_BLAS_H
+#define CHOLMOD_BLAS_H
+
+/* ========================================================================== */
+/* === Architecture ========================================================= */
+/* ========================================================================== */
+
+#if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2)
+#define CHOLMOD_SOL2
+#define CHOLMOD_ARCHITECTURE "Sun Solaris"
+
+#elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI)
+#define CHOLMOD_SGI
+#define CHOLMOD_ARCHITECTURE "SGI Irix"
+
+#elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86)
+#define CHOLMOD_LINUX
+#define CHOLMOD_ARCHITECTURE "Linux"
+
+#elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS)
+#define CHOLMOD_AIX
+#define CHOLMOD_ARCHITECTURE "IBM AIX"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA)
+#define CHOLMOD_ALPHA
+#define CHOLMOD_ARCHITECTURE "Compaq Alpha"
+
+#elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64)
+#if defined (__MINGW32__) || defined (__MINGW32__)
+#define CHOLMOD_MINGW
+#elif defined (__CYGWIN32__) || defined (__CYGWIN32__)
+#define CHOLMOD_CYGWIN
+#else
+#define CHOLMOD_WINDOWS
+#define BLAS_NO_UNDERSCORE
+#endif
+#define CHOLMOD_ARCHITECTURE "Microsoft Windows"
+
+#elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP Unix"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP 700 Unix"
+#define BLAS_NO_UNDERSCORE
+
+#else
+/* If the architecture is unknown, and you call the BLAS, you may need to */
+/* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */
+#define CHOLMOD_ARCHITECTURE "unknown"
+#endif
+
+
+/* ========================================================================== */
+/* === BLAS and LAPACK names ================================================ */
+/* ========================================================================== */
+
+/* Prototypes for the various versions of the BLAS. */
+
+/* Determine if the 64-bit Sun Performance BLAS is to be used */
+#if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(LONG) && defined(LONGBLAS)
+#define SUN64
+#endif
+
+#ifdef SUN64
+
+#define BLAS_DTRSV dtrsv_64_
+#define BLAS_DGEMV dgemv_64_
+#define BLAS_DTRSM dtrsm_64_
+#define BLAS_DGEMM dgemm_64_
+#define BLAS_DSYRK dsyrk_64_
+#define BLAS_DGER dger_64_
+#define BLAS_DSCAL dscal_64_
+#define LAPACK_DPOTRF dpotrf_64_
+
+#define BLAS_ZTRSV ztrsv_64_
+#define BLAS_ZGEMV zgemv_64_
+#define BLAS_ZTRSM ztrsm_64_
+#define BLAS_ZGEMM zgemm_64_
+#define BLAS_ZHERK zherk_64_
+#define BLAS_ZGER zgeru_64_
+#define BLAS_ZSCAL zscal_64_
+#define LAPACK_ZPOTRF zpotrf_64_
+
+#elif defined (BLAS_NO_UNDERSCORE)
+
+#define BLAS_DTRSV dtrsv
+#define BLAS_DGEMV dgemv
+#define BLAS_DTRSM dtrsm
+#define BLAS_DGEMM dgemm
+#define BLAS_DSYRK dsyrk
+#define BLAS_DGER dger
+#define BLAS_DSCAL dscal
+#define LAPACK_DPOTRF dpotrf
+
+#define BLAS_ZTRSV ztrsv
+#define BLAS_ZGEMV zgemv
+#define BLAS_ZTRSM ztrsm
+#define BLAS_ZGEMM zgemm
+#define BLAS_ZHERK zherk
+#define BLAS_ZGER zgeru
+#define BLAS_ZSCAL zscal
+#define LAPACK_ZPOTRF zpotrf
+
+#else
+
+#define BLAS_DTRSV dtrsv_
+#define BLAS_DGEMV dgemv_
+#define BLAS_DTRSM dtrsm_
+#define BLAS_DGEMM dgemm_
+#define BLAS_DSYRK dsyrk_
+#define BLAS_DGER dger_
+#define BLAS_DSCAL dscal_
+#define LAPACK_DPOTRF dpotrf_
+
+#define BLAS_ZTRSV ztrsv_
+#define BLAS_ZGEMV zgemv_
+#define BLAS_ZTRSM ztrsm_
+#define BLAS_ZGEMM zgemm_
+#define BLAS_ZHERK zherk_
+#define BLAS_ZGER zgeru_
+#define BLAS_ZSCAL zscal_
+#define LAPACK_ZPOTRF zpotrf_
+
+#endif
+
+/* ========================================================================== */
+/* === BLAS and LAPACK integer arguments ==================================== */
+/* ========================================================================== */
+
+/* CHOLMOD can be compiled with -D'LONGBLAS=long' for the Sun Performance
+ * Library, or -D'LONGBLAS=long long' for SGI's SCSL BLAS. This defines the
+ * integer used in the BLAS for the cholmod_l_* routines.
+ *
+ * The "int" version of CHOLMOD always uses the "int" version of the BLAS.
+ */
+
+#if defined (LONGBLAS) && defined (LONG)
+#define BLAS_INT LONGBLAS
+#else
+#define BLAS_INT int
+#endif
+
+/* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need
+ * to check for integer overflow when converting from one to the other. If
+ * any integer overflows, the externally-defined blas_ok variable is set to
+ * FALSE. blas_ok should be set to TRUE before calling any BLAS_* macro.
+ */
+
+#define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int))
+#define EQ(K,k) (((BLAS_INT) K) == ((Int) k))
+
+/* ========================================================================== */
+/* === BLAS and LAPACK prototypes and macros ================================ */
+/* ========================================================================== */
+
+void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_dpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_zpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+/* ========================================================================== */
+
+void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+void BLAS_ZGERU (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_2by2.c b/src/C/SuiteSparse/UMFPACK/Source/umf_2by2.c
new file mode 100644
index 0000000..7a4e3e1
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_2by2.c
@@ -0,0 +1,859 @@
+/* ========================================================================== */
+/* === UMF_2by2 ============================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Not user-callable. Computes a row permutation P so that A (P,:) has a
+ * mostly zero-free diagonal, with large entries on the diagonal. It does this
+ * by swapping pairs of rows. Once a row is swapped it is not swapped again.
+ * This is a "cheap" assignment, not a complete max. transversal or
+ * bi-partite matching. It is only a partial matching. For most matrices
+ * for which this algorithm is used, however, the matching is complete (in
+ * UMFPACK this algorithm is used for matrices with roughly symmetric pattern,
+ * and these matrices typically have a mostly-zero-free diagonal to begin with.
+ * This algorithm is not meant to be used on arbitrary unsymmetric matrices
+ * (for those matrices, UMFPACK uses its unsymmetric strategy and does not
+ * use this algorithm).
+ *
+ * Even if incomplete, the matching is usually good enough for UMFPACK's
+ * symmetric strategy, which can easily pivot off the diagonal during numerical
+ * factorization if it finds a weak diagonal entry.
+ *
+ * The algorithms works as follows. First, row scaling factors are computed,
+ * and weak diagonal entries are found. A weak entry is a value A(k,k) whose
+ * absolute value is < tol * max (abs (A (:,k))). For each weak diagonal k in
+ * increasing order of degree in A+A', the algorithm finds an index j such
+ * that A (k,j) and A (j,k) are "large" (greater than or equal to tol times
+ * the largest magnitude in their columns). Row j must also not have already
+ * been swapped. Rows j and k are then swapped. If we come to a diagonal k
+ * that has already been swapped, then it is not modified. This case occurs
+ * for "oxo" pivots:
+ *
+ * k j
+ * k o x
+ * j x o
+ *
+ * which are swapped once to obtain
+ *
+ * k j
+ * j x o
+ * k o x
+ *
+ * These two rows are then not modified any further (A (j,j) was weak, but
+ * after one swap the permuted the jth diagonal entry is strong.
+ *
+ * This algorithm only works on square matrices (real, complex, or pattern-
+ * only). The numerical values are optional. If not present, each entry is
+ * treated as numerically acceptable (tol is ignored), and the algorithm
+ * operates by just using the pattern, not the values. Each column of the
+ * input matrix A must be sorted, with no duplicate entries. The matrix A
+ * can be optionally scaled prior to the numerical test. The matrix A (:,P)
+ * has the same diagonal entries as A (:,P), except in different order. So
+ * the output permutation P can also be used to swap the columns of A.
+ */
+
+#include "umf_internal.h"
+
+#ifndef NDEBUG
+#include "umf_is_permutation.h"
+#endif
+
+/* x is "weak" if it is less than ctol. If x or ctol are NaN, then define
+ * x as not "weak". This is a rather arbitrary choice, made to simplify the
+ * computation. On all but a PC with Microsoft C/C++, this test becomes
+ * ((x) - ctol < 0). */
+#define WEAK(x,ctol) (SCALAR_IS_LTZERO ((x)-(ctol)))
+
+/* For flag value in Next [col] */
+#define IS_WEAK -2
+
+/* ========================================================================== */
+/* === two_by_two =========================================================== */
+/* ========================================================================== */
+
+PRIVATE Int two_by_two /* returns # unmatched weak diagonals */
+(
+ /* input, not modified */
+ Int n2, /* C is n2-by-n2 */
+ Int Cp [ ], /* size n2+1, column pointers for C */
+ Int Ci [ ], /* size snz = Cp [n2], row indices for C */
+ Int Degree [ ], /* Degree [i] = degree of row i of C+C' */
+
+ /* input, not defined on output */
+ Int Next [ ], /* Next [k] == IS_WEAK if k is a weak diagonal */
+ Int Ri [ ], /* Ri [i] is the length of row i in C */
+
+ /* output, not defined on input */
+ Int P [ ],
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ],
+ Int Head [ ]
+)
+{
+ Int deg, newcol, row, col, p, p2, unmatched, k, j, j2, j_best, best, jdiff,
+ jdiff_best, jdeg, jdeg_best, cp, cp1, cp2, rp, rp1, rp2, maxdeg,
+ mindeg ;
+
+ /* ---------------------------------------------------------------------- */
+ /* place weak diagonals in the degree lists */
+ /* ---------------------------------------------------------------------- */
+
+ for (deg = 0 ; deg < n2 ; deg++)
+ {
+ Head [deg] = EMPTY ;
+ }
+
+ maxdeg = 0 ;
+ mindeg = Int_MAX ;
+ for (newcol = n2-1 ; newcol >= 0 ; newcol--)
+ {
+ if (Next [newcol] == IS_WEAK)
+ {
+ /* add this column to the list of weak nodes */
+ DEBUGm1 ((" newcol "ID" has a weak diagonal deg "ID"\n",
+ newcol, deg)) ;
+ deg = Degree [newcol] ;
+ ASSERT (deg >= 0 && deg < n2) ;
+ Next [newcol] = Head [deg] ;
+ Head [deg] = newcol ;
+ maxdeg = MAX (maxdeg, deg) ;
+ mindeg = MIN (mindeg, deg) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct R = C' (C = strong entries in pruned submatrix) */
+ /* ---------------------------------------------------------------------- */
+
+ /* Ri [0..n2-1] is the length of each row of R */
+ /* use P as temporary pointer into the row form of R [ */
+ Rp [0] = 0 ;
+ for (row = 0 ; row < n2 ; row++)
+ {
+ Rp [row+1] = Rp [row] + Ri [row] ;
+ P [row] = Rp [row] ;
+ }
+ /* Ri no longer needed for row counts */
+
+ /* all entries in C are strong */
+ for (col = 0 ; col < n2 ; col++)
+ {
+ p2 = Cp [col+1] ;
+ for (p = Cp [col] ; p < p2 ; p++)
+ {
+ /* place the column index in row = Ci [p] */
+ Ri [P [Ci [p]]++] = col ;
+ }
+ }
+
+ /* contents of P no longer needed ] */
+
+#ifndef NDEBUG
+ DEBUG0 (("==================R: row form of strong entries in A:\n")) ;
+ UMF_dump_col_matrix ((double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+ Ri, Rp, n2, n2, Rp [n2]) ;
+#endif
+ ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* for each weak diagonal, find a pair of strong off-diagonal entries */
+ /* ---------------------------------------------------------------------- */
+
+ for (row = 0 ; row < n2 ; row++)
+ {
+ P [row] = EMPTY ;
+ }
+
+ unmatched = 0 ;
+ best = EMPTY ;
+ jdiff = EMPTY ;
+ jdeg = EMPTY ;
+
+ for (deg = mindeg ; deg <= maxdeg ; deg++)
+ {
+ /* find the next weak diagonal of lowest degree */
+ DEBUGm2 (("---------------------------------- Deg: "ID"\n", deg)) ;
+ for (k = Head [deg] ; k != EMPTY ; k = Next [k])
+ {
+ DEBUGm2 (("k: "ID"\n", k)) ;
+ if (P [k] == EMPTY)
+ {
+ /* C (k,k) is a weak diagonal entry. Find an index j != k such
+ * that C (j,k) and C (k,j) are both strong, and also such
+ * that Degree [j] is minimized. In case of a tie, pick
+ * the smallest index j. C and R contain the pattern of
+ * strong entries only.
+ *
+ * Note that row k of R and column k of C are both sorted. */
+
+ DEBUGm4 (("===== Weak diagonal k = "ID"\n", k)) ;
+ DEBUG1 (("Column k of C:\n")) ;
+ for (p = Cp [k] ; p < Cp [k+1] ; p++)
+ {
+ DEBUG1 ((" "ID": deg "ID"\n", Ci [p], Degree [Ci [p]]));
+ }
+ DEBUG1 (("Row k of R (strong entries only):\n")) ;
+ for (p = Rp [k] ; p < Rp [k+1] ; p++)
+ {
+ DEBUG1 ((" "ID": deg "ID"\n", Ri [p], Degree [Ri [p]]));
+ }
+
+ /* no (C (k,j), C (j,k)) pair exists yet */
+ j_best = EMPTY ;
+ jdiff_best = Int_MAX ;
+ jdeg_best = Int_MAX ;
+
+ /* pointers into column k (including values) */
+ cp1 = Cp [k] ;
+ cp2 = Cp [k+1] ;
+ cp = cp1 ;
+
+ /* pointers into row k (strong entries only, no values) */
+ rp1 = Rp [k] ;
+ rp2 = Rp [k+1] ;
+ rp = rp1 ;
+
+ /* while entries searched in column k and row k */
+ while (TRUE)
+ {
+
+ if (cp >= cp2)
+ {
+ /* no more entries in this column */
+ break ;
+ }
+
+ /* get C (j,k), which is strong */
+ j = Ci [cp] ;
+
+ if (rp >= rp2)
+ {
+ /* no more entries in this column */
+ break ;
+ }
+
+ /* get R (k,j2), which is strong */
+ j2 = Ri [rp] ;
+
+ if (j < j2)
+ {
+ /* C (j,k) is strong, but R (k,j) is not strong */
+ cp++ ;
+ continue ;
+ }
+
+ if (j2 < j)
+ {
+ /* C (k,j2) is strong, but R (j2,k) is not strong */
+ rp++ ;
+ continue ;
+ }
+
+ /* j == j2: C (j,k) is strong and R (k,j) is strong */
+
+ best = FALSE ;
+
+ if (P [j] == EMPTY)
+ {
+ /* j has not yet been matched */
+ jdeg = Degree [j] ;
+ jdiff = SCALAR_ABS (k-j) ;
+
+ DEBUG1 (("Try candidate j "ID" deg "ID" diff "ID
+ "\n", j, jdeg, jdiff)) ;
+
+ if (j_best == EMPTY)
+ {
+ /* this is the first candidate seen */
+ DEBUG1 ((" first\n")) ;
+ best = TRUE ;
+ }
+ else
+ {
+ if (jdeg < jdeg_best)
+ {
+ /* the degree of j is best seen so far. */
+ DEBUG1 ((" least degree\n")) ;
+ best = TRUE ;
+ }
+ else if (jdeg == jdeg_best)
+ {
+ /* degree of j and j_best are the same */
+ /* tie break by nearest node number */
+ if (jdiff < jdiff_best)
+ {
+ DEBUG1 ((" tie degree, closer\n")) ;
+ best = TRUE ;
+ }
+ else if (jdiff == jdiff_best)
+ {
+ /* |j-k| = |j_best-k|. For any given k
+ * and j_best there is only one other j
+ * than can be just as close as j_best.
+ * Tie break by picking the smaller of
+ * j and j_best */
+ DEBUG1 ((" tie degree, as close\n"));
+ best = j < j_best ;
+ }
+ }
+ else
+ {
+ /* j has higher degree than best so far */
+ best = FALSE ;
+ }
+ }
+ }
+
+ if (best)
+ {
+ /* j is best match for k */
+ /* found a strong pair, A (j,k) and A (k,j) */
+ DEBUG1 ((" --- Found pair k: "ID" j: " ID
+ " jdeg: "ID" jdiff: "ID"\n",
+ k, j, jdeg, jdiff)) ;
+ ASSERT (jdiff != EMPTY) ;
+ ASSERT (jdeg != EMPTY) ;
+ j_best = j ;
+ jdeg_best = jdeg ;
+ jdiff_best = jdiff ;
+ }
+
+ /* get the next entries in column k and row k */
+ cp++ ;
+ rp++ ;
+ }
+
+ /* save the pair (j,k), if we found one */
+ if (j_best != EMPTY)
+ {
+ j = j_best ;
+ DEBUGm4 ((" --- best pair j: "ID" for k: "ID"\n", j, k)) ;
+ P [k] = j ;
+ P [j] = k ;
+ }
+ else
+ {
+ /* no match was found for k */
+ unmatched++ ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize the row permutation, P */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n2 ; k++)
+ {
+ if (P [k] == EMPTY)
+ {
+ P [k] = k ;
+ }
+ }
+ ASSERT (UMF_is_permutation (P, Rp, n2, n2)) ;
+
+ return (unmatched) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_2by2 ============================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_2by2
+(
+ /* input, not modified: */
+ Int n, /* A is n-by-n */
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+ const double Ax [ ], /* size nz if present */
+#ifdef COMPLEX
+ const double Az [ ], /* size nz if present */
+#endif
+ double tol, /* tolerance for determining whether or not an
+ * entry is numerically acceptable. If tol <= 0
+ * then all numerical values ignored. */
+ Int scale, /* scaling to perform (none, sum, or max) */
+ Int Cperm1 [ ], /* singleton permutations */
+#ifndef NDEBUG
+ Int Rperm1 [ ], /* not needed, since Rperm1 = Cperm1 for submatrix S */
+#endif
+ Int InvRperm1 [ ], /* inverse of Rperm1 */
+ Int n1, /* number of singletons */
+ Int nempty, /* number of empty rows/cols */
+
+ /* input, contents undefined on output: */
+ Int Degree [ ], /* Degree [j] is the number of off-diagonal
+ * entries in row/column j of S+S', where
+ * where S = A (Cperm1 [n1..], Rperm1 [n1..]).
+ * Note that S is not used, nor formed. */
+
+ /* output: */
+ Int P [ ], /* P [k] = i means original row i is kth row in S(P,:)
+ * where S = A (Cperm1 [n1..], Rperm1 [n1..]) */
+ Int *p_nweak,
+ Int *p_unmatched,
+
+ /* workspace (not defined on input or output): */
+ Int Ri [ ], /* of size >= max (nz, n) */
+ Int Rp [ ], /* of size n+1 */
+ double Rs [ ], /* of size n if present. Rs = sum (abs (A),2) or
+ * max (abs (A),2), the sum or max of each row. Unused
+ * if scale is equal to UMFPACK_SCALE_NONE. */
+ Int Head [ ], /* of size n. Head pointers for bucket sort */
+ Int Next [ ], /* of size n. Next pointers for bucket sort */
+ Int Ci [ ], /* size nz */
+ Int Cp [ ] /* size n+1 */
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry aij ;
+ double cmax, value, rs, ctol, dvalue ;
+ Int k, p, row, col, do_values, do_sum, do_max, do_scale, nweak, weak,
+ p1, p2, dfound, unmatched, n2, oldrow, newrow, oldcol, newcol, pp ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+#ifndef NRECIPROCAL
+ Int do_recip = FALSE ;
+#endif
+
+#ifndef NDEBUG
+ /* UMF_debug += 99 ; */
+ DEBUGm3 (("\n ==================================UMF_2by2: tol %g\n", tol)) ;
+ ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
+ for (k = n1 ; k < n - nempty ; k++)
+ {
+ ASSERT (Cperm1 [k] == Rperm1 [k]) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine scaling options */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the values, but only if they are present */
+ /* ignore the values if tol <= 0 */
+ do_values = (tol > 0) && (Ax != (double *) NULL) ;
+ if (do_values && (Rs != (double *) NULL))
+ {
+ do_sum = (scale == UMFPACK_SCALE_SUM) ;
+ do_max = (scale == UMFPACK_SCALE_MAX) ;
+ }
+ else
+ {
+ /* no scaling */
+ do_sum = FALSE ;
+ do_max = FALSE ;
+ }
+ do_scale = do_max || do_sum ;
+ DEBUGm3 (("do_values "ID" do_sum "ID" do_max "ID" do_scale "ID"\n",
+ do_values, do_sum, do_max, do_scale)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row scaling, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ /* see also umf_kernel_init */
+
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ double rsmin ;
+#endif
+ for (row = 0 ; row < n ; row++)
+ {
+ Rs [row] = 0.0 ;
+ }
+ for (col = 0 ; col < n ; col++)
+ {
+ p2 = Ap [col+1] ;
+ for (p = Ap [col] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ rs = Rs [row] ;
+ if (!SCALAR_IS_NAN (rs))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ /* if any entry in a row is NaN, then the scale factor
+ * for the row is NaN. It will be set to 1 later. */
+ Rs [row] = value ;
+ }
+ else if (do_max)
+ {
+ Rs [row] = MAX (rs, value) ;
+ }
+ else
+ {
+ Rs [row] += value ;
+ }
+ }
+ }
+ }
+#ifndef NRECIPROCAL
+ rsmin = Rs [0] ;
+ if (SCALAR_IS_ZERO (rsmin) || SCALAR_IS_NAN (rsmin))
+ {
+ rsmin = 1.0 ;
+ }
+#endif
+ for (row = 0 ; row < n ; row++)
+ {
+ /* do not scale an empty row, or a row with a NaN */
+ rs = Rs [row] ;
+ if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs))
+ {
+ Rs [row] = 1.0 ;
+ }
+#ifndef NRECIPROCAL
+ rsmin = MIN (rsmin, Rs [row]) ;
+#endif
+ }
+
+#ifndef NRECIPROCAL
+ /* multiply by the reciprocal if Rs is not too small */
+ do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ;
+ if (do_recip)
+ {
+ /* invert the scale factors */
+ for (row = 0 ; row < n ; row++)
+ {
+ Rs [row] = 1.0 / Rs [row] ;
+ }
+ }
+#endif
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the max in each column and find diagonal */
+ /* ---------------------------------------------------------------------- */
+
+ nweak = 0 ;
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n) ;
+ ASSERT (InvRperm1 [Rperm1 [k]] == k) ;
+ }
+#endif
+
+ n2 = n - n1 - nempty ;
+
+ /* use Ri to count the number of strong entries in each row */
+ for (row = 0 ; row < n2 ; row++)
+ {
+ Ri [row] = 0 ;
+ }
+
+ pp = 0 ;
+ ctol = 0 ;
+ dvalue = 1 ;
+
+ /* construct C = pruned submatrix, strong values only, column form */
+
+ for (k = n1 ; k < n - nempty ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ newcol = k - n1 ;
+ Next [newcol] = EMPTY ;
+ DEBUGm1 (("Column "ID" newcol "ID" oldcol "ID"\n", k, newcol, oldcol)) ;
+
+ Cp [newcol] = pp ;
+
+ dfound = FALSE ;
+ p1 = Ap [oldcol] ;
+ p2 = Ap [oldcol+1] ;
+ if (do_values)
+ {
+ cmax = 0 ;
+ dvalue = 0 ;
+
+ if (!do_scale)
+ {
+ /* no scaling */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ /* if either cmax or value is NaN, define cmax as NaN */
+ if (!SCALAR_IS_NAN (cmax))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ cmax = value ;
+ }
+ else
+ {
+ cmax = MAX (cmax, value) ;
+ }
+ }
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ dvalue = value ;
+ dfound = TRUE ;
+ ASSERT (newrow == newcol) ;
+ }
+ }
+ }
+#ifndef NRECIPROCAL
+ else if (do_recip)
+ {
+ /* multiply by the reciprocal */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value *= Rs [oldrow] ;
+ /* if either cmax or value is NaN, define cmax as NaN */
+ if (!SCALAR_IS_NAN (cmax))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ cmax = value ;
+ }
+ else
+ {
+ cmax = MAX (cmax, value) ;
+ }
+ }
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ dvalue = value ;
+ dfound = TRUE ;
+ ASSERT (newrow == newcol) ;
+ }
+ }
+ }
+#endif
+ else
+ {
+ /* divide instead */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value /= Rs [oldrow] ;
+ /* if either cmax or value is NaN, define cmax as NaN */
+ if (!SCALAR_IS_NAN (cmax))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ cmax = value ;
+ }
+ else
+ {
+ cmax = MAX (cmax, value) ;
+ }
+ }
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ dvalue = value ;
+ dfound = TRUE ;
+ ASSERT (newrow == newcol) ;
+ }
+ }
+ }
+
+ ctol = tol * cmax ;
+ DEBUGm1 ((" cmax col "ID" %g ctol %g\n", oldcol, cmax, ctol)) ;
+ }
+ else
+ {
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ Ci [pp++] = newrow ;
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ ASSERT (newrow == newcol) ;
+ dfound = TRUE ;
+ }
+ /* count the entries in each column */
+ Ri [newrow]++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* flag the weak diagonals */
+ /* ------------------------------------------------------------------ */
+
+ if (!dfound)
+ {
+ /* no diagonal entry present */
+ weak = TRUE ;
+ }
+ else
+ {
+ /* diagonal entry is present, check its value */
+ weak = (do_values) ? WEAK (dvalue, ctol) : FALSE ;
+ }
+ if (weak)
+ {
+ /* flag this column as weak */
+ DEBUG0 (("Weak!\n")) ;
+ Next [newcol] = IS_WEAK ;
+ nweak++ ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* count entries in each row that are not numerically weak */
+ /* ------------------------------------------------------------------ */
+
+ if (do_values)
+ {
+ if (!do_scale)
+ {
+ /* no scaling */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ weak = WEAK (value, ctol) ;
+ if (!weak)
+ {
+ DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
+ Ci [pp++] = newrow ;
+ Ri [newrow]++ ;
+ }
+ }
+ }
+#ifndef NRECIPROCAL
+ else if (do_recip)
+ {
+ /* multiply by the reciprocal */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value *= Rs [oldrow] ;
+ weak = WEAK (value, ctol) ;
+ if (!weak)
+ {
+ DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
+ Ci [pp++] = newrow ;
+ Ri [newrow]++ ;
+ }
+ }
+ }
+#endif
+ else
+ {
+ /* divide instead */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value /= Rs [oldrow] ;
+ weak = WEAK (value, ctol) ;
+ if (!weak)
+ {
+ DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
+ Ci [pp++] = newrow ;
+ Ri [newrow]++ ;
+ }
+ }
+ }
+ }
+ }
+ Cp [n2] = pp ;
+ ASSERT (AMD_valid (n2, n2, Cp, Ci) == AMD_OK) ;
+
+ if (nweak == 0)
+ {
+ /* nothing to do, quick return */
+ DEBUGm2 (("\n =============================UMF_2by2: quick return\n")) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = k ;
+ }
+ *p_nweak = 0 ;
+ *p_unmatched = 0 ;
+ return ;
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n2 ; k++)
+ {
+ P [k] = EMPTY ;
+ }
+ for (k = 0 ; k < n2 ; k++)
+ {
+ ASSERT (Degree [k] >= 0 && Degree [k] < n2) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* find the 2-by-2 permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* The matrix S is now mapped to the index range 0 to n2-1. We have
+ * S = A (Rperm [n1 .. n-nempty-1], Cperm [n1 .. n-nempty-1]), and then
+ * C = pattern of strong entries in S. A weak diagonal k in S is marked
+ * with Next [k] = IS_WEAK. */
+
+ unmatched = two_by_two (n2, Cp, Ci, Degree, Next, Ri, P, Rp, Head) ;
+
+ /* ---------------------------------------------------------------------- */
+
+ *p_nweak = nweak ;
+ *p_unmatched = unmatched ;
+
+#ifndef NDEBUG
+ DEBUGm4 (("UMF_2by2: weak "ID" unmatched "ID"\n", nweak, unmatched)) ;
+ for (row = 0 ; row < n ; row++)
+ {
+ DEBUGm2 (("P ["ID"] = "ID"\n", row, P [row])) ;
+ }
+ DEBUGm2 (("\n =============================UMF_2by2: done\n\n")) ;
+#endif
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_2by2.h b/src/C/SuiteSparse/UMFPACK/Source/umf_2by2.h
new file mode 100644
index 0000000..078625e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_2by2.h
@@ -0,0 +1,36 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_2by2
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ double tol,
+ Int scale,
+ Int Cperm1 [ ],
+#ifndef NDEBUG
+ Int Rperm1 [ ],
+#endif
+ Int InvRperm [ ],
+ Int n1,
+ Int nempty,
+ Int Degree [ ],
+ Int P [ ],
+ Int *p_nweak,
+ Int *p_nmatched,
+ Int Ri [ ],
+ Int Rp [ ],
+ double Rs [ ],
+ Int Head [ ],
+ Int Next [ ],
+ Int Si [ ],
+ Int Sp [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_analyze.c b/src/C/SuiteSparse/UMFPACK/Source/umf_analyze.c
new file mode 100644
index 0000000..fa8aecd
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_analyze.c
@@ -0,0 +1,704 @@
+/* ========================================================================== */
+/* === UMF_analyze ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Symbolic LL' factorization of A'*A, to get upper bounds on the size of
+ L and U for LU = PAQ, and to determine the frontal matrices and
+ (supernodal) column elimination tree. No fill-reducing column pre-ordering
+ is used.
+
+ Returns TRUE if successful, FALSE if out of memory. UMF_analyze can only
+ run out of memory if anzmax (which is Ap [n_row]) is too small.
+
+ Uses workspace of size O(nonzeros in A). On input, the matrix A is
+ stored in row-form at the tail end of Ai. It is destroyed on output.
+ The rows of A must be sorted by increasing first column index.
+ The matrix is assumed to be valid.
+
+ Empty rows and columns have already been removed.
+
+*/
+
+#include "umf_internal.h"
+#include "umf_apply_order.h"
+#include "umf_fsize.h"
+
+/* ========================================================================== */
+
+GLOBAL Int UMF_analyze
+(
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ Int Ai [ ], /* Ai [Ap [0]..Ap[n_row]-1]: column indices */
+ /* destroyed on output. Note that this is NOT the */
+ /* user's Ai that was passed to UMFPACK_*symbolic */
+ /* size of Ai, Ap [n_row] = anzmax >= anz + n_col */
+ /* Ap [0] must be => n_col. The space to the */
+ /* front of Ai is used as workspace. */
+
+ Int Ap [ ], /* of size MAX (n_row, n_col) + 1 */
+ /* Ap [0..n_row]: row pointers */
+ /* Row i is in Ai [Ap [i] ... Ap [i+1]-1] */
+
+ /* rows must have smallest col index first, or be */
+ /* in sorted form. Used as workspace of size n_col */
+ /* and destroyed. */
+
+ /* Note that this is NOT the */
+ /* user's Ap that was passed to UMFPACK_*symbolic */
+
+ Int Up [ ], /* workspace of size n_col, and output column perm.
+ * for column etree postorder. */
+
+ Int fixQ,
+
+ /* temporary workspaces: */
+ Int W [ ], /* W [0..n_col-1] */
+ Int Link [ ], /* Link [0..n_col-1] */
+
+ /* output: information about each frontal matrix: */
+ Int Front_ncols [ ], /* size n_col */
+ Int Front_nrows [ ], /* of size n_col */
+ Int Front_npivcol [ ], /* of size n_col */
+ Int Front_parent [ ], /* of size n_col */
+ Int *nfr_out,
+
+ Int *p_ncompactions /* number of compactions in UMF_analyze */
+)
+{
+ /* ====================================================================== */
+ /* ==== local variables ================================================= */
+ /* ====================================================================== */
+
+ Int j, j3, col, k, row, parent, j2, pdest, p, p2, thickness, npivots, nfr,
+ i, *Winv, kk, npiv, jnext, krow, knext, pfirst, jlast, ncompactions,
+ *Front_stack, *Front_order, *Front_child, *Front_sibling,
+ Wflag, npivcol, fallrows, fallcols, fpiv, frows, fcols, *Front_size ;
+
+ nfr = 0 ;
+ DEBUG0 (("UMF_analyze: anzmax "ID" anrow "ID" ancol "ID"\n",
+ Ap [n_row], n_row, n_col)) ;
+
+ /* ====================================================================== */
+ /* ==== initializations ================================================= */
+ /* ====================================================================== */
+
+#pragma ivdep
+ for (j = 0 ; j < n_col ; j++)
+ {
+ Link [j] = EMPTY ;
+ W [j] = EMPTY ;
+ Up [j] = EMPTY ;
+
+ /* Frontal matrix data structure: */
+ Front_npivcol [j] = 0 ; /* number of pivot columns */
+ Front_nrows [j] = 0 ; /* number of rows, incl. pivot rows */
+ Front_ncols [j] = 0 ; /* number of cols, incl. pivot cols */
+ Front_parent [j] = EMPTY ; /* parent front */
+ /* Note that only non-pivotal columns are stored in a front (a "row" */
+ /* of U) during elimination. */
+ }
+
+ /* the rows must be sorted by increasing min col */
+ krow = 0 ;
+ pfirst = Ap [0] ;
+ jlast = EMPTY ;
+ jnext = EMPTY ;
+ Wflag = 0 ;
+
+ /* this test requires the size of Ai to be >= n_col + nz */
+ ASSERT (pfirst >= n_col) ; /* Ai must be large enough */
+
+ /* pdest points to the first free space in Ai */
+ pdest = 0 ;
+ ncompactions = 0 ;
+
+ /* ====================================================================== */
+ /* === compute symbolic LL' factorization (unsorted) ==================== */
+ /* ====================================================================== */
+
+ for (j = 0 ; j < n_col ; j = jnext)
+ {
+ DEBUG1 (("\n\n============Front "ID" starting. nfr = "ID"\n", j, nfr)) ;
+
+ /* ================================================================== */
+ /* === garbage collection =========================================== */
+ /* ================================================================== */
+
+ if (pdest + (n_col-j) > pfirst)
+ {
+ /* we might run out ... compact the rows of U */
+
+#ifndef NDEBUG
+ DEBUG0 (("UMF_analyze COMPACTION, j="ID" pfirst="ID"\n",
+ j, pfirst)) ;
+ for (row = 0 ; row < j ; row++)
+ {
+ if (Up [row] != EMPTY)
+ {
+ /* this is a live row of U */
+ DEBUG1 (("Live row: "ID" cols: ", row)) ;
+ p = Up [row] ;
+ ASSERT (Front_ncols [row] > Front_npivcol [row]) ;
+ p2 = p + (Front_ncols [row] - Front_npivcol [row]) ;
+ for ( ; p < p2 ; p++)
+ {
+ DEBUG1 ((ID, Ai [p])) ;
+ ASSERT (p < pfirst) ;
+ ASSERT (Ai [p] > row && Ai [p] < n_col) ;
+ }
+ DEBUG1 (("\n")) ;
+ }
+ }
+ DEBUG1 (("\nStarting to compact:\n")) ;
+#endif
+
+ pdest = 0 ;
+ ncompactions++ ;
+ for (row = 0 ; row < j ; row++)
+ {
+ if (Up [row] != EMPTY)
+ {
+ /* this is a live row of U */
+ DEBUG1 (("Live row: "ID" cols: ", row)) ;
+ ASSERT (row < n_col) ;
+ p = Up [row] ;
+ ASSERT (Front_ncols [row] > Front_npivcol [row]) ;
+ p2 = p + (Front_ncols [row] - Front_npivcol [row]) ;
+ Up [row] = pdest ;
+ for ( ; p < p2 ; p++)
+ {
+ DEBUG1 ((ID, Ai [p])) ;
+ ASSERT (p < pfirst) ;
+ ASSERT (Ai [p] > row && Ai [p] < n_col) ;
+ Ai [pdest++] = Ai [p] ;
+ ASSERT (pdest <= pfirst) ;
+ }
+ DEBUG1 (("\n")) ;
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("\nAFTER COMPACTION, j="ID" pfirst="ID"\n", j, pfirst)) ;
+ for (row = 0 ; row < j ; row++)
+ {
+ if (Up [row] != EMPTY)
+ {
+ /* this is a live row of U */
+ DEBUG1 (("Live row: "ID" cols: ", row)) ;
+ p = Up [row] ;
+ ASSERT (Front_ncols [row] > Front_npivcol [row]) ;
+ p2 = p + (Front_ncols [row] - Front_npivcol [row]) ;
+ for ( ; p < p2 ; p++)
+ {
+ DEBUG1 ((ID, Ai [p])) ;
+ ASSERT (p < pfirst) ;
+ ASSERT (Ai [p] > row && Ai [p] < n_col) ;
+ }
+ DEBUG1 (("\n")) ;
+ }
+ }
+#endif
+
+ }
+
+ if (pdest + (n_col-j) > pfirst)
+ {
+ /* :: out of memory in umf_analyze :: */
+ /* it can't happen, if pfirst >= n_col */
+ return (FALSE) ; /* internal error! */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* is the last front a child of this one? */
+ /* ------------------------------------------------------------------ */
+
+ if (jlast != EMPTY && Link [j] == jlast)
+ {
+ /* yes - create row j by appending to jlast */
+ DEBUG1 (("GOT:last front is child of this one: j "ID" jlast "ID"\n",
+ j, jlast)) ;
+ ASSERT (jlast >= 0 && jlast < j) ;
+
+ Up [j] = Up [jlast] ;
+ Up [jlast] = EMPTY ;
+
+ /* find the parent, delete column j, and update W */
+ parent = n_col ;
+ for (p = Up [j] ; p < pdest ; )
+ {
+ j3 = Ai [p] ;
+ DEBUG1 (("Initial row of U: col "ID" ", j3)) ;
+ ASSERT (j3 >= 0 && j3 < n_col) ;
+ DEBUG1 (("W: "ID" \n", W [j3])) ;
+ ASSERT (W [j3] == Wflag) ;
+ if (j == j3)
+ {
+ DEBUG1 (("Found column j at p = "ID"\n", p)) ;
+ Ai [p] = Ai [--pdest] ;
+ }
+ else
+ {
+ if (j3 < parent)
+ {
+ parent = j3 ;
+ }
+ p++ ;
+ }
+ }
+
+ /* delete jlast from the link list of j */
+ Link [j] = Link [jlast] ;
+
+ ASSERT (Front_nrows [jlast] > Front_npivcol [jlast]) ;
+ thickness = (Front_nrows [jlast] - Front_npivcol [jlast]) ;
+ DEBUG1 (("initial thickness: "ID"\n", thickness)) ;
+
+ }
+ else
+ {
+ Up [j] = pdest ;
+ parent = n_col ;
+ /* thickness: number of (nonpivotal) rows in frontal matrix j */
+ thickness = 0 ;
+ Wflag = j ;
+ }
+
+ /* ================================================================== */
+ /* === compute row j of A*A' ======================================== */
+ /* ================================================================== */
+
+ /* ------------------------------------------------------------------ */
+ /* flag the diagonal entry in row U, but do not add to pattern */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT (pdest <= pfirst) ;
+ W [j] = Wflag ;
+
+ DEBUG1 (("\nComputing row "ID" of A'*A\n", j)) ;
+ DEBUG2 ((" col: "ID" (diagonal)\n", j)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the rows the contribute to this column j */
+ /* ------------------------------------------------------------------ */
+
+ jnext = n_col ;
+ for (knext = krow ; knext < n_row ; knext++)
+ {
+ ASSERT (Ap [knext] < Ap [knext+1]) ;
+ ASSERT (Ap [knext] >= pfirst && Ap [knext] <= Ap [n_row]) ;
+ jnext = Ai [Ap [knext]] ;
+ ASSERT (jnext >= j) ;
+ if (jnext != j)
+ {
+ break ;
+ }
+ }
+
+ /* rows krow ... knext-1 all have first column index of j */
+ /* (or are empty) */
+
+ /* row knext has first column index of jnext */
+ /* if knext = n_row, then jnext is n_col */
+ if (knext == n_row)
+ {
+ jnext = n_col ;
+ }
+
+ ASSERT (jnext > j) ;
+ ASSERT (jnext <= n_col) ;
+
+ /* ------------------------------------------------------------------ */
+ /* for each nonzero A (k,j) in column j of A do: */
+ /* ------------------------------------------------------------------ */
+
+ for (k = krow ; k < knext ; k++)
+ {
+ p = Ap [k] ;
+ p2 = Ap [k+1] ;
+ ASSERT (p < p2) ;
+
+ /* merge row k of A into W */
+ DEBUG2 ((" ---- A row "ID" ", k)) ;
+ ASSERT (k >= 0 && k < n_row) ;
+ ASSERT (Ai [p] == j) ;
+ DEBUG2 ((" p "ID" p2 "ID"\n cols:", p, p2)) ;
+ ASSERT (p >= pfirst && p < Ap [n_row]) ;
+ ASSERT (p2 > pfirst && p2 <= Ap [n_row]) ;
+ for ( ; p < p2 ; p++)
+ {
+ /* add to pattern if seen for the first time */
+ col = Ai [p] ;
+ ASSERT (col >= j && col < n_col) ;
+ DEBUG3 ((" "ID, col)) ;
+ if (W [col] != Wflag)
+ {
+ Ai [pdest++] = col ;
+ ASSERT (pdest <= pfirst) ;
+ /* flag this column has having been seen for row j */
+ W [col] = Wflag ;
+ if (col < parent)
+ {
+ parent = col ;
+ }
+ }
+ }
+ DEBUG2 (("\n")) ;
+ thickness++ ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("\nRow "ID" of A'A:\n", j)) ;
+ for (p = Up [j] ; p < pdest ; p++)
+ {
+ DEBUG3 ((" "ID, Ai [p])) ;
+ }
+ DEBUG3 (("\n")) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* delete rows up to but not including knext */
+ /* ------------------------------------------------------------------ */
+
+ krow = knext ;
+ pfirst = Ap [knext] ;
+
+ /* we can now use Ai [0..pfirst-1] as workspace for rows of U */
+
+ /* ================================================================== */
+ /* === compute jth row of U ========================================= */
+ /* ================================================================== */
+
+ /* for each nonzero U (k,j) in column j of U (1:j-1,:) do */
+ for (k = Link [j] ; k != EMPTY ; k = Link [k])
+ {
+ /* merge row k of U into W */
+ DEBUG2 ((" ---- U row "ID, k)) ;
+ ASSERT (k >= 0 && k < n_col) ;
+ ASSERT (Up [k] != EMPTY) ;
+ p = Up [k] ;
+ ASSERT (Front_ncols [k] > Front_npivcol [k]) ;
+ p2 = p + (Front_ncols [k] - Front_npivcol [k]) ;
+ DEBUG2 ((" p "ID" p2 "ID"\n cols:", p, p2)) ;
+ ASSERT (p <= pfirst) ;
+ ASSERT (p2 <= pfirst) ;
+ for ( ; p < p2 ; p++)
+ {
+ /* add to pattern if seen for the first time */
+ col = Ai [p] ;
+ ASSERT (col >= j && col < n_col) ;
+ DEBUG3 ((" "ID, col)) ;
+ if (W [col] != Wflag)
+ {
+ Ai [pdest++] = col ;
+ ASSERT (pdest <= pfirst) ;
+ /* flag this col has having been seen for row j */
+ W [col] = Wflag ;
+ if (col < parent)
+ {
+ parent = col ;
+ }
+ }
+ }
+ DEBUG2 (("\n")) ;
+
+ /* mark the row k as deleted */
+ Up [k] = EMPTY ;
+
+ ASSERT (Front_nrows [k] > Front_npivcol [k]) ;
+ thickness += (Front_nrows [k] - Front_npivcol [k]) ;
+ ASSERT (Front_parent [k] == j) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("\nRow "ID" of U prior to supercolumn detection:\n", j));
+ for (p = Up [j] ; p < pdest ; p++)
+ {
+ DEBUG3 ((" "ID, Ai [p])) ;
+ }
+ DEBUG3 (("\n")) ;
+ DEBUG1 (("thickness, prior to supercol detect: "ID"\n", thickness)) ;
+#endif
+
+ /* ================================================================== */
+ /* === quicky mass elimination ====================================== */
+ /* ================================================================== */
+
+ /* this code detects some supernodes, but it might miss */
+ /* some because the elimination tree (created on the fly) */
+ /* is not yet post-ordered, and because the pattern of A'*A */
+ /* is also computed on the fly. */
+
+ /* j2 is incremented because the pivot columns are not stored */
+
+ for (j2 = j+1 ; j2 < jnext ; j2++)
+ {
+ ASSERT (j2 >= 0 && j2 < n_col) ;
+ if (W [j2] != Wflag || Link [j2] != EMPTY)
+ {
+ break ;
+ }
+ }
+
+ /* the loop above terminated with j2 at the first non-supernode */
+ DEBUG1 (("jnext = "ID"\n", jnext)) ;
+ ASSERT (j2 <= jnext) ;
+ jnext = j2 ;
+ j2-- ;
+ DEBUG1 (("j2 = "ID"\n", j2)) ;
+ ASSERT (j2 < n_col) ;
+
+ npivots = j2-j+1 ;
+ DEBUG1 (("Number of pivot columns: "ID"\n", npivots)) ;
+
+ /* rows j:j2 have the same nonzero pattern, except for columns j:j2-1 */
+
+ if (j2 > j)
+ {
+ /* supernode detected, prune the pattern of new row j */
+ ASSERT (parent == j+1) ;
+ ASSERT (j2 < n_col) ;
+ DEBUG1 (("Supernode detected, j "ID" to j2 "ID"\n", j, j2)) ;
+
+ parent = n_col ;
+ p2 = pdest ;
+ pdest = Up [j] ;
+ for (p = Up [j] ; p < p2 ; p++)
+ {
+ col = Ai [p] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (W [col] == Wflag) ;
+ if (col > j2)
+ {
+ /* keep this col in the pattern of the new row j */
+ Ai [pdest++] = col ;
+ if (col < parent)
+ {
+ parent = col ;
+ }
+ }
+ }
+ }
+
+ DEBUG1 (("Parent ["ID"] = "ID"\n", j, parent)) ;
+ ASSERT (parent > j2) ;
+
+ if (parent == n_col)
+ {
+ /* this front has no parent - it is the root of a subtree */
+ parent = EMPTY ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("\nFinal row "ID" of U after supercolumn detection:\n", j)) ;
+ for (p = Up [j] ; p < pdest ; p++)
+ {
+ ASSERT (Ai [p] >= 0 && Ai [p] < n_col) ;
+ DEBUG3 ((" "ID" ("ID")", Ai [p], W [Ai [p]])) ;
+ ASSERT (W [Ai [p]] == Wflag) ;
+ }
+ DEBUG3 (("\n")) ;
+#endif
+
+ /* ================================================================== */
+ /* === frontal matrix =============================================== */
+ /* ================================================================== */
+
+ /* front has Front_npivcol [j] pivot columns */
+ /* entire front is Front_nrows [j] -by- Front_ncols [j] */
+ /* j is first column in the front */
+
+ npivcol = npivots ;
+ fallrows = thickness ;
+ fallcols = npivots + pdest - Up [j] ;
+
+ /* number of pivots in the front (rows and columns) */
+ fpiv = MIN (npivcol, fallrows) ;
+
+ /* size of contribution block */
+ frows = fallrows - fpiv ;
+ fcols = fallcols - fpiv ;
+
+ if (frows == 0 || fcols == 0)
+ {
+ /* front has no contribution block and thus needs no parent */
+ DEBUG1 (("Frontal matrix evaporation\n")) ;
+ Up [j] = EMPTY ;
+ parent = EMPTY ;
+ }
+
+ Front_npivcol [j] = npivots ;
+ Front_nrows [j] = fallrows ;
+ Front_ncols [j] = fallcols ;
+ Front_parent [j] = parent ;
+ ASSERT (npivots > 0) ;
+
+ /* Front_parent [j] is the first column of the parent frontal matrix */
+
+ DEBUG1 (("\n\n==== Front "ID", nfr "ID" pivot columns "ID":"ID
+ " all front: "ID"-by-"ID" Parent: "ID"\n", j, nfr, j,j+npivots-1,
+ Front_nrows [j], Front_ncols [j], Front_parent [j])) ;
+ nfr++ ;
+
+ /* ================================================================== */
+ /* === prepare this row for its parent ============================== */
+ /* ================================================================== */
+
+ if (parent != EMPTY)
+ {
+ Link [j] = Link [parent] ;
+ Link [parent] = j ;
+ }
+
+ ASSERT (jnext > j) ;
+
+ jlast = j ;
+ }
+
+ /* ====================================================================== */
+ /* === postorder the fronts ============================================= */
+ /* ====================================================================== */
+
+ *nfr_out = nfr ;
+
+ Front_order = W ; /* use W for Front_order [ */
+
+ if (fixQ)
+ {
+ /* do not postorder the fronts if Q is fixed */
+ DEBUG1 (("\nNo postorder (Q is fixed)\n")) ;
+ k = 0 ;
+ /* Pragma added May 14, 2003. The Intel compiler icl 6.0 (an old
+ * version) incorrectly vectorizes this loop. */
+#pragma novector
+ for (j = 0 ; j < n_col ; j++)
+ {
+ if (Front_npivcol [j] > 0)
+ {
+ Front_order [j] = k++ ;
+ DEBUG1 (("Front order of j: "ID" is:"ID"\n", j,
+ Front_order [j])) ;
+ }
+ else
+ {
+ Front_order [j] = EMPTY ;
+ }
+ }
+ }
+ else
+ {
+
+ /* use Ap for Front_child and use Link for Front_sibling [ */
+ Front_child = Ap ;
+ Front_sibling = Link ;
+
+ /* use Ai for Front_stack, size of Ai is >= 2*n_col */
+ Front_stack = Ai ;
+ Front_size = Front_stack + n_col ;
+
+ UMF_fsize (n_col, Front_size, Front_nrows, Front_ncols,
+ Front_parent, Front_npivcol) ;
+
+ AMD_postorder (n_col, Front_parent, Front_npivcol, Front_size,
+ Front_order, Front_child, Front_sibling, Front_stack) ;
+
+ /* done with Front_child, Front_sibling, Front_size, and Front_stack ]*/
+
+ /* ------------------------------------------------------------------ */
+ /* construct the column permutation (return in Up) */
+ /* ------------------------------------------------------------------ */
+
+ /* Front_order [i] = k means that front i is kth front in the new order.
+ * i is in the range 0 to n_col-1, and k is in the range 0 to nfr-1 */
+
+ /* Use Ai as workspace for Winv [ */
+ Winv = Ai ;
+ for (k = 0 ; k < nfr ; k++)
+ {
+ Winv [k] = EMPTY ;
+ }
+
+ /* compute the inverse of Front_order, so that Winv [k] = i */
+ /* if Front_order [i] = k */
+
+ DEBUG1 (("\n\nComputing output column permutation:\n")) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ k = Front_order [i] ;
+ if (k != EMPTY)
+ {
+ DEBUG1 (("Front "ID" new order: "ID"\n", i, k)) ;
+ ASSERT (k >= 0 && k < nfr) ;
+ ASSERT (Winv [k] == EMPTY) ;
+ Winv [k] = i ;
+ }
+ }
+
+ /* Use Up as output permutation */
+ kk = 0 ;
+ for (k = 0 ; k < nfr ; k++)
+ {
+ i = Winv [k] ;
+ DEBUG1 (("Old Front "ID" New Front "ID" npivots "ID" nrows "ID
+ " ncols "ID"\n",
+ i, k, Front_npivcol [i], Front_nrows [i], Front_ncols [i])) ;
+ ASSERT (i >= 0 && i < n_col) ;
+ ASSERT (Front_npivcol [i] > 0) ;
+ for (npiv = 0 ; npiv < Front_npivcol [i] ; npiv++)
+ {
+ Up [kk] = i + npiv ;
+ DEBUG1 ((" Cperm ["ID"] = "ID"\n", kk, Up [kk])) ;
+ kk++ ;
+ }
+ }
+ ASSERT (kk == n_col) ;
+
+ /* Winv no longer needed ] */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* apply the postorder traversal to renumber the frontal matrices */
+ /* (or pack them in same order, if fixQ) */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Ai as workspace */
+
+ UMF_apply_order (Front_npivcol, Front_order, Ai, n_col, nfr) ;
+ UMF_apply_order (Front_nrows, Front_order, Ai, n_col, nfr) ;
+ UMF_apply_order (Front_ncols, Front_order, Ai, n_col, nfr) ;
+ UMF_apply_order (Front_parent, Front_order, Ai, n_col, nfr) ;
+
+ /* fix the parent to refer to the new numbering */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ parent = Front_parent [i] ;
+ if (parent != EMPTY)
+ {
+ ASSERT (parent >= 0 && parent < n_col) ;
+ ASSERT (Front_order [parent] >= 0 && Front_order [parent] < nfr) ;
+ Front_parent [i] = Front_order [parent] ;
+ }
+ }
+
+ /* Front_order longer needed ] */
+
+#ifndef NDEBUG
+ DEBUG1 (("\nFinal frontal matrices:\n")) ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ DEBUG1 (("Final front "ID": npiv "ID" nrows "ID" ncols "ID" parent "
+ ID"\n", i, Front_npivcol [i], Front_nrows [i],
+ Front_ncols [i], Front_parent [i])) ;
+ }
+#endif
+
+ *p_ncompactions = ncompactions ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_analyze.h b/src/C/SuiteSparse/UMFPACK/Source/umf_analyze.h
new file mode 100644
index 0000000..c0592a6
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_analyze.h
@@ -0,0 +1,23 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_analyze
+(
+ Int n_row,
+ Int n_col,
+ Int Ai [ ],
+ Int Ap [ ],
+ Int Up [ ],
+ Int fixQ,
+ Int Front_ncols [ ],
+ Int W [ ],
+ Int Link [ ],
+ Int Front_nrows [ ],
+ Int Front_npivcol [ ],
+ Int Front_parent [ ],
+ Int *nfr_out,
+ Int *p_ncompactions
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.c b/src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.c
new file mode 100644
index 0000000..996f2e3
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.c
@@ -0,0 +1,43 @@
+/* ========================================================================== */
+/* === UMF_apply_order ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Apply post-ordering of supernodal elimination tree.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_apply_order
+(
+ Int Front [ ], /* of size nn on input, size nfr on output */
+ const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1,
+ * and k in the range 0..nfr-1, means that node
+ * i is the kth node in the postordered tree. */
+ Int Temp [ ], /* workspace of size nfr */
+ Int nn, /* nodes are numbered in the range 0..nn-1 */
+ Int nfr /* the number of nodes actually in use */
+)
+{
+ Int i, k ;
+ for (i = 0 ; i < nn ; i++)
+ {
+ k = Order [i] ;
+ ASSERT (k >= EMPTY && k < nfr) ;
+ if (k != EMPTY)
+ {
+ Temp [k] = Front [i] ;
+ }
+ }
+
+ for (k = 0 ; k < nfr ; k++)
+ {
+ Front [k] = Temp [k] ;
+ }
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.h b/src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.h
new file mode 100644
index 0000000..8363a96
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_apply_order.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_apply_order
+(
+ Int Front [ ],
+ const Int Order [ ],
+ Int Temp [ ],
+ Int n_col,
+ Int nfr
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_assemble.c b/src/C/SuiteSparse/UMFPACK/Source/umf_assemble.c
new file mode 100644
index 0000000..0bc175f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_assemble.c
@@ -0,0 +1,1215 @@
+/* ========================================================================== */
+/* === UMF_assemble ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Degree update and numerical assembly. This is compiled twice (with and
+ * without FIXQ) for each real/complex int/UF_long version, for a total of 8
+ * versions.*/
+
+#include "umf_internal.h"
+#include "umf_mem_free_tail_block.h"
+
+/* ========================================================================== */
+/* === row_assemble ========================================================= */
+/* ========================================================================== */
+
+PRIVATE void row_assemble
+(
+ Int row,
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+
+ Entry *S, *Fcblock, *Frow ;
+ Int tpi, e, *E, *Fcpos, *Frpos, *Row_degree, *Row_tuples, *Row_tlen, rdeg0,
+ f, nrows, ncols, *Rows, *Cols, col, ncolsleft, j ;
+ Tuple *tp, *tp1, *tp2, *tpend ;
+ Unit *Memory, *p ;
+ Element *ep ;
+
+#ifndef FIXQ
+ Int *Col_degree ;
+ Col_degree = Numeric->Cperm ;
+#endif
+
+ Row_tuples = Numeric->Uip ;
+ tpi = Row_tuples [row] ;
+ if (!tpi) return ;
+
+ Memory = Numeric->Memory ;
+ E = Work->E ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Row_degree = Numeric->Rperm ;
+ Row_tlen = Numeric->Uilen ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ rdeg0 = Work->rdeg0 ;
+ Fcblock = Work->Fcblock ;
+
+#ifndef NDEBUG
+ DEBUG6 (("SCAN2-row: "ID"\n", row)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [row] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = Cols + ep->ncols ;
+ if (Rows [f] == EMPTY) continue ; /* row already assembled */
+ ASSERT (row == Rows [f] && row >= 0 && row < Work->n_row) ;
+
+ if (ep->rdeg == rdeg0)
+ {
+ /* ------------------------------------------------------ */
+ /* this is an old Lson - assemble just one row */
+ /* ------------------------------------------------------ */
+
+ /* flag the row as assembled from the Lson */
+ Rows [f] = EMPTY ;
+
+ nrows = ep->nrows ;
+ ncols = ep->ncols ;
+
+ p += UNITS (Int, ncols + nrows) ;
+ S = ((Entry *) p) + f ;
+
+ DEBUG6 (("Old LSON: "ID"\n", e)) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+
+ ncolsleft = ep->ncolsleft ;
+
+ Frow = Fcblock + Frpos [row] ;
+ DEBUG6 (("LSON found (in scan2-row): "ID"\n", e)) ;
+
+ Row_degree [row] -= ncolsleft ;
+
+ if (ncols == ncolsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no columns assembled out this Lson yet */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+#ifndef FIXQ
+ Col_degree [col] -- ;
+#endif
+ /* Frow [Fcpos [col]] += *S ; */
+ ASSEMBLE (Frow [Fcpos [col]], *S) ;
+ S += nrows ;
+ }
+
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some columns have been assembled out of this Lson */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+ ASSERT (col < Work->n_col) ;
+#ifndef FIXQ
+ Col_degree [col] -- ;
+#endif
+ /* Frow [Fcpos [col]] += *S ; */
+ ASSEMBLE (Frow [Fcpos [col]], *S) ;
+ }
+ S += nrows ;
+ }
+
+ }
+ ep->nrowsleft-- ;
+ ASSERT (ep->nrowsleft > 0) ;
+ }
+ else
+ {
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ }
+ Row_tlen [row] = tp2 - tp1 ;
+
+#ifndef NDEBUG
+ DEBUG7 (("row assembled in scan2-row: "ID"\n", row)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+ DEBUG7 (("Current frontal matrix: (scan 1b)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+}
+
+/* ========================================================================== */
+/* === col_assemble ========================================================= */
+/* ========================================================================== */
+
+PRIVATE void col_assemble
+(
+ Int col,
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+
+ Entry *S, *Fcblock, *Fcol ;
+ Int tpi, e, *E, *Fcpos, *Frpos, *Row_degree, *Col_tuples, *Col_tlen, cdeg0,
+ f, nrows, ncols, *Rows, *Cols, row, nrowsleft, i ;
+ Tuple *tp, *tp1, *tp2, *tpend ;
+ Unit *Memory, *p ;
+ Element *ep ;
+
+#if !defined (FIXQ) || !defined (NDEBUG)
+ Int *Col_degree ;
+ Col_degree = Numeric->Cperm ;
+#endif
+
+ Col_tuples = Numeric->Lip ;
+ tpi = Col_tuples [col] ;
+ if (!tpi) return ;
+
+ Memory = Numeric->Memory ;
+ E = Work->E ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Row_degree = Numeric->Rperm ;
+ Col_tlen = Numeric->Lilen ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ cdeg0 = Work->cdeg0 ;
+ Fcblock = Work->Fcblock ;
+
+ DEBUG6 (("SCAN2-col: "ID"\n", col)) ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [col] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+
+ if (Cols [f] == EMPTY) continue ; /* col already assembled */
+ ASSERT (col == Cols [f] && col >= 0 && col < Work->n_col) ;
+
+ if (ep->cdeg == cdeg0)
+ {
+ /* ------------------------------------------------------ */
+ /* this is an old Uson - assemble just one col */
+ /* ------------------------------------------------------ */
+
+ /* flag the col as assembled from the Uson */
+ Cols [f] = EMPTY ;
+
+ nrows = ep->nrows ;
+ ncols = ep->ncols ;
+ Rows = Cols + ncols ;
+ p += UNITS (Int, ncols + nrows) ;
+ S = ((Entry *) p) + f * nrows ;
+
+ DEBUG6 (("Old USON: "ID"\n", e)) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+
+ nrowsleft = ep->nrowsleft ;
+
+ Fcol = Fcblock + Fcpos [col] ;
+ DEBUG6 (("USON found (in scan2-col): "ID"\n", e)) ;
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ if (nrows == nrowsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no rows assembled out of this Uson yet */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+ Row_degree [row]-- ;
+ /* Fcol [Frpos [row]] += S [i] ; */
+ ASSEMBLE (Fcol [Frpos [row]], S [i]) ;
+ }
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some rows have been assembled out of this Uson */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ ASSERT (row < Work->n_row) ;
+ Row_degree [row]-- ;
+ /* Fcol [Frpos [row]] += S [i] ; */
+ ASSEMBLE (Fcol [Frpos [row]], S [i]) ;
+ }
+ }
+ }
+ ep->ncolsleft-- ;
+ ASSERT (ep->ncolsleft > 0) ;
+ }
+ else
+ {
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ }
+ Col_tlen [col] = tp2 - tp1 ;
+
+#ifndef NDEBUG
+ DEBUG7 (("Column assembled in scan2-col: "ID"\n", col)) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+ DEBUG7 (("Current frontal matrix: after scan2-col\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+}
+
+
+/* ========================================================================== */
+/* === UMF_assemble / UMF_assemble_fixq ===================================== */
+/* ========================================================================== */
+
+#ifndef FIXQ
+GLOBAL void UMF_assemble
+#else
+GLOBAL void UMF_assemble_fixq
+#endif
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int e, i, row, col, i2, nrows, ncols, f, tpi, extcdeg, extrdeg, rdeg0,
+ cdeg0, son_list, next, nrows_to_assemble,
+ ncols_to_assemble, ngetrows, j, j2,
+ nrowsleft, /* number of rows remaining in S */
+ ncolsleft, /* number of columns remaining in S */
+ prior_Lson, prior_Uson, *E, *Cols, *Rows, *Wm, *Woo,
+ *Row_tuples, *Row_degree, *Row_tlen,
+ *Col_tuples, *Col_tlen ;
+ Unit *Memory, *p ;
+ Element *ep ;
+ Tuple *tp, *tp1, *tp2, *tpend ;
+ Entry
+ *S, /* a pointer into the contribution block of a son */
+ *Fcblock, /* current contribution block */
+ *Fcol ; /* a column of FC */
+ Int *Frpos,
+ *Fcpos,
+ fnrows, /* number of rows in contribution block in F */
+ fncols ; /* number of columns in contribution block in F */
+
+#if !defined (FIXQ) || !defined (NDEBUG)
+ Int *Col_degree ;
+#endif
+
+#ifndef NDEBUG
+ Int n_row, n_col ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ DEBUG3 (("::Assemble SCANS 1-4\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+#if !defined (FIXQ) || !defined (NDEBUG)
+ Col_degree = Numeric->Cperm ; /* not updated if FIXQ is true */
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ fncols = Work->fncols ;
+ fnrows = Work->fnrows ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Row_degree = Numeric->Rperm ;
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ Wm = Work->Wm ;
+ Woo = Work->Woo ;
+ rdeg0 = Work->rdeg0 ;
+ cdeg0 = Work->cdeg0 ;
+
+#ifndef NDEBUG
+ DEBUG6 (("============================================\n")) ;
+ DEBUG6 (("Degree update, assembly.\n")) ;
+ DEBUG6 (("pivot row pattern: fncols="ID"\n", fncols)) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Work->Fcols [j] ;
+ DEBUG6 ((ID" ", col)) ;
+ ASSERT (Fcpos [col] == j * Work->fnr_curr) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ }
+ ASSERT (Fcpos [Work->pivcol] >= 0) ;
+ DEBUG6 (("pivcol: "ID" pos "ID" fnr_curr "ID" fncols "ID"\n",
+ Work->pivcol, Fcpos [Work->pivcol], Work->fnr_curr, fncols)) ;
+ ASSERT (Fcpos [Work->pivcol] < fncols * Work->fnr_curr) ;
+ DEBUG6 (("\npivot col pattern: fnrows="ID"\n", fnrows)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Work->Frows [i] ;
+ DEBUG6 ((ID" ", row)) ;
+ ASSERT (Frpos [row] == i) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ }
+ DEBUG6 (("\n")) ;
+ ASSERT (Frpos [Work->pivrow] >= 0) ;
+ ASSERT (Frpos [Work->pivrow] < fnrows) ;
+ ASSERT (Work->Flublock == (Entry *) (Numeric->Memory + E [0])) ;
+ ASSERT (Work->Fcblock == Work->Flublock + Work->nb *
+ (Work->nb + Work->fnr_curr + Work->fnc_curr)) ;
+#endif
+
+ Fcblock = Work->Fcblock ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the largest actual frontal matrix size (for Info only) */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (fnrows == Work->fnrows_new + 1) ;
+ ASSERT (fncols == Work->fncols_new + 1) ;
+
+ Numeric->maxnrows = MAX (Numeric->maxnrows, fnrows) ;
+ Numeric->maxncols = MAX (Numeric->maxncols, fncols) ;
+
+ /* this is safe from integer overflow, since the current frontal matrix
+ * is already allocated. */
+ Numeric->maxfrsize = MAX (Numeric->maxfrsize, fnrows * fncols) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* assemble from prior elements into the current frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG2 (("New assemble start [prior_element:"ID"\n", Work->prior_element)) ;
+
+ /* Currently no rows or columns are marked. No elements are scanned, */
+ /* that is, (ep->next == EMPTY) is true for all elements */
+
+ son_list = 0 ; /* start creating son_list [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if most recent element is Lson or Uson of current front */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Work->do_extend)
+ {
+ prior_Uson = ( Work->pivcol_in_front && !Work->pivrow_in_front) ;
+ prior_Lson = (!Work->pivcol_in_front && Work->pivrow_in_front) ;
+ if (prior_Uson || prior_Lson)
+ {
+ e = Work->prior_element ;
+ if (e != EMPTY)
+ {
+ ASSERT (E [e]) ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ ep->next = son_list ;
+ son_list = e ;
+#ifndef NDEBUG
+ DEBUG2 (("e "ID" is Prior son "ID" "ID"\n",
+ e, prior_Uson, prior_Lson)) ;
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ ASSERT (E [e]) ;
+ }
+ }
+ }
+ Work->prior_element = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN1-row: scan the element lists of each new row in the pivot col */
+ /* and compute the external column degree for each frontal */
+ /* ---------------------------------------------------------------------- */
+
+ for (i2 = Work->fscan_row ; i2 < fnrows ; i2++)
+ {
+ /* Get a row */
+ row = Work->NewRows [i2] ;
+ if (row < 0) row = FLIP (row) ;
+ ASSERT (row >= 0 && row < n_row) ;
+
+ DEBUG6 (("SCAN1-row: "ID"\n", row)) ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ tpi = Row_tuples [row] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [row] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Rows = ((Int *) p) + ep->ncols ;
+ if (Rows [f] == EMPTY) continue ; /* row already assembled */
+ ASSERT (row == Rows [f]) ;
+
+ if (ep->cdeg < cdeg0)
+ {
+ /* first time seen in scan1-row */
+ ep->cdeg = ep->nrowsleft + cdeg0 ;
+ DEBUG6 (("e "ID" First seen: cdeg: "ID" ", e, ep->cdeg-cdeg0)) ;
+ ASSERT (ep->ncolsleft > 0 && ep->nrowsleft > 0) ;
+ }
+
+ ep->cdeg-- ; /* decrement external column degree */
+ DEBUG6 (("e "ID" New ext col deg: "ID"\n", e, ep->cdeg - cdeg0)) ;
+
+ /* this element is not yet in the new son list */
+ if (ep->cdeg == cdeg0 && ep->next == EMPTY)
+ {
+ /* A new LUson or Uson has been found */
+ ep->next = son_list ;
+ son_list = e ;
+ }
+
+ ASSERT (ep->cdeg >= cdeg0) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Row_tlen [row] = tp2 - tp1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN1-col: scan the element lists of each new col in the pivot row */
+ /* and compute the external row degree for each frontal */
+ /* ---------------------------------------------------------------------- */
+
+ for (j2 = Work->fscan_col ; j2 < fncols ; j2++)
+ {
+ /* Get a column */
+ col = Work->NewCols [j2] ;
+ if (col < 0) col = FLIP (col) ;
+ ASSERT (col >= 0 && col < n_col) ;
+
+ DEBUG6 (("SCAN 1-col: "ID"\n", col)) ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ tpi = Col_tuples [col] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [col] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (col == Cols [f]) ;
+
+ if (ep->rdeg < rdeg0)
+ {
+ /* first time seen in scan1-col */
+ ep->rdeg = ep->ncolsleft + rdeg0 ;
+ DEBUG6 (("e "ID" First seen: rdeg: "ID" ", e, ep->rdeg-rdeg0)) ;
+ ASSERT (ep->ncolsleft > 0 && ep->nrowsleft > 0) ;
+ }
+
+ ep->rdeg-- ; /* decrement external row degree */
+ DEBUG6 (("e "ID" New ext row degree: "ID"\n", e, ep->rdeg-rdeg0)) ;
+
+ if (ep->rdeg == rdeg0 && ep->next == EMPTY)
+ {
+ /* A new LUson or Lson has been found */
+ ep->next = son_list ;
+ son_list = e ;
+ }
+
+ ASSERT (ep->rdeg >= rdeg0) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Col_tlen [col] = tp2 - tp1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* assemble new sons via full scans */
+ /* ---------------------------------------------------------------------- */
+
+ next = EMPTY ;
+
+ for (e = son_list ; e > 0 ; e = next)
+ {
+ ASSERT (e > 0 && e <= Work->nel && E [e]) ;
+ p = Memory + E [e] ;
+ DEBUG2 (("New son: "ID"\n", e)) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, S) ;
+ nrowsleft = ep->nrowsleft ;
+ ncolsleft = ep->ncolsleft ;
+ next = ep->next ;
+ ep->next = EMPTY ;
+
+ extrdeg = (ep->rdeg < rdeg0) ? ncolsleft : (ep->rdeg - rdeg0) ;
+ extcdeg = (ep->cdeg < cdeg0) ? nrowsleft : (ep->cdeg - cdeg0) ;
+ ncols_to_assemble = ncolsleft - extrdeg ;
+ nrows_to_assemble = nrowsleft - extcdeg ;
+ DEBUG2 (("extrdeg "ID" extcdeg "ID"\n", extrdeg, extcdeg)) ;
+
+ if (extrdeg == 0 && extcdeg == 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is an LUson - assemble an entire contribution block */
+ /* -------------------------------------------------------------- */
+
+ DEBUG6 (("LUson found: "ID"\n", e)) ;
+
+ if (nrows == nrowsleft)
+ {
+ /* ---------------------------------------------------------- */
+ /* no rows assembled out of this LUson yet */
+ /* ---------------------------------------------------------- */
+
+ /* compute the compressed column offset vector*/
+ /* [ use Wm [0..nrows-1] for offsets */
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ Row_degree [row] -= ncolsleft ;
+ Wm [i] = Frpos [row] ;
+ }
+
+ if (ncols == ncolsleft)
+ {
+ /* ------------------------------------------------------ */
+ /* no rows or cols assembled out of LUson yet */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ /* Fcol [Wm [i]] += S [i] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [i]) ;
+ }
+ S += nrows ;
+ }
+
+
+ }
+ else
+ {
+ /* ------------------------------------------------------ */
+ /* only cols have been assembled out of LUson */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ /* Fcol [Wm [i]] += S [i] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [i]) ;
+ }
+ }
+ S += nrows ;
+ }
+
+ }
+ /* ] done using Wm [0..nrows-1] for offsets */
+ }
+ else
+ {
+ /* ---------------------------------------------------------- */
+ /* some rows have been assembled out of this LUson */
+ /* ---------------------------------------------------------- */
+
+ /* compute the compressed column offset vector*/
+ /* [ use Woo,Wm [0..nrowsleft-1] for offsets */
+ ngetrows = 0 ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ Row_degree [row] -= ncolsleft ;
+ Woo [ngetrows] = i ;
+ Wm [ngetrows++] = Frpos [row] ;
+ }
+ }
+ ASSERT (ngetrows == nrowsleft) ;
+
+ if (ncols == ncolsleft)
+ {
+ /* ------------------------------------------------------ */
+ /* only rows have been assembled out of this LUson */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrowsleft ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ S += nrows ;
+ }
+
+ }
+ else
+ {
+ /* ------------------------------------------------------ */
+ /* both rows and columns have been assembled out of LUson */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrowsleft ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ }
+ S += nrows ;
+ }
+
+ }
+ /* ] done using Woo,Wm [0..nrowsleft-1] */
+ }
+
+ /* deallocate the element: remove from ordered list */
+ UMF_mem_free_tail_block (Numeric, E [e]) ;
+ E [e] = 0 ;
+
+ }
+ else if (extcdeg == 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is a Uson - assemble all possible columns */
+ /* -------------------------------------------------------------- */
+
+ DEBUG6 (("New USON: "ID"\n", e)) ;
+ ASSERT (extrdeg > 0) ;
+
+ DEBUG6 (("New uson "ID" cols to do "ID"\n", e, ncols_to_assemble)) ;
+
+ if (ncols_to_assemble > 0)
+ {
+
+ Int skip = FALSE ;
+ if (ncols_to_assemble * 16 < ncols && nrows == 1)
+ {
+ /* this is a tall and thin frontal matrix consisting of
+ * only one column (most likely an original column). Do
+ * not assemble it. It cannot be the pivot column, since
+ * the pivot column element would be an LU son, not an Lson,
+ * of the current frontal matrix. */
+ ASSERT (nrowsleft == 1) ;
+ ASSERT (Rows [0] >= 0 && Rows [0] < Work->n_row) ;
+ skip = TRUE ;
+ Work->any_skip = TRUE ;
+ }
+
+ if (!skip)
+ {
+
+ if (nrows == nrowsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no rows have been assembled out of this Uson yet */
+ /* -------------------------------------------------- */
+
+ /* compute the compressed column offset vector */
+ /* [ use Wm [0..nrows-1] for offsets */
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ Row_degree [row] -= ncols_to_assemble ;
+ Wm [i] = Frpos [row] ;
+ }
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if ((col >= 0) && (Fcpos [col] >= 0))
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ /* Fcol [Wm [i]] += S [i] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [i]) ;
+ }
+ /* flag the column as assembled from Uson */
+ Cols [j] = EMPTY ;
+ }
+ S += nrows ;
+ }
+
+
+ /* ] done using Wm [0..nrows-1] for offsets */
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some rows have been assembled out of this Uson */
+ /* -------------------------------------------------- */
+
+ /* compute the compressed column offset vector*/
+ /* [ use Woo,Wm [0..nrows-1] for offsets */
+ ngetrows = 0 ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ Row_degree [row] -= ncols_to_assemble ;
+ ASSERT (row < n_row && Frpos [row] >= 0) ;
+ Woo [ngetrows] = i ;
+ Wm [ngetrows++] = Frpos [row] ;
+ }
+ }
+ ASSERT (ngetrows == nrowsleft) ;
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if ((col >= 0) && (Fcpos [col] >= 0))
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrowsleft ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ /* flag the column as assembled from Uson */
+ Cols [j] = EMPTY ;
+ }
+ S += nrows ;
+ }
+
+ /* ] done using Woo,Wm */
+ }
+ ep->ncolsleft = extrdeg ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is an Lson - assemble all possible rows */
+ /* -------------------------------------------------------------- */
+
+ DEBUG6 (("New LSON: "ID"\n", e)) ;
+ ASSERT (extrdeg == 0 && extcdeg > 0) ;
+
+ DEBUG6 (("New lson "ID" rows to do "ID"\n", e, nrows_to_assemble)) ;
+
+ if (nrows_to_assemble > 0)
+ {
+
+ Int skip = FALSE ;
+ if (nrows_to_assemble * 16 < nrows && ncols == 1)
+ {
+ /* this is a tall and thin frontal matrix consisting of
+ * only one column (most likely an original column). Do
+ * not assemble it. It cannot be the pivot column, since
+ * the pivot column element would be an LU son, not an Lson,
+ * of the current frontal matrix. */
+ ASSERT (ncolsleft == 1) ;
+ ASSERT (Cols [0] >= 0 && Cols [0] < Work->n_col) ;
+ Work->any_skip = TRUE ;
+ skip = TRUE ;
+ }
+
+ if (!skip)
+ {
+
+ /* compute the compressed column offset vector */
+ /* [ use Woo,Wm [0..nrows-1] for offsets */
+ ngetrows = 0 ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if ((row >= 0) && (Frpos [row] >= 0))
+ {
+ ASSERT (row < n_row) ;
+ Row_degree [row] -= ncolsleft ;
+ Woo [ngetrows] = i ;
+ Wm [ngetrows++] = Frpos [row] ;
+ /* flag the row as assembled from the Lson */
+ Rows [i] = EMPTY ;
+ }
+ }
+ ASSERT (nrowsleft - ngetrows == extcdeg) ;
+ ASSERT (ngetrows == nrows_to_assemble) ;
+
+ if (ncols == ncolsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no columns assembled out this Lson yet */
+ /* -------------------------------------------------- */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+#ifndef FIXQ
+ Col_degree [col] -= nrows_to_assemble ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows_to_assemble ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ S += nrows ;
+ }
+
+
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some columns have been assembled out of this Lson */
+ /* -------------------------------------------------- */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col < n_col) ;
+ if (col >= 0)
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrows_to_assemble ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows_to_assemble ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ }
+ S += nrows ;
+ }
+
+ }
+
+ /* ] done using Woo,Wm */
+
+ ep->nrowsleft = extcdeg ;
+ }
+ }
+ }
+ }
+
+ /* Note that garbage collection, and build tuples */
+ /* both destroy the son list. */
+
+ /* ] son_list now empty */
+
+ /* ---------------------------------------------------------------------- */
+ /* If frontal matrix extended, assemble old L/Usons from new rows/cols */
+ /* ---------------------------------------------------------------------- */
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN2-row: assemble rows of old Lsons from the new rows */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG7 (("Current frontal matrix: (prior to scan2-row)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ /* rescan the pivot row */
+ if (Work->any_skip)
+ {
+ row_assemble (Work->pivrow, Numeric, Work) ;
+ }
+
+ if (Work->do_scan2row)
+ {
+ for (i2 = Work->fscan_row ; i2 < fnrows ; i2++)
+ {
+ /* Get a row */
+ row = Work->NewRows [i2] ;
+ if (row < 0) row = FLIP (row) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ if (!(row == Work->pivrow && Work->any_skip))
+ {
+ /* assemble it */
+ row_assemble (row, Numeric, Work) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN2-col: assemble columns of old Usons from the new columns */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG7 (("Current frontal matrix: (prior to scan2-col)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ /* rescan the pivot col */
+ if (Work->any_skip)
+ {
+ col_assemble (Work->pivcol, Numeric, Work) ;
+ }
+
+ if (Work->do_scan2col)
+ {
+
+ for (j2 = Work->fscan_col ; j2 < fncols ; j2++)
+ {
+ /* Get a column */
+ col = Work->NewCols [j2] ;
+ if (col < 0) col = FLIP (col) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ if (!(col == Work->pivcol && Work->any_skip))
+ {
+ /* assemble it */
+ col_assemble (col, Numeric, Work) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* done. the remainder of this routine is used only when in debug mode */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+
+ /* ---------------------------------------------------------------------- */
+ /* when debugging: make sure the assembly did everything that it could */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG3 (("::Assemble done\n")) ;
+
+ for (i2 = 0 ; i2 < fnrows ; i2++)
+ {
+ /* Get a row */
+ row = Work->Frows [i2] ;
+ ASSERT (row >= 0 && row < n_row) ;
+
+ DEBUG6 (("DEBUG SCAN 1: "ID"\n", row)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ tpi = Row_tuples [row] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tpend = tp + Row_tlen [row] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = ((Int *) p) + ep->ncols ;
+ if (Rows [f] == EMPTY) continue ; /* row already assembled */
+ ASSERT (row == Rows [f]) ;
+ extrdeg = (ep->rdeg < rdeg0) ? ep->ncolsleft : (ep->rdeg - rdeg0) ;
+ extcdeg = (ep->cdeg < cdeg0) ? ep->nrowsleft : (ep->cdeg - cdeg0) ;
+ DEBUG6 ((
+ "e "ID" After assembly ext row deg: "ID" ext col degree "ID"\n",
+ e, extrdeg, extcdeg)) ;
+
+ if (Work->any_skip)
+ {
+ /* no Lsons in any row, except for very tall and thin ones */
+ ASSERT (extrdeg >= 0) ;
+ if (extrdeg == 0)
+ {
+ /* this is an unassemble Lson */
+ ASSERT (ep->ncols == 1) ;
+ ASSERT (ep->ncolsleft == 1) ;
+ col = Cols [0] ;
+ ASSERT (col != Work->pivcol) ;
+ }
+ }
+ else
+ {
+ /* no Lsons in any row */
+ ASSERT (extrdeg > 0) ;
+ /* Uson external row degree is = number of cols left */
+ ASSERT (IMPLIES (extcdeg == 0, extrdeg == ep->ncolsleft)) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+ for (j2 = 0 ; j2 < fncols ; j2++)
+ {
+ /* Get a column */
+ col = Work->Fcols [j2] ;
+ ASSERT (col >= 0 && col < n_col) ;
+
+ DEBUG6 (("DEBUG SCAN 2: "ID"\n", col)) ;
+#ifndef FIXQ
+ UMF_dump_rowcol (1, Numeric, Work, col, TRUE) ;
+#else
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ tpi = Col_tuples [col] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tpend = tp + Col_tlen [col] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = ((Int *) p) + ep->ncols ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (col == Cols [f]) ;
+ extrdeg = (ep->rdeg < rdeg0) ? ep->ncolsleft : (ep->rdeg - rdeg0) ;
+ extcdeg = (ep->cdeg < cdeg0) ? ep->nrowsleft : (ep->cdeg - cdeg0) ;
+ DEBUG6 (("e "ID" After assembly ext col deg: "ID"\n", e, extcdeg)) ;
+
+ if (Work->any_skip)
+ {
+ /* no Usons in any column, except for very tall and thin ones */
+ ASSERT (extcdeg >= 0) ;
+ if (extcdeg == 0)
+ {
+ /* this is an unassemble Uson */
+ ASSERT (ep->nrows == 1) ;
+ ASSERT (ep->nrowsleft == 1) ;
+ row = Rows [0] ;
+ ASSERT (row != Work->pivrow) ;
+ }
+ }
+ else
+ {
+ /* no Usons in any column */
+ ASSERT (extcdeg > 0) ;
+ /* Lson external column degree is = number of rows left */
+ ASSERT (IMPLIES (extrdeg == 0, extcdeg == ep->nrowsleft)) ;
+ }
+ }
+ }
+#endif /* NDEBUG */
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_assemble.h b/src/C/SuiteSparse/UMFPACK/Source/umf_assemble.h
new file mode 100644
index 0000000..d219e2c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_assemble.h
@@ -0,0 +1,17 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_assemble
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
+
+GLOBAL void UMF_assemble_fixq
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_blas3_update.c b/src/C/SuiteSparse/UMFPACK/Source/umf_blas3_update.c
new file mode 100644
index 0000000..f11fb7b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_blas3_update.c
@@ -0,0 +1,175 @@
+/* ========================================================================== */
+/* === UMF_blas3_update ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_blas3_update
+(
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry *L, *U, *C, *LU ;
+ Int i, j, s, k, m, n, d, nb, dc ;
+
+#ifndef NBLAS
+ Int blas_ok = TRUE ;
+#else
+#define blas_ok FALSE
+#endif
+
+ DEBUG5 (("In UMF_blas3_update "ID" "ID" "ID"\n",
+ Work->fnpiv, Work->fnrows, Work->fncols)) ;
+
+ k = Work->fnpiv ;
+ if (k == 0)
+ {
+ /* no work to do */
+ return ;
+ }
+
+ m = Work->fnrows ;
+ n = Work->fncols ;
+
+ d = Work->fnr_curr ;
+ dc = Work->fnc_curr ;
+ nb = Work->nb ;
+ ASSERT (d >= 0 && (d % 2) == 1) ;
+ C = Work->Fcblock ; /* ldc is fnr_curr */
+ L = Work->Flblock ; /* ldl is fnr_curr */
+ U = Work->Fublock ; /* ldu is fnc_curr, stored by rows */
+ LU = Work->Flublock ; /* nb-by-nb */
+
+#ifndef NDEBUG
+ DEBUG5 (("DO RANK-NB UPDATE of frontal:\n")) ;
+ DEBUG5 (("DGEMM : "ID" "ID" "ID"\n", k, m, n)) ;
+ DEBUG7 (("C block: ")) ; UMF_dump_dense (C, d, m, n) ;
+ DEBUG7 (("A block: ")) ; UMF_dump_dense (L, d, m, k) ;
+ DEBUG7 (("B' block: ")) ; UMF_dump_dense (U, dc, n, k) ;
+ DEBUG7 (("LU block: ")) ; UMF_dump_dense (LU, nb, k, k) ;
+#endif
+
+ if (k == 1)
+ {
+
+#ifndef NBLAS
+ BLAS_GER (m, n, L, U, C, d) ;
+#endif
+
+ if (!blas_ok)
+ {
+ /* rank-1 outer product to update the C block */
+ for (j = 0 ; j < n ; j++)
+ {
+ Entry u_j = U [j] ;
+ if (IS_NONZERO (u_j))
+ {
+ Entry *c_ij, *l_is ;
+ c_ij = & C [j*d] ;
+ l_is = & L [0] ;
+#pragma ivdep
+ for (i = 0 ; i < m ; i++)
+ {
+ /* C [i+j*d]-= L [i] * U [j] */
+ MULT_SUB (*c_ij, *l_is, u_j) ;
+ c_ij++ ;
+ l_is++ ;
+ }
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* triangular solve to update the U block */
+
+#ifndef NBLAS
+ BLAS_TRSM_RIGHT (n, k, LU, nb, U, dc) ;
+#endif
+
+ if (!blas_ok)
+ {
+ /* use plain C code if no BLAS at compile time, or if integer
+ * overflow has occurred */
+ for (s = 0 ; s < k ; s++)
+ {
+ for (i = s+1 ; i < k ; i++)
+ {
+ Entry l_is = LU [i+s*nb] ;
+ if (IS_NONZERO (l_is))
+ {
+ Entry *u_ij, *u_sj ;
+ u_ij = & U [i*dc] ;
+ u_sj = & U [s*dc] ;
+#pragma ivdep
+ for (j = 0 ; j < n ; j++)
+ {
+ /* U [i*dc+j] -= LU [i+s*nb] * U [s*dc+j] ; */
+ MULT_SUB (*u_ij, l_is, *u_sj) ;
+ u_ij++ ;
+ u_sj++ ;
+ }
+ }
+ }
+ }
+ }
+
+ /* rank-k outer product to update the C block */
+ /* C = C - L*U' (U is stored by rows, not columns) */
+
+#ifndef NBLAS
+ BLAS_GEMM (m, n, k, L, U, dc, C, d) ;
+#endif
+
+ if (!blas_ok)
+ {
+ /* use plain C code if no BLAS at compile time, or if integer
+ * overflow has occurred */
+
+ for (s = 0 ; s < k ; s++)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ Entry u_sj = U [j+s*dc] ;
+ if (IS_NONZERO (u_sj))
+ {
+ Entry *c_ij, *l_is ;
+ c_ij = & C [j*d] ;
+ l_is = & L [s*d] ;
+#pragma ivdep
+ for (i = 0 ; i < m ; i++)
+ {
+ /* C [i+j*d]-= L [i+s*d] * U [s*dc+j] */
+ MULT_SUB (*c_ij, *l_is, u_sj) ;
+ c_ij++ ;
+ l_is++ ;
+ }
+ }
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG5 (("RANK-NB UPDATE of frontal done:\n")) ;
+ DEBUG5 (("DGEMM : "ID" "ID" "ID"\n", k, m, n)) ;
+ DEBUG7 (("C block: ")) ; UMF_dump_dense (C, d, m, n) ;
+ DEBUG7 (("A block: ")) ; UMF_dump_dense (L, d, m, k) ;
+ DEBUG7 (("B' block: ")) ; UMF_dump_dense (U, dc, n, k) ;
+ DEBUG7 (("LU block: ")) ; UMF_dump_dense (LU, nb, k, k) ;
+#endif
+
+ DEBUG2 (("blas3 "ID" "ID" "ID"\n", k, Work->fnrows, Work->fncols)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_blas3_update.h b/src/C/SuiteSparse/UMFPACK/Source/umf_blas3_update.h
new file mode 100644
index 0000000..62cea48
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_blas3_update.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_blas3_update
+(
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_build_tuples.c b/src/C/SuiteSparse/UMFPACK/Source/umf_build_tuples.c
new file mode 100644
index 0000000..4895089
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_build_tuples.c
@@ -0,0 +1,159 @@
+/* ========================================================================== */
+/* === UMF_build_tuples ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Construct the tuple lists from a set of packed elements (no holes in
+ elements, no internal or external fragmentation, and a packed (0..Work->nel)
+ element name space). Assume no tuple lists are currently allocated, but
+ that the tuple lengths have been initialized by UMF_tuple_lengths.
+
+ Returns TRUE if successful, FALSE if not enough memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_tail_block.h"
+
+GLOBAL Int UMF_build_tuples
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int e, nrows, ncols, nel, *Rows, *Cols, row, col, n_row, n_col, *E,
+ *Row_tuples, *Row_degree, *Row_tlen,
+ *Col_tuples, *Col_degree, *Col_tlen, n1 ;
+ Element *ep ;
+ Unit *p ;
+ Tuple tuple, *tp ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ E = Work->E ;
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nel = Work->nel ;
+ n1 = Work->n1 ;
+
+ DEBUG3 (("BUILD_TUPLES: n_row "ID" n_col "ID" nel "ID"\n",
+ n_row, n_col, nel)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate space for the tuple lists */
+ /* ---------------------------------------------------------------------- */
+
+ /* Garbage collection and memory reallocation have already attempted to */
+ /* ensure that there is enough memory for all the tuple lists. If */
+ /* memory allocation fails here, then there is nothing more to be done. */
+
+ for (row = n1 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ Row_tuples [row] = UMF_mem_alloc_tail_block (Numeric,
+ UNITS (Tuple, TUPLES (Row_tlen [row]))) ;
+ if (!Row_tuples [row])
+ {
+ /* :: out of memory for row tuples :: */
+ DEBUGm4 (("out of memory: build row tuples\n")) ;
+ return (FALSE) ; /* out of memory for row tuples */
+ }
+ Row_tlen [row] = 0 ;
+ }
+ }
+
+ /* push on stack in reverse order, so column tuples are in the order */
+ /* that they will be deleted. */
+ for (col = n_col-1 ; col >= n1 ; col--)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ Col_tuples [col] = UMF_mem_alloc_tail_block (Numeric,
+ UNITS (Tuple, TUPLES (Col_tlen [col]))) ;
+ if (!Col_tuples [col])
+ {
+ /* :: out of memory for col tuples :: */
+ DEBUGm4 (("out of memory: build col tuples\n")) ;
+ return (FALSE) ; /* out of memory for col tuples */
+ }
+ Col_tlen [col] = 0 ;
+ }
+ }
+
+#ifndef NDEBUG
+ UMF_dump_memory (Numeric) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* create the tuple lists (exclude element 0) */
+ /* ---------------------------------------------------------------------- */
+
+ /* for all elements, in order of creation */
+ for (e = 1 ; e <= nel ; e++)
+ {
+ DEBUG9 (("Adding tuples for element: "ID" at "ID"\n", e, E [e])) ;
+ ASSERT (E [e]) ; /* no external fragmentation */
+ p = Numeric->Memory + E [e] ;
+ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncols) ;
+ nrows = ep->nrows ;
+ ASSERT (e != 0) ;
+ ASSERT (e == 0 || nrows == ep->nrowsleft) ;
+ ASSERT (e == 0 || ncols == ep->ncolsleft) ;
+ tuple.e = e ;
+ for (tuple.f = 0 ; tuple.f < ncols ; tuple.f++)
+ {
+ col = Cols [tuple.f] ;
+ ASSERT (col >= n1 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (Col_tuples [col]) ;
+ tp = ((Tuple *) (Numeric->Memory + Col_tuples [col]))
+ + Col_tlen [col]++ ;
+ *tp = tuple ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+ }
+ for (tuple.f = 0 ; tuple.f < nrows ; tuple.f++)
+ {
+ row = Rows [tuple.f] ;
+ ASSERT (row >= n1 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (Row_tuples [row]) ;
+ tp = ((Tuple *) (Numeric->Memory + Row_tuples [row]))
+ + Row_tlen [row]++ ;
+ *tp = tuple ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+#endif
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* the tuple lists are now valid, and can be scanned */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_memory (Numeric) ;
+ UMF_dump_matrix (Numeric, Work, FALSE) ;
+#endif
+ DEBUG3 (("BUILD_TUPLES: done\n")) ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_build_tuples.h b/src/C/SuiteSparse/UMFPACK/Source/umf_build_tuples.h
new file mode 100644
index 0000000..8ee8052
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_build_tuples.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_build_tuples
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_colamd.c b/src/C/SuiteSparse/UMFPACK/Source/umf_colamd.c
new file mode 100644
index 0000000..edbbad0
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_colamd.c
@@ -0,0 +1,3139 @@
+/* ========================================================================== */
+/* === UMF_colamd =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+UMF_colamd: an approximate minimum degree column ordering algorithm,
+ used as a preordering for UMFPACK.
+
+NOTE: if this routine is used outside of UMFPACK, for a sparse Cholesky
+factorization of (AQ)'*(AQ) or a QR factorization of A, then one line should
+be removed (the "&& pivot_row_thickness > 0" expression). See the comment
+regarding the Cholesky factorization, below.
+
+Purpose:
+
+ Colamd computes a permutation Q such that the Cholesky factorization of
+ (AQ)'(AQ) has less fill-in and requires fewer floating point operations
+ than A'A. This also provides a good ordering for sparse partial
+ pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
+ factorization, and P is computed during numerical factorization via
+ conventional partial pivoting with row interchanges. Colamd is the
+ column ordering method used in SuperLU, part of the ScaLAPACK library.
+ It is also available as built-in function in MATLAB Version 6,
+ available from MathWorks, Inc. (http://www.mathworks.com). This
+ routine can be used in place of colmmd in MATLAB. By default, the \
+ and / operators in MATLAB perform a column ordering (using colmmd
+ or colamd) prior to LU factorization using sparse partial pivoting,
+ in the built-in MATLAB lu(A) routine.
+
+ This code is derived from Colamd Version 2.0.
+
+Authors:
+
+ The authors of the COLAMD code itself are Stefan I. Larimore and Timothy A.
+ Davis, University of Florida. The algorithm was developed in collaboration
+ with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory.
+ The AMD metric on which this is based is by Patrick Amestoy, T. Davis,
+ and Iain Duff.
+
+Date:
+
+ UMFPACK Version: see above.
+ COLAMD Version 2.0 was released on January 31, 2000.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+UMFPACK: Copyright (c) 2003 by Timothy A. Davis. All Rights Reserved.
+
+See the UMFPACK README file for the License for your use of this code.
+
+Availability:
+
+ Both UMFPACK and the original unmodified colamd/symamd library are
+ available at http://www.cise.ufl.edu/research/sparse.
+
+Changes for inclusion in UMFPACK:
+
+ * symamd, symamd_report, and colamd_report removed
+
+ * additional terms added to RowInfo, ColInfo, and stats
+
+ * Frontal matrix information computed for UMFPACK
+
+ * routines renamed
+
+ * column elimination tree post-ordering incorporated. In the original
+ version 2.0, this was performed in colamd.m.
+
+For more information, see:
+
+ Amestoy, P. R. and Davis, T. A. and Duff, I. S.,
+ An approximate minimum degree ordering algorithm,
+ SIAM J. Matrix Analysis and Applic, vol 17, no 4., pp 886-905, 1996.
+
+ Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.,
+ A column approximate minimum degree ordering algorithm,
+ Univ. of Florida, CISE Dept., TR-00-005, Gainesville, FL
+ Oct. 2000. Submitted to ACM Trans. Math. Softw.
+
+*/
+
+/* ========================================================================== */
+/* === Description of user-callable routines ================================ */
+/* ========================================================================== */
+
+/*
+ ----------------------------------------------------------------------------
+ colamd_recommended: removed for UMFPACK
+ ----------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ colamd_set_defaults:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ colamd_set_defaults (double knobs [COLAMD_KNOBS]) ;
+
+ Purpose:
+
+ Sets the default parameters. The use of this routine is optional.
+
+ Arguments:
+
+ double knobs [COLAMD_KNOBS] ; Output only.
+
+ Let c = knobs [COLAMD_DENSE_COL], r = knobs [COLAMD_DENSE_ROW].
+ Colamd: rows with more than max (16, r*16*sqrt(n_col))
+ entries are removed prior to ordering. Columns with more than
+ max (16, c*16*sqrt(n_row)) entries are removed prior to
+ ordering, and placed last in the output column ordering.
+
+ Symamd: removed for UMFPACK.
+
+ COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
+ respectively, in colamd.h. Default values of these two knobs
+ are both 0.5. Currently, only knobs [0] and knobs [1] are
+ used, but future versions may use more knobs. If so, they will
+ be properly set to their defaults by the future version of
+ colamd_set_defaults, so that the code that calls colamd will
+ not need to change, assuming that you either use
+ colamd_set_defaults, or pass a (double *) NULL pointer as the
+ knobs array to colamd or symamd.
+
+ knobs [COLAMD_AGGRESSIVE]: if nonzero, then perform aggressive
+ absorption. Otherwise, do not. This version does aggressive
+ absorption by default. COLAMD v2.1 (in MATLAB) always
+ does aggressive absorption (it doesn't have an option to turn
+ it off).
+
+ ----------------------------------------------------------------------------
+ colamd:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ Int UMF_colamd (Int n_row, Int n_col, Int Alen, Int *A, Int *p,
+ double knobs [COLAMD_KNOBS], Int stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Computes a column ordering (Q) of A such that P(AQ)=LU or
+ (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ operations than factorizing the unpermuted matrix A or A'A,
+ respectively.
+
+ Returns:
+
+ TRUE (1) if successful, FALSE (0) otherwise.
+
+ Arguments:
+
+ Int n_row ; Input argument.
+
+ Number of rows in the matrix A.
+ Restriction: n_row >= 0.
+ Colamd returns FALSE if n_row is negative.
+
+ Int n_col ; Input argument.
+
+ Number of columns in the matrix A.
+ Restriction: n_col >= 0.
+ Colamd returns FALSE if n_col is negative.
+
+ Int Alen ; Input argument.
+
+ Restriction (see note):
+ Alen >= 2*nnz + 8*(n_col+1) + 6*(n_row+1) + n_col
+ Colamd returns FALSE if these conditions are not met.
+
+ Note: this restriction makes an modest assumption regarding
+ the size of the two typedef's structures in colamd.h.
+ We do, however, guarantee that
+
+ Alen >= UMF_COLAMD_RECOMMENDED (nnz, n_row, n_col)
+
+ will be sufficient.
+
+ Int A [Alen] ; Input and output argument.
+
+ A is an integer array of size Alen. Alen must be at least as
+ large as the bare minimum value given above, but this is very
+ low, and can result in excessive run time. For best
+ performance, we recommend that Alen be greater than or equal to
+ UMF_COLAMD_RECOMMENDED (nnz, n_row, n_col), which adds
+ nnz/5 to the bare minimum value given above.
+
+ On input, the row indices of the entries in column c of the
+ matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices
+ in a given column c need not be in ascending order, and
+ duplicate row indices may be be present. However, colamd will
+ work a little faster if both of these conditions are met
+ (Colamd puts the matrix into this format, if it finds that the
+ the conditions are not met).
+
+ The matrix is 0-based. That is, rows are in the range 0 to
+ n_row-1, and columns are in the range 0 to n_col-1. Colamd
+ returns FALSE if any row index is out of range.
+
+ A holds the inverse permutation on output.
+
+ Int p [n_col+1] ; Both input and output argument.
+
+ p is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the matrix A. Column c of
+ the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ for all c in the range 0 to n_col-1. The value p [n_col] is
+ thus the total number of entries in the pattern of the matrix A.
+ Colamd returns FALSE if these conditions are not met.
+
+ On output, if colamd returns TRUE, the array p holds the column
+ permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
+ the first column index in the new ordering, and p [n_col-1] is
+ the last. That is, p [k] = j means that column j of A is the
+ kth pivot column, in AQ, where k is in the range 0 to n_col-1
+ (p [0] = j means that column j of A is the first column in AQ).
+
+ If colamd returns FALSE, then no permutation is returned, and
+ p is undefined on output.
+
+ double knobs [COLAMD_KNOBS] ; Input argument.
+
+ See colamd_set_defaults for a description.
+ The behavior is undefined if knobs contains NaN's.
+ (UMFPACK does not call umf_colamd with NaN-valued knobs).
+
+ Int stats [COLAMD_STATS] ; Output argument.
+
+ Statistics on the ordering, and error status.
+ See colamd.h for related definitions.
+ Colamd returns FALSE if stats is not present.
+
+ stats [0]: number of dense or empty rows ignored.
+
+ stats [1]: number of dense or empty columns ignored (and
+ ordered last in the output permutation p)
+ Note that a row can become "empty" if it
+ contains only "dense" and/or "empty" columns,
+ and similarly a column can become "empty" if it
+ only contains "dense" and/or "empty" rows.
+
+ stats [2]: number of garbage collections performed.
+ This can be excessively high if Alen is close
+ to the minimum required value.
+
+ stats [3]: status code. < 0 is an error code.
+ > 1 is a warning or notice.
+
+ 0 OK. Each column of the input matrix contained
+ row indices in increasing order, with no
+ duplicates.
+
+ -11 Columns of input matrix jumbled
+ (unsorted columns or duplicate entries).
+
+ stats [4]: the bad column index
+ stats [5]: the bad row index
+
+ -1 A is a null pointer
+
+ -2 p is a null pointer
+
+ -3 n_row is negative
+
+ stats [4]: n_row
+
+ -4 n_col is negative
+
+ stats [4]: n_col
+
+ -5 number of nonzeros in matrix is negative
+
+ stats [4]: number of nonzeros, p [n_col]
+
+ -6 p [0] is nonzero
+
+ stats [4]: p [0]
+
+ -7 A is too small
+
+ stats [4]: required size
+ stats [5]: actual size (Alen)
+
+ -8 a column has a zero or negative number of
+ entries (changed for UMFPACK)
+
+ stats [4]: column with <= 0 entries
+ stats [5]: number of entries in col
+
+ -9 a row index is out of bounds
+
+ stats [4]: column with bad row index
+ stats [5]: bad row index
+ stats [6]: n_row, # of rows of matrx
+
+ -10 unused
+
+ -999 (unused; see symamd.c)
+
+ Future versions may return more statistics in the stats array.
+
+ Example:
+
+ See http://www.cise.ufl.edu/~davis/colamd/example.c
+ for a complete example.
+
+ To order the columns of a 5-by-4 matrix with 11 nonzero entries in
+ the following nonzero pattern
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ with default knobs and no output statistics, do the following:
+
+ #include "colamd.h"
+ #define ALEN UMF_COLAMD_RECOMMENDED (11, 5, 4)
+ Int A [ALEN] = {1, 2, 5, 3, 5, 1, 2, 3, 4, 2, 4} ;
+ Int p [ ] = {0, 3, 5, 9, 11} ;
+ Int stats [COLAMD_STATS] ;
+ UMF_colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ;
+
+ The permutation is returned in the array p, and A is destroyed.
+
+
+ ----------------------------------------------------------------------------
+ symamd: does not appear in this version for UMFPACK
+ ----------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ colamd_report: does not appear in this version for UMFPACK
+ ----------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ symamd_report: does not appear in this version for UMFPACK
+ ----------------------------------------------------------------------------
+
+*/
+
+/* ========================================================================== */
+/* === Scaffolding code definitions ======================================== */
+/* ========================================================================== */
+
+/* UMFPACK debugging control moved to amd_internal.h */
+
+/*
+ Our "scaffolding code" philosophy: In our opinion, well-written library
+ code should keep its "debugging" code, and just normally have it turned off
+ by the compiler so as not to interfere with performance. This serves
+ several purposes:
+
+ (1) assertions act as comments to the reader, telling you what the code
+ expects at that point. All assertions will always be true (unless
+ there really is a bug, of course).
+
+ (2) leaving in the scaffolding code assists anyone who would like to modify
+ the code, or understand the algorithm (by reading the debugging output,
+ one can get a glimpse into what the code is doing).
+
+ (3) (gasp!) for actually finding bugs. This code has been heavily tested
+ and "should" be fully functional and bug-free ... but you never know...
+
+ To enable debugging, comment out the "#define NDEBUG" above. For a MATLAB
+ mexFunction, you will also need to modify mexopts.sh to remove the -DNDEBUG
+ definition. The code will become outrageously slow when debugging is
+ enabled. To control the level of debugging output, set an environment
+ variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging,
+ you should see the following message on the standard output:
+
+ colamd: debug version, D = 1 (THIS WILL BE SLOW!)
+
+ or a similar message for symamd. If you don't, then debugging has not
+ been enabled.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+/* ------------------ */
+/* modified for UMFPACK: */
+#include "umf_internal.h"
+#include "umf_colamd.h"
+#include "umf_apply_order.h"
+#include "umf_fsize.h"
+/* ------------------ */
+
+/* ========================================================================== */
+/* === Definitions ========================================================== */
+/* ========================================================================== */
+
+/* ------------------ */
+/* UMFPACK: duplicate definitions moved to umf_internal.h */
+/* ------------------ */
+
+/* Row and column status */
+#define ALIVE (0)
+#define DEAD (-1)
+
+/* Column status */
+#define DEAD_PRINCIPAL (-1)
+#define DEAD_NON_PRINCIPAL (-2)
+
+/* Macros for row and column status update and checking. */
+#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
+#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
+#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
+#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
+#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
+#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
+#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
+#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
+#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
+
+/* ------------------ */
+/* UMFPACK: Colamd reporting mechanism moved to umf_internal.h */
+/* ------------------ */
+
+/* ========================================================================== */
+/* === Prototypes of PRIVATE routines ======================================= */
+/* ========================================================================== */
+
+PRIVATE Int init_rows_cols
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int p []
+ /* Int stats [COLAMD_STATS] */
+) ;
+
+PRIVATE void init_scoring
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ double knobs [COLAMD_KNOBS],
+ Int *p_n_row2,
+ Int *p_n_col2,
+ Int *p_max_deg
+ /* ------------------ */
+ /* added for UMFPACK */
+ , Int *p_ndense_row /* number of dense rows */
+ , Int *p_nempty_row /* number of original empty rows */
+ , Int *p_nnewlyempty_row /* number of newly empty rows */
+ , Int *p_ndense_col /* number of dense cols (excl "empty" cols) */
+ , Int *p_nempty_col /* number of original empty cols */
+ , Int *p_nnewlyempty_col /* number of newly empty cols */
+) ;
+
+PRIVATE Int find_ordering
+(
+ Int n_row,
+ Int n_col,
+ Int Alen,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int n_col2,
+ Int max_deg,
+ Int pfree
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Int Front_npivcol [ ]
+ , Int Front_nrows [ ]
+ , Int Front_ncols [ ]
+ , Int Front_parent [ ]
+ , Int Front_cols [ ]
+ , Int *p_nfr
+ , Int aggressive
+ , Int InFront [ ]
+ /* ------------------ */
+) ;
+
+/* ------------------ */
+/* order_children deleted for UMFPACK: */
+/* ------------------ */
+
+PRIVATE void detect_super_cols
+(
+
+#ifndef NDEBUG
+ Int n_col,
+ Colamd_Row Row [],
+#endif /* NDEBUG */
+
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int row_start,
+ Int row_length
+) ;
+
+PRIVATE Int garbage_collection
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int *pfree
+) ;
+
+PRIVATE Int clear_mark
+(
+ Int n_row,
+ Colamd_Row Row []
+) ;
+
+/* ------------------ */
+/* print_report deleted for UMFPACK */
+/* ------------------ */
+
+/* ========================================================================== */
+/* === Debugging prototypes and definitions ================================= */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+/* ------------------ */
+/* debugging macros moved for UMFPACK */
+/* ------------------ */
+
+PRIVATE void debug_deg_lists
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+) ;
+
+PRIVATE void debug_mark
+(
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+) ;
+
+PRIVATE void debug_matrix
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+) ;
+
+PRIVATE void debug_structures
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+) ;
+
+/* ------------------ */
+/* dump_super added for UMFPACK: */
+PRIVATE void dump_super
+(
+ Int super_c,
+ Colamd_Col Col [],
+ Int n_col
+) ;
+/* ------------------ */
+
+#endif /* NDEBUG */
+
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === USER-CALLABLE ROUTINES: ============================================== */
+/* ========================================================================== */
+
+
+/* ========================================================================== */
+/* === colamd_set_defaults ================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd_set_defaults routine sets the default values of the user-
+ controllable parameters for colamd:
+
+ knobs [0] rows with knobs[0]*n_col entries or more are removed
+ prior to ordering in colamd. Rows and columns with
+ knobs[0]*n_col entries or more are removed prior to
+ ordering in symamd and placed last in the output
+ ordering.
+
+ knobs [1] columns with knobs[1]*n_row entries or more are removed
+ prior to ordering in colamd, and placed last in the
+ column permutation. Symamd ignores this knob.
+
+ knobs [2] if nonzero, then perform aggressive absorption.
+
+ knobs [3..19] unused, but future versions might use this
+*/
+
+GLOBAL void UMF_colamd_set_defaults
+(
+ /* === Parameters ======================================================= */
+
+ double knobs [COLAMD_KNOBS] /* knob array */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+
+#if 0
+ if (!knobs)
+ {
+ return ; /* UMFPACK always passes knobs array */
+ }
+#endif
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [COLAMD_DENSE_ROW] = 0.2 ; /* default changed for UMFPACK */
+ knobs [COLAMD_DENSE_COL] = 0.2 ; /* default changed for UMFPACK */
+ knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default is to do aggressive
+ * absorption */
+}
+
+
+/* ========================================================================== */
+/* === symamd removed for UMFPACK =========================================== */
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === colamd =============================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd routine computes a column ordering Q of a sparse matrix
+ A such that the LU factorization P(AQ) = LU remains sparse, where P is
+ selected via partial pivoting. The routine can also be viewed as
+ providing a permutation Q such that the Cholesky factorization
+ (AQ)'(AQ) = LL' remains sparse.
+*/
+
+/* For UMFPACK: colamd always returns TRUE */
+
+GLOBAL Int UMF_colamd /* returns TRUE if successful, FALSE otherwise*/
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* length of A */
+ Int A [], /* row indices of A */
+ Int p [], /* pointers to columns in A */
+ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ Int stats [COLAMD_STATS] /* output statistics and error codes */
+
+ /* ------------------ */
+ /* added for UMFPACK: each Front_ array is of size n_col+1 */
+ , Int Front_npivcol [ ] /* # pivot cols in each front */
+ , Int Front_nrows [ ] /* # of rows in each front (incl. pivot rows) */
+ , Int Front_ncols [ ] /* # of cols in each front (incl. pivot cols) */
+ , Int Front_parent [ ] /* parent of each front */
+ , Int Front_cols [ ] /* link list of pivot columns for each front */
+ , Int *p_nfr /* total number of frontal matrices */
+ , Int InFront [ ] /* InFront [row] = f if the original row was
+ * absorbed into front f. EMPTY if the row was
+ * empty, dense, or not absorbed. This array
+ * has size n_row+1 */
+ /* ------------------ */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int row ; /* row index */
+ Int i ; /* loop index */
+ Int nnz ; /* nonzeros in A */
+ Int Row_size ; /* size of Row [], in integers */
+ Int Col_size ; /* size of Col [], in integers */
+#if 0
+ Int need ; /* minimum required length of A */
+#endif
+ Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */
+ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int ngarbage ; /* number of garbage collections performed */
+ Int max_deg ; /* maximum row degree */
+ Int aggressive ; /* TRUE if doing aggressive absorption */
+#if 0
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
+#endif
+
+ /* ------------------ */
+ /* debugging initializations moved for UMFPACK */
+ /* ------------------ */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int ndense_row, nempty_row, parent, ndense_col,
+ nempty_col, k, col, nfr, *Front_child, *Front_sibling, *Front_stack,
+ *Front_order, *Front_size ;
+ Int nnewlyempty_col, nnewlyempty_row ;
+ /* ------------------ */
+
+ /* === Check the input arguments ======================================== */
+
+#if 0
+ if (!stats)
+ {
+ DEBUG0 (("colamd: stats not present\n")) ;
+ return (FALSE) ; /* UMFPACK: always passes stats [ ] */
+ }
+#endif
+
+ ASSERT (stats != (Int *) NULL) ;
+
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+#if 0
+ if (!A) /* A is not present */
+ {
+ /* UMFPACK: always passes A [ ] */
+ DEBUG0 (("colamd: A not present\n")) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ /* UMFPACK: always passes p [ ] */
+ DEBUG0 (("colamd: p not present\n")) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ return (FALSE) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ /* UMFPACK: does not call UMF_colamd if n <= 0 */
+ DEBUG0 (("colamd: nrow negative "ID"\n", n_row)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
+ stats [COLAMD_INFO1] = n_row ;
+ return (FALSE) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ /* UMFPACK: does not call UMF_colamd if n <= 0 */
+ DEBUG0 (("colamd: ncol negative "ID"\n", n_col)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n_col ;
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (A != (Int *) NULL) ;
+ ASSERT (p != (Int *) NULL) ;
+ ASSERT (n_row >= 0) ;
+ ASSERT (n_col >= 0) ;
+
+ nnz = p [n_col] ;
+
+#if 0
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ /* UMFPACK: does not call UMF_colamd if nnz < 0 */
+ DEBUG0 (("colamd: number of entries negative "ID"\n", nnz)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0) /* p [0] must be exactly zero */
+ {
+ DEBUG0 (("colamd: p[0] not zero "ID"\n", p [0])) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (nnz >= 0) ;
+ ASSERT (p [0] == 0) ;
+
+ /* === If no knobs, set default knobs =================================== */
+
+#if 0
+ if (!knobs)
+ {
+ /* UMFPACK: always passes the knobs */
+ UMF_colamd_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+#endif
+
+ ASSERT (knobs != (double *) NULL) ;
+
+ /* --------------------- */
+ /* added for UMFPACK v4.1: */
+ aggressive = (knobs [COLAMD_AGGRESSIVE] != 0) ;
+ /* --------------------- */
+
+ /* === Allocate the Row and Col arrays from array A ===================== */
+
+ Col_size = UMF_COLAMD_C (n_col) ;
+ Row_size = UMF_COLAMD_R (n_row) ;
+
+#if 0
+ need = MAX (2*nnz, 4*n_col) + n_col + Col_size + Row_size ;
+ if (need > Alen)
+ {
+ /* UMFPACK: always passes enough space */
+ /* not enough space in array A to perform the ordering */
+ DEBUG0 (("colamd: Need Alen >= "ID", given only Alen = "ID"\n",
+ need, Alen)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
+ stats [COLAMD_INFO1] = need ;
+ stats [COLAMD_INFO2] = Alen ;
+ return (FALSE) ;
+ }
+#endif
+
+ Alen -= Col_size + Row_size ;
+ Col = (Colamd_Col *) &A [Alen] ;
+ Row = (Colamd_Row *) &A [Alen + Col_size] ;
+
+ /* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering
+ * requires Alen >= 2*nnz + n_col, and the postorder requires
+ * Alen >= 5*n_col. */
+
+ /* === Construct the row and column data structures ===================== */
+
+ i = init_rows_cols (n_row, n_col, Row, Col, A, p) ;
+
+#if 0
+ if (!i)
+ {
+ /* input matrix is invalid */
+ DEBUG0 (("colamd: Matrix invalid\n")) ;
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (i) ;
+
+ /* === UMFPACK: Initialize front info =================================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Front_npivcol [col] = 0 ;
+ Front_nrows [col] = 0 ;
+ Front_ncols [col] = 0 ;
+ Front_parent [col] = EMPTY ;
+ Front_cols [col] = EMPTY ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , &ndense_row, &nempty_row, &nnewlyempty_row
+ , &ndense_col, &nempty_col, &nnewlyempty_col
+ /* ------------------ */
+ ) ;
+ ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ;
+ ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+ n_col2, max_deg, 2*nnz
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Front_npivcol, Front_nrows, Front_ncols, Front_parent, Front_cols
+ , &nfr, aggressive, InFront
+ /* ------------------ */
+ ) ;
+
+ /* ------------------ */
+ /* changed for UMFPACK: */
+
+ /* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */
+ /* This step requires Alen >= 5*n_col */
+ Front_child = A ;
+ Front_sibling = Front_child + nfr ;
+ Front_stack = Front_sibling + nfr ;
+ Front_order = Front_stack + nfr ;
+ Front_size = Front_order + nfr ;
+
+ UMF_fsize (nfr, Front_size, Front_nrows, Front_ncols,
+ Front_parent, Front_npivcol) ;
+
+ AMD_postorder (nfr, Front_parent, Front_npivcol, Front_size,
+ Front_order, Front_child, Front_sibling, Front_stack) ;
+
+ /* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */
+
+ /* use A [0..nfr-1] as workspace */
+ UMF_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_nrows, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_ncols, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_parent, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_cols, Front_order, A, nfr, nfr) ;
+
+ /* fix the parent to refer to the new numbering */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ parent = Front_parent [i] ;
+ if (parent != EMPTY)
+ {
+ Front_parent [i] = Front_order [parent] ;
+ }
+ }
+
+ /* fix InFront to refer to the new numbering */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ i = InFront [row] ;
+ ASSERT (i >= EMPTY && i < nfr) ;
+ if (i != EMPTY)
+ {
+ InFront [row] = Front_order [i] ;
+ }
+ }
+
+ /* Front_order longer needed ] */
+
+ /* === Order the columns in the fronts ================================== */
+
+ /* use A [0..n_col-1] as inverse permutation */
+ for (i = 0 ; i < n_col ; i++)
+ {
+ A [i] = EMPTY ;
+ }
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ ASSERT (Front_npivcol [i] > 0) ;
+ for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ ASSERT (col >= 0 && col < n_col) ;
+ DEBUG1 (("Colamd output ordering: k "ID" col "ID"\n", k, col)) ;
+ p [k] = col ;
+ ASSERT (A [col] == EMPTY) ;
+ A [col] = k ;
+ k++ ;
+ }
+ }
+
+ /* === Order the "dense" and null columns =============================== */
+
+ ASSERT (k == n_col2) ;
+ if (n_col2 < n_col)
+ {
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (A [col] == EMPTY)
+ {
+ k = Col [col].shared2.order ;
+ ASSERT (k >= n_col2 && k < n_col) ;
+ DEBUG1 (("Colamd output ordering: k "ID" col "ID
+ " (dense or null col)\n", k, col)) ;
+ p [k] = col ;
+ A [col] = k ;
+ }
+ }
+ }
+
+ /* ------------------ */
+
+ /* === Return statistics in stats ======================================= */
+
+ /* ------------------ */
+ /* modified for UMFPACK */
+ stats [COLAMD_DENSE_ROW] = ndense_row ;
+ stats [COLAMD_EMPTY_ROW] = nempty_row ;
+ stats [COLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ;
+ stats [COLAMD_DENSE_COL] = ndense_col ;
+ stats [COLAMD_EMPTY_COL] = nempty_col ;
+ stats [COLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ;
+ ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ;
+ /* ------------------ */
+ stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
+ *p_nfr = nfr ;
+ DEBUG1 (("colamd: done.\n")) ;
+ return (TRUE) ;
+}
+
+
+
+
+/* ========================================================================== */
+/* === colamd_report removed for UMFPACK ==================================== */
+/* ========================================================================== */
+
+/* ========================================================================== */
+/* === symamd_report removed for UMFPACK ==================================== */
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns FALSE if the matrix is invalid,
+ TRUE otherwise. Not user-callable.
+*/
+
+/* For UMFPACK, this always returns TRUE */
+
+PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A, of size Alen */
+ Int p [] /* pointers to columns in A, of size n_col+1 */
+/*
+ Int stats [COLAMD_STATS] colamd statistics, removed for UMFPACK
+*/
+)
+{
+ /* === Local variables ================================================== */
+
+ Int col ; /* a column index */
+ Int row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int *cp_end ; /* a pointer to the end of a column */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+#if 0
+ if (Col [col].length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = Col [col].length ;
+ DEBUG0 (("colamd: col "ID" length "ID" <= 0\n",
+ col, Col [col].length));
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (Col [col].length >= 0) ;
+
+ /* added for UMFPACK v4.1 */
+ ASSERT (Col [col].length > 0) ;
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = EMPTY ;
+ Col [col].shared4.degree_next = EMPTY ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Col [col].nextcol = EMPTY ;
+ Col [col].lastcol = col ;
+ /* ------------------ */
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ /* ------------------ */
+ /* stats [COLAMD_INFO3] = 0 ; */
+ /* number of duplicate or unsorted row indices - not computed in UMFPACK */
+ /* ------------------ */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ /* ------------------ */
+ /* removed for UMFPACK */
+ /* Row [row].shared2.mark = -1 ; */
+ /* ------------------ */
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Row [row].thickness = 1 ;
+ Row [row].front = EMPTY ;
+ /* ------------------ */
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+#ifndef NDEBUG
+ Int last_row = -1 ;
+#endif
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+
+#if 0
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ /* ------------------ */
+ /* not needed in UMFPACK: */
+ /* stats [COLAMD_INFO3] = n_row ; */
+ /* ------------------ */
+ DEBUG0 (("colamd: row "ID" col "ID" out of bounds\n", row,col));
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (row >= 0 && row < n_row) ;
+
+#if 0
+ /* ------------------ */
+ /* changed for UMFPACK */
+ if (row <= last_row)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is an error condition for UMFPACK */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_jumbled_matrix ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ DEBUG1 (("colamd: row "ID" col "ID" unsorted/duplicate\n",
+ row, col)) ;
+ return (FALSE) ;
+ }
+ /* ------------------ */
+#endif
+
+ ASSERT (row > last_row) ;
+
+ /* ------------------ */
+ /* changed for UMFPACK - jumbled columns not tolerated */
+ Row [row].length++ ;
+ /* ------------------ */
+
+#ifndef NDEBUG
+ last_row = row ;
+#endif
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ /* ------------------ */
+ /* removed for UMFPACK */
+ /* Row [0].shared2.mark = -1 ; */
+ /* ------------------ */
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ /* ------------------ */
+ /* removed for UMFPACK */
+ /* Row [row].shared2.mark = -1 ; */
+ /* ------------------ */
+ }
+
+ /* === Create row form ================================================== */
+
+ /* ------------------ */
+ /* jumbled matrix case removed for UMFPACK */
+ /* ------------------ */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* ------------------ */
+ /* recreate columns for jumbled matrix case removed for UMFPACK */
+ /* ------------------ */
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+
+PRIVATE void init_scoring
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameters */
+ Int *p_n_row2, /* number of non-dense, non-empty rows */
+ Int *p_n_col2, /* number of non-dense, non-empty columns */
+ Int *p_max_deg /* maximum row degree */
+ /* ------------------ */
+ /* added for UMFPACK */
+ , Int *p_ndense_row /* number of dense rows */
+ , Int *p_nempty_row /* number of original empty rows */
+ , Int *p_nnewlyempty_row /* number of newly empty rows */
+ , Int *p_ndense_col /* number of dense cols (excl "empty" cols) */
+ , Int *p_nempty_col /* number of original empty cols */
+ , Int *p_nnewlyempty_col /* number of newly empty cols */
+ /* ------------------ */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int c ; /* a column index */
+ Int r, row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int deg ; /* degree of a row or column */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *new_cp ; /* new column pointer */
+ Int col_length ; /* length of pruned column */
+ Int score ; /* current column score */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int dense_row_count ; /* remove rows with more entries than this */
+ Int dense_col_count ; /* remove cols with more entries than this */
+ Int min_score ; /* smallest column score */
+ Int max_deg ; /* maximum row degree */
+ Int next_col ; /* Used to add to degree list.*/
+
+ /* ------------------ */
+ /* added for UMFPACK */
+ Int ndense_row ; /* number of dense rows */
+ Int nempty_row ; /* number of empty rows */
+ Int nnewlyempty_row ; /* number of newly empty rows */
+ Int ndense_col ; /* number of dense cols (excl "empty" cols) */
+ Int nempty_col ; /* number of original empty cols */
+ Int nnewlyempty_col ; /* number of newly empty cols */
+ Int ne ;
+ /* ------------------ */
+
+#ifndef NDEBUG
+ Int debug_count ; /* debug only. */
+#endif /* NDEBUG */
+
+ /* === Extract knobs ==================================================== */
+
+ /* --------------------- */
+ /* old dense row/column knobs:
+ dense_row_count = MAX (0, MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ;
+ dense_col_count = MAX (0, MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ;
+ */
+ /* new, for UMFPACK: */
+ /* Note: if knobs contains a NaN, this is undefined: */
+ dense_row_count =
+ UMFPACK_DENSE_DEGREE_THRESHOLD (knobs [COLAMD_DENSE_ROW], n_col) ;
+ dense_col_count =
+ UMFPACK_DENSE_DEGREE_THRESHOLD (knobs [COLAMD_DENSE_COL], n_row) ;
+ /* Make sure dense_*_count is between 0 and n: */
+ dense_row_count = MAX (0, MIN (dense_row_count, n_col)) ;
+ dense_col_count = MAX (0, MIN (dense_col_count, n_row)) ;
+ /* --------------------- */
+
+ DEBUG1 (("colamd: densecount: "ID" "ID"\n",
+ dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* --------------------- */
+ /* added for UMFPACK */
+ ndense_col = 0 ;
+ nempty_col = 0 ;
+ nnewlyempty_col = 0 ;
+ ndense_row = 0 ;
+ nempty_row = 0 ;
+ nnewlyempty_row = 0 ;
+ /* --------------------- */
+
+ /* === Kill empty columns =============================================== */
+
+ /* removed for UMFPACK v4.1. prune_singletons has already removed empty
+ * columns and empty rows */
+
+#if 0
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ nempty_col++ ;
+ /* --------------------- */
+ }
+ }
+ DEBUG1 (("colamd: null columns killed: "ID"\n", n_col - n_col2)) ;
+#endif
+
+#ifndef NDEBUG
+ for (c = 0 ; c < n_col ; c++)
+ {
+ ASSERT (Col [c].length > 0) ;
+ }
+#endif
+
+ /* === Count null rows ================================================== */
+
+#if 0
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ if (deg == 0)
+ {
+ /* this is an original empty row */
+ nempty_row++ ;
+ }
+ }
+#endif
+
+#ifndef NDEBUG
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared1.degree > 0) ;
+ ASSERT (Row [r].length > 0) ;
+ }
+#endif
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+
+ /* ----------------------------------------------------------------- */
+#if 0
+ /* removed for UMFPACK v4.1: no empty columns */
+ /* skip any dead columns */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+#endif
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].length > 0) ;
+ /* ----------------------------------------------------------------- */
+
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ ndense_col++ ;
+ /* --------------------- */
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("colamd: Dense and null columns killed: "ID"\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ /* Note that there can now be empty rows, since dense columns have
+ * been deleted. These are "newly" empty rows. */
+
+ ne = 0 ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ ASSERT (deg >= 0 && deg <= n_col) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ if (deg > dense_row_count)
+ {
+ /* There is at least one dense row. Continue ordering, but */
+ /* symbolic factorization will be redone after UMF_colamd is done.*/
+ ndense_row++ ;
+ }
+ if (deg == 0)
+ {
+ /* this is a newly empty row, or original empty row */
+ ne++ ;
+ }
+ /* --------------------- */
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ KILL_ROW (r) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ Row [r].thickness = 0 ;
+ /* --------------------- */
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = MAX (max_deg, deg) ;
+ }
+ }
+ nnewlyempty_row = ne - nempty_row ;
+ DEBUG1 (("colamd: Dense rows killed: "ID"\n", ndense_row)) ;
+ DEBUG1 (("colamd: Dense and null rows killed: "ID"\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial matlab score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = MIN (score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (Int) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ DEBUG2 (("Newly null killed: "ID"\n", c)) ;
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ nnewlyempty_col++ ;
+ /* --------------------- */
+ }
+ else
+ {
+ /* set column length and set score */
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ DEBUG1 (("colamd: Dense, null, and newly-null columns killed: "ID"\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+#ifndef NDEBUG
+ debug_structures (n_row, n_col, Row, Col, A, n_col2) ;
+#endif /* NDEBUG */
+
+ /* === Initialize degree lists ========================================== */
+
+#ifndef NDEBUG
+ debug_count = 0 ;
+#endif /* NDEBUG */
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = EMPTY ;
+ }
+ min_score = n_col ;
+ /* place in reverse order, so low column indices are at the front */
+ /* of the lists. This is to encourage natural tie-breaking */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* only add principal columns to degree lists */
+ if (COL_IS_ALIVE (c))
+ {
+ DEBUG4 (("place "ID" score "ID" minscore "ID" ncol "ID"\n",
+ c, Col [c].shared2.score, min_score, n_col)) ;
+
+ /* === Add columns score to DList =============================== */
+
+ score = Col [c].shared2.score ;
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ ASSERT (head [score] >= EMPTY) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [c].shared3.prev = EMPTY ;
+ Col [c].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = c ;
+ }
+ head [score] = c ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, score) ;
+
+#ifndef NDEBUG
+ debug_count++ ;
+#endif /* NDEBUG */
+
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("colamd: Live cols "ID" out of "ID", non-princ: "ID"\n",
+ debug_count, n_col, n_col-debug_count)) ;
+ ASSERT (debug_count == n_col2) ;
+ debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+
+ /* --------------------- */
+ /* added for UMFPACK */
+ *p_ndense_row = ndense_row ;
+ *p_nempty_row = nempty_row ; /* original empty rows */
+ *p_nnewlyempty_row = nnewlyempty_row ;
+ *p_ndense_col = ndense_col ;
+ *p_nempty_col = nempty_col ; /* original empty cols */
+ *p_nnewlyempty_col = nnewlyempty_col ;
+ /* --------------------- */
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ Order the principal columns of the supercolumn form of the matrix
+ (no supercolumns on input). Uses a minimum approximate column minimum
+ degree ordering method. Not user-callable.
+*/
+
+PRIVATE Int find_ordering /* return the number of garbage collections */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int Alen, /* size of A, 2*nnz + n_col or larger */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ Int n_col2, /* Remaining columns to order */
+ Int max_deg, /* Maximum row degree */
+ Int pfree /* index of first free slot (2*nnz on entry) */
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Int Front_npivcol [ ]
+ , Int Front_nrows [ ]
+ , Int Front_ncols [ ]
+ , Int Front_parent [ ]
+ , Int Front_cols [ ]
+ , Int *p_nfr /* number of fronts */
+ , Int aggressive
+ , Int InFront [ ]
+ /* ------------------ */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int k ; /* current pivot ordering step */
+ Int pivot_col ; /* current pivot column */
+ Int *cp ; /* a column pointer */
+ Int *rp ; /* a row pointer */
+ Int pivot_row ; /* current pivot row */
+ Int *new_cp ; /* modified column pointer */
+ Int *new_rp ; /* modified row pointer */
+ Int pivot_row_start ; /* pointer to start of pivot row */
+ Int pivot_row_degree ; /* number of columns in pivot row */
+ Int pivot_row_length ; /* number of supercolumns in pivot row */
+ Int pivot_col_score ; /* score of pivot column */
+ Int needed_memory ; /* free space needed for pivot row */
+ Int *cp_end ; /* pointer to the end of a column */
+ Int *rp_end ; /* pointer to the end of a row */
+ Int row ; /* a row index */
+ Int col ; /* a column index */
+ Int max_score ; /* maximum possible score */
+ Int cur_score ; /* score of current column */
+ unsigned Int hash ; /* hash value for supernode detection */
+ Int head_column ; /* head of hash bucket */
+ Int first_col ; /* first column in hash bucket */
+ Int tag_mark ; /* marker value for mark array */
+ Int row_mark ; /* Row [row].shared2.mark */
+ Int set_difference ; /* set difference size of row with pivot row */
+ Int min_score ; /* smallest column score */
+ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ Int max_mark ; /* maximum value of tag_mark */
+ Int pivot_col_thickness ; /* number of columns represented by pivot col */
+ Int prev_col ; /* Used by Dlist operations. */
+ Int next_col ; /* Used by Dlist operations. */
+ Int ngarbage ; /* number of garbage collections performed */
+
+#ifndef NDEBUG
+ Int debug_d ; /* debug loop counter */
+ Int debug_step = 0 ; /* debug loop counter */
+#endif /* NDEBUG */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int pivot_row_thickness ; /* number of rows represented by pivot row */
+ Int nfr = 0 ; /* number of fronts */
+ Int child ;
+ /* ------------------ */
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = MAX_MARK (n_col) ; /* defined in umfpack.h */
+ tag_mark = clear_mark (n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ DEBUG1 (("colamd: Ordering, n_col2="ID"\n", n_col2)) ;
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = EMPTY ;
+ }
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
+ {
+
+#ifndef NDEBUG
+ if (debug_step % 100 == 0)
+ {
+ DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
+ }
+ else
+ {
+ DEBUG3 (("\n-----Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
+ }
+ debug_step++ ;
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+
+ /* === Select pivot column, and order it ============================ */
+
+ /* make sure degree list isn't empty */
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (head [min_score] >= EMPTY) ;
+
+#ifndef NDEBUG
+ for (debug_d = 0 ; debug_d < min_score ; debug_d++)
+ {
+ ASSERT (head [debug_d] == EMPTY) ;
+ }
+#endif /* NDEBUG */
+
+ /* get pivot column from head of minimum degree list */
+ while (head [min_score] == EMPTY && min_score < n_col)
+ {
+ min_score++ ;
+ }
+ pivot_col = head [min_score] ;
+ ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = EMPTY ;
+ }
+
+ ASSERT (COL_IS_ALIVE (pivot_col)) ;
+ DEBUG3 (("Pivot col: "ID"\n", pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ k += pivot_col_thickness ;
+ /* ------------------ */
+ ASSERT (pivot_col_thickness > 0) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = MIN (pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out the Row[].shared2.mark array */
+ tag_mark = clear_mark (n_row, Row) ;
+
+#ifndef NDEBUG
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ pivot_row_thickness = 0 ;
+ /* ------------------ */
+
+ /* [ tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ DEBUG4 (("Pivot col pattern %d "ID"\n", ROW_IS_ALIVE(row), row)) ;
+ /* skip if row is dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* sum the thicknesses of all the rows */
+ /* ASSERT (Row [row].thickness > 0) ; */
+ pivot_row_thickness += Row [row].thickness ;
+ /* ------------------ */
+
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && COL_IS_ALIVE (col))
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ /* ------------------ */
+ /* added for UMFPACK: */
+ DEBUG4 (("\t\t\tNew live column in pivot row: "ID"\n",col));
+ /* ------------------ */
+ }
+ /* ------------------ */
+ /* added for UMFPACK */
+#ifndef NDEBUG
+ if (col_thickness < 0 && COL_IS_ALIVE (col))
+ {
+ DEBUG4 (("\t\t\tOld live column in pivot row: "ID"\n",col));
+ }
+#endif
+ /* ------------------ */
+ }
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* pivot_row_thickness is the number of rows in frontal matrix */
+ /* both pivotal rows and nonpivotal rows */
+ /* ------------------ */
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ; /* ] */
+ max_deg = MAX (max_deg, pivot_row_degree) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check2\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+
+ DEBUG2 (("Kill row in pivot col: "ID" alive? %d, front "ID"\n",
+ row, ROW_IS_ALIVE (row), Row [row].front)) ;
+
+ /* added for UMFPACK: */
+ if (ROW_IS_ALIVE (row))
+ {
+ if (Row [row].front != EMPTY)
+ {
+ /* This row represents a frontal matrix. */
+ /* Row [row].front is a child of current front */
+ child = Row [row].front ;
+ Front_parent [child] = nfr ;
+ DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr));
+ }
+ else
+ {
+ /* This is an original row. Keep track of which front
+ * is its parent in the row-merge tree. */
+ InFront [row] = nfr ;
+ DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ;
+ }
+ }
+
+ KILL_ROW (row) ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Row [row].thickness = 0 ;
+ /* ------------------ */
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ DEBUG3 (("Pivotal row is "ID"\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = EMPTY ;
+ ASSERT (pivot_row_length == 0) ;
+ }
+ ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ DEBUG3 (("Pivot row: \n")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ DEBUG3 ((" Col: "ID"\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (cur_score >= EMPTY) ;
+ if (prev_col == EMPTY)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ ASSERT (set_difference >= 0) ;
+ ASSERT (ROW_IS_ALIVE (row)) ;
+
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0 && aggressive)
+ {
+ /* v4.1: do aggressive absorption */
+ DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ;
+
+ if (Row [row].front != EMPTY)
+ {
+ /* Row [row].front is a child of current front. */
+ child = Row [row].front ;
+ Front_parent [child] = nfr ;
+ DEBUG1 (("Front "ID" => front "ID", aggressive\n",
+ child, nfr)) ;
+ }
+ else
+ {
+ /* this is an original row. Keep track of which front
+ * assembles it, for the row-merge tree */
+ InFront [row] = nfr ;
+ DEBUG1 (("Row "ID" => front "ID", aggressive\n",
+ row, nfr)) ;
+ }
+
+ KILL_ROW (row) ;
+
+ /* sum the thicknesses of all the rows */
+ /* ASSERT (Row [row].thickness > 0) ; */
+ pivot_row_thickness += Row [row].thickness ;
+ Row [row].thickness = 0 ;
+
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k-pivot_row_degree, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Add up set differences for each column ======================= */
+
+ DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ DEBUG4 (("Adding set diffs for Col: "ID".\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ ASSERT(row >= 0 && row < n_row) ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ DEBUG4 ((" Row "ID", dead\n", row)) ;
+ /* ------------------ */
+ continue ;
+ }
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ /* ASSERT (row_mark > tag_mark) ; */
+ DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark));
+ ASSERT (row_mark >= tag_mark) ;
+ /* ------------------ */
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = MIN (cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0)
+ {
+ DEBUG4 (("further mass elimination. Col: "ID"\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ KILL_PRINCIPAL_COL (col) ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ pivot_col_thickness += Col [col].shared1.thickness ;
+
+ /* add to column list of front ... */
+#ifndef NDEBUG
+ DEBUG1 (("Mass")) ;
+ dump_super (col, Col, n_col) ;
+#endif
+ Col [Col [col].lastcol].nextcol = Front_cols [nfr] ;
+ Front_cols [nfr] = col ;
+ /* ------------------ */
+
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col));
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ /* NOTE: hash is an unsigned Int to avoid a problem in ANSI C.
+ * The sign of the expression a % b is not defined when a and/or
+ * b are negative. Since hash is unsigned and n_col >= 0,
+ * this problem is avoided. */
+ hash %= n_col + 1 ;
+
+ DEBUG4 ((" Hash = "ID", n_col = "ID".\n", (Int) hash, n_col)) ;
+ ASSERT (((Int) hash) <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (Int) hash ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ detect_super_cols (
+
+#ifndef NDEBUG
+ n_col, Row,
+#endif /* NDEBUG */
+
+ Col, A, head, pivot_row_start, pivot_row_length) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ KILL_PRINCIPAL_COL (pivot_col) ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* add columns to column list of front */
+#ifndef NDEBUG
+ DEBUG1 (("Pivot")) ;
+ dump_super (pivot_col, Col, n_col) ;
+#endif
+ Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ;
+ Front_cols [nfr] = pivot_col ;
+ /* ------------------ */
+
+ /* === Clear mark =================================================== */
+
+ tag_mark += (max_deg + 1) ;
+ if (tag_mark >= max_mark)
+ {
+ DEBUG2 (("clearing tag_mark\n")) ;
+ tag_mark = clear_mark (n_row, Row) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("check3\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ DEBUG3 (("** Finalize scores phase. **\n")) ;
+ DEBUG3 (("pivot_row_degree "ID"\n", pivot_row_degree)) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ DEBUG3 (("Col "ID" \n", col)) ;
+ /* skip dead columns */
+ if (COL_IS_DEAD (col))
+ {
+ DEBUG3 (("dead\n")) ;
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+ DEBUG3 ((" cur_score "ID" ", cur_score)) ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+ DEBUG3 ((" max_score "ID" ", max_score)) ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+ DEBUG3 ((" cur_score "ID" ", cur_score)) ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = MIN (cur_score, max_score) ;
+ ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+ DEBUG3 ((" "ID"\n", cur_score)) ;
+
+ /* === Place column back in degree list ========================= */
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (head [cur_score] >= EMPTY) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = EMPTY ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, cur_score) ;
+
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+#endif /* NDEBUG */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* frontal matrix can have more pivot cols than pivot rows for */
+ /* singular matrices. */
+
+ /* number of candidate pivot columns */
+ Front_npivcol [nfr] = pivot_col_thickness ;
+
+ /* all rows (not just size of contrib. block) */
+ Front_nrows [nfr] = pivot_row_thickness ;
+
+ /* all cols */
+ Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ;
+
+ Front_parent [nfr] = EMPTY ;
+
+ pivot_row_thickness -= pivot_col_thickness ;
+ DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n",
+ nfr, pivot_row_thickness)) ;
+ pivot_row_thickness = MAX (0, pivot_row_thickness) ;
+ /* ------------------ */
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if (pivot_row_degree > 0
+ /* ------------------ */
+ /* added for UMFPACK. Note that this part of the expression should be
+ * removed if this routine is used outside of UMFPACK, for a Cholesky
+ * factorization of (AQ)'(AQ) */
+ && pivot_row_thickness > 0
+ /* ------------------ */
+ )
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ;
+ ASSERT (Row [pivot_row].length > 0) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Row [pivot_row].thickness = pivot_row_thickness ;
+ Row [pivot_row].front = nfr ;
+ /* ------------------ */
+ /* pivot row is no longer dead */
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+
+#ifndef NDEBUG
+ DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr,
+ Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ;
+ DEBUG1 ((" cols:[ ")) ;
+ debug_d = 0 ;
+ for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ DEBUG1 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (COL_IS_DEAD (col)) ;
+ debug_d++ ;
+ ASSERT (debug_d <= pivot_col_thickness) ;
+ }
+ ASSERT (debug_d == pivot_col_thickness) ;
+ DEBUG1 ((" ]\n ")) ;
+#endif
+ nfr++ ; /* one more front */
+ /* ------------------ */
+
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ *p_nfr = nfr ;
+ /* ------------------ */
+
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === order_children deleted for UMFPACK =================================== */
+/* ========================================================================== */
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ Detects supercolumns by finding matches between columns in the hash buckets.
+ Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ The columns under consideration are currently *not* in the degree lists,
+ and have already been placed in the hash buckets.
+
+ The hash bucket for columns whose hash function is equal to h is stored
+ as follows:
+
+ if head [h] is >= 0, then head [h] contains a degree list, so:
+
+ head [h] is the first column in degree bucket h.
+ Col [head [h]].headhash gives the first column in hash bucket h.
+
+ otherwise, the degree list is empty, and:
+
+ -(head [h] + 2) is the first column in hash bucket h.
+
+ For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ column" pointer. Col [c].shared3.hash is used instead as the hash number
+ for that column. The value of Col [c].shared4.hash_next is the next column
+ in the same hash bucket.
+
+ Assuming no, or "few" hash collisions, the time taken by this routine is
+ linear in the sum of the sizes (lengths) of each column whose score has
+ just been computed in the approximate degree computation.
+ Not user-callable.
+*/
+
+PRIVATE void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+#ifndef NDEBUG
+ /* these two parameters are only needed when debugging is enabled: */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+#endif /* NDEBUG */
+
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A */
+ Int head [], /* head of degree lists and hash buckets */
+ Int row_start, /* pointer to set of columns to check */
+ Int row_length /* number of columns to check */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int hash ; /* hash value for a column */
+ Int *rp ; /* pointer to a row */
+ Int c ; /* a column index */
+ Int super_c ; /* column index of the column to absorb into */
+ Int *cp1 ; /* column pointer for column super_c */
+ Int *cp2 ; /* column pointer for column c */
+ Int length ; /* length of column super_c */
+ Int prev_c ; /* column preceding c in hash bucket */
+ Int i ; /* loop counter */
+ Int *rp_end ; /* pointer to the end of the row */
+ Int col ; /* a column index in the row to check */
+ Int head_column ; /* first column in hash bucket or degree list */
+ Int first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != EMPTY ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ ASSERT (COL_IS_ALIVE (super_c)) ;
+ ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != EMPTY ; c = Col [c].shared4.hash_next)
+ {
+ ASSERT (c != super_c) ;
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ ASSERT (ROW_IS_ALIVE (*cp1)) ;
+ ASSERT (ROW_IS_ALIVE (*cp2)) ;
+ /* row indices will same order for both supercols, */
+ /* no gather scatter nessasary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ KILL_NON_PRINCIPAL_COL (c) ;
+
+ Col [c].shared2.order = EMPTY ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* add c to end of list of super_c */
+ ASSERT (Col [super_c].lastcol >= 0) ;
+ ASSERT (Col [super_c].lastcol < n_col) ;
+ Col [Col [super_c].lastcol].nextcol = c ;
+ Col [super_c].lastcol = Col [c].lastcol ;
+#ifndef NDEBUG
+ /* dump the supercolumn */
+ DEBUG1 (("Super")) ;
+ dump_super (super_c, Col, n_col) ;
+#endif
+ /* ------------------ */
+
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > EMPTY)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = EMPTY ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = EMPTY ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ Defragments and compacts columns and rows in the workspace A. Used when
+ all avaliable memory has been used while performing row merging. Returns
+ the index of the first free position in A, after garbage collection. The
+ time taken by this routine is linear is the size of the array A, which is
+ itself linear in the number of nonzeros in the input matrix.
+ Not user-callable.
+*/
+
+PRIVATE Int garbage_collection /* returns the new value of pfree */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows */
+ Int n_col, /* number of columns */
+ Colamd_Row Row [], /* row info */
+ Colamd_Col Col [], /* column info */
+ Int A [], /* A [0 ... Alen-1] holds the matrix */
+ Int *pfree /* &A [0] ... pfree is in use */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *psrc ; /* source pointer */
+ Int *pdest ; /* destination pointer */
+ Int j ; /* counter */
+ Int r ; /* a row index */
+ Int c ; /* a column index */
+ Int length ; /* length of a row or column */
+
+#ifndef NDEBUG
+ Int debug_rows ;
+ DEBUG2 (("Defrag..\n")) ;
+ for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ;
+ debug_rows = 0 ;
+#endif /* NDEBUG */
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ ASSERT (pdest <= psrc) ;
+ Col [c].start = (Int) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (ROW_IS_ALIVE (r))
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (Int) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ if (Row [r].length == 0)
+ {
+ /* :: defrag row kill :: */
+ /* This row is of zero length. cannot compact it, so kill it.
+ * NOTE: in the current version, there are no zero-length live
+ * rows when garbage_collection is called. So this code will
+ * never trigger. However, if the code is modified, or if
+ * garbage_collection is called at a different place, then rows
+ * can be of zero length. So this test is kept, just in case.
+ */
+ DEBUGm4 (("Defrag row kill\n")) ;
+ KILL_ROW (r) ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ONES_COMPLEMENT (r) ;
+#ifndef NDEBUG
+ debug_rows++ ;
+#endif /* NDEBUG */
+ }
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ONES_COMPLEMENT (*psrc) ;
+ ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+
+ /* move and compact the row */
+ ASSERT (pdest <= psrc) ;
+ Row [r].start = (Int) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (Int) (pdest - &A [Row [r].start]) ;
+
+#ifndef NDEBUG
+ debug_rows-- ;
+#endif /* NDEBUG */
+
+ }
+ }
+ /* ensure we found all the rows */
+ ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((Int) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Clears the Row [].shared2.mark array, and returns the new tag_mark.
+ Return value is the new tag_mark. Not user-callable.
+*/
+
+PRIVATE Int clear_mark /* return the new value for tag_mark */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Colamd_Row Row [] /* Row [0 ... n-1].shared2.mark is set to zero */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+
+ /* ------------------ */
+ return (1) ;
+ /* ------------------ */
+
+}
+
+
+/* ========================================================================== */
+/* === print_report removed for UMFPACK ===================================== */
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === colamd debugging routines ============================================ */
+/* ========================================================================== */
+
+/* When debugging is disabled, the remainder of this file is ignored. */
+
+#ifndef NDEBUG
+
+
+/* ========================================================================== */
+/* === debug_structures ===================================================== */
+/* ========================================================================== */
+
+/*
+ At this point, all empty rows and columns are dead. All live columns
+ are "clean" (containing no dead rows) and simplicial (no supercolumns
+ yet). Rows may contain dead columns, but all live rows contain at
+ least one live column.
+*/
+
+PRIVATE void debug_structures
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+ Int c ;
+ Int *cp ;
+ Int *cp_end ;
+ Int len ;
+ Int score ;
+ Int r ;
+ Int *rp ;
+ Int *rp_end ;
+ Int deg ;
+
+ /* === Check A, Row, and Col ============================================ */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ len = Col [c].length ;
+ score = Col [c].shared2.score ;
+ DEBUG4 (("initial live col "ID" "ID" "ID"\n", c, len, score)) ;
+ ASSERT (len > 0) ;
+ ASSERT (score >= 0) ;
+ ASSERT (Col [c].shared1.thickness == 1) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + len ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ }
+ }
+ else
+ {
+ i = Col [c].shared2.order ;
+ ASSERT (i >= n_col2 && i < n_col) ;
+ }
+ }
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ i = 0 ;
+ len = Row [r].length ;
+ deg = Row [r].shared1.degree ;
+ ASSERT (len > 0) ;
+ ASSERT (deg > 0) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + len ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ i++ ;
+ }
+ }
+ ASSERT (i > 0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_deg_lists ====================================================== */
+/* ========================================================================== */
+
+/*
+ Prints the contents of the degree lists. Counts the number of columns
+ in the degree list and compares it to the total it should have. Also
+ checks the row degrees.
+*/
+
+PRIVATE void debug_deg_lists
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+)
+{
+ /* === Local variables ================================================== */
+
+ Int deg ;
+ Int col ;
+ Int have ;
+ Int row ;
+
+ /* === Check the degree lists =========================================== */
+
+ if (n_col > 10000 && UMF_debug <= 0)
+ {
+ return ;
+ }
+ have = 0 ;
+ DEBUG4 (("Degree lists: "ID"\n", min_score)) ;
+ for (deg = 0 ; deg <= n_col ; deg++)
+ {
+ col = head [deg] ;
+ if (col == EMPTY)
+ {
+ continue ;
+ }
+ DEBUG4 ((ID":", deg)) ;
+ while (col != EMPTY)
+ {
+ DEBUG4 ((" "ID, col)) ;
+ have += Col [col].shared1.thickness ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ col = Col [col].shared4.degree_next ;
+ }
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("should "ID" have "ID"\n", should, have)) ;
+ ASSERT (should == have) ;
+
+ /* === Check the row degrees ============================================ */
+
+ if (n_row > 10000 && UMF_debug <= 0)
+ {
+ return ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (ROW_IS_ALIVE (row))
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Ensures that the tag_mark is less that the maximum and also ensures that
+ each entry in the mark array is less than the tag mark.
+*/
+
+PRIVATE void debug_mark
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ /* === Check the Row marks ============================================== */
+
+ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ;
+ if (n_row > 10000 && UMF_debug <= 0)
+ {
+ return ;
+ }
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared2.mark < tag_mark) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_matrix ========================================================= */
+/* ========================================================================== */
+
+/*
+ Prints out the contents of the columns and the rows.
+*/
+
+PRIVATE void debug_matrix
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+ Int c ;
+ Int *rp ;
+ Int *rp_end ;
+ Int *cp ;
+ Int *cp_end ;
+
+ /* === Dump the rows and columns of the matrix ========================== */
+
+ if (UMF_debug < 3)
+ {
+ return ;
+ }
+ DEBUG3 (("DUMP MATRIX:\n")) ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ DEBUG3 (("Row "ID" alive? %d\n", r, ROW_IS_ALIVE (r))) ;
+ if (ROW_IS_DEAD (r))
+ {
+ continue ;
+ }
+
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ DEBUG3 (("start "ID" length "ID" degree "ID" thickness "ID"\n",
+ Row [r].start, Row [r].length, Row [r].shared1.degree,
+ Row [r].thickness)) ;
+ /* ------------------ */
+
+ rp = &A [Row [r].start] ;
+ rp_end = rp + Row [r].length ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ DEBUG4 ((" %d col "ID"\n", COL_IS_ALIVE (c), c)) ;
+ }
+ }
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ DEBUG3 (("Col "ID" alive? %d\n", c, COL_IS_ALIVE (c))) ;
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ DEBUG3 (("start "ID" length "ID" shared1[thickness,parent] "ID
+ " shared2 [order,score] "ID"\n", Col [c].start, Col [c].length,
+ Col [c].shared1.thickness, Col [c].shared2.score));
+ /* ------------------ */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ DEBUG4 ((" %d row "ID"\n", ROW_IS_ALIVE (r), r)) ;
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ DEBUG1 (("Col")) ;
+ dump_super (c, Col, n_col) ;
+ /* ------------------ */
+
+ }
+}
+
+/* ------------------ */
+/* dump_super added for UMFPACK: */
+PRIVATE void dump_super
+(
+ Int super_c,
+ Colamd_Col Col [],
+ Int n_col
+)
+{
+ Int col, ncols ;
+
+ DEBUG1 ((" =[ ")) ;
+ ncols = 0 ;
+ for (col = super_c ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ DEBUG1 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ if (col != super_c)
+ {
+ ASSERT (COL_IS_DEAD (col)) ;
+ }
+ if (Col [col].nextcol == EMPTY)
+ {
+ ASSERT (col == Col [super_c].lastcol) ;
+ }
+ ncols++ ;
+ ASSERT (ncols <= Col [super_c].shared1.thickness) ;
+ }
+ ASSERT (ncols == Col [super_c].shared1.thickness) ;
+ DEBUG1 (("]\n")) ;
+}
+/* ------------------ */
+
+
+#endif /* NDEBUG */
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_colamd.h b/src/C/SuiteSparse/UMFPACK/Source/umf_colamd.h
new file mode 100644
index 0000000..c7d9167
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_colamd.h
@@ -0,0 +1,255 @@
+/* ========================================================================== */
+/* === umf_colamd.h ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+
+Authors:
+
+ The authors of the COLAMD code itself are Stefan I. Larimore and Timothy A.
+ Davis, University of Florida. The algorithm was developed in collaboration
+ with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory.
+
+Date:
+
+ UMFPACK Version: see above.
+ COLAMD Version 2.0 was released on January 31, 2000.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+UMFPACK: Copyright (c) 2003 by Timothy A. Davis. All Rights Reserved.
+
+See the UMFPACK README file for the License for your use of this code.
+
+Availability:
+
+ Both UMFPACK and the original unmodified colamd/symamd library are
+ available at http://www.cise.ufl.edu/research/sparse.
+
+*/
+
+#ifndef COLAMD_H
+#define COLAMD_H
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..2] are currently used. */
+#define COLAMD_KNOBS 20
+
+/* number of output statistics. Only stats [0..8] are currently used. */
+#define COLAMD_STATS 20
+
+/* knobs [0] and stats [0]: dense row knob and output statistic. */
+#define COLAMD_DENSE_ROW 0
+
+/* knobs [1] and stats [1]: dense column knob and output statistic. */
+#define COLAMD_DENSE_COL 1
+
+/* knobs [2]: aggressive absorption option */
+#define COLAMD_AGGRESSIVE 2
+
+/* stats [2]: memory defragmentation count output statistic */
+#define COLAMD_DEFRAG_COUNT 2
+
+/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
+#define COLAMD_STATUS 3
+
+/* stats [4..6]: error info, or info on jumbled columns */
+#define COLAMD_INFO1 4
+#define COLAMD_INFO2 5
+#define COLAMD_INFO3 6
+
+/* ------------------ */
+/* added for UMFPACK: */
+/* stats [7]: number of originally empty rows */
+#define COLAMD_EMPTY_ROW 7
+/* stats [8]: number of originally empty cols */
+#define COLAMD_EMPTY_COL 8
+/* stats [9]: number of rows with entries only in dense cols */
+#define COLAMD_NEWLY_EMPTY_ROW 9
+/* stats [10]: number of cols with entries only in dense rows */
+#define COLAMD_NEWLY_EMPTY_COL 10
+/* ------------------ */
+
+/* error codes returned in stats [3]: */
+#define COLAMD_OK (0)
+#define COLAMD_ERROR_jumbled_matrix (-11)
+#define COLAMD_ERROR_A_not_present (-1)
+#define COLAMD_ERROR_p_not_present (-2)
+#define COLAMD_ERROR_nrow_negative (-3)
+#define COLAMD_ERROR_ncol_negative (-4)
+#define COLAMD_ERROR_nnz_negative (-5)
+#define COLAMD_ERROR_p0_nonzero (-6)
+#define COLAMD_ERROR_A_too_small (-7)
+#define COLAMD_ERROR_col_length_negative (-8)
+#define COLAMD_ERROR_row_index_out_of_bounds (-9)
+#define COLAMD_ERROR_out_of_memory (-10)
+#define COLAMD_ERROR_internal_error (-999)
+
+/* ========================================================================== */
+/* === Row and Column structures ============================================ */
+/* ========================================================================== */
+
+/* User code that makes use of the colamd/symamd routines need not directly */
+/* reference these structures. They are used only for the COLAMD_RECOMMENDED */
+/* macro. */
+
+typedef struct Colamd_Col_struct
+{
+ Int start ; /* index for A of first row in this column, or DEAD */
+ /* if column is dead */
+ Int length ; /* number of rows in this column */
+ union
+ {
+ Int thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ Int parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ Int score ; /* the score used to maintain heap, if col is alive */
+ Int order ; /* pivot ordering of this column, if col is dead */
+ } shared2 ;
+ union
+ {
+ Int headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ Int hash ; /* hash value, if col is not in a degree list */
+ Int prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ Int degree_next ; /* next column, if col is in a degree list */
+ Int hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int nextcol ; /* next column in this supercolumn */
+ Int lastcol ; /* last column in this supercolumn */
+ /* ------------------ */
+
+} Colamd_Col ;
+
+typedef struct Colamd_Row_struct
+{
+ Int start ; /* index for A of first col in this row */
+ Int length ; /* number of principal columns in this row */
+ union
+ {
+ Int degree ; /* number of principal & non-principal columns in row */
+ Int p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ Int mark ; /* for computing set differences and marking dead rows*/
+ Int first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int thickness ; /* number of original rows represented by this row */
+ /* that are not yet pivotal */
+ Int front ; /* -1 if an original row */
+ /* k if this row represents the kth frontal matrix */
+ /* where k goes from 0 to at most n_col-1 */
+ /* ------------------ */
+
+} Colamd_Row ;
+
+
+
+/* ========================================================================== */
+/* === Colamd recommended memory size ======================================= */
+/* ========================================================================== */
+
+/*
+ The recommended length Alen of the array A passed to colamd is given by
+ the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any
+ argument is negative. 2*nnz space is required for the row and column
+ indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is
+ required for the Col and Row arrays, respectively, which are internal to
+ colamd. An additional n_col space is the minimal amount of "elbow room",
+ and nnz/5 more space is recommended for run time efficiency.
+
+ This macro is not needed when using symamd.
+*/
+
+/* about 8*(n_col+1) integers: */
+#define UMF_COLAMD_C(n_col) ((n_col + 1) * sizeof (Colamd_Col) / sizeof (Int))
+
+/* about 6*(n_row+1) integers: */
+#define UMF_COLAMD_R(n_row) ((n_row + 1) * sizeof (Colamd_Row) / sizeof (Int))
+
+/* UMFPACK: make sure Alen is >= 5*n_col + size of Col and Row structures.
+ * Alen is typically about 2.2*nz + 9*n_col + 6*n_row, or 2.2nz+15n for
+ * square matrices. */
+#define UMF_COLAMD_RECOMMENDED(nnz, n_row, n_col) \
+( \
+((nnz) < 0 || (n_row) < 0 || (n_col) < 0) \
+? \
+ (-1) \
+: \
+ (MAX (2 * (nnz), 4 * (n_col)) + \
+ (Int) UMF_COLAMD_C (n_col) + \
+ (Int) UMF_COLAMD_R (n_row) + (n_col) + ((nnz) / 5)) \
+)
+
+/* ========================================================================== */
+/* === Prototypes of user-callable routines ================================= */
+/* ========================================================================== */
+
+/* colamd_recommended removed for UMFPACK */
+
+void UMF_colamd_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */
+) ;
+
+Int UMF_colamd /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* size of the array A */
+ Int A [], /* row indices of A, of size Alen */
+ Int p [], /* column pointers of A, of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */
+ Int stats [COLAMD_STATS] /* colamd output statistics and error codes */
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Int Front_npivcol [ ]
+ , Int Front_nrows [ ]
+ , Int Front_ncols [ ]
+ , Int Front_parent [ ]
+ , Int Front_cols [ ]
+ , Int *p_nfr
+ , Int InFront [ ]
+ /* ------------------ */
+) ;
+
+/* symamd deleted for UMFPACK */
+
+/* colamd_report deleted for UMFPACK */
+
+/* symamd_report deleted for UMFPACK */
+
+#endif /* COLAMD_H */
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_config.h b/src/C/SuiteSparse/UMFPACK/Source/umf_config.h
new file mode 100644
index 0000000..224cf52
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_config.h
@@ -0,0 +1,324 @@
+/* ========================================================================== */
+/* === umf_config.h ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This file controls the compile-time configuration of UMFPACK. Modify the
+ UFconfig/UFconfig.mk file and this file if necessary, to control these
+ options. The following flags may be given as options to your C compiler
+ (as in "cc -DNSUNPERF", for example). These flags are normally placed in
+ your UMFPACK_CONFIG string, defined in the UFconfig/UFconfig.mk file.
+
+ All of these options, except for the timer, are for accessing the BLAS.
+
+ -DNSUNPERF
+
+ Applies only to Sun Solaris. If -DNSUNPERF is set, then the Sun
+ Performance Library BLAS will not be used.
+
+ The Sun Performance Library BLAS is used by default when compiling
+ the C-callable libumfpack.a library on Sun Solaris.
+
+ -DLONGBLAS
+
+ -DNPOSIX
+
+ If -DNPOSIX is set, then your Unix operating system is not POSIX-
+ compliant, and the POSIX routines sysconf ( ) and times ( )
+ routines are not used. These routines provide CPU time and
+ wallclock time information. If -DNPOSIX is set, then the ANSI
+ C clock ( ) routine is used. If -DNPOSIX is not set, then
+ sysconf ( ) and times ( ) are used in umfpack_tic and umfpack_toc.
+ See umfpack_tictoc.c for more information.
+ The default is to use the POSIX routines, except for Windows,
+ which is not POSIX-compliant.
+
+ -DGETRUSAGE
+
+ If -DGETRUSAGE is set, then your system's getrusage ( ) routine
+ will be used for getting the process CPU time. Otherwise the ANSI
+ C clock ( ) routine will be used. The default is to use getrusage
+ ( ) on Unix systems, and to use clock on all other architectures.
+
+ -DNO_TIMER
+
+ If -DNO_TIMER is set, then no timing routines are used at all.
+
+ -DNRECIPROCAL
+
+ This option controls a tradeoff between speed and accuracy. Using
+ -DNRECIPROCAL can lead to more accurate results, but with perhaps
+ some cost in performance, particularly if floating-point division
+ is much more costly than floating-point multiplication.
+
+ This option determines the method used to scale the pivot column.
+ If set, or if the absolute value of the pivot is < 1e-12 (or is a
+ NaN), then the pivot column is divided by the pivot value.
+ Otherwise, the reciprocal of the pivot value is computed, and the
+ pivot column is multiplied by (1/pivot). Multiplying by the
+ reciprocal can be slightly less accurate than dividing by the
+ pivot, but it is often faster. See umf_scale.c.
+
+ This has a small effect on the performance of UMFPACK, at least on
+ a Pentium 4M. It may have a larger effect on other architectures
+ where floating-point division is much more costly than floating-
+ point multiplication. The RS 6000 is one such example.
+
+ By default, the method chosen is to multiply by the reciprocal
+ (sacrificing accuracy for speed), except when compiling UMFPACK
+ as a built-in routine in MATLAB, or when gcc is being used.
+
+ When MATHWORKS is defined, -DNRECIPROCAL is forced on, and the pivot
+ column is divided by the pivot value. The only way of using the
+ other method in this case is to edit this file.
+
+ If -DNRECIPROCAL is enabled, then the row scaling factors are always
+ applied by dividing each row by the scale factor, rather than
+ multiplying by the reciprocal. If -DNRECIPROCAL is not enabled
+ (the default case), then the scale factors are normally applied by
+ multiplying by the reciprocal. If, however, the smallest scale
+ factor is tiny, then the scale factors are applied via division.
+
+ -DNO_DIVIDE_BY_ZERO
+
+ If the pivot is zero, and this flag is set, then no divide-by-zero
+ occurs.
+
+ The following options are controlled by amd_internal.h:
+
+ -DMATLAB_MEX_FILE
+
+ This flag is turned on when compiling the umfpack mexFunction for
+ use in MATLAB. The -DNRECIPROCAL flag is forced on (more accurate,
+ slightly slower). The umfpack mexFunction always returns
+ L*U = P*(R\A)*Q.
+
+ -DMATHWORKS
+
+ This flag is turned on when compiling umfpack as a built-in routine
+ in MATLAB. The -DNRECIPROCAL flag is forced on.
+
+ -DNDEBUG
+
+ Debugging mode (if NDEBUG is not defined). The default, of course,
+ is no debugging. Turning on debugging takes some work (see below).
+ If you do not edit this file, then debugging is turned off anyway,
+ regardless of whether or not -DNDEBUG is specified in your compiler
+ options.
+*/
+
+/* ========================================================================== */
+/* === AMD configuration ==================================================== */
+/* ========================================================================== */
+
+/* NDEBUG, PRINTF defined in amd_internal.h */
+
+/* ========================================================================== */
+/* === reciprocal option ==================================================== */
+/* ========================================================================== */
+
+/* Force the definition NRECIPROCAL when MATHWORKS or MATLAB_MEX_FILE
+ * are defined. Do not multiply by the reciprocal in those cases. */
+
+#ifndef NRECIPROCAL
+#if defined (MATHWORKS) || defined (MATLAB_MEX_FILE)
+#define NRECIPROCAL
+#endif
+#endif
+
+/* ========================================================================== */
+/* === Microsoft Windows configuration ====================================== */
+/* ========================================================================== */
+
+#if defined (UMF_WINDOWS) || defined (UMF_MINGW)
+/* Windows isn't Unix. Profound. */
+#define NPOSIX
+#endif
+
+/* ========================================================================== */
+/* === 0-based or 1-based printing ========================================== */
+/* ========================================================================== */
+
+#if defined (MATLAB_MEX_FILE) && defined (NDEBUG)
+/* In MATLAB, matrices are 1-based to the user, but 0-based internally. */
+/* One is added to all row and column indices when printing matrices */
+/* for the MATLAB user. The +1 shift is turned off when debugging. */
+#define INDEX(i) ((i)+1)
+#else
+/* In ANSI C, matrices are 0-based and indices are reported as such. */
+/* This mode is also used for debug mode, and if MATHWORKS is defined rather */
+/* than MATLAB_MEX_FILE. */
+#define INDEX(i) (i)
+#endif
+
+/* ========================================================================== */
+/* === Timer ================================================================ */
+/* ========================================================================== */
+
+/*
+ If you have the getrusage routine (all Unix systems I've test do), then use
+ that. Otherwise, use the ANSI C clock function. Note that on many
+ systems, the ANSI clock function wraps around after only 2147 seconds, or
+ about 36 minutes. BE CAREFUL: if you compare the run time of UMFPACK with
+ other sparse matrix packages, be sure to use the same timer. See
+ umfpack_tictoc.c for the timer used internally by UMFPACK. See also
+ umfpack_timer.c for the timer used in an earlier version of UMFPACK.
+ That timer is still available as a user-callable routine, but it is no
+ longer used internally by UMFPACK.
+*/
+
+/* Sun Solaris, SGI Irix, Linux, Compaq Alpha, and IBM RS 6000 all have */
+/* getrusage. It's in BSD unix, so perhaps all unix systems have it. */
+#if defined (UMF_SOL2) || defined (UMF_SGI) || defined (UMF_LINUX) \
+|| defined (UMF_ALPHA) || defined (UMF_AIX) || defined (UMF_CYGWIN)
+#define GETRUSAGE
+#endif
+
+
+/* ========================================================================== */
+/* === BLAS ================================================================= */
+/* ========================================================================== */
+
+#include "cholmod_blas.h"
+
+
+/* -------------------------------------------------------------------------- */
+/* DGEMM */
+/* -------------------------------------------------------------------------- */
+
+/* C = C - A*B', where:
+ * A is m-by-k with leading dimension ldac
+ * B is k-by-n with leading dimension ldb
+ * C is m-by-n with leading dimension ldac */
+#ifdef COMPLEX
+#define BLAS_GEMM(m,n,k,A,B,ldb,C,ldac) \
+{ \
+ double alpha [2] = {-1,0}, beta [2] = {1,0} ; \
+ BLAS_zgemm ("N", "T", m, n, k, alpha, (double *) A, ldac, \
+ (double *) B, ldb, beta, (double *) C, ldac) ; \
+}
+#else
+#define BLAS_GEMM(m,n,k,A,B,ldb,C,ldac) \
+{ \
+ double alpha = -1, beta = 1 ; \
+ BLAS_dgemm ("N", "T", m, n, k, &alpha, A, ldac, B, ldb, &beta, C, ldac) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* GER */
+/* -------------------------------------------------------------------------- */
+
+/* A = A - x*y', where:
+ * A is m-by-n with leading dimension d
+ x is a column vector with stride 1
+ y is a column vector with stride 1 */
+#ifdef COMPLEX
+#define BLAS_GER(m,n,x,y,A,d) \
+{ \
+ double alpha [2] = {-1,0} ; \
+ BLAS_zgeru (m, n, alpha, (double *) x, 1, (double *) y, 1, \
+ (double *) A, d) ; \
+}
+#else
+#define BLAS_GER(m,n,x,y,A,d) \
+{ \
+ double alpha = -1 ; \
+ BLAS_dger (m, n, &alpha, x, 1, y, 1, A, d) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* GEMV */
+/* -------------------------------------------------------------------------- */
+
+/* y = y - A*x, where A is m-by-n with leading dimension d,
+ x is a column vector with stride 1
+ y is a column vector with stride 1 */
+#ifdef COMPLEX
+#define BLAS_GEMV(m,n,A,x,y,d) \
+{ \
+ double alpha [2] = {-1,0}, beta [2] = {1,0} ; \
+ BLAS_zgemv ("N", m, n, alpha, (double *) A, d, (double *) x, 1, beta, \
+ (double *) y, 1) ; \
+}
+#else
+#define BLAS_GEMV(m,n,A,x,y,d) \
+{ \
+ double alpha = -1, beta = 1 ; \
+ BLAS_dgemv ("N", m, n, &alpha, A, d, x, 1, &beta, y, 1) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* TRSV */
+/* -------------------------------------------------------------------------- */
+
+/* solve Lx=b, where:
+ * B is a column vector (m-by-1) with leading dimension d
+ * A is m-by-m with leading dimension d */
+#ifdef COMPLEX
+#define BLAS_TRSV(m,A,b,d) \
+{ \
+ BLAS_ztrsv ("L", "N", "U", m, (double *) A, d, (double *) b, 1) ; \
+}
+#else
+#define BLAS_TRSV(m,A,b,d) \
+{ \
+ BLAS_dtrsv ("L", "N", "U", m, A, d, b, 1) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* TRSM */
+/* -------------------------------------------------------------------------- */
+
+/* solve XL'=B where:
+ * B is m-by-n with leading dimension ldb
+ * A is n-by-n with leading dimension lda */
+#ifdef COMPLEX
+#define BLAS_TRSM_RIGHT(m,n,A,lda,B,ldb) \
+{ \
+ double alpha [2] = {1,0} ; \
+ BLAS_ztrsm ("R", "L", "T", "U", m, n, alpha, (double *) A, lda, \
+ (double *) B, ldb) ; \
+}
+#else
+#define BLAS_TRSM_RIGHT(m,n,A,lda,B,ldb) \
+{ \
+ double alpha = 1 ; \
+ BLAS_dtrsm ("R", "L", "T", "U", m, n, &alpha, A, lda, B, ldb) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* SCAL */
+/* -------------------------------------------------------------------------- */
+
+/* x = s*x, where x is a stride-1 vector of length n */
+#ifdef COMPLEX
+#define BLAS_SCAL(n,s,x) \
+{ \
+ double alpha [2] ; \
+ alpha [0] = REAL_COMPONENT (s) ; \
+ alpha [1] = IMAG_COMPONENT (s) ; \
+ BLAS_zscal (n, alpha, (double *) x, 1) ; \
+}
+#else
+#define BLAS_SCAL(n,s,x) \
+{ \
+ double alpha = REAL_COMPONENT (s) ; \
+ BLAS_dscal (n, &alpha, (double *) x, 1) ; \
+}
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_create_element.c b/src/C/SuiteSparse/UMFPACK/Source/umf_create_element.c
new file mode 100644
index 0000000..2588a64
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_create_element.c
@@ -0,0 +1,592 @@
+/* ========================================================================== */
+/* === UMF_create_element =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Factorization of a frontal matrix is complete. Create a new element for
+ later assembly into a subsequent frontal matrix. Returns TRUE if
+ successful, FALSE if out of memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_element.h"
+#include "umf_mem_alloc_tail_block.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_get_memory.h"
+
+/* ========================================================================== */
+/* === copy_column ========================================================== */
+/* ========================================================================== */
+
+PRIVATE void copy_column (Int len, Entry *X, Entry *Y)
+{
+ Int i ;
+#pragma ivdep
+ for (i = 0 ; i < len ; i++)
+ {
+ Y [i] = X [i] ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_create_element =================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_create_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int j, col, row, *Fcols, *Frows, fnrows, fncols, *Cols, len, needunits, t1,
+ t2, size, e, i, *E, *Fcpos, *Frpos, *Rows, eloc, fnr_curr, f,
+ got_memory, *Row_tuples, *Row_degree, *Row_tlen, *Col_tuples, max_mark,
+ *Col_degree, *Col_tlen, nn, n_row, n_col, r2, c2, do_Fcpos ;
+ Entry *C, *Fcol ;
+ Element *ep ;
+ Unit *p, *Memory ;
+ Tuple *tp, *tp1, *tp2, tuple, *tpend ;
+#ifndef NDEBUG
+ DEBUG2 (("FRONTAL WRAPUP\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Work->fnpiv == 0) ;
+ ASSERT (Work->fnzeros == 0) ;
+ Row_degree = Numeric->Rperm ;
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_degree = Numeric->Cperm ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nn = MAX (n_row, n_col) ;
+ Fcols = Work->Fcols ;
+ Frows = Work->Frows ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Memory = Numeric->Memory ;
+ fncols = Work->fncols ;
+ fnrows = Work->fnrows ;
+
+ tp = (Tuple *) NULL ;
+ tp1 = (Tuple *) NULL ;
+ tp2 = (Tuple *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* add the current frontal matrix to the degrees of each column */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Symbolic->fixQ)
+ {
+ /* but only if the column ordering is not fixed */
+#pragma ivdep
+ for (j = 0 ; j < fncols ; j++)
+ {
+ /* add the current frontal matrix to the degree */
+ ASSERT (Fcols [j] >= 0 && Fcols [j] < n_col) ;
+ Col_degree [Fcols [j]] += fnrows ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* add the current frontal matrix to the degrees of each row */
+ /* ---------------------------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ /* add the current frontal matrix to the degree */
+ ASSERT (Frows [i] >= 0 && Frows [i] < n_row) ;
+ Row_degree [Frows [i]] += fncols ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Reset the external degree counters */
+ /* ---------------------------------------------------------------------- */
+
+ E = Work->E ;
+ max_mark = MAX_MARK (nn) ;
+
+ if (!Work->pivcol_in_front)
+ {
+ /* clear the external column degrees. no more Usons of current front */
+ Work->cdeg0 += (nn + 1) ;
+ if (Work->cdeg0 >= max_mark)
+ {
+ /* guard against integer overflow. This is very rare */
+ DEBUG1 (("Integer overflow, cdeg\n")) ;
+ Work->cdeg0 = 1 ;
+#pragma ivdep
+ for (e = 1 ; e <= Work->nel ; e++)
+ {
+ if (E [e])
+ {
+ ep = (Element *) (Memory + E [e]) ;
+ ep->cdeg = 0 ;
+ }
+ }
+ }
+ }
+
+ if (!Work->pivrow_in_front)
+ {
+ /* clear the external row degrees. no more Lsons of current front */
+ Work->rdeg0 += (nn + 1) ;
+ if (Work->rdeg0 >= max_mark)
+ {
+ /* guard against integer overflow. This is very rare */
+ DEBUG1 (("Integer overflow, rdeg\n")) ;
+ Work->rdeg0 = 1 ;
+#pragma ivdep
+ for (e = 1 ; e <= Work->nel ; e++)
+ {
+ if (E [e])
+ {
+ ep = (Element *) (Memory + E [e]) ;
+ ep->rdeg = 0 ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear row/col offsets */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Work->pivrow_in_front)
+ {
+#pragma ivdep
+ for (j = 0 ; j < fncols ; j++)
+ {
+ Fcpos [Fcols [j]] = EMPTY ;
+ }
+ }
+
+ if (!Work->pivcol_in_front)
+ {
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Frpos [Frows [i]] = EMPTY ;
+ }
+ }
+
+ if (fncols <= 0 || fnrows <= 0)
+ {
+ /* no element to create */
+ DEBUG2 (("Element evaporation\n")) ;
+ Work->prior_element = EMPTY ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create element for later assembly */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0)
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage collection (create)\n"));
+ }
+#endif
+
+ needunits = 0 ;
+ got_memory = FALSE ;
+ eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C,
+ &needunits, &ep) ;
+
+ /* if UMF_get_memory needs to be called */
+ if (Work->do_grow)
+ {
+ /* full compaction of current frontal matrix, since UMF_grow_front will
+ * be called next anyway. */
+ r2 = fnrows ;
+ c2 = fncols ;
+ do_Fcpos = FALSE ;
+ }
+ else
+ {
+ /* partial compaction. */
+ r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ c2 = MAX (fncols, Work->fncols_new + 1) ;
+ /* recompute Fcpos if pivot row is in the front */
+ do_Fcpos = Work->pivrow_in_front ;
+ }
+
+ if (!eloc)
+ {
+ /* Do garbage collection, realloc, and try again. */
+ /* Compact the current front if it needs to grow anyway. */
+ /* Note that there are no pivot rows or columns in the current front */
+ DEBUGm3 (("get_memory from umf_create_element, 1\n")) ;
+ if (!UMF_get_memory (Numeric, Work, needunits, r2, c2, do_Fcpos))
+ {
+ /* :: out of memory in umf_create_element (1) :: */
+ DEBUGm4 (("out of memory: create element (1)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ got_memory = TRUE ;
+ Memory = Numeric->Memory ;
+ eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C,
+ &needunits, &ep) ;
+ ASSERT (eloc >= 0) ;
+ if (!eloc)
+ {
+ /* :: out of memory in umf_create_element (2) :: */
+ DEBUGm4 (("out of memory: create element (2)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ }
+
+ e = ++(Work->nel) ; /* get the name of this new frontal matrix */
+ Work->prior_element = e ;
+ DEBUG8 (("wrapup e "ID" nel "ID"\n", e, Work->nel)) ;
+
+ ASSERT (e > 0 && e < Work->elen) ;
+ ASSERT (E [e] == 0) ;
+ E [e] = eloc ;
+
+ if (Work->pivcol_in_front)
+ {
+ /* the new element is a Uson of the next frontal matrix */
+ ep->cdeg = Work->cdeg0 ;
+ }
+
+ if (Work->pivrow_in_front)
+ {
+ /* the new element is an Lson of the next frontal matrix */
+ ep->rdeg = Work->rdeg0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* copy frontal matrix into the new element */
+ /* ---------------------------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Rows [i] = Frows [i] ;
+ }
+#pragma ivdep
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Cols [i] = Fcols [i] ;
+ }
+ Fcol = Work->Fcblock ;
+ DEBUG0 (("copy front "ID" by "ID"\n", fnrows, fncols)) ;
+ fnr_curr = Work->fnr_curr ;
+ ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ copy_column (fnrows, Fcol, C) ;
+ Fcol += fnr_curr ;
+ C += fnrows ;
+ }
+
+ DEBUG8 (("element copied\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* add tuples for the new element */
+ /* ---------------------------------------------------------------------- */
+
+ tuple.e = e ;
+
+ if (got_memory)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* UMF_get_memory ensures enough space exists for each new tuple */
+ /* ------------------------------------------------------------------ */
+
+ /* place (e,f) in the element list of each column */
+ for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++)
+ {
+ col = Fcols [tuple.f] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (Col_tuples [col]) ;
+ tp = ((Tuple *) (Memory + Col_tuples [col])) + Col_tlen [col]++ ;
+ *tp = tuple ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ /* place (e,f) in the element list of each row */
+ for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++)
+ {
+ row = Frows [tuple.f] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Row_tuples [row]) ;
+ tp = ((Tuple *) (Memory + Row_tuples [row])) + Row_tlen [row]++ ;
+ *tp = tuple ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* place (e,f) in the element list of each column */
+ /* ------------------------------------------------------------------ */
+
+ /* might not have enough space for each tuple */
+
+ for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++)
+ {
+ col = Fcols [tuple.f] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ t1 = Col_tuples [col] ;
+ DEBUG1 (("Placing on col:"ID" , tuples at "ID"\n",
+ col, Col_tuples [col])) ;
+
+ size = 0 ;
+ len = 0 ;
+
+ if (t1)
+ {
+ p = Memory + t1 ;
+ tp = (Tuple *) p ;
+ size = GET_BLOCK_SIZE (p) ;
+ len = Col_tlen [col] ;
+ tp2 = tp + len ;
+ }
+
+ needunits = UNITS (Tuple, len + 1) ;
+ DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n",
+ len, size, needunits));
+
+ if (needunits > size && t1)
+ {
+ /* prune the tuples */
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + len ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ ;
+ if (Cols [f] == EMPTY) continue ; /* already assembled */
+ ASSERT (col == Cols [f]) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ len = tp2 - tp1 ;
+ Col_tlen [col] = len ;
+ needunits = UNITS (Tuple, len + 1) ;
+ }
+
+ if (needunits > size)
+ {
+ /* no room exists - reallocate elsewhere */
+ DEBUG1 (("REALLOCATE Col: "ID", size "ID" to "ID"\n",
+ col, size, 2*needunits)) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
+ {
+ double rrr = ((double) (rand ( ))) /
+ (((double) RAND_MAX) + 1) ;
+ DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random gar. (col tuple)\n")) ;
+ }
+#endif
+
+ needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ;
+ t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ;
+ if (!t2)
+ {
+ /* :: get memory in umf_create_element (1) :: */
+ /* get memory, reconstruct all tuple lists, and return */
+ /* Compact the current front if it needs to grow anyway. */
+ /* Note: no pivot rows or columns in the current front */
+ DEBUGm4 (("get_memory from umf_create_element, 1\n")) ;
+ return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+ }
+ Col_tuples [col] = t2 ;
+ tp2 = (Tuple *) (Memory + t2) ;
+ if (t1)
+ {
+ for (i = 0 ; i < len ; i++)
+ {
+ *tp2++ = *tp1++ ;
+ }
+ UMF_mem_free_tail_block (Numeric, t1) ;
+ }
+ }
+
+ /* place the new (e,f) tuple in the element list of the column */
+ Col_tlen [col]++ ;
+ *tp2 = tuple ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* place (e,f) in the element list of each row */
+ /* ------------------------------------------------------------------ */
+
+ for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++)
+ {
+ row = Frows [tuple.f] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ t1 = Row_tuples [row] ;
+ DEBUG1 (("Placing on row:"ID" , tuples at "ID"\n",
+ row, Row_tuples [row])) ;
+
+ size = 0 ;
+ len = 0 ;
+ if (t1)
+ {
+ p = Memory + t1 ;
+ tp = (Tuple *) p ;
+ size = GET_BLOCK_SIZE (p) ;
+ len = Row_tlen [row] ;
+ tp2 = tp + len ;
+ }
+
+ needunits = UNITS (Tuple, len + 1) ;
+ DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n",
+ len, size, needunits)) ;
+
+ if (needunits > size && t1)
+ {
+ /* prune the tuples */
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + len ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e])
+ {
+ continue ; /* element already deallocated */
+ }
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = Cols + (ep->ncols) ;
+ if (Rows [f] == EMPTY) continue ; /* already assembled */
+ ASSERT (row == Rows [f]) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ len = tp2 - tp1 ;
+ Row_tlen [row] = len ;
+ needunits = UNITS (Tuple, len + 1) ;
+ }
+
+ if (needunits > size)
+ {
+ /* no room exists - reallocate elsewhere */
+ DEBUG1 (("REALLOCATE Row: "ID", size "ID" to "ID"\n",
+ row, size, 2*needunits)) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
+ {
+ double rrr = ((double) (rand ( ))) /
+ (((double) RAND_MAX) + 1) ;
+ DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random gar. (row tuple)\n")) ;
+ }
+#endif
+
+ needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ;
+ t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ;
+ if (!t2)
+ {
+ /* :: get memory in umf_create_element (2) :: */
+ /* get memory, reconstruct all tuple lists, and return */
+ /* Compact the current front if it needs to grow anyway. */
+ /* Note: no pivot rows or columns in the current front */
+ DEBUGm4 (("get_memory from umf_create_element, 2\n")) ;
+ return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+ }
+ Row_tuples [row] = t2 ;
+ tp2 = (Tuple *) (Memory + t2) ;
+ if (t1)
+ {
+ for (i = 0 ; i < len ; i++)
+ {
+ *tp2++ = *tp1++ ;
+ }
+ UMF_mem_free_tail_block (Numeric, t1) ;
+ }
+ }
+
+ /* place the new (e,f) tuple in the element list of the row */
+ Row_tlen [row]++ ;
+ *tp2 = tuple ;
+ }
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG1 (("Done extending\nFINAL: element row pattern: len="ID"\n", fncols));
+ for (j = 0 ; j < fncols ; j++) DEBUG1 ((""ID"\n", Fcols [j])) ;
+ DEBUG1 (("FINAL: element col pattern: len="ID"\n", fnrows)) ;
+ for (j = 0 ; j < fnrows ; j++) DEBUG1 ((""ID"\n", Frows [j])) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
+ }
+ for (j = 0 ; j < fnrows ; j++)
+ {
+ row = Frows [j] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+ }
+ if (n_row < 1000 && n_col < 1000)
+ {
+ UMF_dump_memory (Numeric) ;
+ }
+ DEBUG1 (("New element, after filling with stuff: "ID"\n", e)) ;
+ UMF_dump_element (Numeric, Work, e, TRUE) ;
+ if (nn < 1000)
+ {
+ DEBUG4 (("Matrix dump, after New element: "ID"\n", e)) ;
+ UMF_dump_matrix (Numeric, Work, TRUE) ;
+ }
+ DEBUG3 (("FRONTAL WRAPUP DONE\n")) ;
+#endif
+
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_create_element.h b/src/C/SuiteSparse/UMFPACK/Source/umf_create_element.h
new file mode 100644
index 0000000..f2beda6
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_create_element.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_create_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_dump.c b/src/C/SuiteSparse/UMFPACK/Source/umf_dump.c
new file mode 100644
index 0000000..962ad9c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_dump.c
@@ -0,0 +1,1209 @@
+/* ========================================================================== */
+/* === UMF_dump ============================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* These routines, and external variables, are used only when debugging. */
+/* If debugging is disabled (for normal operation) then this entire file */
+/* becomes empty */
+
+#include "umf_internal.h"
+
+#ifndef NDEBUG
+
+/* These global debugging variables and arrays do not exist if debugging */
+/* is disabled at compile time (which is the default). */
+GLOBAL Int UMF_debug = -999 ;
+GLOBAL Int UMF_allocfail = FALSE ;
+GLOBAL double UMF_gprob = -1.0 ;
+
+/* static debugging arrays used only in UMF_dump_rowcol */
+PRIVATE Int UMF_DBflag = 0 ;
+PRIVATE Int UMF_DBpacked [UMF_DBMAX+1] ;
+PRIVATE Int UMF_DBscatter [UMF_DBMAX+1] ;
+
+/* ========================================================================== */
+/* === UMF_DBinit =========================================================== */
+/* ========================================================================== */
+
+/* clear the debugging arrays */
+
+PRIVATE void UMF_DBinit
+(
+ void
+)
+{
+ Int i ;
+
+ /* Int_MAX is defined in umfpack.h */
+ if (UMF_DBflag < 1 || UMF_DBflag == Int_MAX)
+ {
+ /* clear the debugging arrays */
+ UMF_DBflag = 0 ;
+ for (i = 0 ; i <= UMF_DBMAX ; i++)
+ {
+ UMF_DBscatter [i] = 0 ;
+ UMF_DBpacked [i] = 0 ;
+ }
+ }
+
+ UMF_DBflag++ ;
+
+ /* UMF_DBflag > UMF_DBscatter [0...UMF_DBmax] is now true */
+}
+
+/* ========================================================================== */
+/* === UMF_dump_dense ======================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_dense
+(
+ Entry *C,
+ Int dim,
+ Int m,
+ Int n
+)
+{
+
+ /* dump C [1..m,1..n], with column dimenstion dim */
+ Int i, j;
+
+ if (UMF_debug < 7) return ;
+ if (C == (Entry *) NULL)
+ {
+ DEBUG7 (("No dense matrix allocated\n")) ;
+ return ;
+ }
+ DEBUG8 ((" dimension= "ID" rows= "ID" cols= "ID"\n", dim, m, n)) ;
+
+ for (i = 0 ; i < m ; i++)
+ {
+ DEBUG9 ((ID": ", i)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ EDEBUG9 (C [i+j*dim]) ;
+ if (j % 6 == 5) DEBUG9 (("\n ")) ;
+ }
+ DEBUG9 (("\n")) ;
+ }
+
+ for (i = 0 ; i < m ; i++)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ if (IS_ZERO (C [i+j*dim]))
+ {
+ DEBUG8 ((".")) ;
+ }
+ else
+ {
+ DEBUG8 (("X")) ;
+ }
+ }
+ DEBUG8 (("\n")) ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_dump_element ===================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int e,
+ Int clean
+)
+{
+
+ Int i, j, k, *Rows, *Cols, nrows, ncols, *E, row, col,
+ *Row_degree, *Col_degree ;
+ Entry *C ;
+ Element *ep ;
+ Unit *p ;
+
+ if (UMF_debug < 7) return ;
+
+ if (e == 0)
+ {
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ return ;
+ }
+
+ DEBUG7 (("\n====================ELEMENT: "ID" ", e)) ;
+ if (!Numeric || !Work || !Numeric->Memory)
+ {
+ DEBUG7 ((" No Numeric, Work\n")) ;
+ return ;
+ }
+ DEBUG7 ((" nel: "ID" of "ID, e, Work->nel)) ;
+ E = Work->E ;
+ if (!E)
+ {
+ DEBUG7 ((" No elements\n")) ;
+ return ;
+ }
+ if (e < 0 || e > Work->nel)
+ {
+ DEBUG7 (("e out of range!\n")) ;
+ return ;
+ }
+ if (!E [e])
+ {
+ DEBUG7 ((" deallocated\n")) ;
+ return ;
+ }
+ DEBUG7 (("\n")) ;
+ Col_degree = Numeric->Cperm ;
+ Row_degree = Numeric->Rperm ;
+
+ p = Numeric->Memory + E [e] ;
+ DEBUG7 (("ep "ID"\n", (Int) (p-Numeric->Memory))) ;
+ GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, C) ;
+ DEBUG7 (("nrows "ID" nrowsleft "ID"\n", nrows, ep->nrowsleft)) ;
+ DEBUG7 (("ncols "ID" ncolsleft "ID"\n", ncols, ep->ncolsleft)) ;
+ DEBUG7 (("cdeg-cdeg0 "ID" rdeg-rdeg0 "ID" next "ID"\n",
+ ep->cdeg - Work->cdeg0, ep->rdeg - Work->rdeg0, ep->next)) ;
+
+ DEBUG8 (("rows: ")) ;
+ k = 0 ;
+ for (i = 0 ; i < ep->nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ DEBUG8 ((" "ID, row)) ;
+ ASSERT (row < Work->n_row) ;
+ if ((k++ % 10) == 9) DEBUG8 (("\n")) ;
+ ASSERT (IMPLIES (clean, NON_PIVOTAL_ROW (row))) ;
+ }
+ }
+
+ DEBUG8 (("\ncols: ")) ;
+ k = 0 ;
+ for (j = 0 ; j < ep->ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+ DEBUG8 ((" "ID, col)) ;
+ ASSERT (col < Work->n_col) ;
+ if ((k++ % 10) == 9) DEBUG8 (("\n")) ;
+ ASSERT (IMPLIES (clean, NON_PIVOTAL_COL (col))) ;
+ }
+ }
+
+ DEBUG8 (("\nvalues:\n")) ;
+ if (UMF_debug >= 9)
+ {
+ for (i = 0 ; i < ep->nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ DEBUG9 ((ID": ", row)) ;
+ k = 0 ;
+ for (j = 0 ; j < ep->ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+ EDEBUG9 (C [i+j*ep->nrows]) ;
+ if (k++ % 6 == 5) DEBUG9 (("\n ")) ;
+ }
+ }
+ DEBUG9 (("\n")) ;
+ }
+ }
+ }
+
+ DEBUG7 (("====================\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_rowcol ====================================================== */
+/* ========================================================================== */
+
+/* dump a row or a column, from one or more memory spaces */
+/* return exact degree */
+
+GLOBAL void UMF_dump_rowcol
+(
+ Int dumpwhich, /* 0 for row, 1 for column */
+ NumericType *Numeric,
+ WorkType *Work,
+ Int dumpindex, /* row or column index to dump */
+ Int check_degree /* true if degree is to be checked */
+)
+{
+ Entry value ;
+ Entry *C ;
+ Int f, nrows, j, jj, len, e, deg, index, n_row, n_col, *Cols, *Rows, nn,
+ dumpdeg, ncols, preve, *E, tpi, *Pattern, approx_deg, not_in_use ;
+ Tuple *tp, *tend ;
+ Element *ep ;
+ Int *Row_tuples, *Row_degree, *Row_tlen ;
+ Int *Col_tuples, *Col_degree, *Col_tlen ;
+ Unit *p ;
+ Int is_there ;
+
+ /* clear the debugging arrays */
+ UMF_DBinit () ;
+
+ if (dumpwhich == 0)
+ {
+ DEBUG7 (("\n====================ROW: "ID, dumpindex)) ;
+ }
+ else
+ {
+ DEBUG7 (("\n====================COL: "ID, dumpindex)) ;
+ }
+
+ if (dumpindex == EMPTY)
+ {
+ DEBUG7 ((" (EMPTY)\n")) ;
+ return ;
+ }
+
+ deg = 0 ;
+ approx_deg = 0 ;
+
+ if (!Numeric || !Work)
+ {
+ DEBUG7 ((" No Numeric, Work\n")) ;
+ return ;
+ }
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nn = MAX (n_row, n_col) ;
+ E = Work->E ;
+
+ Col_degree = Numeric->Cperm ;
+ Row_degree = Numeric->Rperm ;
+
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+
+ if (!E
+ || !Row_tuples || !Row_degree || !Row_tlen
+ || !Col_tuples || !Col_degree || !Col_tlen)
+ {
+ DEBUG7 ((" No E, Rows, Cols\n")) ;
+ return ;
+ }
+
+ if (dumpwhich == 0)
+ {
+ /* dump a row */
+ ASSERT (dumpindex >= 0 && dumpindex < n_row) ;
+ if (!NON_PIVOTAL_ROW (dumpindex))
+ {
+ DEBUG7 ((" Pivotal\n")) ;
+ return ;
+ }
+ len = Row_tlen [dumpindex] ;
+ dumpdeg = Row_degree [dumpindex] ;
+ tpi = Row_tuples [dumpindex] ;
+ }
+ else
+ {
+ /* dump a column */
+ ASSERT (dumpindex >= 0 && dumpindex < n_col) ;
+ if (!NON_PIVOTAL_COL (dumpindex))
+ {
+ DEBUG7 ((" Pivotal\n")) ;
+ return ;
+ }
+ len = Col_tlen [dumpindex] ;
+ dumpdeg = Col_degree [dumpindex] ;
+ tpi = Col_tuples [dumpindex] ;
+ }
+
+ p = Numeric->Memory + tpi ;
+ tp = (Tuple *) p ;
+ if (!tpi)
+ {
+ DEBUG7 ((" Nonpivotal, No tuple list tuples "ID" tlen "ID"\n",
+ tpi, len)) ;
+ return ;
+ }
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+
+ DEBUG7 ((" degree: "ID" len: "ID"\n", dumpdeg, len)) ;
+ not_in_use = (p-1)->header.size - UNITS (Tuple, len) ;
+ DEBUG7 ((" Tuple list: p+1: "ID" size: "ID" units, "ID" not in use\n",
+ (Int) (p-Numeric->Memory), (p-1)->header.size, not_in_use)) ;
+ ASSERT (not_in_use >= 0) ;
+ tend = tp + len ;
+ preve = 0 ;
+ for ( ; tp < tend ; tp++)
+ {
+ /* row/col of element e, offset is f: */
+ /* DEBUG8 ((" (tp="ID")\n", tp)) ; */
+ e = tp->e ;
+ f = tp->f ;
+ DEBUG8 ((" (e="ID", f="ID")\n", e, f)) ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ /* dump the pattern and values */
+ if (E [e])
+ {
+ p = Numeric->Memory + E [e] ;
+ GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, C) ;
+ if (dumpwhich == 0)
+ {
+ Pattern = Cols ;
+ jj = ep->ncols ;
+ is_there = Rows [f] >= 0 ;
+ if (is_there) approx_deg += ep->ncolsleft ;
+ }
+ else
+ {
+ Pattern = Rows ;
+ jj = ep->nrows ;
+ is_there = Cols [f] >= 0 ;
+ if (is_there) approx_deg += ep->nrowsleft ;
+ }
+ if (!is_there)
+ {
+ DEBUG8 (("\t\tnot present\n")) ;
+ }
+ else
+ {
+ for (j = 0 ; j < jj ; j++)
+ {
+ index = Pattern [j] ;
+ value =
+ C [ (dumpwhich == 0) ? (f+nrows*j) : (j+nrows*f) ] ;
+ if (index >= 0)
+ {
+ DEBUG8 (("\t\t"ID":", index)) ;
+ EDEBUG8 (value) ;
+ DEBUG8 (("\n")) ;
+ if (dumpwhich == 0)
+ {
+ /* col must be in the range 0..n_col-1 */
+ ASSERT (index < n_col) ;
+ }
+ else
+ {
+ /* row must be in the range 0..n_row-1 */
+ ASSERT (index < n_row) ;
+ }
+
+ if (nn <= UMF_DBMAX)
+ {
+ if (UMF_DBscatter [index] != UMF_DBflag)
+ {
+ UMF_DBpacked [deg++] = index ;
+ UMF_DBscatter [index] = UMF_DBflag ;
+ }
+ }
+ }
+ }
+ }
+ /* the (e,f) tuples should be in order of their creation */
+ /* this means that garbage collection will not jumble them */
+ ASSERT (preve < e) ;
+ preve = e ;
+ }
+ else
+ {
+ DEBUG8 (("\t\tdeallocated\n")) ;
+ }
+ }
+
+ if (nn <= UMF_DBMAX)
+ {
+ if (deg > 0)
+ {
+ DEBUG7 ((" Assembled, actual deg: "ID" : ", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ index = UMF_DBpacked [j] ;
+ DEBUG8 ((ID" ", index)) ;
+ if (j % 20 == 19) DEBUG8 (("\n ")) ;
+ ASSERT (UMF_DBscatter [index] == UMF_DBflag) ;
+ }
+ DEBUG7 (("\n")) ;
+ }
+ }
+
+ /* Col_degree is not maintained when fixQ is true */
+ if (check_degree)
+ {
+ DEBUG8 ((" approx_deg "ID" dumpdeg "ID"\n", approx_deg, dumpdeg)) ;
+ ASSERT (approx_deg == dumpdeg) ;
+ }
+
+ DEBUG7 (("====================\n")) ;
+
+ /* deg is now the exact degree */
+ /* if nn <= UMF_DBMAX, then UMF_DBscatter [i] == UMF_DBflag for every i */
+ /* in the row or col, and != UMF_DBflag if not */
+
+ return ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_matrix ====================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_matrix
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check_degree
+)
+{
+
+ Int e, row, col, intfrag, frag, n_row, n_col, *E, fullsize, actualsize ;
+ Element *ep ;
+ Unit *p ;
+
+ DEBUG6 (("=================================================== MATRIX:\n")) ;
+ if (!Numeric || !Work)
+ {
+ DEBUG6 (("No Numeric or Work allocated\n")) ;
+ return ;
+ }
+ if (!Numeric->Memory)
+ {
+ DEBUG6 (("No Numeric->Memory\n")) ;
+ return ;
+ }
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ DEBUG6 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, Work->nz)) ;
+ DEBUG6 (("============================ ELEMENTS: "ID" \n", Work->nel)) ;
+ intfrag = 0 ;
+ E = Work->E ;
+ if (!E)
+ {
+ DEBUG6 (("No elements allocated\n")) ;
+ }
+ else
+ {
+ for (e = 0 ; e <= Work->nel ; e++)
+ {
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+ if (e > 0 && E [e])
+ {
+ p = Numeric->Memory + E [e] ;
+ ep = (Element *) p ;
+ ASSERT (ep->nrowsleft > 0 || ep->ncolsleft > 0) ;
+ fullsize = GET_BLOCK_SIZE (p) ;
+ actualsize = GET_ELEMENT_SIZE (ep->nrowsleft,ep->ncolsleft);
+ frag = fullsize - actualsize ;
+ intfrag += frag ;
+ DEBUG7 (("dump el: "ID", full "ID" actual "ID" frag: "ID
+ " intfrag: "ID"\n", e, fullsize, actualsize, frag,
+ intfrag)) ;
+ }
+ }
+ }
+
+ DEBUG6 (("CURRENT INTERNAL FRAG in elements: "ID" \n", intfrag)) ;
+
+
+
+ DEBUG6 (("======================================== ROWS: "ID"\n", n_row)) ;
+ UMF_debug -= 2 ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ UMF_dump_rowcol (0, Numeric, Work, row, check_degree) ;
+ }
+ UMF_debug += 2 ;
+ DEBUG6 (("======================================== COLS: "ID"\n", n_col)) ;
+ UMF_debug -= 2 ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+ }
+ UMF_debug += 2 ;
+ DEBUG6 (("============================================= END OF MATRIX:\n"));
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_current_front =============================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_current_front
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check
+)
+{
+
+ Entry *Flublock, *Flblock, *Fublock, *Fcblock ;
+ Int fnrows_max, fncols_max, fnrows, fncols, fnpiv, *Frows, *Fcols,
+ i, j, *Fcpos, *Frpos, fnr_curr, fnc_curr, *E ;
+ if (!Work) return ;
+ DEBUG7 (("\n\n========CURRENT FRONTAL MATRIX:\n")) ;
+
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fcblock = Work->Fcblock ;
+
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+ fnrows_max = Work->fnrows_max ;
+ fncols_max = Work->fncols_max ;
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ fnpiv = Work->fnpiv ;
+ E = Work->E ;
+
+ DEBUG6 (("=== fnpiv= "ID"\n", fnpiv)) ;
+ DEBUG6 (("fnrows_max fncols_max "ID" "ID"\n",fnrows_max, fncols_max)) ;
+ DEBUG6 (("fnr_curr fnc_curr "ID" "ID"\n",fnr_curr, fnc_curr)) ;
+ DEBUG6 (("fnrows fncols "ID" "ID"\n",fnrows, fncols)) ;
+ ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ;
+ DEBUG6 (("Pivot row pattern:\n")) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG7 ((ID" "ID" "ID" %d\n", j, Fcols [j], Fcpos [Fcols [j]],
+ j < fncols)) ;
+ if (check)
+ {
+ ASSERT (Fcols [j] >= 0 && Fcols [j] < Work->n_col) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+ }
+ DEBUG6 (("Pivot col pattern:\n")) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG7 ((ID" "ID" "ID" %d\n", i, Frows [i], Frpos [Frows [i]],
+ i < fnrows)) ;
+ if (check)
+ {
+ ASSERT (Frows [i] >= 0 && Frows [i] < Work->n_row) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+ }
+ if (UMF_debug < 7) return ;
+
+ if (!E [0])
+ {
+ DEBUG6 (("current front not allocated\n")) ;
+ ASSERT (!Work->Flublock) ;
+ return ;
+ }
+
+ ASSERT (Work->Flublock == (Entry *) (Numeric->Memory + E [0])) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv) ;
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, Work->nb, fnpiv, fnpiv) ;
+ if (fnpiv > 0)
+ {
+ DEBUG7 (("Pivot entry: ")) ;
+ EDEBUG7 (Flublock [(fnpiv-1)+(fnpiv-1)*Work->nb]) ;
+ DEBUG7 (("\n")) ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_dump_lu ========================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_lu
+(
+ NumericType *Numeric
+)
+{
+ Int i, n_row, n_col, *Cperm, *Rperm ;
+
+ DEBUG6 (("=============================================== LU factors:\n")) ;
+ if (!Numeric)
+ {
+ DEBUG6 (("No LU factors allocated\n")) ;
+ return ;
+ }
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ DEBUG6 (("n_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
+ DEBUG6 (("nLentries: "ID" nUentries: "ID"\n",
+ Numeric->nLentries, Numeric->nUentries)) ;
+
+ if (Numeric->Cperm)
+ {
+ Cperm = Numeric->Cperm ;
+ DEBUG7 (("Column permutations: (new: old)\n")) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ if (Cperm [i] != EMPTY)
+ {
+ DEBUG7 ((ID": "ID"\n", i, Cperm [i])) ;
+ }
+ }
+ }
+ else
+ {
+ DEBUG7 (("No Numeric->Cperm allocatated\n")) ;
+ }
+
+ if (Numeric->Rperm)
+ {
+ Rperm = Numeric->Rperm ;
+ DEBUG7 (("row permutations: (new: old)\n")) ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ if (Rperm [i] != EMPTY)
+ {
+ DEBUG7 ((ID": "ID"\n", i, Rperm [i])) ;
+ }
+ }
+ }
+ else
+ {
+ DEBUG7 (("No Numeric->Rperm allocatated\n")) ;
+ }
+
+ DEBUG6 (("========================================= END OF LU factors:\n"));
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_memory ====================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_memory
+(
+ NumericType *Numeric
+)
+{
+
+ Unit *p ;
+ Int prevsize, s ;
+ Int found ;
+
+ if (!Numeric)
+ {
+ DEBUG6 (("No memory space S allocated\n")) ;
+ return ;
+ }
+
+ DEBUG6 (("\n ============================================== MEMORY:\n")) ;
+ if (!Numeric || !Numeric->Memory)
+ {
+ DEBUG6 (("No memory space Numeric allocated\n")) ;
+ return ;
+ }
+
+ DEBUG6 (("S: "ID"\n", (Int) Numeric)) ;
+ DEBUG6 (("S->ihead : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 (("S->itail : "ID"\n", Numeric->itail)) ;
+ DEBUG6 (("S->size : "ID"\n", Numeric->size)) ;
+ DEBUG6 (("S->ngarbage : "ID"\n", Numeric->ngarbage)) ;
+ DEBUG6 (("S->nrealloc : "ID"\n", Numeric->nrealloc)) ;
+ DEBUG6 ((" in use at head : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 ((" free space : "ID"\n",
+ Numeric->itail - Numeric->ihead)) ;
+ DEBUG6 ((" blocks in use at tail : "ID"\n",
+ Numeric->size - Numeric->itail)) ;
+ DEBUG6 ((" total in use : "ID"\n",
+ Numeric->size - (Numeric->itail - Numeric->ihead))) ;
+
+ prevsize = 0 ;
+ found = FALSE ;
+
+ ASSERT (0 <= Numeric->ihead) ;
+ ASSERT (Numeric->ihead <= Numeric->itail) ;
+ ASSERT (Numeric->itail <= Numeric->size) ;
+
+ p = Numeric->Memory + Numeric->itail ;
+
+ while (p < Numeric->Memory + Numeric->size)
+ {
+ DEBUG8 (("p: "ID" p+1: "ID" prevsize: "ID" size: "ID,
+ (Int) (p-Numeric->Memory), (Int) (p+1-Numeric->Memory),
+ p->header.prevsize, p->header.size)) ;
+ if (p->header.size < 0)
+ {
+ DEBUG8 ((" free")) ;
+ }
+
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ ASSERT (p->header.prevsize == 0) ;
+ }
+ else
+ {
+ ASSERT (p->header.prevsize > 0) ;
+ }
+
+ ASSERT (p->header.size != 0) ;
+ s = prevsize >= 0 ? prevsize : -prevsize ;
+ ASSERT (p->header.prevsize == s) ;
+ /* no adjacent free blocks */
+ ASSERT (p->header.size > 0 || prevsize > 0) ;
+ if (Numeric->ibig != EMPTY)
+ {
+ if (p == Numeric->Memory + Numeric->ibig)
+ {
+ ASSERT (p->header.size < 0) ;
+ DEBUG8 ((" <===== Numeric->ibig")) ;
+ found = TRUE ;
+ }
+ }
+ s = p->header.size ;
+ prevsize = s ;
+ s = s >= 0 ? s : -s ;
+ p = p + 1 + s ;
+ DEBUG8 (("\n")) ;
+ }
+
+ ASSERT (p == Numeric->Memory + Numeric->size) ;
+ ASSERT (IMPLIES (Numeric->ibig != EMPTY, found)) ;
+ DEBUG6 (("============================================= END OF MEMORY:\n"));
+
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_packed_memory =============================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_packed_memory
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ Unit *p, *p3 ;
+ Int prevsize, col, row, *Rows, *Cols, ncols, nrows, k, esize,
+ *Row_tuples, *Row_degree, *Col_tuples, *Col_degree ;
+ Entry *C ;
+ Element *ep ;
+
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Row_tuples = Numeric->Uip ;
+ Col_tuples = Numeric->Lip ;
+
+ DEBUG6 (("============================================ PACKED MEMORY:\n")) ;
+ if (!Numeric || !Numeric->Memory)
+ {
+ DEBUG6 (("No memory space S allocated\n")) ;
+ return ;
+ }
+ DEBUG6 (("S: "ID"\n", (Int) Numeric)) ;
+ DEBUG6 (("S->ihead : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 (("S->itail : "ID"\n", Numeric->itail)) ;
+ DEBUG6 (("S->size : "ID"\n", Numeric->size)) ;
+ DEBUG6 (("S->ngarbage : "ID"\n", Numeric->ngarbage)) ;
+ DEBUG6 (("S->nrealloc : "ID"\n", Numeric->nrealloc)) ;
+ DEBUG6 ((" in use at head : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 ((" free space : "ID"\n",
+ Numeric->itail - Numeric->ihead)) ;
+ DEBUG6 ((" blocks in use at tail : "ID"\n",
+ Numeric->size - Numeric->itail)) ;
+ DEBUG6 ((" total in use : "ID"\n",
+ Numeric->size - (Numeric->itail - Numeric->ihead))) ;
+
+ ASSERT (0 <= Numeric->ihead) ;
+ ASSERT (Numeric->ihead <= Numeric->itail) ;
+ ASSERT (Numeric->itail <= Numeric->size) ;
+
+ for (row = 0 ; row < Work->n_row ; row++)
+ {
+ ASSERT (IMPLIES (NON_PIVOTAL_ROW (row), !Row_tuples [row])) ;
+ }
+ for (col = 0 ; col < Work->n_col ; col++)
+ {
+ ASSERT (IMPLIES (NON_PIVOTAL_COL (col), !Col_tuples [col])) ;
+ }
+
+ prevsize = 0 ;
+ p = Numeric->Memory + Numeric->itail ;
+ while (p < Numeric->Memory + Numeric->size)
+ {
+ DEBUG9 (("====================\n")) ;
+ DEBUG7 (("p: "ID" p+1: "ID" prevsize: "ID" size: "ID"\n",
+ (Int) (p-Numeric->Memory), (Int) (p+1-Numeric->Memory),
+ p->header.prevsize, p->header.size)) ;
+ ASSERT (p->header.size > 0) ;
+
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ ASSERT (p->header.prevsize == 0) ;
+ }
+ else
+ {
+ ASSERT (p->header.prevsize > 0) ;
+ }
+
+ ASSERT (p->header.prevsize == prevsize) ;
+ prevsize = p->header.size ;
+
+ if (p != Numeric->Memory + Numeric->size - 2)
+ {
+
+ p3 = p + 1 ;
+ if (p3 == Numeric->Memory + Work->E [0])
+ {
+ /* this is the current frontal matrix */
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ }
+ else
+ {
+
+ /* this is a packed element */
+ GET_ELEMENT (ep, p3, Cols, Rows, ncols, nrows, C) ;
+ DEBUG9 (("ep "ID"\n nrows "ID" ncols "ID"\n",
+ (Int) ((p+1)-Numeric->Memory), ep->nrows, ep->ncols)) ;
+ DEBUG9 (("rows:")) ;
+ for (k = 0 ; k < ep->nrows; k++)
+ {
+ row = Rows [k] ;
+ DEBUG9 ((" "ID, row)) ;
+ ASSERT (row >= 0 && row <= Work->n_row) ;
+ if ((k % 10) == 9) DEBUG9 (("\n")) ;
+ }
+ DEBUG9 (("\ncols:")) ;
+ for (k = 0 ; k < ep->ncols; k++)
+ {
+ col = Cols [k] ;
+ DEBUG9 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col <= Work->n_col) ;
+ if ((k % 10) == 9) DEBUG9 (("\n")) ;
+ }
+ DEBUG9 (("\nvalues: ")) ;
+ if (UMF_debug >= 9)
+ {
+ UMF_dump_dense (C, ep->nrows, ep->nrows, ep->ncols) ;
+ }
+ esize = GET_ELEMENT_SIZE (ep->nrows, ep->ncols) ;
+ DEBUG9 (("esize: "ID"\n", esize)) ;
+ ASSERT (esize <= p->header.size) ;
+ }
+
+ }
+ else
+ {
+ /* this is the final marker block */
+ ASSERT (p->header.size == 1) ;
+ }
+ p = p + 1 + p->header.size ;
+ }
+
+ ASSERT (Numeric->ibig == EMPTY) ;
+ ASSERT (p == Numeric->Memory + Numeric->size) ;
+ DEBUG6 (("======================================END OF PACKED MEMORY:\n")) ;
+
+}
+
+/* ========================================================================== */
+/* === UMF_dump_col_matrix ================================================== */
+/* ========================================================================== */
+
+/* This code is the same for real or complex matrices. */
+
+GLOBAL void UMF_dump_col_matrix
+(
+ const double Ax [ ], /* Ax [0..nz-1]: real values, in column order */
+#ifdef COMPLEX
+ const double Az [ ], /* Az [0..nz-1]: imag values, in column order */
+#endif
+ const Int Ai [ ], /* Ai [0..nz-1]: row indices, in column order */
+ const Int Ap [ ], /* Ap [0..n_col]: column pointers */
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int nz /* number of entries */
+)
+{
+ Int col, p, p1, p2, row ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+
+ if (!Ai || !Ap) return ;
+ DEBUG6 (("============================================ COLUMN FORM:\n")) ;
+
+ ASSERT (n_col >= 0) ;
+ nz = Ap [n_col] ;
+ DEBUG2 (("UMF_dump_col: nz "ID"\n", nz)) ;
+ DEBUG2 (("n_row "ID" \n", n_row)) ;
+ DEBUG2 (("n_col "ID" \n", n_col)) ;
+
+ DEBUG6 ((" n_row = "ID", n_col ="ID" nz = "ID" Ap [0] "ID", Ap [n] "ID"\n",
+ n_row, n_col, nz, Ap [0], Ap [n_col])) ;
+ ASSERT (Ap [0] == 0) ;
+ ASSERT (Ap [n_col] == nz) ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p1 = Ap [col] ;
+ p2 = Ap [col+1] ;
+ DEBUG6 (("col: "ID", length "ID"\n", col, p2 - p1)) ;
+ ASSERT (p2 >= p1) ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ DEBUG6 (("\t"ID" ", row)) ;
+ if (Ax != (double *) NULL)
+ {
+#ifdef COMPLEX
+ if (split)
+ {
+ DEBUG6 ((" (%e+%ei) ", Ax [p], Az [p])) ;
+ }
+ else
+ {
+ DEBUG6 ((" (%e+%ei) ", Ax [2*p], Ax [2*p+1])) ;
+ }
+#else
+ DEBUG6 ((" %e", Ax [p])) ;
+#endif
+ }
+ DEBUG6 (("\n")) ;
+ }
+ }
+ DEBUG6 (("========================================== COLUMN FORM done\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_chain ======================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_chain
+(
+ Int frontid,
+ Int Front_parent [ ],
+ Int Front_npivcol [ ],
+ Int Front_nrows [ ],
+ Int Front_ncols [ ],
+ Int nfr
+)
+{
+ Int i, len = 0 ;
+
+ /* print a list of contiguous parents */
+ i = frontid ;
+ ASSERT (Front_parent [i] == EMPTY ||
+ (Front_parent [i] > i && Front_parent [i] < nfr)) ;
+
+ len++ ;
+ DEBUG3 (("Chain:\n "ID" ["ID","ID"]("ID"-by-"ID")\n", i,
+ Front_npivcol [i],
+ MIN (Front_npivcol [i], Front_nrows [i]),
+ Front_nrows [i],
+ Front_ncols [i])) ;
+
+ for (i = frontid ; i < nfr ; i++)
+ {
+ ASSERT (Front_parent [i] == EMPTY ||
+ (Front_parent [i] > i && Front_parent [i] < nfr)) ;
+ if (Front_parent [i] == i+1)
+ {
+ len++ ;
+ DEBUG3 (("\t"ID" ["ID","ID"]("ID"-by-"ID")\n", i+1,
+ Front_npivcol [i+1],
+ MIN (Front_npivcol [i+1], Front_nrows [i+1]),
+ Front_nrows [i+1],
+ Front_ncols [i+1])) ;
+ }
+ else
+ {
+ DEBUG2 (("Length of chain: "ID"\n", len)) ;
+ return ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_start ======================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_start
+(
+ void
+)
+{
+ FILE *ff ;
+
+ AMD_debug_init ("from umfpack") ;
+
+ /* get the debug print level from the "debug.umf" file, if it exists */
+ UMF_debug = -999 ;
+ ff = fopen ("debug.umf", "r") ;
+ if (ff)
+ {
+ (void) fscanf (ff, ID, &UMF_debug) ;
+ (void) fclose (ff) ;
+ }
+
+ DEBUG0 (("umfpack: debug version (SLOW!) ")) ;
+
+ DEBUG0 ((" MATLAB: ")) ;
+#ifdef MATLAB_MEX_FILE
+ DEBUG0 (("mexFunction.\n")) ;
+#else
+#ifdef MATHWORKS
+ DEBUG0 (("yes.\n")) ;
+#else
+ DEBUG0 (("no.\n")) ;
+#endif
+#endif
+
+ UMF_gprob = -1.0 ;
+ ff = fopen ("gprob.umf", "r") ;
+ if (ff)
+ {
+ (void) fscanf (ff, "%lg", &UMF_gprob) ;
+ (void) fclose (ff) ;
+ srand (1) ; /* restart the random number generator */
+ }
+
+ if (UMF_gprob > 1.0) UMF_gprob = 1.0 ;
+ DEBUG1 (("factor: UMF_gprob: %e UMF_debug "ID"\n", UMF_gprob, UMF_debug)) ;
+
+ DEBUG2 (("sizeof: (bytes / int / Units) \n")) ;
+ DEBUG2 (("sizeof (Int) %u %u %u\n",
+ sizeof (Int), sizeof (Int) / sizeof (int), UNITS (Int, 1) )) ;
+ DEBUG2 (("sizeof (int) %u %u %u\n",
+ sizeof (int), sizeof (int) / sizeof (int), UNITS (int, 1) )) ;
+ DEBUG2 (("sizeof (size_t) %u %u %u\n",
+ sizeof (size_t), sizeof (size_t) / sizeof (size_t), UNITS (size_t, 1) )) ;
+ DEBUG2 (("sizeof (UF_long) %u %u %u\n",
+ sizeof (UF_long), sizeof (UF_long) / sizeof (UF_long), UNITS (UF_long, 1)));
+ DEBUG2 (("sizeof (double) %u %u %u\n",
+ sizeof (double), sizeof (double) / sizeof (int), UNITS (double, 1) )) ;
+ DEBUG2 (("sizeof (Unit) %u %u %u\n",
+ sizeof (Unit), sizeof (Unit) / sizeof (int), UNITS (Unit, 1) )) ;
+ DEBUG2 (("sizeof (Entry) %u %u %u\n",
+ sizeof (Entry), sizeof (Entry) / sizeof (int), UNITS (Entry, 1) )) ;
+ DEBUG2 (("sizeof (Tuple) %u %u %u\n",
+ sizeof (Tuple), sizeof (Tuple) / sizeof (int), UNITS (Tuple, 1) )) ;
+ DEBUG2 (("sizeof (Tuple *) %u %u %u\n",
+ sizeof (Tuple *), sizeof (Tuple *) / sizeof (int), UNITS (Tuple *, 1) )) ;
+ DEBUG2 (("sizeof (Element) %u %u %u\n",
+ sizeof (Element), sizeof (Element) / sizeof (int), UNITS (Element, 1) )) ;
+ DEBUG2 (("sizeof (Element *) %u %u %u\n",
+ sizeof (Element *), sizeof (Element *) / sizeof (int),
+ UNITS (Element *, 1) )) ;
+ DEBUG2 (("sizeof (WorkType) %u %u %u\n",
+ sizeof (WorkType), sizeof (WorkType) / sizeof (int),
+ UNITS (WorkType, 1) )) ;
+ DEBUG2 (("sizeof (NumericType) %u %u %u\n",
+ sizeof (NumericType), sizeof (NumericType) / sizeof (int),
+ UNITS (NumericType, 1) )) ;
+ DEBUG2 (("sizeof (SymbolicType) %u %u %u\n",
+ sizeof (SymbolicType), sizeof (SymbolicType) / sizeof (int),
+ UNITS (SymbolicType, 1) )) ;
+
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_rowmerge ==================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_rowmerge
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+)
+{
+ Int *Front_leftmostdesc, *Front_1strow, *Front_new1strow, row1, row2,
+ fleftmost, nfr, n_row, *Row_degree, i, frontid, row ;
+
+ nfr = Symbolic->nfr ;
+ DEBUG3 (("\n================== Row merge sets: nfr "ID"\n", nfr)) ;
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_new1strow = Work->Front_new1strow ;
+ n_row = Symbolic->n_row ;
+ Row_degree = Numeric->Rperm ;
+ frontid = Work->frontid ;
+
+ for (i = frontid ; i <= nfr ; i++)
+ {
+ DEBUG3 (("----------------------\n")) ;
+ if (i == nfr) DEBUG3 (("Dummy: ")) ;
+ DEBUG3 (("Front "ID" 1strow "ID" new1strow "ID" leftmostdesc "ID,
+ i, Front_1strow [i], Front_new1strow [i], Front_leftmostdesc [i])) ;
+ DEBUG3 ((" parent "ID" pivcol "ID"\n", Symbolic->Front_parent [i],
+ Symbolic->Front_npivcol [i])) ;
+
+ if (i == nfr)
+ {
+ fleftmost = -1 ;
+ row1 = Front_new1strow [i] ;
+ row2 = n_row-1 ;
+ }
+ else
+ {
+ fleftmost = Front_leftmostdesc [i] ;
+ row1 = Front_new1strow [fleftmost] ;
+ row2 = Front_1strow [i+1] - 1 ;
+ }
+ DEBUG3 (("Leftmost: "ID" Rows ["ID" to "ID"], search ["ID" to "ID"]\n",
+ fleftmost, Front_1strow [i], row2, row1, row2)) ;
+
+ for (row = row1 ; row <= row2 ; row++)
+ {
+ ASSERT (row >= 0 && row < n_row) ;
+ DEBUG3 ((" Row "ID" live: %d\n", row, NON_PIVOTAL_ROW (row))) ;
+ }
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_dump_diagonal_map ================================================ */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_diagonal_map
+(
+ Int Diagonal_map [ ],
+ Int Diagonal_imap [ ],
+ Int n1,
+ Int nn,
+ Int nempty
+)
+{
+ Int row, col ;
+ if (Diagonal_map != (Int *) NULL)
+ {
+ DEBUG2 (("\nDump the Diagonal_map: n1 "ID" nn "ID" nempty "ID"\n",
+ n1, nn, nempty)) ;
+ for (col = n1 ; col < nn - nempty ; col++)
+ {
+ row = Diagonal_map [col] ;
+ DEBUG2 ((" Diagonal_map [col = "ID"] gives "ID": ",
+ col, row)) ;
+ row = UNFLIP (row) ;
+ DEBUG2 ((" row "ID"\n", row)) ;
+ ASSERT (Diagonal_imap [row] == col) ;
+ }
+ }
+}
+
+#endif /* NDEBUG */
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_dump.h b/src/C/SuiteSparse/UMFPACK/Source/umf_dump.h
new file mode 100644
index 0000000..2e0e512
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_dump.h
@@ -0,0 +1,191 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* umf_dump.h: debugging definitions. */
+
+#ifndef NDEBUG
+
+GLOBAL void UMF_dump_dense
+(
+ Entry *C,
+ Int dim,
+ Int m,
+ Int n
+) ;
+
+GLOBAL void UMF_dump_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int e,
+ Int clean
+) ;
+
+GLOBAL void UMF_dump_rowcol
+(
+ Int dump_which,
+ NumericType *Numeric,
+ WorkType *Work,
+ Int dump_index,
+ Int check_degree
+) ;
+
+GLOBAL void UMF_dump_matrix
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check_degree
+) ;
+
+GLOBAL void UMF_dump_current_front
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check
+) ;
+
+GLOBAL void UMF_dump_lu
+(
+ NumericType *Numeric
+) ;
+
+GLOBAL void UMF_dump_memory
+(
+ NumericType *Numeric
+) ;
+
+GLOBAL void UMF_dump_packed_memory
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
+
+GLOBAL void UMF_dump_col_matrix
+(
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ const Int Ai [ ],
+ const Int Ap [ ],
+ Int n_row,
+ Int n_col,
+ Int nz
+) ;
+
+GLOBAL void UMF_dump_chain
+(
+ Int frontid,
+ Int Front_parent [ ],
+ Int Front_npivcol [ ],
+ Int Front_nrows [ ],
+ Int Front_ncols [ ],
+ Int nfr
+) ;
+
+GLOBAL void UMF_dump_rowmerge
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+) ;
+
+GLOBAL void UMF_dump_start
+(
+ void
+) ;
+
+
+GLOBAL void UMF_dump_diagonal_map
+(
+ Int Diagonal_map [ ],
+ Int Diagonal_imap [ ],
+ Int n1,
+ Int nn,
+ Int nempty
+) ;
+
+#define UMF_DBMAX 50000
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+GLOBAL EXTERN Int UMF_debug ;
+GLOBAL EXTERN Int UMF_allocfail ;
+GLOBAL EXTERN double UMF_gprob ;
+
+#define DEBUGk(k,params) { if (UMF_debug >= (k)) { PRINTF (params) ; } }
+
+#define DEBUGm4(params) DEBUGk (-4, params)
+#define DEBUGm3(params) DEBUGk (-3, params)
+#define DEBUGm2(params) DEBUGk (-2, params)
+#define DEBUGm1(params) DEBUGk (-1, params)
+#define DEBUG0(params) DEBUGk (0, params)
+#define DEBUG1(params) DEBUGk (1, params)
+#define DEBUG2(params) DEBUGk (2, params)
+#define DEBUG3(params) DEBUGk (3, params)
+#define DEBUG4(params) DEBUGk (4, params)
+#define DEBUG5(params) DEBUGk (5, params)
+#define DEBUG6(params) DEBUGk (6, params)
+#define DEBUG7(params) DEBUGk (7, params)
+#define DEBUG8(params) DEBUGk (8, params)
+#define DEBUG9(params) DEBUGk (9, params)
+
+#define EDEBUGk(k,a) { if (UMF_debug >= (k)) { PRINT_ENTRY (a) ; } }
+
+#define EDEBUG0(a) EDEBUGk (0, a)
+#define EDEBUG1(a) EDEBUGk (1, a)
+#define EDEBUG2(a) EDEBUGk (2, a)
+#define EDEBUG3(a) EDEBUGk (3, a)
+#define EDEBUG4(a) EDEBUGk (4, a)
+#define EDEBUG5(a) EDEBUGk (5, a)
+#define EDEBUG6(a) EDEBUGk (6, a)
+#define EDEBUG7(a) EDEBUGk (7, a)
+#define EDEBUG8(a) EDEBUGk (8, a)
+#define EDEBUG9(a) EDEBUGk (9, a)
+
+/* ASSERT defined in amd_dump.h */
+
+#else
+
+/* ========================================================================== */
+/* === No debugging ========================================================= */
+/* ========================================================================== */
+
+/* turn off all debugging macros */
+
+#define DEBUGk(k,params)
+
+#define DEBUGm4(params)
+#define DEBUGm3(params)
+#define DEBUGm2(params)
+#define DEBUGm1(params)
+#define DEBUG0(params)
+#define DEBUG1(params)
+#define DEBUG2(params)
+#define DEBUG3(params)
+#define DEBUG4(params)
+#define DEBUG5(params)
+#define DEBUG6(params)
+#define DEBUG7(params)
+#define DEBUG8(params)
+#define DEBUG9(params)
+
+#define EDEBUGk(k,a)
+
+#define EDEBUG0(a)
+#define EDEBUG1(a)
+#define EDEBUG2(a)
+#define EDEBUG3(a)
+#define EDEBUG4(a)
+#define EDEBUG5(a)
+#define EDEBUG6(a)
+#define EDEBUG7(a)
+#define EDEBUG8(a)
+#define EDEBUG9(a)
+
+#endif /* NDEBUG */
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_extend_front.c b/src/C/SuiteSparse/UMFPACK/Source/umf_extend_front.c
new file mode 100644
index 0000000..ee17d7f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_extend_front.c
@@ -0,0 +1,392 @@
+/* ========================================================================== */
+/* === UMF_extend_front ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Called by kernel. */
+
+#include "umf_internal.h"
+#include "umf_grow_front.h"
+
+/* ========================================================================== */
+/* === zero_front =========================================================== */
+/* ========================================================================== */
+
+PRIVATE void zero_front (
+ Entry *Flblock, Entry *Fublock, Entry *Fcblock,
+ Int fnrows, Int fncols, Int fnr_curr, Int fnc_curr,
+ Int fnpiv, Int fnrows_extended, Int fncols_extended)
+{
+ Int j, i ;
+ Entry *F, *Fj, *Fi ;
+
+ Fj = Fcblock + fnrows ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ /* zero the new rows in the contribution block: */
+ F = Fj ;
+ Fj += fnr_curr ;
+#pragma ivdep
+ for (i = fnrows ; i < fnrows_extended ; i++)
+ {
+ /* CLEAR (Fcblock [i + j*fnr_curr]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+ Fj -= fnrows ;
+ for (j = fncols ; j < fncols_extended ; j++)
+ {
+ /* zero the new columns in the contribution block: */
+ F = Fj ;
+ Fj += fnr_curr ;
+#pragma ivdep
+ for (i = 0 ; i < fnrows_extended ; i++)
+ {
+ /* CLEAR (Fcblock [i + j*fnr_curr]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+ Fj = Flblock + fnrows ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ /* zero the new rows in L block: */
+ F = Fj ;
+ Fj += fnr_curr ;
+#pragma ivdep
+ for (i = fnrows ; i < fnrows_extended ; i++)
+ {
+ /* CLEAR (Flblock [i + j*fnr_curr]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+ Fi = Fublock + fncols ;
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ /* zero the new columns in U block: */
+ F = Fi ;
+ Fi += fnc_curr ;
+#pragma ivdep
+ for (j = fncols ; j < fncols_extended ; j++)
+ {
+ /* CLEAR (Fublock [i*fnc_curr + j]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+}
+
+/* ========================================================================== */
+/* === UMF_extend_front ===================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_extend_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int j, i, *Frows, row, col, *Wrow, fnr2, fnc2, *Frpos, *Fcpos, *Fcols,
+ fnrows_extended, rrdeg, ccdeg, fncols_extended, fnr_curr, fnc_curr,
+ fnrows, fncols, pos, fnpiv, *Wm ;
+ Entry *Wx, *Wy, *Fu, *Fl ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get current frontal matrix and check for frontal growth */
+ /* ---------------------------------------------------------------------- */
+
+ fnpiv = Work->fnpiv ;
+
+#ifndef NDEBUG
+ DEBUG2 (("EXTEND FRONT\n")) ;
+ DEBUG2 (("Work->fnpiv "ID"\n", fnpiv)) ;
+ ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ;
+ ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ;
+ ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, Work->fnr_curr, Work->fnrows, Work->fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, Work->fnr_curr, Work->fnrows, fnpiv);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, Work->fnc_curr, Work->fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, Work->nb, fnpiv, fnpiv) ;
+#endif
+
+ if (Work->do_grow)
+ {
+ fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ;
+ fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ;
+ if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, 1))
+ {
+ DEBUGm4 (("out of memory: extend front\n")) ;
+ return (FALSE) ;
+ }
+ }
+
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ ASSERT (Work->fnrows_new + 1 <= fnr_curr) ;
+ ASSERT (Work->fncols_new + 1 <= fnc_curr) ;
+ ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Frows = Work->Frows ;
+ Frpos = Work->Frpos ;
+ Fcols = Work->Fcols ;
+ Fcpos = Work->Fcpos ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ rrdeg = Work->rrdeg ;
+ ccdeg = Work->ccdeg ;
+
+ /* scan starts at the first new column in Fcols */
+ /* also scan the pivot column if it was not in the front */
+ Work->fscan_col = fncols ;
+ Work->NewCols = Fcols ;
+
+ /* scan1 starts at the first new row in Frows */
+ /* also scan the pivot row if it was not in the front */
+ Work->fscan_row = fnrows ;
+ Work->NewRows = Frows ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extend row pattern of the front with the new pivot column */
+ /* ---------------------------------------------------------------------- */
+
+ fnrows_extended = fnrows ;
+ fncols_extended = fncols ;
+
+#ifndef NDEBUG
+ DEBUG2 (("Pivot col, before extension: "ID"\n", fnrows)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG2 ((" "ID": row "ID"\n", i, Frows [i])) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+ DEBUG2 (("Extending pivot column: pivcol_in_front: "ID"\n",
+ Work->pivcol_in_front)) ;
+#endif
+
+ Fl = Work->Flblock + fnpiv * fnr_curr ;
+
+ if (Work->pivcol_in_front)
+ {
+ /* extended pattern and position already in Frows, Frpos. Values above
+ * the diagonal are already in LU block. Values on and below the
+ * diagonal are in Wy [0 .. fnrows_extended-1]. Copy into the L
+ * block. */
+ fnrows_extended += ccdeg ;
+ Wy = Work->Wy ;
+
+ for (i = 0 ; i < fnrows_extended ; i++)
+ {
+ Fl [i] = Wy [i] ;
+#ifndef NDEBUG
+ row = Frows [i] ;
+ DEBUG2 ((" "ID": row "ID" ", i, row)) ;
+ EDEBUG2 (Fl [i]) ;
+ if (row == Work->pivrow) DEBUG2 ((" <- pivrow")) ;
+ DEBUG2 (("\n")) ;
+ if (i == fnrows - 1) DEBUG2 ((" :::::::\n")) ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+ ASSERT (Frpos [row] == i) ;
+#endif
+ }
+
+ }
+ else
+ {
+ /* extended pattern,values is in (Wm,Wx), not yet in the front */
+ Entry *F ;
+ Fu = Work->Flublock + fnpiv * Work->nb ;
+ Wm = Work->Wm ;
+ Wx = Work->Wx ;
+ F = Fu ;
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ F = Fl ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ for (i = 0 ; i < ccdeg ; i++)
+ {
+ row = Wm [i] ;
+#ifndef NDEBUG
+ DEBUG2 ((" "ID": row "ID" (ext) ", fnrows_extended, row)) ;
+ EDEBUG2 (Wx [i]) ;
+ if (row == Work->pivrow) DEBUG2 ((" <- pivrow")) ;
+ DEBUG2 (("\n")) ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+#endif
+ pos = Frpos [row] ;
+ if (pos < 0)
+ {
+ pos = fnrows_extended++ ;
+ Frows [pos] = row ;
+ Frpos [row] = pos ;
+ }
+ Fl [pos] = Wx [i] ;
+ }
+ }
+
+ ASSERT (fnrows_extended <= fnr_curr) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extend the column pattern of the front with the new pivot row */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG6 (("Pivot row, before extension: "ID"\n", fncols)) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG7 ((" "ID": col "ID"\n", j, Fcols [j])) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+ DEBUG6 (("Extending pivot row:\n")) ;
+#endif
+
+ if (Work->pivrow_in_front)
+ {
+ if (Work->pivcol_in_front)
+ {
+ ASSERT (Fcols == Work->Wrow) ;
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+#ifndef NDEBUG
+ col = Fcols [j] ;
+ DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ;
+ ASSERT (col != Work->pivcol) ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] < 0) ;
+#endif
+ Fcpos [Fcols [j]] = j * fnr_curr ;
+ }
+ }
+ else
+ {
+ /* OUT-IN option: pivcol not in front, but pivrow is in front */
+ Wrow = Work->Wrow ;
+ ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ;
+ if (Wrow == Fcols)
+ {
+ /* Wrow and Fcols are equivalenced */
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ;
+ ASSERT (Fcpos [col] < 0) ;
+ /* Fcols [j] = col ; not needed */
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ else
+ {
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ;
+ ASSERT (Fcpos [col] < 0) ;
+ Fcols [j] = col ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ }
+ fncols_extended = rrdeg ;
+ }
+ else
+ {
+ ASSERT (Fcols != Work->Wrow) ;
+ Wrow = Work->Wrow ;
+ for (j = 0 ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ if (Fcpos [col] < 0)
+ {
+ DEBUG2 ((" col:: "ID" (ext)\n", col)) ;
+ Fcols [fncols_extended] = col ;
+ Fcpos [col] = fncols_extended * fnr_curr ;
+ fncols_extended++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* pivot row and column have been extended */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ ASSERT (fncols_extended <= fnc_curr) ;
+ ASSERT (fnrows_extended <= fnr_curr) ;
+
+ DEBUG6 (("Pivot col, after ext: "ID" "ID"\n", fnrows,fnrows_extended)) ;
+ for (i = 0 ; i < fnrows_extended ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG7 ((" "ID": row "ID" pos "ID" old: %d", i, row, Frpos [row],
+ i < fnrows)) ;
+ if (row == Work->pivrow ) DEBUG7 ((" <-- pivrow")) ;
+ DEBUG7 (("\n")) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+
+ DEBUG6 (("Pivot row position: "ID"\n", Frpos [Work->pivrow])) ;
+ ASSERT (Frpos [Work->pivrow] >= 0) ;
+ ASSERT (Frpos [Work->pivrow] < fnrows_extended) ;
+
+ DEBUG6 (("Pivot row, after ext: "ID" "ID"\n", fncols,fncols_extended)) ;
+ for (j = 0 ; j < fncols_extended ; j++)
+ {
+ col = Fcols [j] ;
+ DEBUG7 ((" "ID": col "ID" pos "ID" old: %d", j, col, Fcpos [col],
+ j < fncols)) ;
+ if (col == Work->pivcol ) DEBUG7 ((" <-- pivcol")) ;
+ DEBUG7 (("\n")) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+
+ DEBUG6 (("Pivot col position: "ID"\n", Fcpos [Work->pivcol])) ;
+ ASSERT (Fcpos [Work->pivcol] >= 0) ;
+ ASSERT (Fcpos [Work->pivcol] < fncols_extended * fnr_curr) ;
+
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* Zero the newly extended frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ zero_front (Work->Flblock, Work->Fublock, Work->Fcblock,
+ fnrows, fncols, fnr_curr, fnc_curr,
+ fnpiv, fnrows_extended, fncols_extended) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize extended row and column pattern of the frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Work->fnrows = fnrows_extended ;
+ Work->fncols = fncols_extended ;
+
+ ASSERT (fnrows_extended == Work->fnrows_new + 1) ;
+ ASSERT (fncols_extended == Work->fncols_new + 1) ;
+
+ return (TRUE) ;
+
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_extend_front.h b/src/C/SuiteSparse/UMFPACK/Source/umf_extend_front.h
new file mode 100644
index 0000000..cfb284e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_extend_front.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_extend_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_free.c b/src/C/SuiteSparse/UMFPACK/Source/umf_free.c
new file mode 100644
index 0000000..864d3d6
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_free.c
@@ -0,0 +1,45 @@
+/* ========================================================================== */
+/* === UMF_free ============================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Free a block previously allocated by UMF_malloc and return NULL.
+ Usage is p = UMF_free (p), to ensure that we don't free it twice.
+ Also maintains the UMFPACK malloc count.
+*/
+
+#include "umf_internal.h"
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+#include "umf_malloc.h"
+#endif
+
+GLOBAL void *UMF_free
+(
+ void *p
+)
+{
+ DEBUG0 (("UMF_free: "ID"\n", (Int) p)) ;
+ if (p)
+ {
+
+ /* see AMD/Source/amd_global.c for the memory allocator selection */
+ amd_free (p) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ /* One more object has been free'd. Keep track of the count. */
+ /* (purely for sanity checks). */
+ UMF_malloc_count-- ;
+ DEBUG0 ((" new malloc count: "ID"\n", UMF_malloc_count)) ;
+#endif
+
+ }
+
+ return ((void *) NULL) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_free.h b/src/C/SuiteSparse/UMFPACK/Source/umf_free.h
new file mode 100644
index 0000000..045e40b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_free.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void *UMF_free
+(
+ void *p
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_fsize.c b/src/C/SuiteSparse/UMFPACK/Source/umf_fsize.c
new file mode 100644
index 0000000..6411bf9
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_fsize.c
@@ -0,0 +1,69 @@
+/* ========================================================================== */
+/* === UMF_fsize ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Determine the largest frontal matrix size for each subtree. Called by
+ * UMF_colamd and UMF_analyze. Only required to sort the children of each
+ * node prior to AMD_postorder. */
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_fsize
+(
+ Int nn,
+ Int Fsize [ ],
+ Int Fnrows [ ],
+ Int Fncols [ ],
+ Int Parent [ ],
+ Int Npiv [ ]
+)
+{
+ Int j, parent, frsize, r, c ;
+
+ for (j = 0 ; j < nn ; j++)
+ {
+ Fsize [j] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find max front size for tree rooted at node j, for each front j */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("\n\n========================================FRONTS:\n")) ;
+ for (j = 0 ; j < nn ; j++)
+ {
+ if (Npiv [j] > 0)
+ {
+ /* this is a frontal matrix */
+ parent = Parent [j] ;
+ r = Fnrows [j] ;
+ c = Fncols [j] ;
+ frsize = r * c ;
+ /* avoid integer overflow */
+ if (INT_OVERFLOW (((double) r) * ((double) c)))
+ {
+ /* :: frsize int overflow :: */
+ frsize = Int_MAX ;
+ }
+ DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ",
+ j, Npiv [j], frsize, parent)) ;
+ Fsize [j] = MAX (Fsize [j], frsize) ;
+ DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ;
+ if (parent != EMPTY)
+ {
+ /* find the maximum frontsize of self and children */
+ ASSERT (Npiv [parent] > 0) ;
+ ASSERT (parent > j) ;
+ Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ;
+ DEBUG1 (("Fsize [parent = "ID"] = "ID"\n",
+ parent, Fsize [parent]));
+ }
+ }
+ }
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_fsize.h b/src/C/SuiteSparse/UMFPACK/Source/umf_fsize.h
new file mode 100644
index 0000000..27601be
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_fsize.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_fsize
+(
+ Int nn,
+ Int MaxFsize [ ],
+ Int Fnrows [ ],
+ Int Fncols [ ],
+ Int Parent [ ],
+ Int Npiv [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_garbage_collection.c b/src/C/SuiteSparse/UMFPACK/Source/umf_garbage_collection.c
new file mode 100644
index 0000000..15e7163
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_garbage_collection.c
@@ -0,0 +1,695 @@
+/* ========================================================================== */
+/* === UMF_garbage_collection =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Compress the elements at the tail of Numeric->Memory, and delete the tuples.
+ Elements are renumbered. The new numbering space is compressed, and
+ in the order of element creation (original elements of A first, followed
+ by the new elements in the order that they were formed).
+
+ Only called by UMF_get_memory.
+
+ There are 5 ways in which garbage collection can be performed:
+
+ Allocate a new working array for the current frontal matrix. In this
+ case, there are never any pivot rows/columns in the current frontal
+ matrix (fnpiv = 0), and the old working array for the current frontal
+ matrix can always be fully compacted, to fnrows-by-fncols.
+
+ UMF_kernel : UMF_extend : UMF_grow_front : UMF_get_memory
+ UMF_kernel : UMF_init_front : UMF_grow_front : UMF_get_memory
+ UMF_kernel : UMF_start_front : UMF_grow_front : UMF_get_memory
+
+ Allocate a new element. In this case, UMF_grow_front may or may not
+ be subsequently called, depending on Work->do_grow. There are never
+ any pivot rows/columns in the current frontal matrix (fnpiv=0), but one
+ may be added if UMF_init_front is to be called just after
+ UMF_create_element. If do_grow is true, then the current front can be
+ fully compacted, to fnrows-by-fncols. Otherwise, it can only be
+ partially compacted, to MAX (fnrows, fnrows_new + 1) -by-
+ MAX (fncols, fncols_new + 1).
+
+ UMF_kernel : UMF_create_element : UMF_get_memory
+
+ Allocate rows of L and columns of U. In this case, the current
+ frontal matrix is only partially compacted, to (fnrows_new + 1)-by-
+ (fncols_new + 1). There are pivots in the frontal matrix (fnpiv > 0).
+
+ UMF_kernel : UMF_store_lu : UMF_get_memory
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_garbage_collection
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int drnew, /* compact current front to drnew-by-dcnew */
+ Int dcnew,
+ Int do_Fcpos
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int size, e, n_row, n_col, nrows, ncols, nrowsleft, ncolsleft, prevsize,
+ csize, size2, i2, j2, i, j, cdeg, rdeg, *E, row, col,
+ *Rows, *Cols, *Rows2, *Cols2, nel, e2, *Row_tuples, *Col_tuples,
+ *Row_degree, *Col_degree ;
+ Entry *C, *C1, *C3, *C2 ;
+ Unit *psrc, *pdest, *p, *pnext ;
+ Element *epsrc, *epdest ;
+
+#ifndef NDEBUG
+ Int nmark ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Row_tuples = Numeric->Uip ;
+ Col_tuples = Numeric->Lip ;
+ E = Work->E ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+
+ /* note that the tuple lengths (Col_tlen and Row_tlen) are updated, but */
+ /* the tuple lists themselves are stale and are about to be destroyed */
+ /* and recreated. Do not attempt to scan them until they are recreated. */
+
+#ifndef NDEBUG
+ DEBUGm1 (("::::GARBAGE COLLECTION::::\n")) ;
+ UMF_dump_memory (Numeric) ;
+#endif
+
+ Numeric->ngarbage++ ;
+
+ /* ---------------------------------------------------------------------- */
+ /* delete the tuple lists by marking the blocks as free */
+ /* ---------------------------------------------------------------------- */
+
+ /* do not modify Row_tlen and Col_tlen */
+ /* those are needed for UMF_build_tuples */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row) && Row_tuples [row])
+ {
+ DEBUG2 (("row "ID" tuples "ID"\n", row, Row_tuples [row])) ;
+ p = Numeric->Memory + Row_tuples [row] - 1 ;
+ DEBUG2 (("Freeing tuple list row "ID", p-S "ID", size "ID"\n",
+ row, (Int) (p-Numeric->Memory), p->header.size)) ;
+ ASSERT (p->header.size > 0) ;
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+ p->header.size = -p->header.size ;
+ Row_tuples [row] = 0 ;
+ }
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col) && Col_tuples [col])
+ {
+ DEBUG2 (("col "ID" tuples "ID"\n", col, Col_tuples [col])) ;
+ p = Numeric->Memory + Col_tuples [col] - 1 ;
+ DEBUG2 (("Freeing tuple list col "ID", p-S "ID", size "ID"\n",
+ col, (Int) (p-Numeric->Memory), p->header.size)) ;
+ ASSERT (p->header.size > 0) ;
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+ p->header.size = -p->header.size ;
+ Col_tuples [col] = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* mark the elements, and compress the name space */
+ /* ---------------------------------------------------------------------- */
+
+ nel = Work->nel ;
+ ASSERT (nel < Work->elen) ;
+
+#ifndef NDEBUG
+ nmark = 0 ;
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ DEBUGm1 (("E [0] "ID" \n", E [0])) ;
+ ASSERT (IMPLIES (E [0],
+ Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ;
+ ASSERT (IMPLIES (Work->Flublock,
+ Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ;
+ ASSERT ((E [0] != 0) == (Work->Flublock != (Entry *) NULL)) ;
+#endif
+
+ e2 = 0 ;
+
+ for (e = 0 ; e <= nel ; e++) /* for all elements in order of creation */
+ {
+ if (E [e])
+ {
+ psrc = Numeric->Memory + E [e] ;
+ psrc-- ; /* get the header of this block */
+ if (e > 0)
+ {
+ e2++ ; /* do not renumber element zero */
+ }
+ ASSERT (psrc->header.size > 0) ;
+ psrc->header.size = e2 ; /* store the new name in the header */
+#ifndef NDEBUG
+ nmark++ ;
+#endif
+ DEBUG7 ((ID":: Mark e "ID" at psrc-S "ID", new e "ID"\n",
+ nmark, e, (Int) (psrc-Numeric->Memory), e2)) ;
+ E [e] = 0 ;
+ if (e == Work->prior_element)
+ {
+ Work->prior_element = e2 ;
+ }
+ }
+ }
+
+ /* all 1..e2 are now in use (element zero may or may not be in use) */
+ Work->nel = e2 ;
+ nel = Work->nel ;
+
+#ifndef NDEBUG
+ for (e = 0 ; e < Work->elen ; e++)
+ {
+ ASSERT (!E [e]) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* compress the elements */
+ /* ---------------------------------------------------------------------- */
+
+ /* point to tail marker block of size 1 + header */
+ psrc = Numeric->Memory + Numeric->size - 2 ;
+ pdest = psrc ;
+ prevsize = psrc->header.prevsize ;
+ DEBUG7 (("Starting the compression:\n")) ;
+
+ while (prevsize > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* move up to the next element above the current header, and */
+ /* get the element name and size */
+ /* (if it is an element, the name will be positive) */
+ /* ------------------------------------------------------------------ */
+
+ size = prevsize ;
+ psrc -= (size + 1) ;
+ e = psrc->header.size ;
+ prevsize = psrc->header.prevsize ;
+ /* top block at tail has prevsize of 0 */
+
+ /* a free block will have a negative size, so skip it */
+ /* otherwise, if size >= 0, it holds the element name, not the size */
+
+ DEBUG8 (("psrc-S: "ID" prevsize: "ID" size: "ID,
+ (Int) (psrc-Numeric->Memory), prevsize, size)) ;
+
+ if (e == 0)
+ {
+ /* -------------------------------------------------------------- */
+ /* this is the current frontal matrix */
+ /* -------------------------------------------------------------- */
+
+ Entry *F1, *F2, *Fsrc, *Fdst ;
+ Int c, r, k, dr, dc, gap, gap1, gap2, nb ;
+
+ /* shift the frontal matrix down */
+ F1 = (Entry *) (psrc + 1) ;
+
+ /* get the size of the current front. r and c could be zero */
+ k = Work->fnpiv ;
+ dr = Work->fnr_curr ;
+ dc = Work->fnc_curr ;
+ r = Work->fnrows ;
+ c = Work->fncols ;
+ nb = Work->nb ;
+
+ ASSERT ((dr >= 0 && (dr % 2) == 1) || dr == 0) ;
+ ASSERT (drnew >= 0) ;
+ if (drnew % 2 == 0)
+ {
+ /* make sure leading frontal matrix dimension is always odd */
+ drnew++ ;
+ }
+ drnew = MIN (dr, drnew) ;
+ ASSERT ((drnew >= 0 && (drnew % 2) == 1) || drnew == 0) ;
+
+ pnext = pdest ;
+
+#ifndef NDEBUG
+ DEBUGm2 (("move front: dr "ID" dc "ID" r "ID" drnew "ID" c "ID
+ " dcnew " ID" k "ID"\n", dr, dc, r, drnew, c, dcnew, k)) ;
+ DEBUG7 (("\n")) ;
+ DEBUG7 ((ID":: Move current frontal matrix from: psrc-S: "ID" \n",
+ nmark, (Int) (psrc-Numeric->Memory))) ;
+ nmark-- ;
+ ASSERT (E [e] == 0) ;
+ ASSERT (Work->Flublock == F1) ;
+ ASSERT (Work->Flblock == Work->Flublock + nb*nb) ;
+ ASSERT (Work->Fublock == Work->Flblock + dr*nb) ;
+ ASSERT (Work->Fcblock == Work->Fublock + nb*dc) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, dr, r, c) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, dr, r, k);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, dc, c, k) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, nb, k, k) ;
+ ASSERT (r <= drnew && c <= dcnew && drnew <= dr && dcnew <= dc) ;
+#endif
+
+ /* compact frontal matrix to drnew-by-dcnew before moving it */
+
+ /* do not compact the LU block (nb-by-nb) */
+
+ /* compact the columns of L (from dr-by-nb to drnew-by-nb) */
+ Fsrc = Work->Flblock ;
+ Fdst = Work->Flblock ;
+ ASSERT (Fdst == F1 + nb*nb) ;
+ gap1 = dr - r ;
+ gap2 = drnew - r ;
+ ASSERT (gap1 >= 0) ;
+ for (j = 0 ; j < k ; j++)
+ {
+ for (i = 0 ; i < r ; i++)
+ {
+ *Fdst++ = *Fsrc++ ;
+ }
+ Fsrc += gap1 ;
+ Fdst += gap2 ;
+ }
+ ASSERT (Fdst == F1 + nb*nb + drnew*k) ;
+ Fdst += drnew * (nb - k) ;
+
+ /* compact the rows of U (U' from dc-by-nb to dcnew-by-nb) */
+ Fsrc = Work->Fublock ;
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb) ;
+ gap1 = dc - c ;
+ gap2 = dcnew - c ;
+ for (i = 0 ; i < k ; i++)
+ {
+ for (j = 0 ; j < c ; j++)
+ {
+ *Fdst++ = *Fsrc++ ;
+ }
+ Fsrc += gap1 ;
+ Fdst += gap2 ;
+ }
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb + dcnew*k) ;
+ Fdst += dcnew * (nb - k) ;
+
+ /* compact the columns of C (from dr-by-dc to drnew-by-dcnew) */
+ Fsrc = Work->Fcblock ;
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew) ;
+ gap1 = dr - r ;
+ gap2 = drnew - r ;
+ for (j = 0 ; j < c ; j++)
+ {
+ for (i = 0 ; i < r ; i++)
+ {
+ *Fdst++ = *Fsrc++ ;
+ }
+ Fsrc += gap1 ;
+ Fdst += gap2 ;
+ }
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c) ;
+
+ /* recompute Fcpos, if necessary */
+ if (do_Fcpos)
+ {
+ Int *Fcols, *Fcpos ;
+ Fcols = Work->Fcols ;
+ Fcpos = Work->Fcpos ;
+ for (j = 0 ; j < c ; j++)
+ {
+ col = Fcols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] == j * dr) ;
+ Fcpos [col] = j * drnew ;
+ }
+#ifndef NDEBUG
+ {
+ Int cnt = 0 ;
+ for (j = 0 ; j < Work->n_col ; j++)
+ {
+ if (Fcpos [j] != EMPTY) cnt++ ;
+ }
+ DEBUGm2 (("Recompute Fcpos cnt "ID" c "ID"\n", cnt, c)) ;
+ ASSERT (cnt == c) ;
+ }
+#endif
+ }
+
+#ifndef NDEBUG
+ DEBUGm2 (("Compacted front, drnew "ID" dcnew "ID"\n", drnew, dcnew)) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (F1 + nb*nb + drnew*nb + nb*dcnew, drnew, r, c) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (F1 + nb*nb, drnew, r, k) ;
+ DEBUG7 (("U block: ")) ;
+ UMF_dump_dense (F1 + nb*nb + drnew*nb, nb, k, c) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (F1, nb, k, k) ;
+#endif
+
+ /* Compacted dimensions of the new frontal matrix. */
+ Work->fnr_curr = drnew ;
+ Work->fnc_curr = dcnew ;
+ Work->fcurr_size = (drnew + nb) * (dcnew + nb) ;
+ size = UNITS (Entry, Work->fcurr_size) ;
+
+ /* make sure the object doesn't evaporate. The front can have
+ * zero size (Work->fcurr_size = 0), but the size of the memory
+ * block containing it cannot have zero size. */
+ size = MAX (1, size) ;
+
+ /* get the destination of frontal matrix */
+ pnext->header.prevsize = size ;
+ pdest -= (size + 1) ;
+ F2 = (Entry *) (pdest + 1) ;
+
+ ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ;
+ ASSERT (psrc <= pdest) ;
+ ASSERT (F1 <= F2) ;
+
+ /* move the C block first */
+ Fsrc = F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c ;
+ Fdst = F2 + nb*nb + drnew*nb + nb*dcnew + drnew*c ;
+ gap = drnew - r ;
+ for (j = c-1 ; j >= 0 ; j--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ /* move column j of C */
+ for (i = r-1 ; i >= 0 ; i--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1 + nb*nb + drnew*nb + nb*dcnew) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*nb + nb*dcnew) ;
+
+ /* move the U block */
+ Fsrc -= dcnew * (nb - k) ;
+ Fdst -= dcnew * (nb - k) ;
+ ASSERT (Fsrc == F1 + nb*nb + drnew*nb + dcnew*k) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*nb + dcnew*k) ;
+ gap = dcnew - c ;
+ for (i = k-1 ; i >= 0 ; i--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ for (j = c-1 ; j >= 0 ; j--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1 + nb*nb + drnew*nb) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*nb) ;
+
+ /* move the L block */
+ Fsrc -= drnew * (nb - k) ;
+ Fdst -= drnew * (nb - k) ;
+ ASSERT (Fsrc == F1 + nb*nb + drnew*k) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*k) ;
+ gap = drnew - r ;
+ for (j = k-1 ; j >= 0 ; j--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ for (i = r-1 ; i >= 0 ; i--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1 + nb*nb) ;
+ ASSERT (Fdst == F2 + nb*nb) ;
+
+ /* move the LU block */
+ Fsrc -= nb * (nb - k) ;
+ Fdst -= nb * (nb - k) ;
+ ASSERT (Fsrc == F1 + nb*k) ;
+ ASSERT (Fdst == F2 + nb*k) ;
+ gap = nb - k ;
+ for (j = k-1 ; j >= 0 ; j--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ for (i = k-1 ; i >= 0 ; i--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1) ;
+ ASSERT (Fdst == F2) ;
+
+ E [0] = (pdest + 1) - Numeric->Memory ;
+
+ Work->Flublock = (Entry *) (Numeric->Memory + E [0]) ;
+ ASSERT (Work->Flublock == F2) ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + drnew * nb ;
+ Work->Fcblock = Work->Fublock + nb * dcnew ;
+
+ pdest->header.prevsize = 0 ;
+ pdest->header.size = size ;
+
+#ifndef NDEBUG
+ DEBUG7 (("After moving compressed current frontal matrix:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, drnew, r, c) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, drnew, r, k);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, dcnew, c, k) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, nb, k, k) ;
+#endif
+
+ }
+ else if (e > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is an element, compress and move from psrc down to pdest */
+ /* -------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG7 (("\n")) ;
+ DEBUG7 ((ID":: Move element "ID": from: "ID" \n",
+ nmark, e, (Int) (psrc-Numeric->Memory))) ;
+ nmark-- ;
+ ASSERT (e <= nel) ;
+ ASSERT (E [e] == 0) ;
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* get the element scalars, and pointers to C, Rows, and Cols: */
+ /* -------------------------------------------------------------- */
+
+ p = psrc + 1 ;
+ GET_ELEMENT (epsrc, p, Cols, Rows, ncols, nrows, C) ;
+ nrowsleft = epsrc->nrowsleft ;
+ ncolsleft = epsrc->ncolsleft ;
+ cdeg = epsrc->cdeg ;
+ rdeg = epsrc->rdeg ;
+
+#ifndef NDEBUG
+ DEBUG7 ((" nrows "ID" nrowsleft "ID"\n", nrows, nrowsleft)) ;
+ DEBUG7 ((" ncols "ID" ncolsleft "ID"\n", ncols, ncolsleft)) ;
+ DEBUG8 ((" Rows:")) ;
+ for (i = 0 ; i < nrows ; i++) DEBUG8 ((" "ID, Rows [i])) ;
+ DEBUG8 (("\n Cols:")) ;
+ for (j = 0 ; j < ncols ; j++) DEBUG8 ((" "ID, Cols [j])) ;
+ DEBUG8 (("\n")) ;
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* determine the layout of the new element */
+ /* -------------------------------------------------------------- */
+
+ csize = nrowsleft * ncolsleft ;
+ size2 = UNITS (Element, 1)
+ + UNITS (Int, nrowsleft + ncolsleft)
+ + UNITS (Entry, csize) ;
+
+ DEBUG7 (("Old size "ID" New size "ID"\n", size, size2)) ;
+
+ pnext = pdest ;
+ pnext->header.prevsize = size2 ;
+ pdest -= (size2 + 1) ;
+
+ ASSERT (size2 <= size) ;
+ ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ;
+ ASSERT (psrc <= pdest) ;
+
+ p = pdest + 1 ;
+ epdest = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols2 = (Int *) p ;
+ Rows2 = Cols2 + ncolsleft ;
+ p += UNITS (Int, nrowsleft + ncolsleft) ;
+ C2 = (Entry *) p ;
+
+ ASSERT (epdest >= epsrc) ;
+ ASSERT (Rows2 >= Rows) ;
+ ASSERT (Cols2 >= Cols) ;
+ ASSERT (C2 >= C) ;
+ ASSERT (p + UNITS (Entry, csize) == pnext) ;
+
+ /* -------------------------------------------------------------- */
+ /* move the contribution block */
+ /* -------------------------------------------------------------- */
+
+ /* overlap = psrc + size + 1 > pdest ; */
+
+ if (nrowsleft < nrows || ncolsleft < ncols)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* compress contribution block in place prior to moving it */
+ /* ---------------------------------------------------------- */
+
+ DEBUG7 (("Compress C in place prior to move:\n"));
+#ifndef NDEBUG
+ UMF_dump_dense (C, nrows, nrows, ncols) ;
+#endif
+ C1 = C ;
+ C3 = C ;
+ for (j = 0 ; j < ncols ; j++)
+ {
+ if (Cols [j] >= 0)
+ {
+ for (i = 0 ; i < nrows ; i++)
+ {
+ if (Rows [i] >= 0)
+ {
+ *C3++ = C1 [i] ;
+ }
+ }
+ }
+ C1 += nrows ;
+ }
+ ASSERT (C3-C == csize) ;
+ DEBUG8 (("Newly compressed contrib. block (all in use):\n")) ;
+#ifndef NDEBUG
+ UMF_dump_dense (C, nrowsleft, nrowsleft, ncolsleft) ;
+#endif
+ }
+
+ /* shift the contribution block down */
+ C += csize ;
+ C2 += csize ;
+ for (i = 0 ; i < csize ; i++)
+ {
+ *--C2 = *--C ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* move the row indices */
+ /* -------------------------------------------------------------- */
+
+ i2 = nrowsleft ;
+ for (i = nrows - 1 ; i >= 0 ; i--)
+ {
+ ASSERT (Rows2+i2 >= Rows+i) ;
+ if (Rows [i] >= 0)
+ {
+ Rows2 [--i2] = Rows [i] ;
+ }
+ }
+ ASSERT (i2 == 0) ;
+
+ j2 = ncolsleft ;
+ for (j = ncols - 1 ; j >= 0 ; j--)
+ {
+ ASSERT (Cols2+j2 >= Cols+j) ;
+ if (Cols [j] >= 0)
+ {
+ Cols2 [--j2] = Cols [j] ;
+ }
+ }
+ ASSERT (j2 == 0) ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the new header */
+ /* -------------------------------------------------------------- */
+
+ /* E [0...e] is now valid */
+ E [e] = (pdest + 1) - Numeric->Memory ;
+ epdest = (Element *) (pdest + 1) ;
+
+ epdest->next = EMPTY ; /* destroys the son list */
+ epdest->ncols = ncolsleft ;
+ epdest->nrows = nrowsleft ;
+ epdest->ncolsleft = ncolsleft ;
+ epdest->nrowsleft = nrowsleft ;
+ epdest->rdeg = rdeg ;
+ epdest->cdeg = cdeg ;
+
+ ASSERT (size2 <= size) ;
+ pdest->header.prevsize = 0 ;
+ pdest->header.size = size2 ;
+
+ DEBUG7 (("After moving it:\n")) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ }
+
+#ifndef NDEBUG
+ else
+ {
+ DEBUG8 ((" free\n")) ;
+ }
+#endif
+ DEBUG7 (("psrc "ID" tail "ID"\n",
+ (Int) (psrc-Numeric->Memory), Numeric->itail)) ;
+ }
+
+ ASSERT (psrc == Numeric->Memory + Numeric->itail) ;
+ ASSERT (nmark == 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* final tail pointer */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (pdest >= Numeric->Memory + Numeric->itail) ;
+ Numeric->itail = pdest - Numeric->Memory ;
+ pdest->header.prevsize = 0 ;
+ Numeric->ibig = EMPTY ;
+ Numeric->tail_usage = Numeric->size - Numeric->itail ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear the unused E [nel+1 .. Work->elen - 1] */
+ /* ---------------------------------------------------------------------- */
+
+ for (e = nel+1 ; e < Work->elen ; e++)
+ {
+ E [e] = 0 ;
+ }
+
+#ifndef NDEBUG
+ UMF_dump_packed_memory (Numeric, Work) ;
+#endif
+
+ DEBUG8 (("::::GARBAGE COLLECTION DONE::::\n")) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_garbage_collection.h b/src/C/SuiteSparse/UMFPACK/Source/umf_garbage_collection.h
new file mode 100644
index 0000000..69d25d9
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_garbage_collection.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_garbage_collection
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int drnew,
+ Int dcnew,
+ Int do_Fcpos
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.c b/src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.c
new file mode 100644
index 0000000..bbef6be
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.c
@@ -0,0 +1,222 @@
+/* ========================================================================== */
+/* === UMF_get_memory ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Reallocate the workspace (Numeric->Memory) and shift elements downwards.
+ needunits: increase in size so that the free space is at least this many
+ Units (to which the tuple lengths is added).
+
+ Return TRUE if successful, FALSE if out of memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_garbage_collection.h"
+#include "umf_tuple_lengths.h"
+#include "umf_build_tuples.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_realloc.h"
+
+GLOBAL Int UMF_get_memory
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int needunits,
+ Int r2, /* compact current front to r2-by-c2 */
+ Int c2,
+ Int do_Fcpos
+)
+{
+ double nsize, bsize, tsize ;
+ Int i, minsize, newsize, newmem, costly, row, col, *Row_tlen, *Col_tlen,
+ n_row, n_col, *Row_degree, *Col_degree ;
+ Unit *mnew, *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get and check parameters */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG1 (("::::GET MEMORY::::\n")) ;
+ UMF_dump_memory (Numeric) ;
+#endif
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_tlen = Numeric->Uilen ;
+ Col_tlen = Numeric->Lilen ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize the tuple list lengths */
+ /* ---------------------------------------------------------------------- */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ Row_tlen [row] = 0 ;
+ }
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ Col_tlen [col] = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine how much memory is needed for the tuples */
+ /* ---------------------------------------------------------------------- */
+
+ nsize = (double) needunits + 2 ;
+ needunits += UMF_tuple_lengths (Numeric, Work, &tsize) ;
+ nsize += tsize ;
+ needunits += 2 ; /* add 2, so that newmem >= 2 is true if realloc'd */
+
+ /* note: Col_tlen and Row_tlen are updated, but the tuple lists */
+ /* themselves are not. Do not attempt to scan the tuple lists. */
+ /* They are now stale, and are about to be destroyed and recreated. */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the desired new size of memory */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG0 (("UMF_get_memory: needunits: "ID"\n", needunits)) ;
+
+ minsize = Numeric->size + needunits ;
+ nsize += (double) Numeric->size ;
+
+ bsize = ((double) Int_MAX) / sizeof (Unit) - 1 ;
+
+ newsize = (Int) (UMF_REALLOC_INCREASE * ((double) minsize)) ;
+ nsize *= UMF_REALLOC_INCREASE ;
+ nsize += 1 ;
+
+ if (newsize < 0 || nsize > bsize)
+ {
+ /* :: realloc Numeric->Memory int overflow :: */
+ DEBUGm3 (("Realloc hit integer limit\n")) ;
+ newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */
+ }
+ else
+ {
+ ASSERT (newsize <= nsize) ;
+ newsize = MAX (newsize, minsize) ;
+ }
+ newsize = MAX (newsize, Numeric->size) ;
+
+ DEBUG0 ((
+ "REALLOC MEMORY: needunits "ID" old size: "ID" new size: "ID" Units \n",
+ needunits, Numeric->size, newsize)) ;
+
+ /* Forget where the biggest free block is (we no longer need it) */
+ /* since garbage collection will occur shortly. */
+ Numeric->ibig = EMPTY ;
+
+ DEBUG0 (("Before realloc E [0] "ID"\n", Work->E [0])) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reallocate the memory, if possible, and make it bigger */
+ /* ---------------------------------------------------------------------- */
+
+ mnew = (Unit *) NULL ;
+ while (!mnew)
+ {
+ mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ;
+ if (!mnew)
+ {
+ if (newsize == minsize) /* last realloc attempt failed */
+ {
+ /* We failed to get the minimum. Just stick with the */
+ /* current allocation and hope that garbage collection */
+ /* can recover enough space. */
+ mnew = Numeric->Memory ; /* no new memory available */
+ newsize = Numeric->size ;
+ }
+ else
+ {
+ /* otherwise, reduce the request and keep trying */
+ newsize = (Int) (UMF_REALLOC_REDUCTION * ((double) newsize)) ;
+ newsize = MAX (minsize, newsize) ;
+ }
+ }
+ }
+ ASSERT (mnew != (Unit *) NULL) ;
+
+ /* see if realloc had to copy, rather than just extend memory */
+ costly = (mnew != Numeric->Memory) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extend the tail portion of memory downwards */
+ /* ---------------------------------------------------------------------- */
+
+ Numeric->Memory = mnew ;
+ if (Work->E [0])
+ {
+ Int nb, dr, dc ;
+ nb = Work->nb ;
+ dr = Work->fnr_curr ;
+ dc = Work->fnc_curr ;
+ Work->Flublock = (Entry *) (Numeric->Memory + Work->E [0]) ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + dr * nb ;
+ Work->Fcblock = Work->Fublock + nb * dc ;
+ DEBUG0 (("after realloc E [0] "ID"\n", Work->E [0])) ;
+ }
+ ASSERT (IMPLIES (!(Work->E [0]), Work->Flublock == (Entry *) NULL)) ;
+
+ newmem = newsize - Numeric->size ;
+ ASSERT (newmem == 0 || newmem >= 2) ;
+
+ if (newmem >= 2)
+ {
+ /* reallocation succeeded */
+
+ /* point to the old tail marker block of size 1 + header */
+ p = Numeric->Memory + Numeric->size - 2 ;
+
+ /* create a new block out of the newly extended memory */
+ p->header.size = newmem - 1 ;
+ i = Numeric->size - 1 ;
+ p += newmem ;
+
+ /* create a new tail marker block */
+ p->header.prevsize = newmem - 1 ;
+ p->header.size = 1 ;
+
+ Numeric->size = newsize ;
+
+ /* free the new block */
+ UMF_mem_free_tail_block (Numeric, i) ;
+
+ Numeric->nrealloc++ ;
+
+ if (costly)
+ {
+ Numeric->ncostly++ ;
+ }
+
+ }
+ DEBUG1 (("Done with realloc memory\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* garbage collection on the tail of Numeric->memory (destroys tuples) */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_garbage_collection (Numeric, Work, r2, c2, do_Fcpos) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* rebuild the tuples */
+ /* ---------------------------------------------------------------------- */
+
+ return (UMF_build_tuples (Numeric, Work)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.h b/src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.h
new file mode 100644
index 0000000..6131478
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_get_memory.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_get_memory
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int needunits,
+ Int r2,
+ Int c2,
+ Int do_Fcpos
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.c b/src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.c
new file mode 100644
index 0000000..9afa6d6
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.c
@@ -0,0 +1,293 @@
+/* ========================================================================== */
+/* === UMF_grow_front ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Current frontal matrix is too small. Make it bigger. */
+
+#include "umf_internal.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_mem_alloc_tail_block.h"
+#include "umf_get_memory.h"
+
+GLOBAL Int UMF_grow_front
+(
+ NumericType *Numeric,
+ Int fnr2, /* desired size is fnr2-by-fnc2 */
+ Int fnc2,
+ WorkType *Work,
+ Int do_what /* -1: UMF_start_front
+ * 0: UMF_init_front, do not recompute Fcpos
+ * 1: UMF_extend_front
+ * 2: UMF_init_front, recompute Fcpos */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double s ;
+ Entry *Fcold, *Fcnew ;
+ Int j, i, col, *Fcpos, *Fcols, fnrows_max, fncols_max, fnr_curr, nb,
+ fnrows_new, fncols_new, fnr_min, fnc_min, minsize,
+ newsize, fnrows, fncols, *E, eloc ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ if (do_what != -1) UMF_debug++ ;
+ DEBUG0 (("\n\n====================GROW FRONT: do_what: "ID"\n", do_what)) ;
+ if (do_what != -1) UMF_debug-- ;
+ ASSERT (Work->do_grow) ;
+ ASSERT (Work->fnpiv == 0) ;
+#endif
+
+ Fcols = Work->Fcols ;
+ Fcpos = Work->Fcpos ;
+ E = Work->E ;
+
+ /* ---------------------------------------------------------------------- */
+ /* The current front is too small, find the new size */
+ /* ---------------------------------------------------------------------- */
+
+ /* maximum size of frontal matrix for this chain */
+ nb = Work->nb ;
+ fnrows_max = Work->fnrows_max + nb ;
+ fncols_max = Work->fncols_max + nb ;
+ ASSERT (fnrows_max >= 0 && (fnrows_max % 2) == 1) ;
+ DEBUG0 (("Max size: "ID"-by-"ID" (incl. "ID" pivot block\n",
+ fnrows_max, fncols_max, nb)) ;
+
+ /* current dimensions of frontal matrix: fnr-by-fnc */
+ DEBUG0 (("Current : "ID"-by-"ID" (excl "ID" pivot blocks)\n",
+ Work->fnr_curr, Work->fnc_curr, nb)) ;
+ ASSERT (Work->fnr_curr >= 0) ;
+ ASSERT ((Work->fnr_curr % 2 == 1) || Work->fnr_curr == 0) ;
+
+ /* required dimensions of frontal matrix: fnr_min-by-fnc_min */
+ fnrows_new = Work->fnrows_new + 1 ;
+ fncols_new = Work->fncols_new + 1 ;
+ ASSERT (fnrows_new >= 0) ;
+ if (fnrows_new % 2 == 0) fnrows_new++ ;
+ fnrows_new += nb ;
+ fncols_new += nb ;
+ fnr_min = MIN (fnrows_new, fnrows_max) ;
+ fnc_min = MIN (fncols_new, fncols_max) ;
+ minsize = fnr_min * fnc_min ;
+ if (INT_OVERFLOW ((double) fnr_min * (double) fnc_min * sizeof (Entry)))
+ {
+ /* :: the minimum front size is bigger than the integer maximum :: */
+ return (FALSE) ;
+ }
+ ASSERT (fnr_min >= 0) ;
+ ASSERT (fnr_min % 2 == 1) ;
+
+ DEBUG0 (("Min : "ID"-by-"ID"\n", fnr_min, fnc_min)) ;
+
+ /* grow the front to fnr2-by-fnc2, but no bigger than the maximum,
+ * and no smaller than the minumum. */
+ DEBUG0 (("Desired : ("ID"+"ID")-by-("ID"+"ID")\n", fnr2, nb, fnc2, nb)) ;
+ fnr2 += nb ;
+ fnc2 += nb ;
+ ASSERT (fnr2 >= 0) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ fnr2 = MAX (fnr2, fnr_min) ;
+ fnc2 = MAX (fnc2, fnc_min) ;
+ fnr2 = MIN (fnr2, fnrows_max) ;
+ fnc2 = MIN (fnc2, fncols_max) ;
+ DEBUG0 (("Try : "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnr2 % 2 == 1) ;
+
+ s = ((double) fnr2) * ((double) fnc2) ;
+ if (INT_OVERFLOW (s * sizeof (Entry)))
+ {
+ /* :: frontal matrix size int overflow :: */
+ /* the desired front size is bigger than the integer maximum */
+ /* compute a such that a*a*s < Int_MAX / sizeof (Entry) */
+ double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ;
+ fnr2 = MAX (fnr_min, a * fnr2) ;
+ fnc2 = MAX (fnc_min, a * fnc2) ;
+ /* the new frontal size is a*r*a*c = a*a*s */
+ newsize = fnr2 * fnc2 ;
+ ASSERT (fnr2 >= 0) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ fnc2 = newsize / fnr2 ;
+ }
+
+ fnr2 = MAX (fnr2, fnr_min) ;
+ fnc2 = MAX (fnc2, fnc_min) ;
+ newsize = fnr2 * fnc2 ;
+
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnr2 % 2 == 1) ;
+ ASSERT (fnr2 >= fnr_min) ;
+ ASSERT (fnc2 >= fnc_min) ;
+ ASSERT (newsize >= minsize) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the current front if it is empty of any numerical values */
+ /* ---------------------------------------------------------------------- */
+
+ if (E [0] && do_what != 1)
+ {
+ /* free the current front, if it exists and has nothing in it */
+ DEBUG0 (("Freeing empty front\n")) ;
+ UMF_mem_free_tail_block (Numeric, E [0]) ;
+ E [0] = 0 ;
+ Work->Flublock = (Entry *) NULL ;
+ Work->Flblock = (Entry *) NULL ;
+ Work->Fublock = (Entry *) NULL ;
+ Work->Fcblock = (Entry *) NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the new front, doing garbage collection if necessary */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage collection (grow)\n")) ;
+ }
+#endif
+
+ DEBUG0 (("Attempt size: "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+
+ if (!eloc)
+ {
+ /* Do garbage collection, realloc, and try again. Compact the current
+ * contribution block in the front to fnrows-by-fncols. Note that
+ * there are no pivot rows/columns in current front. Do not recompute
+ * Fcpos in UMF_garbage_collection. */
+ DEBUGm3 (("get_memory from umf_grow_front\n")) ;
+ if (!UMF_get_memory (Numeric, Work, 1 + UNITS (Entry, newsize),
+ Work->fnrows, Work->fncols, FALSE))
+ {
+ /* :: out of memory in umf_grow_front :: */
+ return (FALSE) ; /* out of memory */
+ }
+ DEBUG0 (("Attempt size: "ID"-by-"ID" again\n", fnr2, fnc2)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+ }
+
+ /* try again with something smaller */
+ while ((fnr2 != fnr_min || fnc2 != fnc_min) && !eloc)
+ {
+ fnr2 = MIN (fnr2 - 2, fnr2 * UMF_REALLOC_REDUCTION) ;
+ fnc2 = MIN (fnc2 - 2, fnc2 * UMF_REALLOC_REDUCTION) ;
+ ASSERT (fnr_min >= 0) ;
+ ASSERT (fnr_min % 2 == 1) ;
+ fnr2 = MAX (fnr_min, fnr2) ;
+ fnc2 = MAX (fnc_min, fnc2) ;
+ ASSERT (fnr2 >= 0) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ newsize = fnr2 * fnc2 ;
+ DEBUGm3 (("Attempt smaller size: "ID"-by-"ID" minsize "ID"-by-"ID"\n",
+ fnr2, fnc2, fnr_min, fnc_min)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+ }
+
+ /* try again with the smallest possible size */
+ if (!eloc)
+ {
+ fnr2 = fnr_min ;
+ fnc2 = fnc_min ;
+ newsize = minsize ;
+ DEBUG0 (("Attempt minsize: "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+ }
+
+ if (!eloc)
+ {
+ /* out of memory */
+ return (FALSE) ;
+ }
+
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnr2 % 2 == 1) ;
+ ASSERT (fnr2 >= fnr_min && fnc2 >= fnc_min) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the old frontal matrix into the new one */
+ /* ---------------------------------------------------------------------- */
+
+ /* old contribution block (if any) */
+ fnr_curr = Work->fnr_curr ; /* garbage collection can change fn*_curr */
+ ASSERT (fnr_curr >= 0) ;
+ ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ Fcold = Work->Fcblock ;
+
+ /* remove nb from the sizes */
+ fnr2 -= nb ;
+ fnc2 -= nb ;
+
+ /* new frontal matrix */
+ Work->Flublock = (Entry *) (Numeric->Memory + eloc) ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + nb * fnr2 ;
+ Work->Fcblock = Work->Fublock + nb * fnc2 ;
+ Fcnew = Work->Fcblock ;
+
+ if (E [0])
+ {
+ /* copy the old contribution block into the new one */
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ DEBUG1 (("copy col "ID" \n",col)) ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Fcnew [i] = Fcold [i] ;
+ }
+ Fcnew += fnr2 ;
+ Fcold += fnr_curr ;
+ DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ;
+ Fcpos [col] = j * fnr2 ;
+ }
+ }
+ else if (do_what == 2)
+ {
+ /* just find the new column offsets */
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ;
+ Fcpos [col] = j * fnr2 ;
+ }
+ }
+
+ /* free the old frontal matrix */
+ UMF_mem_free_tail_block (Numeric, E [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* new frontal matrix size */
+ /* ---------------------------------------------------------------------- */
+
+ E [0] = eloc ;
+ Work->fnr_curr = fnr2 ; /* C block is fnr2-by-fnc2 */
+ Work->fnc_curr = fnc2 ;
+ Work->fcurr_size = newsize ; /* including LU, L, U, and C blocks */
+ Work->do_grow = FALSE ; /* the front has just been grown */
+
+ ASSERT (Work->fnr_curr >= 0) ;
+ ASSERT (Work->fnr_curr % 2 == 1) ;
+ DEBUG0 (("Newly grown front: "ID"+"ID" by "ID"+"ID"\n", Work->fnr_curr,
+ nb, Work->fnc_curr, nb)) ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.h b/src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.h
new file mode 100644
index 0000000..e63acd3
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_grow_front.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_grow_front
+(
+ NumericType *Numeric,
+ Int fnr2,
+ Int fnc2,
+ WorkType *Work,
+ Int do_what
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_init_front.c b/src/C/SuiteSparse/UMFPACK/Source/umf_init_front.c
new file mode 100644
index 0000000..b82be9f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_init_front.c
@@ -0,0 +1,267 @@
+/* ========================================================================== */
+/* === UMF_init_front ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+#include "umf_grow_front.h"
+
+/* ========================================================================== */
+/* === zero_init_front ====================================================== */
+/* ========================================================================== */
+
+/* Set the initial frontal matrix to zero. */
+
+PRIVATE void zero_init_front (Int m, Int n, Entry *Fcblock, Int d)
+{
+ Int i, j ;
+ Entry *F, *Fj = Fcblock ;
+ for (j = 0 ; j < m ; j++)
+ {
+ F = Fj ;
+ Fj += d ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* CLEAR (Fcblock [i + j*d]) ; */
+ CLEAR (*F) ;
+ F++ ;
+ }
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_init_front ======================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMF_init_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int i, j, fnr_curr, row, col, *Frows, *Fcols,
+ *Fcpos, *Frpos, fncols, fnrows, *Wrow, fnr2, fnc2, rrdeg, ccdeg, *Wm,
+ fnrows_extended ;
+ Entry *Fcblock, *Fl, *Wy, *Wx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get current frontal matrix and check for frontal growth */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG0 (("INIT FRONT\n")) ;
+ DEBUG1 (("CURR before init:\n")) ;
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+#endif
+ if (Work->do_grow)
+ {
+ fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ;
+ fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ;
+ if (!UMF_grow_front (Numeric, fnr2, fnc2, Work,
+ Work->pivrow_in_front ? 2 : 0))
+ {
+ /* :: out of memory in umf_init_front :: */
+ DEBUGm4 (("out of memory: init front\n")) ;
+ return (FALSE) ;
+ }
+ }
+#ifndef NDEBUG
+ DEBUG1 (("CURR after grow:\n")) ;
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ DEBUG1 (("fnrows new "ID" fncols new "ID"\n",
+ Work->fnrows_new, Work->fncols_new)) ;
+#endif
+ ASSERT (Work->fnpiv == 0) ;
+ fnr_curr = Work->fnr_curr ;
+ ASSERT (Work->fnrows_new + 1 <= fnr_curr) ;
+ ASSERT (Work->fncols_new + 1 <= Work->fnc_curr) ;
+ ASSERT (fnr_curr >= 0) ;
+ ASSERT (fnr_curr % 2 == 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ /* current front is defined by pivot row and column */
+
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+
+ Work->fnzeros = 0 ;
+
+ ccdeg = Work->ccdeg ;
+ rrdeg = Work->rrdeg ;
+
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+
+ /* if both pivrow and pivcol are in front, then we extend the old one */
+ /* in UMF_extend_front, rather than starting a new one here. */
+ ASSERT (! (Work->pivrow_in_front && Work->pivcol_in_front)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* place pivot column pattern in frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Fl = Work->Flblock ;
+
+ if (Work->pivcol_in_front)
+ {
+ /* Append the pivot column extension.
+ * Note that all we need to do is increment the size, since the
+ * candidate pivot column pattern is already in place in
+ * Frows [0 ... fnrows-1] (the old pattern), and
+ * Frows [fnrows ... fnrows + Work->ccdeg - 1] (the new
+ * pattern). Frpos is also properly defined. */
+ /* make a list of the new rows to scan */
+ Work->fscan_row = fnrows ; /* only scan the new rows */
+ Work->NewRows = Work->Wrp ;
+ Wy = Work->Wy ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Fl [i] = Wy [i] ;
+ }
+ fnrows_extended = fnrows + ccdeg ;
+ for (i = fnrows ; i < fnrows_extended ; i++)
+ {
+ Fl [i] = Wy [i] ;
+ /* flip the row index, since Wrp must be < 0 */
+ row = Frows [i] ;
+ Work->NewRows [i] = FLIP (row) ;
+ }
+ fnrows = fnrows_extended ;
+ }
+ else
+ {
+ /* this is a completely new column */
+ Work->fscan_row = 0 ; /* scan all the rows */
+ Work->NewRows = Frows ;
+ Wm = Work->Wm ;
+ Wx = Work->Wx ;
+ for (i = 0 ; i < ccdeg ; i++)
+ {
+ Fl [i] = Wx [i] ;
+ row = Wm [i] ;
+ Frows [i] = row ;
+ Frpos [row] = i ;
+ }
+ fnrows = ccdeg ;
+ }
+
+ Work->fnrows = fnrows ;
+
+#ifndef NDEBUG
+ DEBUG3 (("New Pivot col "ID" now in front, length "ID"\n",
+ Work->pivcol, fnrows)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG4 ((" "ID": row "ID"\n", i, Frows [i])) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* place pivot row pattern in frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Wrow = Work->Wrow ;
+ if (Work->pivrow_in_front)
+ {
+ /* append the pivot row extension */
+ Work->fscan_col = fncols ; /* only scan the new columns */
+ Work->NewCols = Work->Wp ;
+#ifndef NDEBUG
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] == j * fnr_curr) ;
+ }
+#endif
+ /* Wrow == Fcol for the IN_IN case, and for the OUT_IN case when
+ * the pivrow [IN][IN] happens to be the same as pivrow [OUT][IN].
+ * See UMF_local_search for more details. */
+ ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ;
+ if (Wrow == Fcols)
+ {
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ /* Fcols [j] = col ; not needed */
+ /* flip the col index, since Wp must be < 0 */
+ Work->NewCols [j] = FLIP (col) ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ else
+ {
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ Fcols [j] = col ;
+ /* flip the col index, since Wp must be < 0 */
+ Work->NewCols [j] = FLIP (col) ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ }
+ else
+ {
+ /* this is a completely new row */
+ Work->fscan_col = 0 ; /* scan all the columns */
+ Work->NewCols = Fcols ;
+ for (j = 0 ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ Fcols [j] = col ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+
+ DEBUGm1 (("rrdeg "ID" fncols "ID"\n", rrdeg, fncols)) ;
+ fncols = rrdeg ;
+ Work->fncols = fncols ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear the frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (fnrows == Work->fnrows_new + 1) ;
+ ASSERT (fncols == Work->fncols_new + 1) ;
+
+ Fcblock = Work->Fcblock ;
+ ASSERT (Fcblock != (Entry *) NULL) ;
+
+ zero_init_front (fncols, fnrows, Fcblock, fnr_curr) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("New Pivot row "ID" now in front, length "ID" fnr_curr "ID"\n",
+ Work->pivrow, fncols, fnr_curr)) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG4 (("col "ID" position "ID"\n", j, Fcols [j])) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* current workspace usage: */
+ /* ---------------------------------------------------------------------- */
+
+ /* Fcblock [0..fnr_curr-1, 0..fnc_curr-1]: space for the new frontal
+ * matrix. Fcblock (i,j) is located at Fcblock [i+j*fnr_curr] */
+
+ return (TRUE) ;
+
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_init_front.h b/src/C/SuiteSparse/UMFPACK/Source/umf_init_front.h
new file mode 100644
index 0000000..b7115fb
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_init_front.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_init_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_internal.h b/src/C/SuiteSparse/UMFPACK/Source/umf_internal.h
new file mode 100644
index 0000000..7c231e8
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_internal.h
@@ -0,0 +1,734 @@
+/* ========================================================================== */
+/* === umf_internal.h ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This file is for internal use in UMFPACK itself, and should not be included
+ in user code. Use umfpack.h instead. User-accessible file names and
+ routine names all start with the letters "umfpack_". Non-user-accessible
+ file names and routine names all start with "umf_".
+*/
+
+#ifndef _UMF_INTERNAL
+#define _UMF_INTERNAL
+
+/* -------------------------------------------------------------------------- */
+/* ANSI standard include files */
+/* -------------------------------------------------------------------------- */
+
+/* from float.h: DBL_EPSILON */
+#include <float.h>
+
+/* from string.h: strcmp */
+#include <string.h>
+
+/* when debugging, assert.h and the assert macro are used (see umf_dump.h) */
+
+/* -------------------------------------------------------------------------- */
+/* Architecture */
+/* -------------------------------------------------------------------------- */
+
+#if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2)
+#define UMF_SOL2
+#define UMFPACK_ARCHITECTURE "Sun Solaris"
+
+#elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI)
+#define UMF_SGI
+#define UMFPACK_ARCHITECTURE "SGI Irix"
+
+#elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86)
+#define UMF_LINUX
+#define UMFPACK_ARCHITECTURE "Linux"
+
+#elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS)
+#define UMF_AIX
+#define UMFPACK_ARCHITECTURE "IBM AIX"
+
+#elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA)
+#define UMF_ALPHA
+#define UMFPACK_ARCHITECTURE "Compaq Alpha"
+
+#elif defined (_WIN32) || defined (WIN32)
+#if defined (__MINGW32__)
+#define UMF_MINGW
+#elif defined (__CYGWIN32__)
+#define UMF_CYGWIN
+#else
+#define UMF_WINDOWS
+#endif
+#define UMFPACK_ARCHITECTURE "Microsoft Windows"
+
+#elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX)
+#define UMF_HP
+#define UMFPACK_ARCHITECTURE "HP Unix"
+
+#elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700)
+#define UMF_HP
+#define UMFPACK_ARCHITECTURE "HP 700 Unix"
+
+#else
+/* If the architecture is unknown, and you call the BLAS, you may need to */
+/* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */
+#define UMFPACK_ARCHITECTURE "unknown"
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* basic definitions (see also amd_internal.h) */
+/* -------------------------------------------------------------------------- */
+
+#define ONES_COMPLEMENT(r) (-(r)-1)
+
+/* -------------------------------------------------------------------------- */
+/* AMD include file */
+/* -------------------------------------------------------------------------- */
+
+/* stdio.h, stdlib.h, limits.h, and math.h, NDEBUG definition, assert.h */
+#include "amd_internal.h"
+
+/* -------------------------------------------------------------------------- */
+/* MATLAB include files */
+/* -------------------------------------------------------------------------- */
+
+/* only used when compiling the UMFPACK mexFunction */
+#ifdef MATLAB_MEX_FILE
+#include "matrix.h"
+#include "mex.h"
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Real/complex and int/UF_long definitions, double relops */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_version.h"
+
+/* -------------------------------------------------------------------------- */
+/* Compile-time configurations */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_config.h"
+
+/* -------------------------------------------------------------------------- */
+/* umfpack include file */
+/* -------------------------------------------------------------------------- */
+
+#include "umfpack.h"
+
+/* -------------------------------------------------------------------------- */
+/* for contents of Info. This must correlate with umfpack.h */
+/* -------------------------------------------------------------------------- */
+
+#define ESTIMATE (UMFPACK_NUMERIC_SIZE_ESTIMATE - UMFPACK_NUMERIC_SIZE)
+#define ACTUAL 0
+
+/* -------------------------------------------------------------------------- */
+/* get a parameter from the Control array */
+/* -------------------------------------------------------------------------- */
+
+#define GET_CONTROL(i,default) \
+ ((Control != (double *) NULL) ? \
+ (SCALAR_IS_NAN (Control [i]) ? default : Control [i]) \
+ : default)
+
+/* -------------------------------------------------------------------------- */
+/* for clearing the external degree counters */
+/* -------------------------------------------------------------------------- */
+
+#define MAX_MARK(n) Int_MAX - (2*(n)+1)
+
+/* -------------------------------------------------------------------------- */
+/* convert number of Units to MBytes */
+/* -------------------------------------------------------------------------- */
+
+#define MBYTES(units) (((units) * sizeof (Unit)) / 1048576.0)
+
+/* -------------------------------------------------------------------------- */
+/* dense row/column macro */
+/* -------------------------------------------------------------------------- */
+
+/* In order for a row or column to be treated as "dense", it must have more */
+/* entries than the value returned by this macro. n is the dimension of the */
+/* matrix, and alpha is the dense row/column control parameter. */
+
+/* Note: this is not defined if alpha is NaN or Inf: */
+#define UMFPACK_DENSE_DEGREE_THRESHOLD(alpha,n) \
+ ((Int) MAX (16.0, (alpha) * 16.0 * sqrt ((double) (n))))
+
+/* -------------------------------------------------------------------------- */
+/* PRINTF */
+/* -------------------------------------------------------------------------- */
+
+#define PRINTFk(k,params) { if (prl >= (k)) { PRINTF (params) ; } }
+#define PRINTF1(params) PRINTFk (1, params)
+#define PRINTF2(params) PRINTFk (2, params)
+#define PRINTF3(params) PRINTFk (3, params)
+#define PRINTF4(params) PRINTFk (4, params)
+#define PRINTF5(params) PRINTFk (5, params)
+#define PRINTF6(params) PRINTFk (6, params)
+
+/* -------------------------------------------------------------------------- */
+/* Fixed control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* maximum number of columns to consider at one time, in a single front */
+#define MAX_CANDIDATES 128
+
+/* reduce Numeric->Memory request by this ratio, if allocation fails */
+#define UMF_REALLOC_REDUCTION (0.95)
+
+/* increase Numeric->Memory request by this ratio, if we need more */
+#define UMF_REALLOC_INCREASE (1.2)
+
+/* increase the dimensions of the current frontal matrix by this factor
+ * when it needs to grow. */
+#define UMF_FRONTAL_GROWTH (1.2)
+
+/* largest BLAS block size permitted */
+#define MAXNB 64
+
+/* if abs (y) < RECIPROCAL_TOLERANCE, then compute x/y. Otherwise x*(1/y).
+ * Ignored if NRECIPROCAL is defined */
+#define RECIPROCAL_TOLERANCE 1e-12
+
+/* -------------------------------------------------------------------------- */
+/* Memory allocator */
+/* -------------------------------------------------------------------------- */
+
+/* See AMD/Source/amd_global.c and AMD/Source/amd.h for the
+ * definition of the memory allocator used by UMFPACK. Versions 4.4 and
+ * earlier had their memory allocator definitions here. Other global
+ * function pointers for UMFPACK are located in umf_global.c.
+ *
+ * The MATLAB mexFunction uses MATLAB's memory manager and mexPrintf, while the
+ * C-callable AMD library uses the ANSI C malloc, free, realloc, and printf
+ * routines.
+ */
+
+/* -------------------------------------------------------------------------- */
+/* Memory space definitions */
+/* -------------------------------------------------------------------------- */
+
+/* for memory alignment - assume double has worst case alignment */
+typedef double Align ;
+
+/* get number of bytes required to hold n items of a type: */
+/* note that this will not overflow, because sizeof (type) is always */
+/* greater than or equal to sizeof (Int) >= 2 */
+#define BYTES(type,n) (sizeof (type) * (n))
+
+/* ceiling of (b/u). Assumes b >= 0 and u > 0 */
+#define CEILING(b,u) (((b) + (u) - 1) / (u))
+
+/* get number of Units required to hold n items of a type: */
+#define UNITS(type,n) (CEILING (BYTES (type, n), sizeof (Unit)))
+
+/* same as DUNITS, but use double instead of int to avoid overflow */
+#define DUNITS(type,n) (ceil (BYTES (type, (double) n) / sizeof (Unit)))
+
+union Unit_union
+{ /* memory is allocated in multiples of Unit */
+ struct
+ {
+ Int
+ size, /* size, in Units, of the block, excl. header block */
+ /* size >= 0: block is in use */
+ /* size < 0: block is free, of |size| Units */
+ prevsize ; /* size, in Units, of preceding block in S->Memory */
+ /* during garbage_collection, prevsize is set to -e-1 */
+ /* for element e, or positive (and thus a free block) */
+ /* otherwise */
+ } header ; /* block header */
+ Align xxxxxx ; /* force alignment of blocks (xxxxxx is never used) */
+} ;
+
+typedef union Unit_union Unit ;
+
+/* get the size of an allocated block */
+#define GET_BLOCK_SIZE(p) (((p)-1)->header.size)
+
+/* -------------------------------------------------------------------------- */
+/* Numeric */
+/* -------------------------------------------------------------------------- */
+
+/*
+ NUMERIC_VALID and SYMBOLIC_VALID:
+ The different values of SYBOLIC_VALID and NUMERIC_VALID are chosen as a
+ first defense against corrupted *Symbolic or *Numeric pointers passed to an
+ UMFPACK routine. They also ensure that the objects are used only by the
+ same version that created them (umfpack_di_*, umfpack_dl_*, umfpack_zi_*,
+ or umfpack_zl_*). The values have also been changed since prior releases of
+ the code to ensure that all routines that operate on the objects are of the
+ same release. The values themselves are purely arbitrary. The are less
+ than the ANSI C required minimums of INT_MAX and LONG_MAX, respectively.
+*/
+
+#ifdef DINT
+#define NUMERIC_VALID 15977
+#define SYMBOLIC_VALID 41937
+#endif
+#ifdef DLONG
+#define NUMERIC_VALID 399789720
+#define SYMBOLIC_VALID 399192713
+#endif
+#ifdef ZINT
+#define NUMERIC_VALID 17957
+#define SYMBOLIC_VALID 40927
+#endif
+#ifdef ZLONG
+#define NUMERIC_VALID 129987754
+#define SYMBOLIC_VALID 110291734
+#endif
+
+typedef struct /* NumericType */
+{
+ double
+ flops, /* "true" flop count */
+ relpt, /* relative pivot tolerance used */
+ relpt2, /* relative pivot tolerance used for sym. */
+ droptol,
+ alloc_init, /* initial allocation of Numeric->memory */
+ front_alloc_init, /* frontal matrix allocation parameter */
+ rsmin, /* smallest row sum */
+ rsmax, /* largest row sum */
+ min_udiag, /* smallest abs value on diagonal of D */
+ max_udiag, /* smallest abs value on diagonal of D */
+ rcond ; /* min (D) / max (D) */
+
+ Int
+ scale ;
+
+ Int valid ; /* set to NUMERIC_VALID, for validity check */
+
+ /* Memory space for A and LU factors */
+ Unit
+ *Memory ; /* working memory for A and LU factors */
+ Int
+ ihead, /* pointer to tail of LU factors, in Numeric->Memory */
+ itail, /* pointer to top of elements & tuples, */
+ /* in Numeric->Memory */
+ ibig, /* pointer to largest free block seen in tail */
+ size ; /* size of Memory, in Units */
+
+ Int
+ *Rperm, /* pointer to row perm array, size: n+1 */
+ /* after UMF_kernel: Rperm [new] = old */
+ /* during UMF_kernel: Rperm [old] = new */
+ *Cperm, /* pointer to col perm array, size: n+1 */
+ /* after UMF_kernel: Cperm [new] = old */
+ /* during UMF_kernel: Cperm [old] = new */
+
+ *Upos, /* see UMFPACK_get_numeric for a description */
+ *Lpos,
+ *Lip,
+ *Lilen,
+ *Uip,
+ *Uilen,
+ *Upattern ; /* pattern of last row of U (if singular) */
+
+ Int
+ ulen, /* length of Upattern */
+ npiv, /* number of structural pivots found (sprank approx) */
+ nnzpiv ; /* number of numerical (nonzero) pivots found */
+
+ Entry
+ *D ; /* D [i] is the diagonal entry of U */
+
+ Int do_recip ;
+ double *Rs ; /* scale factors for the rows of A and b */
+ /* do_recip FALSE: Divide row i by Rs [i] */
+ /* do_recip TRUE: Multiply row i by Rs [i] */
+
+ Int
+ n_row, n_col, /* A is n_row-by-n_row */
+ n1 ; /* number of singletons */
+
+ /* for information only: */
+ Int
+ tail_usage, /* amount of memory allocated in tail */
+ /* head_usage is Numeric->ihead */
+ init_usage, /* memory usage just after UMF_kernel_init */
+ max_usage, /* peak memory usage (excludes internal and external */
+ /* fragmentation in the tail) */
+ ngarbage, /* number of garbage collections performed */
+ nrealloc, /* number of reallocations performed */
+ ncostly, /* number of costly reallocations performed */
+ isize, /* size of integer pattern of L and U */
+ nLentries, /* number of entries in L, excluding diagonal */
+ nUentries, /* number of entries in U, including diagonal */
+ /* Some entries may be numerically zero. */
+ lnz, /* number of nonzero entries in L, excl. diagonal */
+ all_lnz, /* lnz plus entries dropped from L */
+ unz, /* number of nonzero entries in U, excl. diagonal */
+ all_unz, /* unz plus entries dropped form U */
+ maxfrsize ; /* largest actual front size */
+
+ Int maxnrows, maxncols ; /* not the same as Symbolic->maxnrows/cols* */
+
+} NumericType ;
+
+
+
+/* -------------------------------------------------------------------------- */
+/* Element tuples for connecting elements together in a matrix */
+/* -------------------------------------------------------------------------- */
+
+typedef struct /* Tuple */
+{
+ /* The (e,f) tuples for the element lists */
+ Int
+ e, /* element */
+ f ; /* contribution to the row/col appears at this offset */
+
+} Tuple ;
+
+#define TUPLES(t) MAX (4, (t) + 1)
+
+/* Col_degree is aliased with Cperm, and Row_degree with Rperm */
+#define NON_PIVOTAL_COL(col) (Col_degree [col] >= 0)
+#define NON_PIVOTAL_ROW(row) (Row_degree [row] >= 0)
+
+/* -------------------------------------------------------------------------- */
+/* An element */
+/* -------------------------------------------------------------------------- */
+
+typedef struct /* Element */
+{
+ Int
+
+ cdeg, /* external column degree + cdeg0 offset */
+ rdeg, /* external row degree + rdeg0 offset */
+ nrowsleft, /* number of rows remaining */
+ ncolsleft, /* number of columns remaining */
+ nrows, /* number of rows */
+ ncols, /* number of columns */
+ next ; /* for list link of sons, used during assembly only */
+
+ /* followed in memory by:
+ Int
+ col [0..ncols-1], column indices of this element
+ row [0..nrows-1] ; row indices of this element
+ Entry (suitably aligned, see macro below)
+ C [0...nrows-1, 0...ncols-1] ;
+ size of C is nrows*ncols Entry's
+ */
+
+} Element ;
+
+/* macros for computing pointers to row/col indices, and contribution block: */
+
+#define GET_ELEMENT_SIZE(nr,nc) \
+(UNITS (Element, 1) + UNITS (Int, (nc) + (nr)) + UNITS (Entry, (nc) * (nr)))
+
+#define DGET_ELEMENT_SIZE(nr,nc) \
+(DUNITS (Element, 1) + DUNITS (Int, (nc) + (nr)) + DUNITS (Entry, (nc) * (nr)))
+
+#define GET_ELEMENT_COLS(ep,p,Cols) { \
+ ASSERT (p != (Unit *) NULL) ; \
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ; \
+ ASSERT (p <= Numeric->Memory + Numeric->size) ; \
+ ep = (Element *) p ; \
+ p += UNITS (Element, 1) ; \
+ Cols = (Int *) p ; \
+}
+
+#define GET_ELEMENT_PATTERN(ep,p,Cols,Rows,ncm) { \
+ GET_ELEMENT_COLS (ep, p, Cols) ; \
+ ncm = ep->ncols ; \
+ Rows = Cols + ncm ; \
+}
+
+#define GET_ELEMENT(ep,p,Cols,Rows,ncm,nrm,C) { \
+ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncm) ; \
+ nrm = ep->nrows ; \
+ p += UNITS (Int, ncm + nrm) ; \
+ C = (Entry *) p ; \
+}
+
+/* -------------------------------------------------------------------------- */
+/* Work data structure */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This data structure holds items needed only during factorization.
+ All of this is freed when UMFPACK_numeric completes. Note that some of
+ it is stored in the tail end of Numeric->S (namely, the Tuples and the
+ Elements).
+*/
+
+typedef struct /* WorkType */
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* information about each row and col of A */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ Row_tuples: pointer to tuple list (alias with Numeric->Uip)
+ Row_tlen: number of tuples (alias with Numeric->Uilen)
+ Col_tuples: pointer to tuple list (alias with Numeric->Lip)
+ Col_tlen: number of tuples (alias with Numeric->Lilen)
+ Row_degree: degree of the row or column (alias Numeric->Rperm)
+ Col_degree: degree of the row or column (alias Numeric->Cperm)
+
+ The Row_degree and Col_degree are MATLAB-style colmmd approximations,
+ are equal to the sum of the sizes of the elements (contribution blocks)
+ in each row and column. They are maintained when elements are created
+ and assembled. They are used only during the pivot row and column
+ search. They are not needed to represent the pattern of the remaining
+ matrix.
+ */
+
+ /* ---------------------------------------------------------------------- */
+ /* information about each element */
+ /* ---------------------------------------------------------------------- */
+
+ Int *E ; /* E [0 .. Work->elen-1] element "pointers" */
+ /* (offsets in Numeric->Memory) */
+
+ /* ---------------------------------------------------------------------- */
+ /* generic workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Entry *Wx, *Wy ; /* each of size maxnrows+1 */
+
+ Int /* Sizes: nn = MAX (n_row, n_col) */
+ *Wp, /* nn+1 */
+ *Wrp, /* n_col+1 */
+ *Wm, /* maxnrows+1 */
+ *Wio, /* maxncols+1 */
+ *Woi, /* maxncols+1 */
+ *Woo, /* MAX (maxnrows,maxncols)+1 */
+ *Wrow, /* pointer to Fcols, Wio, or Woi */
+ *NewRows, /* list of rows to scan */
+ *NewCols ; /* list of cols to scan */
+
+ /* ---------------------------------------------------------------------- */
+
+ Int
+ *Lpattern, /* pattern of column of L, for one Lchain */
+ *Upattern, /* pattern of row of U, for one Uchain */
+ ulen, llen ; /* length of Upattern and Lpattern */
+
+ Int
+ *Diagonal_map, /* used for symmetric pivoting, of size nn+1 */
+ *Diagonal_imap ;/* used for symmetric pivoting, of size nn+1 */
+
+ /* ---------------------------------------------------------------------- */
+
+ Int
+ n_row, n_col, /* matrix is n_row-by-n_col */
+ nz, /* nonzeros in the elements for this matrix */
+ n1, /* number of row and col singletons */
+ elen, /* max possible number of elements */
+ npiv, /* number of pivot rows and columns so far */
+ ndiscard, /* number of discarded pivot columns */
+ Wrpflag,
+ nel, /* elements in use are in the range 1..nel */
+ noff_diagonal,
+ prior_element,
+ rdeg0, cdeg0,
+ rrdeg, ccdeg,
+ Candidates [MAX_CANDIDATES], /* current candidate pivot columns */
+ nCandidates, /* number of candidates in Candidate set */
+ ksuper,
+ firstsuper,
+ jsuper,
+ ncand, /* number of candidates (some not in Candidates[ ]) */
+ nextcand, /* next candidate to place in Candidate search set */
+ lo,
+ hi,
+ pivrow, /* current pivot row */
+ pivcol, /* current pivot column */
+ do_extend, /* true if the next pivot extends the current front */
+ do_update, /* true if update should be applied */
+ nforced, /* number of forced updates because of frontal growth */
+ any_skip,
+ do_scan2row,
+ do_scan2col,
+ do_grow,
+ pivot_case,
+ frontid, /* id of current frontal matrix */
+ nfr ; /* number of frontal matrices */
+
+ /* ---------------------------------------------------------------------- */
+ /* For row-merge tree */
+ /* ---------------------------------------------------------------------- */
+
+ Int
+ *Front_new1strow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* current frontal matrix, F */
+ /* ---------------------------------------------------------------------- */
+
+ Int Pivrow [MAXNB],
+ Pivcol [MAXNB] ;
+
+ Entry
+ *Flublock, /* LU block, nb-by-nb */
+ *Flblock, /* L block, fnr_curr-by-nb */
+ *Fublock, /* U block, nb-by-fnc_curr, or U' fnc_curr-by-nb */
+ *Fcblock ; /* C block, fnr_curr-by-fnc_curr */
+
+ Int
+ *Frows, /* Frows [0.. ]: row indices of F */
+
+ *Fcols, /* Fcols [0.. ]: column indices of F */
+
+ *Frpos, /* position of row indices in F, or -1 if not present */
+ /* if Frows[i] == row, then Frpos[row] == i */
+
+ *Fcpos, /* position of col indices in F, or -1 if not present */
+ /* if Fcols[j] == col, then */
+ /* Fcpos[col] == j*Work->fnr_curr */
+
+ fnrows, /* number of rows in contribution block in F */
+ fncols, /* number of columns in contribution block in F */
+ fnr_curr, /* maximum # of rows in F (leading dimension) */
+ fnc_curr, /* maximum # of columns in F */
+ fcurr_size, /* current size of F */
+ fnrows_max, /* max possible column-dimension (max # of rows) of F */
+ fncols_max, /* max possible row-dimension (max # of columns) of F */
+ nb,
+ fnpiv, /* number of pivots in F */
+ fnzeros, /* number of explicit zero entries in LU block */
+ fscan_row, /* where to start scanning rows of F in UMF_assemble */
+ fscan_col, /* where to start scanning cols of F in UMF_assemble */
+ fnrows_new, /* number of new row indices in F after pivot added */
+ fncols_new, /* number of new col indices in F after pivot added */
+ pivrow_in_front, /* true if current pivot row in Frows */
+ pivcol_in_front ; /* true if current pivot column in Fcols */
+
+ /* ----------------------------------------------------------------------
+ * Current frontal matrix
+ * ----------------------------------------------------------------------
+ * The current frontal matrix is held as a single block of memory allocated
+ * from the "tail" end of Numeric->Memory. It is subdivided into four
+ * parts: an LU block, an L block, a U block, and a C block.
+ *
+ * Let k = fnpiv, r = fnrows, and c = fncols for the following discussion.
+ * Let dr = fnr_curr and dc = fnc_curr. Note that r <= dr and c <= dc.
+ *
+ * The LU block is of dimension nb-by-nb. The first k-by-k part holds the
+ * "diagonal" part of the LU factors for these k pivot rows and columns.
+ * The k pivot row and column indices in this part are Pivrow [0..k-1] and
+ * Pivcol [0..k-1], respectively.
+ *
+ * The L block is of dimension dr-by-nb. It holds the k pivot columns,
+ * except for the leading k-by-k part in the LU block. Only the leading
+ * r-by-k part is in use.
+ *
+ * The U block is of dimension dc-by-nb. It holds the k pivot rows,
+ * except for the leading k-by-k part in the LU block. It is stored in
+ * row-oriented form. Only the leading c-by-k part is in use.
+ *
+ * The C block is of dimension dr-by-dc. It holds the current contribution
+ * block. Only the leading r-by-c part is in use. The column indices in
+ * the C block are Fcols [0..c-1], and the row indices are Frows [0..r-1].
+ *
+ * dr is always odd, to avoid bad cache behavior.
+ */
+
+} WorkType ;
+
+
+/* -------------------------------------------------------------------------- */
+/* Symbolic */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This is is constructed by UMFPACK_symbolic, and is needed by UMFPACK_numeric
+ to factor the matrix.
+*/
+
+typedef struct /* SymbolicType */
+{
+
+ double
+ num_mem_usage_est, /* estimated max Numeric->Memory size */
+ num_mem_size_est, /* estimated final Numeric->Memory size */
+ peak_sym_usage, /* peak Symbolic and SymbolicWork usage */
+ sym, /* symmetry of pattern */
+ dnum_mem_init_usage, /* min Numeric->Memory for UMF_kernel_init */
+ amd_lunz, /* nz in LU for AMD, with symmetric pivoting */
+ lunz_bound ; /* max nx in LU, for arbitrary row pivoting */
+
+ Int valid, /* set to SYMBOLIC_VALID, for validity check */
+ max_nchains,
+ nchains,
+ *Chain_start,
+ *Chain_maxrows,
+ *Chain_maxcols,
+ maxnrows, /* largest number of rows in any front */
+ maxncols, /* largest number of columns in any front */
+ *Front_npivcol, /* Front_npivcol [j] = size of jth supercolumn*/
+ *Front_1strow, /* first row index in front j */
+ *Front_leftmostdesc, /* leftmost desc of front j */
+ *Front_parent, /* super-column elimination tree */
+ *Cperm_init, /* initial column ordering */
+ *Rperm_init, /* initial row ordering */
+ *Cdeg, *Rdeg,
+ *Esize,
+ dense_row_threshold,
+ n1, /* number of singletons */
+ nempty, /* MIN (nempty_row, nempty_col) */
+ *Diagonal_map, /* initial "diagonal" (after 2by2) */
+ esize, /* size of Esize array */
+ nfr,
+ n_row, n_col, /* matrix A is n_row-by-n_col */
+ nz, /* nz of original matrix */
+ nb, /* block size for BLAS 3 */
+ num_mem_init_usage, /* min Numeric->Memory for UMF_kernel_init */
+ nempty_row, nempty_col,
+
+ strategy,
+ ordering,
+ fixQ,
+ prefer_diagonal,
+ nzaat,
+ nzdiag,
+ amd_dmax ;
+
+} SymbolicType ;
+
+
+/* -------------------------------------------------------------------------- */
+/* for debugging only: */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_dump.h"
+
+/* -------------------------------------------------------------------------- */
+/* for statement coverage testing only: */
+/* -------------------------------------------------------------------------- */
+
+#ifdef TESTING
+
+/* for testing integer overflow: */
+#ifdef TEST_FOR_INTEGER_OVERFLOW
+#undef MAX_MARK
+#define MAX_MARK(n) (3*(n))
+#endif
+
+/* for testing out-of-memory conditions: */
+#define UMF_TCOV_TEST
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+GLOBAL EXTERN int umf_fail, umf_fail_lo, umf_fail_hi ;
+GLOBAL EXTERN int umf_realloc_fail, umf_realloc_lo, umf_realloc_hi ;
+
+/* for testing malloc count: */
+#define UMF_MALLOC_COUNT
+
+#endif
+
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_is_permutation.c b/src/C/SuiteSparse/UMFPACK/Source/umf_is_permutation.c
new file mode 100644
index 0000000..05ff965
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_is_permutation.c
@@ -0,0 +1,55 @@
+/* ========================================================================== */
+/* === UMF_is_permutation =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Return TRUE if P is a r-permutation vector, FALSE otherwise */
+/* P [0..r-1] must be an r-permutation of 0..n-1 */
+
+#include "umf_internal.h"
+
+GLOBAL Int UMF_is_permutation
+(
+ const Int P [ ], /* permutation of size r */
+ Int W [ ], /* workspace of size n */
+ Int n,
+ Int r
+)
+{
+ Int i, k ;
+
+ if (!P)
+ {
+ /* if P is (Int *) NULL, this is the identity permutation */
+ return (TRUE) ;
+ }
+
+ ASSERT (W != (Int *) NULL) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = FALSE ;
+ }
+ for (k = 0 ; k < r ; k++)
+ {
+ i = P [k] ;
+ DEBUG5 (("k "ID" i "ID"\n", k, i)) ;
+ if (i < 0 || i >= n)
+ {
+ DEBUG0 (("i out of range "ID" "ID"\n", i, n)) ;
+ return (FALSE) ;
+ }
+ if (W [i])
+ {
+ DEBUG0 (("i duplicate "ID"\n", i)) ;
+ return (FALSE) ;
+ }
+ W [i] = TRUE ;
+ }
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_is_permutation.h b/src/C/SuiteSparse/UMFPACK/Source/umf_is_permutation.h
new file mode 100644
index 0000000..89256bd
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_is_permutation.h
@@ -0,0 +1,13 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_is_permutation
+(
+ const Int P [ ],
+ Int W [ ],
+ Int n,
+ Int r
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_kernel.c b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel.c
new file mode 100644
index 0000000..e94522c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel.c
@@ -0,0 +1,299 @@
+/* ========================================================================== */
+/* === UMF_kernel =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Primary factorization routine. Called by UMFPACK_numeric.
+ Returns:
+ UMFPACK_OK if successful,
+ UMFPACK_ERROR_out_of_memory if out of memory, or
+ UMFPACK_ERROR_different_pattern if pattern of matrix (Ap and/or Ai)
+ has changed since the call to UMFPACK_*symbolic.
+*/
+
+#include "umf_internal.h"
+#include "umf_kernel_init.h"
+#include "umf_init_front.h"
+#include "umf_start_front.h"
+#include "umf_assemble.h"
+#include "umf_scale_column.h"
+#include "umf_local_search.h"
+#include "umf_create_element.h"
+#include "umf_extend_front.h"
+#include "umf_blas3_update.h"
+#include "umf_store_lu.h"
+#include "umf_kernel_wrapup.h"
+
+/* perform an action, and return if out of memory */
+#define DO(action) { if (! (action)) { return (UMFPACK_ERROR_out_of_memory) ; }}
+
+GLOBAL Int UMF_kernel
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int j, f1, f2, chain, nchains, *Chain_start, status, fixQ, evaporate,
+ *Front_npivcol, jmax, nb, drop ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize memory space and load the matrix. Optionally scale. */
+ /* ---------------------------------------------------------------------- */
+
+ if (!UMF_kernel_init (Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Numeric, Work, Symbolic))
+ {
+ /* UMF_kernel_init is guaranteed to succeed, since UMFPACK_numeric */
+ /* either allocates enough space or if not, UMF_kernel does not get */
+ /* called. So running out of memory here is a fatal error, and means */
+ /* that the user changed Ap and/or Ai since the call to */
+ /* UMFPACK_*symbolic. */
+ DEBUGm4 (("kernel init failed\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ nchains = Symbolic->nchains ;
+ Chain_start = Symbolic->Chain_start ;
+ Front_npivcol = Symbolic->Front_npivcol ;
+ nb = Symbolic->nb ;
+ fixQ = Symbolic->fixQ ;
+ drop = Numeric->droptol > 0.0 ;
+
+#ifndef NDEBUG
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ Int i ;
+ f1 = Chain_start [chain] ;
+ f2 = Chain_start [chain+1] - 1 ;
+ DEBUG1 (("\nCHain: "ID" start "ID" end "ID"\n", chain, f1, f2)) ;
+ for (i = f1 ; i <= f2 ; i++)
+ {
+ DEBUG1 (("Front "ID", npivcol "ID"\n", i, Front_npivcol [i])) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize each chain of frontal matrices */
+ /* ---------------------------------------------------------------------- */
+
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ f1 = Chain_start [chain] ;
+ f2 = Chain_start [chain+1] - 1 ;
+
+ /* ------------------------------------------------------------------ */
+ /* get the initial frontal matrix size for this chain */
+ /* ------------------------------------------------------------------ */
+
+ DO (UMF_start_front (chain, Numeric, Work, Symbolic)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factorize each front in the chain */
+ /* ------------------------------------------------------------------ */
+
+ for (Work->frontid = f1 ; Work->frontid <= f2 ; Work->frontid++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Initialize the pivot column candidate set */
+ /* -------------------------------------------------------------- */
+
+ Work->ncand = Front_npivcol [Work->frontid] ;
+ Work->lo = Work->nextcand ;
+ Work->hi = Work->nextcand + Work->ncand - 1 ;
+ jmax = MIN (MAX_CANDIDATES, Work->ncand) ;
+ DEBUGm1 ((">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Starting front "
+ ID", npivcol: "ID"\n", Work->frontid, Work->ncand)) ;
+ if (fixQ)
+ {
+ /* do not modify the column order */
+ jmax = 1 ;
+ }
+ DEBUGm1 (("Initial candidates: ")) ;
+ for (j = 0 ; j < jmax ; j++)
+ {
+ DEBUGm1 ((" "ID, Work->nextcand)) ;
+ ASSERT (Work->nextcand <= Work->hi) ;
+ Work->Candidates [j] = Work->nextcand++ ;
+ }
+ Work->nCandidates = jmax ;
+ DEBUGm1 (("\n")) ;
+
+ /* -------------------------------------------------------------- */
+ /* Assemble and factorize the current frontal matrix */
+ /* -------------------------------------------------------------- */
+
+ while (Work->ncand > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* get the pivot row and column */
+ /* ---------------------------------------------------------- */
+
+ status = UMF_local_search (Numeric, Work, Symbolic) ;
+ if (status == UMFPACK_ERROR_different_pattern)
+ {
+ /* :: pattern change detected in umf_local_search :: */
+ /* input matrix has changed since umfpack_*symbolic */
+ DEBUGm4 (("local search failed\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ /* no pivot found, discard and try again */
+ continue ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* update if front not extended or too many zeros in L,U */
+ /* ---------------------------------------------------------- */
+
+ if (Work->do_update)
+ {
+ UMF_blas3_update (Work) ;
+ if (drop)
+ {
+ DO (UMF_store_lu_drop (Numeric, Work)) ;
+ }
+ else
+ {
+ DO (UMF_store_lu (Numeric, Work)) ;
+ }
+ }
+
+ /* ---------------------------------------------------------- */
+ /* extend the frontal matrix, or start a new one */
+ /* ---------------------------------------------------------- */
+
+ if (Work->do_extend)
+ {
+ /* extend the current front */
+ DO (UMF_extend_front (Numeric, Work)) ;
+ }
+ else
+ {
+ /* finish the current front (if any) and start a new one */
+ DO (UMF_create_element (Numeric, Work, Symbolic)) ;
+ DO (UMF_init_front (Numeric, Work)) ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* Numerical & symbolic assembly into current frontal matrix */
+ /* ---------------------------------------------------------- */
+
+ if (fixQ)
+ {
+ UMF_assemble_fixq (Numeric, Work) ;
+ }
+ else
+ {
+ UMF_assemble (Numeric, Work) ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* scale the pivot column */
+ /* ---------------------------------------------------------- */
+
+ UMF_scale_column (Numeric, Work) ;
+
+ /* ---------------------------------------------------------- */
+ /* Numerical update if enough pivots accumulated */
+ /* ---------------------------------------------------------- */
+
+ evaporate = Work->fnrows == 0 || Work->fncols == 0 ;
+ if (Work->fnpiv >= nb || evaporate)
+ {
+ UMF_blas3_update (Work) ;
+ if (drop)
+ {
+ DO (UMF_store_lu_drop (Numeric, Work)) ;
+ }
+ else
+ {
+ DO (UMF_store_lu (Numeric, Work)) ;
+ }
+
+ }
+
+ Work->pivrow_in_front = FALSE ;
+ Work->pivcol_in_front = FALSE ;
+
+ /* ---------------------------------------------------------- */
+ /* If front is empty, evaporate it */
+ /* ---------------------------------------------------------- */
+
+ if (evaporate)
+ {
+ /* This does not create an element, just evaporates it.
+ * It ensures that a front is not 0-by-c or r-by-0. No
+ * memory is allocated, so it is guaranteed to succeed. */
+ (void) UMF_create_element (Numeric, Work, Symbolic) ;
+ Work->fnrows = 0 ;
+ Work->fncols = 0 ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------
+ * Wrapup the current frontal matrix. This is the last in a chain
+ * in the column elimination tree. The next frontal matrix
+ * cannot overlap with the current one, which will be its sibling
+ * in the column etree.
+ * ------------------------------------------------------------------ */
+
+ UMF_blas3_update (Work) ;
+ if (drop)
+ {
+ DO (UMF_store_lu_drop (Numeric, Work)) ;
+ }
+ else
+ {
+ DO (UMF_store_lu (Numeric, Work)) ;
+ }
+ Work->fnrows_new = Work->fnrows ;
+ Work->fncols_new = Work->fncols ;
+ DO (UMF_create_element (Numeric, Work, Symbolic)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* current front is now empty */
+ /* ------------------------------------------------------------------ */
+
+ Work->fnrows = 0 ;
+ Work->fncols = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* end the last Lchain and Uchain and finalize the LU factors */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_kernel_wrapup (Numeric, Symbolic, Work) ;
+
+ /* note that the matrix may be singular (this is OK) */
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_kernel.h b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel.h
new file mode 100644
index 0000000..4acd2ae
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel.h
@@ -0,0 +1,18 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_kernel
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.c b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.c
new file mode 100644
index 0000000..b15db9c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.c
@@ -0,0 +1,1056 @@
+/* ========================================================================== */
+/* === UMF_kernel_init ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Initialize the kernel: scale the matrix, load the initial elements, and
+ build the tuple lists.
+
+ Returns TRUE if successful, FALSE if out of memory or if the pattern has
+ changed since UMFPACK_*symbolic. UMFPACK_numeric allocates at least enough
+ space for UMF_kernel_init to succeed; otherwise it does not call
+ UMF_kernel_init. So an out-of-memory condition means that the pattern must
+ have gotten larger.
+*/
+
+#include "umf_internal.h"
+#include "umf_tuple_lengths.h"
+#include "umf_build_tuples.h"
+#include "umf_mem_init_memoryspace.h"
+#include "umf_mem_alloc_element.h"
+#include "umf_mem_alloc_head_block.h"
+#include "umf_mem_alloc_tail_block.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_scale.h"
+
+/* ========================================================================== */
+/* === packsp =============================================================== */
+/* ========================================================================== */
+
+/* remove zero or small entries from a column of L or a row of U */
+
+PRIVATE Int packsp /* returns new value of pnew */
+(
+ Int pnew, /* index into Memory of next free space */
+ Int *p_p, /* ptr to index of old pattern in Memory on input,
+ new pattern on output */
+ Int *p_len, /* ptr to length of old pattern on input,
+ new pattern on output */
+ Int drop, /* TRUE if small nonzero entries are to be dropped */
+ double droptol, /* the drop tolerance */
+ Unit *Memory /* contains the sparse vector on input and output */
+)
+{
+ Entry x ;
+ double s ;
+ Entry *Bx, *Bx2 ;
+ Int p, i, len, len_new, *Bi, *Bi2 ;
+
+ /* get the pointers to the sparse vector, and its length */
+ p = *p_p ;
+ len = *p_len ;
+ Bi = (Int *) (Memory + p) ; p += UNITS (Int, len) ;
+ Bx = (Entry *) (Memory + p) ; p += UNITS (Entry, len) ;
+ DEBUGm4 ((" p "ID" len "ID" pnew "ID"\n", p, len, pnew)) ;
+
+ /* the vector resides in Bi [0..len-1] and Bx [0..len-1] */
+
+ /* first, compact the vector in place */
+ len_new = 0 ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Bi [p] ;
+ x = Bx [p] ;
+ DEBUGm4 ((" old vector: i "ID" value: ", i)) ;
+ EDEBUGk (-4, x) ;
+ DEBUGm4 (("\n")) ;
+ ASSERT (i >= 0) ;
+ /* skip if zero or below drop tolerance */
+ if (IS_ZERO (x)) continue ;
+ if (drop)
+ {
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ }
+ /* store the value back into the vector */
+ if (len_new != p)
+ {
+ Bi [len_new] = i ;
+ Bx [len_new] = x ;
+ }
+ len_new++ ;
+ }
+ ASSERT (len_new <= len) ;
+
+ /* the vector is now in Bi [0..len_new-1] and Bx [0..len_new-1] */
+
+#ifndef NDEBUG
+ for (p = 0 ; p < len_new ; p++)
+ {
+ DEBUGm4 ((" new vector: i "ID" value: ", Bi [p])) ;
+ EDEBUGk (-4, Bx [p]) ;
+ DEBUGm4 (("\n")) ;
+ ASSERT (Bi [p] >= 0) ;
+ }
+#endif
+
+ /* allocate new space for the compacted vector */
+ *p_p = pnew ;
+ *p_len = len_new ;
+ Bi2 = (Int *) (Memory + pnew) ; pnew += UNITS (Int, len_new) ;
+ Bx2 = (Entry *) (Memory + pnew) ; pnew += UNITS (Entry, len_new) ;
+ DEBUGm4 ((" pnew "ID" len_new "ID"\n", pnew, len_new)) ;
+
+ /* shift the vector upwards, into its new space */
+ for (p = 0 ; p < len_new ; p++)
+ {
+ Bi2 [p] = Bi [p] ;
+ }
+ for (p = 0 ; p < len_new ; p++)
+ {
+ Bx2 [p] = Bx [p] ;
+ }
+
+#ifndef NDEBUG
+ for (p = 0 ; p < len_new ; p++)
+ {
+ DEBUGm4 ((" packed vec: i "ID" value: ", Bi2 [p])) ;
+ EDEBUGk (-4, Bx2 [p]) ;
+ DEBUGm4 (("\n")) ;
+ ASSERT (Bi2 [p] >= 0) ;
+ }
+#endif
+
+ /* return the pointer to the space just after the new vector */
+ return (pnew) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_kernel_init ====================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_kernel_init
+(
+ const Int Ap [ ], /* user's input matrix (not modified) */
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry x, pivot_value ;
+ double unused = 0, rsmin, rsmax, rs, droptol ;
+ Entry *D, *C, *Lval, **Rpx ;
+ double *Rs ;
+ Int row, k, oldcol, size, e, p1, p2, p, nz, *Rows, *Cols, *E, i, *Upos,
+ *Lpos, n_row, n_col, *Wp, *Cperm_init, *Frpos, *Fcpos, *Row_degree, nn,
+ *Row_tlen, *Col_degree, *Col_tlen, oldrow, newrow, ilast, *Wrp,
+ *Rperm_init, col, n_inner, prefer_diagonal, *Diagonal_map, nempty,
+ *Diagonal_imap, fixQ, rdeg, cdeg, nempty_col, *Esize, esize, pnew,
+ *Lip, *Uip, *Lilen, *Uilen, llen, pa, *Cdeg, *Rdeg, n1, clen, do_scale,
+ lnz, unz, lip, uip, k1, *Rperm, *Cperm, pivcol, *Li, lilen, drop,
+ **Rpi, nempty_row, dense_row_threshold, empty_elements, rpi, rpx ;
+ Element *ep ;
+ Unit *Memory ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+#ifndef NRECIPROCAL
+ Int do_recip = FALSE ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG0 (("KERNEL INIT\n")) ;
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ nempty_col = Symbolic->nempty_col ;
+ nempty_row = Symbolic->nempty_row ;
+ nempty = MIN (nempty_row, nempty_col) ;
+ ASSERT (n_row > 0 && n_col > 0) ;
+ Cperm_init = Symbolic->Cperm_init ;
+ Rperm_init = Symbolic->Rperm_init ;
+ Cdeg = Symbolic->Cdeg ;
+ Rdeg = Symbolic->Rdeg ;
+ n1 = Symbolic->n1 ;
+ dense_row_threshold = Symbolic->dense_row_threshold ;
+ DEBUG0 (("Singletons: "ID"\n", n1)) ;
+ Work->nforced = 0 ;
+ Work->ndiscard = 0 ;
+ Work->noff_diagonal = 0 ;
+
+ nz = Ap [n_col] ;
+ if (nz < 0 || Ap [0] != 0 || nz != Symbolic->nz)
+ {
+ DEBUGm4 (("nz or Ap [0] bad\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ prefer_diagonal = Symbolic->prefer_diagonal ;
+ Diagonal_map = Work->Diagonal_map ;
+ Diagonal_imap = Work->Diagonal_imap ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize the Numeric->Memory space for LU, elements, and tuples */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_mem_init_memoryspace (Numeric) ;
+ DEBUG1 (("Kernel init head usage, before allocs: "ID"\n", Numeric->ihead)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize the Work and Numeric objects */
+ /* ---------------------------------------------------------------------- */
+
+ /* current front is empty */
+ Work->fnpiv = 0 ;
+ Work->fncols = 0 ;
+ Work->fnrows = 0 ;
+ Work->fncols_max = 0 ;
+ Work->fnrows_max = 0 ;
+ Work->fnzeros = 0 ;
+ Work->fcurr_size = 0 ;
+ Work->fnr_curr = 0 ;
+ Work->fnc_curr = 0 ;
+
+ Work->nz = nz ;
+ Work->prior_element = EMPTY ;
+ Work->ulen = 0 ;
+ Work->llen = 0 ;
+ Work->npiv = n1 ;
+ Work->frontid = 0 ;
+ Work->nextcand = n1 ;
+
+ Memory = Numeric->Memory ;
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+ Row_degree = Numeric->Rperm ;
+ Col_degree = Numeric->Cperm ;
+ /* Row_tuples = Numeric->Uip ; not needed */
+ Row_tlen = Numeric->Uilen ;
+ /* Col_tuples = Numeric->Lip ; not needed */
+ Col_tlen = Numeric->Lilen ;
+
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ Lilen = Numeric->Lilen ;
+ Uilen = Numeric->Uilen ;
+
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+ Wp = Work->Wp ;
+ Wrp = Work->Wrp ;
+
+ D = Numeric->D ;
+ Upos = Numeric->Upos ;
+ Lpos = Numeric->Lpos ;
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ CLEAR (D [k]) ;
+ }
+
+ Rs = Numeric->Rs ;
+
+ for (row = 0 ; row <= n_row ; row++)
+ {
+ Lpos [row] = EMPTY ;
+ /* Row_tuples [row] = 0 ; set in UMF_build_tuples */
+ /* Row_degree [row] = 0 ; initialized below */
+ Row_tlen [row] = 0 ;
+ /* Frpos [row] = EMPTY ; do this later */
+ }
+
+ for (col = 0 ; col <= n_col ; col++)
+ {
+ Upos [col] = EMPTY ;
+ /* Col_tuples [col] = 0 ; set in UMF_build_tuples */
+ /* Col_degree [col] = 0 ; initialized below */
+ Col_tlen [col] = 0 ;
+ Fcpos [col] = EMPTY ;
+ Wrp [col] = 0 ;
+ }
+ Work->Wrpflag = 1 ;
+
+ /* When cleared, Wp [0..nn] is < 0 */
+ for (i = 0 ; i <= nn ; i++)
+ {
+ Wp [i] = EMPTY ;
+ }
+ /* In col search, Wp [row] is set to a position, which is >= 0. */
+
+ /* When cleared, Wrp [0..n_col] is < Wrpflag */
+ /* In row search, Wrp [col] is set to Wrpflag. */
+
+ /* no need to initialize Wm, Wio, Woi, and Woo */
+
+ /* clear the external degree counters */
+ Work->cdeg0 = 1 ;
+ Work->rdeg0 = 1 ;
+
+ fixQ = Symbolic->fixQ ;
+
+ E = Work->E ;
+
+ Numeric->n_row = n_row ;
+ Numeric->n_col = n_col ;
+ Numeric->npiv = 0 ;
+ Numeric->nnzpiv = 0 ;
+ Numeric->min_udiag = 0.0 ;
+ Numeric->max_udiag = 0.0 ;
+ Numeric->rcond = 0.0 ;
+ Numeric->isize = 0 ;
+ Numeric->nLentries = 0 ;
+ Numeric->nUentries = 0 ;
+ Numeric->lnz = 0 ;
+ Numeric->unz = 0 ;
+ Numeric->all_lnz = 0 ;
+ Numeric->all_unz = 0 ;
+ Numeric->maxfrsize = 0 ;
+ Numeric->maxnrows = 0 ;
+ Numeric->maxncols = 0 ;
+ Numeric->flops = 0. ;
+ Numeric->n1 = n1 ;
+ droptol = Numeric->droptol ;
+ drop = (droptol > 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the scale factors, if requested, and check the input matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* UMFPACK_SCALE_SUM: Rs [i] = sum of the absolute values in row i.
+ * UMFPACK_SCALE_MAX: Rs [i] = max of the absolute values in row i.
+ *
+ * If A is complex, an approximate abs is used (|xreal| + |ximag|).
+ *
+ * If min (Rs [0..n_row]) >= RECIPROCAL_TOLERANCE, then the scale
+ * factors are inverted, and the rows of A are multiplied by the scale
+ * factors. Otherwise, the rows are divided by the scale factors. If
+ * NRECIPROCAL is defined, then the rows are always divided by the scale
+ * factors.
+ *
+ * For MATLAB (either built-in routine or mexFunction), or for gcc,
+ * the rows are always divided by the scale factors.
+ */
+
+ do_scale = (Numeric->scale != UMFPACK_SCALE_NONE) ;
+
+ if (do_scale)
+ {
+ int do_max = Numeric->scale == UMFPACK_SCALE_MAX ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rs [row] = 0.0 ;
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ ilast = EMPTY ;
+ p1 = Ap [col] ;
+ p2 = Ap [col+1] ;
+ if (p1 > p2)
+ {
+ /* invalid matrix */
+ DEBUGm4 (("invalid matrix (Ap)\n")) ;
+ return (FALSE) ;
+ }
+ for (p = p1 ; p < p2 ; p++)
+ {
+ Entry aij ;
+ double value ;
+ row = Ai [p] ;
+ if (row <= ilast || row >= n_row)
+ {
+ /* invalid matrix, columns must be sorted, no duplicates */
+ DEBUGm4 (("invalid matrix (Ai)\n")) ;
+ return (FALSE) ;
+ }
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ rs = Rs [row] ;
+ if (!SCALAR_IS_NAN (rs))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ /* if any entry in the row is NaN, then the scale factor
+ * is NaN too (for now) and then set to 1.0 below */
+ Rs [row] = value ;
+ }
+ else if (do_max)
+ {
+ Rs [row] = MAX (rs, value) ;
+ }
+ else
+ {
+ Rs [row] += value ;
+ }
+ }
+ DEBUG4 (("i "ID" j "ID" value %g, Rs[i]: %g\n",
+ row, col, value, Rs[row])) ;
+ ilast = row ;
+ }
+ }
+ DEBUG2 (("Rs[0] = %30.20e\n", Rs [0])) ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rs = Rs [row] ;
+ if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs))
+ {
+ /* don't scale a completely zero row, or one with NaN's */
+ Rs [row] = 1.0 ;
+ }
+ }
+ rsmin = Rs [0] ;
+ rsmax = Rs [0] ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ DEBUG2 (("sum %30.20e ", Rs [row])) ;
+ rsmin = MIN (rsmin, Rs [row]) ;
+ rsmax = MAX (rsmax, Rs [row]) ;
+ DEBUG2 (("Rs["ID"] = %30.20e\n", row, Rs [row])) ;
+ }
+#ifndef NRECIPROCAL
+ /* multiply by the reciprocal if Rs is not too small */
+ do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ;
+ if (do_recip)
+ {
+ /* invert the scale factors */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rs [row] = 1.0 / Rs [row] ;
+ }
+ }
+#endif
+ }
+ else
+ {
+ /* no scaling, rsmin and rsmax not computed */
+ rsmin = -1 ;
+ rsmax = -1 ;
+#ifndef NRECIPROCAL
+ do_recip = FALSE ;
+#endif
+ /* check the input matrix */
+ if (AMD_valid (n_row, n_col, Ap, Ai) != AMD_OK)
+ {
+ /* matrix is invalid */
+ return (FALSE) ;
+ }
+ }
+
+ Numeric->rsmin = rsmin ;
+ Numeric->rsmax = rsmax ;
+#ifndef NRECIPROCAL
+ Numeric->do_recip = do_recip ;
+#else
+ Numeric->do_recip = FALSE ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the inverse row Rperm_init permutation (use Frpos as temp) */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG3 (("\n\n===================LOAD_MATRIX:\n")) ;
+
+ for (newrow = 0 ; newrow < n_row ; newrow++)
+ {
+ oldrow = Rperm_init [newrow] ;
+ ASSERT (oldrow >= 0 && oldrow < n_row) ;
+ Frpos [oldrow] = newrow ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the diagonal imap if doing symmetric pivoting */
+ /* ---------------------------------------------------------------------- */
+
+ if (prefer_diagonal)
+ {
+ ASSERT (n_row == n_col) ;
+ ASSERT (nempty_col == Symbolic->nempty_row) ;
+ ASSERT (nempty_col == nempty) ;
+ for (i = 0 ; i < nn ; i++)
+ {
+ Diagonal_map [i] = EMPTY ;
+ Diagonal_imap [i] = EMPTY ;
+ }
+ for (k = n1 ; k < nn - nempty ; k++)
+ {
+ newrow = Symbolic->Diagonal_map [k] ;
+ Diagonal_map [k] = newrow ;
+ Diagonal_imap [newrow] = k ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate O (n_row) workspace at the tail end of Memory */
+ /* ---------------------------------------------------------------------- */
+
+ rpi = UMF_mem_alloc_tail_block (Numeric, UNITS (Int *, n_row+1)) ;
+ rpx = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry *, n_row+1)) ;
+ if (!rpi || !rpx)
+ {
+ /* :: pattern change (out of memory for Rpx, Rpx) :: */
+ /* out of memory, which can only mean that the pattern has changed */
+ return (FALSE) ; /* pattern changed */
+ }
+ Rpi = (Int **) (Memory + rpx) ;
+ Rpx = (Entry **) (Memory + rpi) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the LU factors for the columns of the singletons */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("Allocating singletons:\n")) ;
+ for (k = 0 ; k < n1 ; k++)
+ {
+ lnz = Cdeg [k] - 1 ;
+ unz = Rdeg [k] - 1 ;
+
+ DEBUG1 (("Singleton k "ID" pivrow "ID" pivcol "ID" cdeg "ID" rdeg "
+ ID"\n", k, Rperm_init [k], Cperm_init [k], Cdeg [k], Rdeg [k])) ;
+ ASSERT (unz >= 0 && lnz >= 0 && (lnz == 0 || unz == 0)) ;
+ DEBUG1 ((" lnz "ID" unz "ID"\n", lnz, unz)) ;
+
+ size = UNITS (Int, lnz) + UNITS (Entry, lnz)
+ + UNITS (Int, unz) + UNITS (Entry, unz) ;
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ DEBUG1 (("Kernel init head usage: "ID"\n", Numeric->ihead)) ;
+ if (!p)
+ {
+ /* :: pattern change (out of memory for singletons) :: */
+ DEBUG0 (("Pattern has gotten larger - kernel init failed\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ Numeric->all_lnz += lnz ;
+ Numeric->all_unz += unz ;
+
+ /* allocate the column of L */
+ lip = p ;
+ p += UNITS (Int, lnz) ;
+ p += UNITS (Entry, lnz) ;
+
+ /* allocate the row of U */
+ uip = p ;
+ Rpi [k] = (Int *) (Memory + p) ;
+ p += UNITS (Int, unz) ;
+ Rpx [k] = (Entry *) (Memory + p) ;
+ /* p += UNITS (Entry, unz) ; (not needed) */
+
+ /* a single column of L (no Lchains) */
+ Lip [k] = lip ;
+ Lilen [k] = lnz ;
+
+ /* a single row of L (no Uchains) */
+ Uip [k] = uip ;
+ Uilen [k] = unz ;
+
+ Wp [k] = unz ;
+
+ /* save row and column inverse permutation */
+ k1 = ONES_COMPLEMENT (k) ;
+ Rperm [k] = k1 ; /* aliased with Row_degree */
+ Cperm [k] = k1 ; /* aliased with Col_degree */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* current frontal matrix is empty */
+ /* ---------------------------------------------------------------------- */
+
+ e = 0 ;
+ E [e] = 0 ;
+ Work->Flublock = (Entry *) NULL ;
+ Work->Flblock = (Entry *) NULL ;
+ Work->Fublock = (Entry *) NULL ;
+ Work->Fcblock = (Entry *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the column elements */
+ /* ---------------------------------------------------------------------- */
+
+ Esize = Symbolic->Esize ;
+ empty_elements = FALSE ;
+ for (k = n1 ; k < n_col - nempty_col ; k++)
+ {
+ e = k - n1 + 1 ;
+ ASSERT (e < Work->elen) ;
+ esize = Esize ? Esize [k-n1] : Cdeg [k] ;
+ if (esize > 0)
+ {
+ /* allocate an element for this column */
+ E [e] = UMF_mem_alloc_element (Numeric, esize, 1, &Rows, &Cols, &C,
+ &size, &ep) ;
+ if (E [e] <= 0)
+ {
+ /* :: pattern change (out of memory for column elements) :: */
+ return (FALSE) ; /* pattern has changed */
+ }
+ Cols [0] = k ;
+ DEBUG0 (("Got column element e "ID" esize "ID"\n", e, esize)) ;
+ }
+ else
+ {
+ /* all rows in this column are dense, or empty */
+ E [e] = 0 ;
+ empty_elements = TRUE ;
+ DEBUG0 (("column element e is empty "ID"\n", e)) ;
+ }
+ }
+ DEBUG0 (("e "ID" n_col "ID" nempty_col "ID" n1 "ID"\n", e, n_col,
+ nempty_col, n1)) ;
+ ASSERT (e == n_col - nempty_col - n1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the row elements for dense rows of A (if any) */
+ /* ---------------------------------------------------------------------- */
+
+ if (Esize)
+ {
+ for (k = n1 ; k < n_row - nempty_row ; k++)
+ {
+ rdeg = Rdeg [k] ;
+ if (rdeg > dense_row_threshold)
+ {
+ /* allocate an element for this dense row */
+ e++ ;
+ ASSERT (e < Work->elen) ;
+ E [e] = UMF_mem_alloc_element (Numeric, 1, rdeg, &Rows, &Cols,
+ &C, &size, &ep) ;
+ if (E [e] <= 0)
+ {
+ /* :: pattern change (out of memory for row elements) :: */
+ return (FALSE) ; /* pattern has changed */
+ }
+ Rows [0] = k ;
+ Rpi [k] = Cols ;
+ Rpx [k] = C ;
+ Wp [k] = rdeg ;
+ DEBUG0 (("Got row element e "ID" rdeg "ID"\n", e, rdeg)) ;
+ }
+ }
+ }
+
+ /* elements are currently in the range 0 to e */
+ Work->nel = e ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create the first n1 columns of L and U */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ pivcol = Cperm_init [k] ;
+ p2 = Ap [pivcol+1] ;
+
+ /* get the kth column of L */
+ p = Lip [k] ;
+ Li = (Int *) (Memory + p) ;
+ lilen = Lilen [k] ;
+ p += UNITS (Int, lilen) ;
+ Lval = (Entry *) (Memory + p) ;
+
+ llen = 0 ;
+
+ for (pa = Ap [pivcol] ; pa < p2 ; pa++)
+ {
+ oldrow = Ai [pa] ;
+ newrow = Frpos [oldrow] ;
+ ASSIGN (x, Ax, Az, pa, split) ;
+
+ /* scale the value using the scale factors, Rs */
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ SCALE (x, Rs [oldrow]) ;
+ }
+ else
+#endif
+ {
+ SCALE_DIV (x, Rs [oldrow]) ;
+ }
+ }
+
+ if (newrow == k)
+ {
+ /* this is the pivot entry itself */
+ ASSERT (oldrow == Rperm_init [k]) ;
+ D [k] = x ;
+ }
+ else if (newrow < k)
+ {
+ /* this entry goes in a row of U */
+ DEBUG1 (("Singleton row of U: k "ID" newrow "ID"\n",
+ k, newrow)) ;
+ if (--(Wp [newrow]) < 0)
+ {
+ /* :: pattern change (singleton row too lengthy) :: */
+ DEBUGm4 (("bad U singleton row (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ *(Rpi [newrow]++) = k ;
+ *(Rpx [newrow]++) = x ;
+ }
+ else
+ {
+ /* this entry goes in a column of L */
+ DEBUG1 (("Singleton col of L: k "ID" newrow "ID"\n",
+ k, newrow)) ;
+ if (llen >= lilen)
+ {
+ DEBUGm4 (("bad L singleton col (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ Li [llen] = newrow ;
+ Lval [llen] = x ;
+ llen++ ;
+ }
+ }
+
+ if (llen != lilen)
+ {
+ /* :: pattern change (singleton column too lengthy) :: */
+ DEBUGm4 (("bad L singleton col (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ /* scale the column of L */
+ if (llen > 0)
+ {
+ pivot_value = D [k] ;
+ UMF_scale (llen, pivot_value, Lval) ;
+ }
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the elements and copy the columns of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* also apply the row and column pre-ordering. */
+ for (k = n1 ; k < n_col ; k++)
+ {
+ /* The newcol is k, which is what the name of the column is in the
+ * UMFPACK kernel. The user's name for the column is oldcol. */
+ oldcol = Cperm_init [k] ;
+
+ ASSERT (oldcol >= 0 && oldcol < n_col) ;
+
+ p2 = Ap [oldcol+1] ;
+
+ cdeg = Cdeg [k] ;
+ ASSERT (cdeg >= 0) ;
+ ASSERT (IMPLIES (
+ (Symbolic->ordering != UMFPACK_ORDERING_GIVEN) && n1 > 0,
+ cdeg > 1 || cdeg == 0)) ;
+
+ /* if fixQ: set Col_degree to 0 for the NON_PIVOTAL_COL macro */
+ Col_degree [k] = fixQ ? 0 : cdeg ;
+
+ /* get the element for this column (if any) */
+ e = k - n1 + 1 ;
+ if (k < n_col - nempty_col)
+ {
+ esize = Esize ? Esize [k-n1] : cdeg ;
+ if (E [e])
+ {
+ Int ncols, nrows ;
+ Unit *pp ;
+ pp = Memory + E [e] ;
+ GET_ELEMENT (ep, pp, Cols, Rows, ncols, nrows, C) ;
+ ASSERT (ncols == 1) ;
+ ASSERT (nrows == esize) ;
+ ASSERT (Cols [0] == k) ;
+ }
+ }
+ else
+ {
+ ASSERT (cdeg == 0) ;
+ esize = 0 ;
+ }
+
+ clen = 0 ;
+
+ for (pa = Ap [oldcol] ; pa < p2 ; pa++)
+ {
+ oldrow = Ai [pa] ;
+ newrow = Frpos [oldrow] ;
+ ASSIGN (x, Ax, Az, pa, split) ;
+
+ /* scale the value using the scale factors, Rs */
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the reciprocal */
+ SCALE (x, Rs [oldrow]) ;
+ }
+ else
+#endif
+ {
+ /* divide instead */
+ SCALE_DIV (x, Rs [oldrow]) ;
+ }
+ }
+
+ rdeg = Rdeg [newrow] ;
+ if (newrow < n1 || rdeg > dense_row_threshold)
+ {
+ /* this entry goes in a row of U or into a dense row */
+ DEBUG1 (("Singleton/dense row of U: k "ID" newrow "ID"\n",
+ k, newrow)) ;
+ if (--(Wp [newrow]) < 0)
+ {
+ DEBUGm4 (("bad row of U or A (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ *(Rpi [newrow]++) = k ;
+ *(Rpx [newrow]++) = x ;
+ }
+ else
+ {
+ /* this entry goes in an initial element */
+ DEBUG1 (("In element k "ID" e "ID" newrow "ID"\n",
+ k, e, newrow)) ;
+ if (clen >= esize)
+ {
+ DEBUGm4 (("bad A column (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ ASSERT (E [e]) ;
+ ASSERT (k < n_col - nempty_col) ;
+ Rows [clen] = newrow ;
+ C [clen] = x ;
+ clen++ ;
+#ifndef NDEBUG
+ if (Diagonal_map && (newrow == Diagonal_map [k]))
+ {
+ DEBUG0 (("Diagonal: old: row "ID" col "ID" : "
+ "new: row "ID" col "ID" : ",
+ oldrow, oldcol, newrow, k)) ;
+ EDEBUGk (0, x) ;
+ }
+#endif
+ }
+ }
+
+ if (clen != esize)
+ {
+ /* :: pattern change (singleton column too short) :: */
+ DEBUGm4 (("bad A column (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the Rpi and Rpx workspace at the tail end of memory */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_mem_free_tail_block (Numeric, rpi) ;
+ UMF_mem_free_tail_block (Numeric, rpx) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* prune zeros and small entries from the singleton rows and columns */
+ /* ---------------------------------------------------------------------- */
+
+ if (n1 > 0)
+ {
+ pnew = Lip [0] ;
+ ASSERT (pnew == 1) ;
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUGm4 (("\nPrune singleton L col "ID"\n", k)) ;
+ pnew = packsp (pnew, &Lip [k], &Lilen [k], drop, droptol, Memory) ;
+ Numeric->lnz += Lilen [k] ;
+ DEBUGm4 (("\nPrune singleton U row "ID"\n", k)) ;
+ pnew = packsp (pnew, &Uip [k], &Uilen [k], drop, droptol, Memory) ;
+ Numeric->unz += Uilen [k] ;
+ }
+ /* free the unused space at the head of memory */
+ Numeric->ihead = pnew ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize row degrees */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ if (Wp [k] != 0)
+ {
+ /* :: pattern change (singleton row too short) :: */
+ DEBUGm4 (("bad U singleton row (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ }
+
+ for (k = n1 ; k < n_row ; k++)
+ {
+ DEBUG1 (("Initial row degree k "ID" oldrow "ID" Rdeg "ID"\n",
+ k, Rperm_init [k], Rdeg [k])) ;
+ rdeg = Rdeg [k] ;
+ Row_degree [k] = rdeg ;
+ if (rdeg > dense_row_threshold && Wp [k] != 0)
+ {
+ /* :: pattern change (dense row too short) :: */
+ DEBUGm4 (("bad dense row (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ }
+
+#ifndef NDEBUG
+ if (prefer_diagonal)
+ {
+ Entry aij ;
+ Int *InvCperm, newcol ;
+ UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, n1, nn, nempty) ;
+ InvCperm = (Int *) malloc (n_col * sizeof (Int)) ;
+ ASSERT (InvCperm != (Int *) NULL) ;
+ for (newcol = 0 ; newcol < n_col ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ InvCperm [oldcol] = newcol ;
+ }
+ DEBUGm3 (("Diagonal of P2*A:\n")) ;
+ for (oldcol = 0 ; oldcol < n_col ; oldcol++)
+ {
+ newcol = InvCperm [oldcol] ;
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Frpos [oldrow] ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ if (newrow == Diagonal_map [newcol])
+ {
+ DEBUG0 (("old row "ID" col "ID" new row "ID" col "ID,
+ oldrow, oldcol, newrow, newcol)) ;
+ EDEBUGk (0, aij) ;
+ DEBUG0 ((" scaled ")) ;
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ SCALE (aij, Rs [oldrow]) ;
+ }
+ else
+#endif
+ {
+ SCALE_DIV (aij, Rs [oldrow]) ;
+ }
+ }
+ EDEBUGk (0, aij) ;
+ DEBUG0 (("\n")) ;
+ }
+ }
+ }
+ free (InvCperm) ;
+ }
+#endif
+
+ Col_degree [n_col] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* pack the element name space */
+ /* ---------------------------------------------------------------------- */
+
+ if (empty_elements)
+ {
+ Int e2 = 0 ;
+ DEBUG0 (("\n\n============= Packing element space\n")) ;
+ for (e = 1 ; e <= Work->nel ; e++)
+ {
+ if (E [e])
+ {
+ e2++ ;
+ E [e2] = E [e] ;
+ }
+ }
+ Work->nel = e2 ;
+ }
+
+#ifndef NDEBUG
+ DEBUG0 (("Number of initial elements: "ID"\n", Work->nel)) ;
+ for (e = 0 ; e <= Work->nel ; e++) UMF_dump_element (Numeric, Work,e,TRUE) ;
+#endif
+
+ for (e = Work->nel + 1 ; e < Work->elen ; e++)
+ {
+ E [e] = 0 ;
+ }
+
+ /* Frpos no longer needed */
+ for (row = 0 ; row <= n_row ; row++)
+ {
+ Frpos [row] = EMPTY ;
+ }
+
+ /* clear Wp */
+ for (i = 0 ; i <= nn ; i++)
+ {
+ Wp [i] = EMPTY ;
+ }
+
+ DEBUG1 (("Kernel init head usage: "ID"\n", Numeric->ihead)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* build the tuple lists */
+ /* ---------------------------------------------------------------------- */
+
+ /* if the memory usage changes, then the pattern has changed */
+
+ (void) UMF_tuple_lengths (Numeric, Work, &unused) ;
+ if (!UMF_build_tuples (Numeric, Work))
+ {
+ /* :: pattern change (out of memory in umf_build_tuples) :: */
+ /* We ran out of memory, which can only mean that */
+ /* the pattern (Ap and or Ai) has changed (gotten larger). */
+ DEBUG0 (("Pattern has gotten larger - build tuples failed\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ Numeric->init_usage = Numeric->max_usage ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row merge sets */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i <= Symbolic->nfr ; i++)
+ {
+ Work->Front_new1strow [i] = Symbolic->Front_1strow [i] ;
+ }
+
+#ifndef NDEBUG
+ UMF_dump_rowmerge (Numeric, Symbolic, Work) ;
+ DEBUG6 (("Column form of original matrix:\n")) ;
+ UMF_dump_col_matrix (Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Ai, Ap, n_row, n_col, nz) ;
+ UMF_dump_memory (Numeric) ;
+ UMF_dump_matrix (Numeric, Work, FALSE) ;
+ DEBUG0 (("kernel init done...\n")) ;
+#endif
+
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.h b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.h
new file mode 100644
index 0000000..312e8e8
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_init.h
@@ -0,0 +1,18 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_kernel_init
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c
new file mode 100644
index 0000000..98f2821
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c
@@ -0,0 +1,466 @@
+/* ========================================================================== */
+/* === UMF_kernel_wrapup ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The matrix is factorized. Finish the LU data structure. */
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_kernel_wrapup
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry pivot_value ;
+ double d ;
+ Entry *D ;
+ Int i, k, col, row, llen, ulen, *ip, *Rperm, *Cperm, *Lilen, npiv, lp,
+ *Uilen, *Lip, *Uip, *Cperm_init, up, pivrow, pivcol, *Lpos, *Upos, *Wr,
+ *Wc, *Wp, *Frpos, *Fcpos, *Row_degree, *Col_degree, *Rperm_init,
+ n_row, n_col, n_inner, zero_pivot, nan_pivot, n1 ;
+
+#ifndef NDEBUG
+ UMF_dump_matrix (Numeric, Work, FALSE) ;
+#endif
+
+ DEBUG0 (("Kernel complete, Starting Kernel wrapup\n")) ;
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+ Lilen = Numeric->Lilen ;
+ Uilen = Numeric->Uilen ;
+ Upos = Numeric->Upos ;
+ Lpos = Numeric->Lpos ;
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+
+ npiv = Work->npiv ;
+ Numeric->npiv = npiv ;
+ Numeric->ulen = Work->ulen ;
+
+ ASSERT (n_row == Numeric->n_row) ;
+ ASSERT (n_col == Symbolic->n_col) ;
+ DEBUG0 (("Wrap-up: npiv "ID" ulen "ID"\n", npiv, Numeric->ulen)) ;
+ ASSERT (npiv <= n_inner) ;
+
+ /* this will be nonzero only if matrix is singular or rectangular */
+ ASSERT (IMPLIES (npiv == n_col, Work->ulen == 0)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the smallest and largest entries in D */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivot_value = D [k] ;
+ ABS (d, pivot_value) ;
+ zero_pivot = SCALAR_IS_ZERO (d) ;
+ nan_pivot = SCALAR_IS_NAN (d) ;
+
+ if (!zero_pivot)
+ {
+ /* the pivot is nonzero, but might be Inf or NaN */
+ Numeric->nnzpiv++ ;
+ }
+
+ if (k == 0)
+ {
+ Numeric->min_udiag = d ;
+ Numeric->max_udiag = d ;
+ }
+ else
+ {
+ /* min (abs (diag (U))) behaves as follows: If any entry is zero,
+ then the result is zero (regardless of the presence of NaN's).
+ Otherwise, if any entry is NaN, then the result is NaN.
+ Otherwise, the result is the smallest absolute value on the
+ diagonal of U.
+ */
+
+ if (SCALAR_IS_NONZERO (Numeric->min_udiag))
+ {
+ if (zero_pivot || nan_pivot)
+ {
+ Numeric->min_udiag = d ;
+ }
+ else if (!SCALAR_IS_NAN (Numeric->min_udiag))
+ {
+ /* d and min_udiag are both non-NaN */
+ Numeric->min_udiag = MIN (Numeric->min_udiag, d) ;
+ }
+ }
+
+ /*
+ max (abs (diag (U))) behaves as follows: If any entry is NaN
+ then the result is NaN. Otherise, the result is the largest
+ absolute value on the diagonal of U.
+ */
+
+ if (nan_pivot)
+ {
+ Numeric->max_udiag = d ;
+ }
+ else if (!SCALAR_IS_NAN (Numeric->max_udiag))
+ {
+ /* d and max_udiag are both non-NaN */
+ Numeric->max_udiag = MAX (Numeric->max_udiag, d) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check if matrix is singular or rectangular */
+ /* ---------------------------------------------------------------------- */
+
+ Col_degree = Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Rperm ; /* for NON_PIVOTAL_ROW macro */
+
+ if (npiv < n_row)
+ {
+ /* finalize the row permutation */
+ k = npiv ;
+ DEBUGm3 (("Singular pivot rows "ID" to "ID"\n", k, n_row-1)) ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ Rperm [row] = ONES_COMPLEMENT (k) ;
+ DEBUGm3 (("Singular row "ID" is k: "ID" pivot row\n", row, k)) ;
+ ASSERT (!NON_PIVOTAL_ROW (row)) ;
+ Lpos [row] = EMPTY ;
+ Uip [row] = EMPTY ;
+ Uilen [row] = 0 ;
+ k++ ;
+ }
+ }
+ ASSERT (k == n_row) ;
+ }
+
+ if (npiv < n_col)
+ {
+ /* finalize the col permutation */
+ k = npiv ;
+ DEBUGm3 (("Singular pivot cols "ID" to "ID"\n", k, n_col-1)) ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ Cperm [col] = ONES_COMPLEMENT (k) ;
+ DEBUGm3 (("Singular col "ID" is k: "ID" pivot row\n", col, k)) ;
+ ASSERT (!NON_PIVOTAL_COL (col)) ;
+ Upos [col] = EMPTY ;
+ Lip [col] = EMPTY ;
+ Lilen [col] = 0 ;
+ k++ ;
+ }
+ }
+ ASSERT (k == n_col) ;
+ }
+
+ if (npiv < n_inner)
+ {
+ /* finalize the diagonal of U */
+ DEBUGm3 (("Diag of U is zero, "ID" to "ID"\n", npiv, n_inner-1)) ;
+ for (k = npiv ; k < n_inner ; k++)
+ {
+ CLEAR (D [k]) ;
+ }
+ }
+
+ /* save the pattern of the last row of U */
+ if (Numeric->ulen > 0)
+ {
+ DEBUGm3 (("Last row of U is not empty\n")) ;
+ Numeric->Upattern = Work->Upattern ;
+ Work->Upattern = (Int *) NULL ;
+ }
+
+ DEBUG2 (("Nnzpiv: "ID" npiv "ID"\n", Numeric->nnzpiv, npiv)) ;
+ ASSERT (Numeric->nnzpiv <= npiv) ;
+ if (Numeric->nnzpiv < n_inner && !SCALAR_IS_NAN (Numeric->min_udiag))
+ {
+ /* the rest of the diagonal is zero, so min_udiag becomes 0,
+ * unless it is already NaN. */
+ Numeric->min_udiag = 0.0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* size n_row, n_col workspaces that can be used here: */
+ /* ---------------------------------------------------------------------- */
+
+ Frpos = Work->Frpos ; /* of size n_row+1 */
+ Fcpos = Work->Fcpos ; /* of size n_col+1 */
+ Wp = Work->Wp ; /* of size MAX(n_row,n_col)+1 */
+ /* Work->Upattern ; cannot be used (in Numeric) */
+ Wr = Work->Lpattern ; /* of size n_row+1 */
+ Wc = Work->Wrp ; /* of size n_col+1 or bigger */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct Rperm from inverse permutations */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Frpos for temporary copy of inverse row permutation [ */
+
+ for (pivrow = 0 ; pivrow < n_row ; pivrow++)
+ {
+ k = Rperm [pivrow] ;
+ ASSERT (k < 0) ;
+ k = ONES_COMPLEMENT (k) ;
+ ASSERT (k >= 0 && k < n_row) ;
+ Wp [k] = pivrow ;
+ Frpos [pivrow] = k ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rperm [k] = Wp [k] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct Cperm from inverse permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Fcpos for temporary copy of inverse column permutation [ */
+
+ for (pivcol = 0 ; pivcol < n_col ; pivcol++)
+ {
+ k = Cperm [pivcol] ;
+ ASSERT (k < 0) ;
+ k = ONES_COMPLEMENT (k) ;
+ ASSERT (k >= 0 && k < n_col) ;
+ Wp [k] = pivcol ;
+ /* save a copy of the inverse column permutation in Fcpos */
+ Fcpos [pivcol] = k ;
+ }
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm [k] = Wp [k] ;
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n_col ; k++)
+ {
+ col = Cperm [k] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (Fcpos [col] == k) ; /* col is the kth pivot */
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ row = Rperm [k] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == k) ; /* row is the kth pivot */
+ }
+#endif
+
+#ifndef NDEBUG
+ UMF_dump_lu (Numeric) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* permute Lpos, Upos, Lilen, Lip, Uilen, and Uip */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivrow = Rperm [k] ;
+ Wr [k] = Uilen [pivrow] ;
+ Wp [k] = Uip [pivrow] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Uilen [k] = Wr [k] ;
+ Uip [k] = Wp [k] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivrow = Rperm [k] ;
+ Wp [k] = Lpos [pivrow] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Lpos [k] = Wp [k] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivcol = Cperm [k] ;
+ Wc [k] = Lilen [pivcol] ;
+ Wp [k] = Lip [pivcol] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Lilen [k] = Wc [k] ;
+ Lip [k] = Wp [k] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivcol = Cperm [k] ;
+ Wp [k] = Upos [pivcol] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Upos [k] = Wp [k] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* terminate the last Uchain and last Lchain */
+ /* ---------------------------------------------------------------------- */
+
+ Upos [npiv] = EMPTY ;
+ Lpos [npiv] = EMPTY ;
+ Uip [npiv] = EMPTY ;
+ Lip [npiv] = EMPTY ;
+ Uilen [npiv] = 0 ;
+ Lilen [npiv] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert U to the new pivot order */
+ /* ---------------------------------------------------------------------- */
+
+ n1 = Symbolic->n1 ;
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ /* this is a singleton row of U */
+ ulen = Uilen [k] ;
+ DEBUG4 (("K "ID" New U. ulen "ID" Singleton 1\n", k, ulen)) ;
+ if (ulen > 0)
+ {
+ up = Uip [k] ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = *ip ;
+ DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col]));
+ ASSERT (col >= 0 && col < n_col) ;
+ *ip++ = Fcpos [col] ;
+ }
+ }
+ }
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+ up = Uip [k] ;
+ if (up < 0)
+ {
+ /* this is the start of a new Uchain (with a pattern) */
+ ulen = Uilen [k] ;
+ DEBUG4 (("K "ID" New U. ulen "ID" End_Uchain 1\n", k, ulen)) ;
+ if (ulen > 0)
+ {
+ up = -up ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = *ip ;
+ DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col]));
+ ASSERT (col >= 0 && col < n_col) ;
+ *ip++ = Fcpos [col] ;
+ }
+ }
+ }
+ }
+
+ ulen = Numeric->ulen ;
+ if (ulen > 0)
+ {
+ /* convert last pivot row of U to the new pivot order */
+ DEBUG4 (("K "ID" (last)\n", k)) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = Numeric->Upattern [i] ;
+ DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col])) ;
+ Numeric->Upattern [i] = Fcpos [col] ;
+ }
+ }
+
+ /* Fcpos no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to the new pivot order */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ llen = Lilen [k] ;
+ DEBUG4 (("K "ID" New L. llen "ID" Singleton col\n", k, llen)) ;
+ if (llen > 0)
+ {
+ lp = Lip [k] ;
+ ip = (Int *) (Numeric->Memory + lp) ;
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = *ip ;
+ DEBUG4 ((" old row "ID" new row "ID"\n", row, Frpos [row])) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ *ip++ = Frpos [row] ;
+ }
+ }
+ }
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+ llen = Lilen [k] ;
+ DEBUG4 (("K "ID" New L. llen "ID" \n", k, llen)) ;
+ if (llen > 0)
+ {
+ lp = Lip [k] ;
+ if (lp < 0)
+ {
+ /* this starts a new Lchain */
+ lp = -lp ;
+ }
+ ip = (Int *) (Numeric->Memory + lp) ;
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = *ip ;
+ DEBUG4 ((" old row "ID" new row "ID"\n", row, Frpos [row])) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ *ip++ = Frpos [row] ;
+ }
+ }
+ }
+
+ /* Frpos no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* combine symbolic and numeric permutations */
+ /* ---------------------------------------------------------------------- */
+
+ Cperm_init = Symbolic->Cperm_init ;
+ Rperm_init = Symbolic->Rperm_init ;
+
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rperm [k] = Rperm_init [Rperm [k]] ;
+ }
+
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm [k] = Cperm_init [Cperm [k]] ;
+ }
+
+ /* Work object will be freed immediately upon return (to UMF_kernel */
+ /* and then to UMFPACK_numeric). */
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.h b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.h
new file mode 100644
index 0000000..2cee302
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_kernel_wrapup
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_local_search.c b/src/C/SuiteSparse/UMFPACK/Source/umf_local_search.c
new file mode 100644
index 0000000..6bc59a0
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_local_search.c
@@ -0,0 +1,1952 @@
+/* ========================================================================== */
+/* === UMF_local_search ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Perform pivot search to find pivot row and pivot column.
+ The pivot column is selected from the candidate set. The candidate set
+ corresponds to a supercolumn from colamd or UMF_analyze. The pivot column
+ is then removed from that set. Constructs the pivot column pattern and
+ values. Called by umf_kernel. Returns UMFPACK_OK if successful, or
+ UMFPACK_WARNING_singular_matrix or UMFPACK_ERROR_different_pattern if not.
+*/
+
+#include "umf_internal.h"
+#include "umf_row_search.h"
+#include "umf_mem_free_tail_block.h"
+
+/* relaxed amalgamation control parameters are fixed at compile time */
+#define RELAX1 0.25
+#define SYM_RELAX1 0.0
+#define RELAX2 0.1
+#define RELAX3 0.125
+
+/* ========================================================================== */
+/* === remove_candidate ===================================================== */
+/* ========================================================================== */
+
+/* Remove a column from the set of candidate pivot columns. */
+
+PRIVATE void remove_candidate (Int jj, WorkType *Work, SymbolicType *Symbolic)
+{
+
+#ifndef NDEBUG
+ Int j ;
+ DEBUGm2 (("pivot column Candidates before remove: nCand "ID" ncand "ID
+ " lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand,
+ Work->lo, Work->hi, jj)) ;
+ for (j = 0 ; j < Work->nCandidates ; j++)
+ {
+ Int col = Work->Candidates [j] ;
+ DEBUGm2 ((ID" ", col));
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ /* ASSERT (NON_PIVOTAL_COL (col)) ; */
+ ASSERT (col >= Work->lo && col <= Work->hi) ;
+ }
+ DEBUGm2 (("\n")) ;
+#endif
+
+ if (Symbolic->fixQ)
+ {
+ DEBUGm2 (("FixQ\n")) ;
+ /* do not modify the column ordering */
+ ASSERT (Work->nCandidates == 1) ;
+ ASSERT (jj == 0) ;
+ if (Work->ncand > 1)
+ {
+ Work->Candidates [0] = Work->nextcand++ ;
+ }
+ else
+ {
+ Work->nCandidates = 0 ;
+ }
+ }
+ else
+ {
+ /* place the next candidate in the set */
+ if (Work->ncand > MAX_CANDIDATES)
+ {
+ Work->Candidates [jj] = Work->nextcand++ ;
+ }
+ else
+ {
+ ASSERT (Work->nCandidates == Work->ncand) ;
+ Work->Candidates [jj] = Work->Candidates [Work->ncand - 1] ;
+ Work->Candidates [Work->ncand - 1] = EMPTY ;
+ Work->nCandidates-- ;
+ }
+ }
+ Work->ncand-- ;
+
+#ifndef NDEBUG
+ DEBUGm2 (("pivot column Candidates after remove: nCand "ID" ncand "ID
+ " lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand, Work->lo,
+ Work->hi, jj)) ;
+ for (j = 0 ; j < Work->nCandidates ; j++)
+ {
+ Int col = Work->Candidates [j] ;
+ DEBUGm2 ((ID" ", col));
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ /* ASSERT (NON_PIVOTAL_COL (col)) ; */
+ ASSERT (col >= Work->lo && col <= Work->hi) ;
+ }
+ DEBUGm2 (("\n")) ;
+ ASSERT (Work->ncand >= 0) ;
+ ASSERT (Work->nCandidates <= Work->ncand) ;
+#endif
+}
+
+/* ========================================================================== */
+/* === UMF_local_search ===================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_local_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double relax1 ;
+ Entry *Flblock, *Fublock, *Fs, *Fcblock, *C, *Wx, *Wy, *Fu, *Flublock,
+ *Flu ;
+ Int pos, nrows, *Cols, *Rows, e, f, status, max_cdeg, fnzeros, nb, j, col,
+ i, row, cdeg_in, rdeg [2][2], fnpiv, nothing [2], new_LUsize,
+ pivrow [2][2], pivcol [2], *Wp, *Fcpos, *Frpos, new_fnzeros, cdeg_out,
+ *Wm, *Wio, *Woi, *Woo, *Frows, *Fcols, fnrows, fncols, *E, deg, nr_in,
+ nc, thiscost, bestcost, nr_out, do_update, extra_cols, extra_rows,
+ extra_zeros, relaxed_front, do_extend, fnr_curr, fnc_curr, tpi,
+ *Col_tuples, *Col_degree, *Col_tlen, jj, jcand [2], freebie [2],
+ did_rowmerge, fnrows_new [2][2], fncols_new [2][2], search_pivcol_out,
+ *Diagonal_map, *Diagonal_imap, row2, col2 ;
+ Unit *Memory, *p ;
+ Tuple *tp, *tpend, *tp1, *tp2 ;
+ Element *ep ;
+
+#ifndef NBLAS
+ Int blas_ok = TRUE ;
+#else
+#define blas_ok FALSE
+#endif
+
+#ifndef NDEBUG
+ Int debug_ok, n_row, n_col, *Row_degree ;
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Memory = Numeric->Memory ;
+ E = Work->E ;
+ Col_degree = Numeric->Cperm ;
+
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+
+ Wx = Work->Wx ;
+ Wy = Work->Wy ;
+ Wp = Work->Wp ;
+ Wm = Work->Wm ;
+ Woi = Work->Woi ;
+ Wio = Work->Wio ;
+ Woo = Work->Woo ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ nb = Work->nb ;
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ fnpiv = Work->fnpiv ;
+ nothing [0] = EMPTY ;
+ nothing [1] = EMPTY ;
+ relax1 = (Symbolic->prefer_diagonal) ? SYM_RELAX1 : RELAX1 ;
+ fnzeros = Work->fnzeros ;
+ new_fnzeros = fnzeros ;
+ jj = EMPTY ;
+
+ Fcblock = Work->Fcblock ; /* current contribution block */
+ Flblock = Work->Flblock ; /* current L block */
+ Fublock = Work->Fublock ; /* current U block */
+ Flublock = Work->Flublock ; /* current LU block */
+
+ /* The pivot column degree cannot exceed max_cdeg */
+ max_cdeg = Work->fnrows_max ;
+ ASSERT (Work->fnrows_max <= Symbolic->maxnrows) ;
+ ASSERT (Work->fncols_max <= Symbolic->maxncols) ;
+
+ if (fnrows == 0 && fncols == 0)
+ {
+ /* frontal matrix is empty */
+ Work->firstsuper = Work->ksuper ;
+ }
+
+#ifndef NDEBUG
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ DEBUG2 (("\n========LOCAL SEARCH: current frontal matrix: ========= \n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+ if (UMF_debug > 0 || MAX (n_row, n_col) < 1000)
+ {
+ for (i = 0 ; i < MAX (n_row, n_col) ; i++)
+ {
+ ASSERT (Wp [i] < 0) ;
+ }
+ }
+
+ DEBUGm2 ((ID" pivot column Candidates: lo "ID" hi "ID"\n",
+ Work->nCandidates, Work->lo, Work->hi)) ;
+ for (j = 0 ; j < Work->nCandidates ; j++)
+ {
+ col = Work->Candidates [j] ;
+ DEBUGm2 ((ID" ", col));
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (col >= Work->lo && col <= Work->hi) ;
+ }
+
+ DEBUGm2 (("\n")) ;
+ /* there are no 0-by-c or r-by-0 fronts, where c and r are > 0 */
+ /* a front is either 0-by-0, or r-by-c */
+ DEBUG2 (("\n\n::: "ID" : Npiv: "ID" + fnpiv "ID" = "ID". "
+ "size "ID"-by-"ID"\n", Work->frontid,
+ Work->npiv, Work->fnpiv, Work->npiv + Work->fnpiv, fnrows, fncols)) ;
+ ASSERT ((fnrows == 0 && fncols == 0) ||(fnrows != 0 && fncols != 0)) ;
+#endif
+
+ /* ====================================================================== */
+ /* === PIVOT SEARCH ===================================================== */
+ /* ====================================================================== */
+
+ /* initialize */
+
+ pivcol [IN] = EMPTY ;
+ pivcol [OUT] = EMPTY ;
+
+ cdeg_in = Int_MAX ;
+ cdeg_out = Int_MAX ;
+
+ pivrow [IN][IN] = EMPTY ;
+ pivrow [IN][OUT] = EMPTY ;
+ pivrow [OUT][IN] = EMPTY ;
+ pivrow [OUT][OUT] = EMPTY ;
+
+ rdeg [IN][IN] = Int_MAX ;
+ rdeg [IN][OUT] = Int_MAX ;
+ rdeg [OUT][IN] = Int_MAX ;
+ rdeg [OUT][OUT] = Int_MAX ;
+
+ freebie [IN] = FALSE ;
+ freebie [OUT] = FALSE ;
+
+ Work->pivot_case = EMPTY ;
+ bestcost = EMPTY ;
+
+ nr_out = EMPTY ;
+ nr_in = EMPTY ;
+
+ jcand [IN] = EMPTY ;
+ jcand [OUT] = EMPTY ;
+
+ fnrows_new [IN][IN] = EMPTY ;
+ fnrows_new [IN][OUT] = EMPTY ;
+ fnrows_new [OUT][IN] = EMPTY ;
+ fnrows_new [OUT][OUT] = EMPTY ;
+
+ fncols_new [IN][IN] = EMPTY ;
+ fncols_new [IN][OUT] = EMPTY ;
+ fncols_new [OUT][IN] = EMPTY ;
+ fncols_new [OUT][OUT] = EMPTY ;
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("Check Frpos : fnrows "ID" col "ID" maxcdeg "ID"\n",
+ fnrows, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ DEBUG4 (("All:\n")) ;
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = fnrows ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
+ }
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* find shortest column in the front, and shortest column not in the */
+ /* front, from the candidate pivot column set */
+ /* ---------------------------------------------------------------------- */
+
+ /* If there are too many candidates, then only look at the first */
+ /* MAX_CANDIDATES of them. Otherwise, if there are O(n) candidates, */
+ /* this code could take O(n^2) time. */
+
+ /* ------------------------------------------------------------------ */
+ /* look in the candidate set for the best column */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG2 (("Max candidates %d, Work->ncand "ID" jmax "ID"\n",
+ MAX_CANDIDATES, Work->ncand, Work->nCandidates)) ;
+ col = Work->Candidates [0] ;
+ ASSERT (Work->nCandidates > 0) ;
+ DEBUG3 (("Pivot column candidate: "ID" j = "ID"\n", col, j)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+
+ /* there is no Col_degree if fixQ is true */
+ deg = Symbolic->fixQ ? EMPTY : Col_degree [col] ;
+
+#ifndef NDEBUG
+ DEBUG3 (("Pivot column candidate: "ID" cost: "ID" Fcpos[col] "ID"\n",
+ col, deg, Fcpos [col])) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
+ if (Symbolic->fixQ)
+ {
+ DEBUG1 (("FIXQ: Candidates "ID" pivcol "ID" npiv "ID" fnpiv "ID
+ " ndiscard "ID "\n", Work->nCandidates, col, Work->npiv,
+ Work->fnpiv, Work->ndiscard)) ;
+ ASSERT (Work->nCandidates == 1) ;
+ ASSERT (col == Work->npiv + Work->fnpiv + Work->ndiscard) ;
+ }
+#endif
+
+ if (Fcpos [col] >= 0)
+ {
+ /* best column in front, so far */
+ pivcol [IN] = col ;
+ cdeg_in = deg ; /* ignored, if fixQ is true */
+ jcand [IN] = 0 ;
+ }
+ else
+ {
+ /* best column not in front, so far */
+ pivcol [OUT] = col ;
+ cdeg_out = deg ; /* ignored, if fixQ is true */
+ jcand [OUT] = 0 ;
+ }
+
+ /* look at the rest of the candidates */
+ for (j = 1 ; j < Work->nCandidates ; j++)
+ {
+ col = Work->Candidates [j] ;
+
+ DEBUG3 (("Pivot col candidate: "ID" j = "ID"\n", col, j)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (!Symbolic->fixQ) ;
+ deg = Col_degree [col] ;
+#ifndef NDEBUG
+ DEBUG3 (("Pivot col candidate: "ID" cost: "ID" Fcpos[col] "ID"\n",
+ col, deg, Fcpos [col])) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
+#endif
+ if (Fcpos [col] >= 0)
+ {
+#ifndef NDEBUG
+ Int fs ;
+ fs = Fcpos [col] / fnr_curr ;
+ ASSERT (fs >= 0 && fs < fncols) ;
+#endif
+ if (deg < cdeg_in || (deg == cdeg_in && col < pivcol [IN]))
+ {
+ /* best column in front, so far */
+ pivcol [IN] = col ;
+ cdeg_in = deg ;
+ jcand [IN] = j ;
+ }
+ }
+ else
+ {
+ if (deg < cdeg_out || (deg == cdeg_out && col < pivcol [OUT]))
+ {
+ /* best column not in front, so far */
+ pivcol [OUT] = col ;
+ cdeg_out = deg ;
+ jcand [OUT] = j ;
+ }
+ }
+ }
+
+ DEBUG2 (("Pivcol in "ID" out "ID"\n", pivcol [IN], pivcol [OUT])) ;
+ ASSERT ((pivcol [IN] >= 0 && pivcol [IN] < n_col)
+ || (pivcol [OUT] >= 0 && pivcol [OUT] < n_col)) ;
+
+ cdeg_in = EMPTY ;
+ cdeg_out = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct candidate column in front, and search for pivot rows */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("Prior to col update: fnrows "ID" col "ID" maxcdeg "ID"\n",
+ fnrows, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ DEBUG4 (("All:\n")) ;
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = fnrows ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
+ }
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+ if (pivcol [IN] != EMPTY)
+ {
+
+#ifndef NDEBUG
+ DEBUG2 (("col[IN] column "ID" in front at position = "ID"\n",
+ pivcol [IN], Fcpos [pivcol [IN]])) ;
+ UMF_dump_rowcol (1, Numeric, Work, pivcol [IN], !Symbolic->fixQ) ;
+#endif
+
+ /* the only way we can have a pivcol[IN] is if the front is not empty */
+ ASSERT (fnrows > 0 && fncols > 0) ;
+
+ DEBUG4 (("Update pivot column:\n")) ;
+ Fs = Fcblock + Fcpos [pivcol [IN]] ;
+ Fu = Fublock + (Fcpos [pivcol [IN]] / fnr_curr) ;
+ Flu = Flublock + fnpiv * nb ;
+
+ /* ------------------------------------------------------------------ */
+ /* copy the pivot column from the U block into the LU block */
+ /* ------------------------------------------------------------------ */
+
+ /* This copy is permanent if the pivcol [IN] is chosen. */
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ Flu [i] = Fu [i*fnc_curr] ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* update the pivot column in the LU block using a triangular solve */
+ /* ------------------------------------------------------------------ */
+
+ /* This work will be discarded if the pivcol [OUT] is chosen instead.
+ * It is permanent if the pivcol [IN] is chosen. */
+
+ if (fnpiv > 1)
+ {
+ /* solve Lx=b, where b = U (:,k), stored in the LU block */
+
+#ifndef NBLAS
+ BLAS_TRSV (fnpiv, Flublock, Flu, nb) ;
+#endif
+ if (!blas_ok)
+ {
+ /* use plain C code if no BLAS, or on integer overflow */
+ Entry *Flub = Flublock ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ Entry Fuj = Flu [j] ;
+#pragma ivdep
+ for (i = j+1 ; i < fnpiv ; i++)
+ {
+ /* Flu [i] -= Flublock [i + j*nb] * Flu [j] ; */
+ MULT_SUB (Flu [i], Flub [i], Fuj) ;
+ }
+ Flub += nb ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* copy the pivot column from the C block into Wy */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Wy [i] = Fs [i] ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* update the pivot column of L using a matrix-vector multiply */
+ /* ------------------------------------------------------------------ */
+
+ /* this work will be discarded if the pivcol [OUT] is chosen instead */
+
+#ifdef NBLAS
+ /* no BLAS available - use plain C code instead */
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ Entry Fuj, *Flub = Flblock + j * fnr_curr ;
+ Fuj = Flu [j] ;
+ if (IS_NONZERO (Fuj))
+ {
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ /* Wy [i] -= Flblock [i+j*fnr_curr] * Fuj ; */
+ MULT_SUB (Wy [i], Flub [i], Fuj) ;
+ }
+ }
+ /* Flblock += fnr_curr ; */
+ }
+#else
+ /* Using 1-based notation:
+ * Wy (1:fnrows) -= Flblock (1:fnrows,1:fnpiv) * Flu (1:fnpiv) */
+ BLAS_GEMV (fnrows, fnpiv, Flblock, Flu, Wy, fnr_curr) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ DEBUG2 (("Wy after update: fnrows="ID"\n", fnrows)) ;
+ DEBUG4 ((" fnpiv="ID" \n", fnpiv)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG4 ((ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ;
+ EDEBUG4 (Wy [i]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* construct the candidate column */
+ /* ------------------------------------------------------------------ */
+
+ cdeg_in = fnrows ;
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("After col update: fnrows "ID" col "ID" maxcdeg "ID"\n",
+ fnrows, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ DEBUG4 (("All:\n")) ;
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = fnrows ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
+ }
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("COL ASSEMBLE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n",
+ cdeg_in, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < cdeg_in ; i++)
+ {
+ row = Frows [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = cdeg_in ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY) cnt++ ;
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+ /* assemble column into Wy */
+
+ ASSERT (pivcol [IN] >= 0 && pivcol [IN] < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol [IN])) ;
+
+ tpi = Col_tuples [pivcol [IN]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [pivcol [IN]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (pivcol [IN] == Cols [f]) ;
+
+ Rows = Cols + ep->ncols ;
+ nrows = ep->nrows ;
+ p += UNITS (Int, ep->ncols + nrows) ;
+ C = ((Entry *) p) + f * nrows ;
+
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0) /* skip this if already gone from element */
+ {
+ ASSERT (row < n_row) ;
+ pos = Frpos [row] ;
+ if (pos < 0)
+ {
+ /* new entry in the pattern - save Frpos */
+ ASSERT (cdeg_in < n_row) ;
+ if (cdeg_in >= max_cdeg)
+ {
+ /* :: pattern change (cdeg in failure) :: */
+ DEBUGm4 (("cdeg_in failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Frpos [row] = cdeg_in ;
+ Frows [cdeg_in] = row ;
+ Wy [cdeg_in++] = C [i] ;
+ }
+ else
+ {
+ /* entry already in pattern - sum values in Wy */
+ /* Wy [pos] += C [i] ; */
+ ASSERT (pos < max_cdeg) ;
+ ASSEMBLE (Wy [pos], C [i]) ;
+ }
+ }
+ }
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Col_tlen [pivcol [IN]] = tp2 - tp1 ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ /* check Frpos again */
+ DEBUG4 (("COL DONE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n",
+ cdeg_in, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < cdeg_in ; i++)
+ {
+ row = Frows [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = cdeg_in ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY) cnt++ ;
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced column: cdeg in "ID" fnrows_max "ID"\n",
+ cdeg_in, Work->fnrows_max)) ;
+ for (i = 0 ; i < cdeg_in ; i++)
+ {
+ DEBUG4 ((" "ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ;
+ EDEBUG4 (Wy [i]) ;
+ DEBUG4 (("\n")) ;
+ ASSERT (i == Frpos [Frows [i]]) ;
+ }
+ ASSERT (cdeg_in <= Work->fnrows_max) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* cdeg_in is now the exact degree of this column */
+ /* ------------------------------------------------------------------ */
+
+ nr_in = cdeg_in - fnrows ;
+
+ /* since there are no 0-by-x fronts, if there is a pivcol [IN] the */
+ /* front must have at least one row. */
+ ASSERT (cdeg_in > 0) ;
+
+ /* new degree of pivcol [IN], excluding current front is nr_in */
+ /* column expands by nr_in rows */
+
+ /* ------------------------------------------------------------------ */
+ /* search for two candidate pivot rows */
+ /* ------------------------------------------------------------------ */
+
+ /* for the IN_IN pivot row (if any), */
+ /* extend the pattern in place, using Fcols */
+ status = UMF_row_search (Numeric, Work, Symbolic,
+ fnrows, cdeg_in, Frows, Frpos, /* pattern of column to search */
+ pivrow [IN], rdeg [IN], Fcols, Wio, nothing, Wy,
+ pivcol [IN], freebie) ;
+ ASSERT (!freebie [IN] && !freebie [OUT]) ;
+
+ /* ------------------------------------------------------------------ */
+ /* fatal error if matrix pattern has changed since symbolic analysis */
+ /* ------------------------------------------------------------------ */
+
+ if (status == UMFPACK_ERROR_different_pattern)
+ {
+ /* :: pattern change (row search IN failure) :: */
+ DEBUGm4 (("row search IN failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* we now must have a structural pivot */
+ /* ------------------------------------------------------------------ */
+
+ /* Since the pivcol[IN] exists, there must be at least one row in the */
+ /* current frontal matrix, and so we must have found a structural */
+ /* pivot. The numerical value might be zero, of course. */
+
+ ASSERT (status != UMFPACK_WARNING_singular_matrix) ;
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate IN_IN option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [IN][IN] != EMPTY)
+ {
+ /* The current front would become an (implicit) LUson.
+ * Both candidate pivot row and column are in the current front.
+ * Cost is how much the current front would expand */
+
+ /* pivrow[IN][IN] candidates are not found via row merge search */
+
+ ASSERT (fnrows >= 0 && fncols >= 0) ;
+
+ ASSERT (cdeg_in > 0) ;
+ nc = rdeg [IN][IN] - fncols ;
+
+ thiscost =
+ /* each column in front (except pivot column) grows by nr_in: */
+ (nr_in * (fncols - 1)) +
+ /* new columns not in old front: */
+ (nc * (cdeg_in - 1)) ;
+
+ /* no extra cost to relaxed amalgamation */
+
+ ASSERT (fnrows + nr_in == cdeg_in) ;
+ ASSERT (fncols + nc == rdeg [IN][IN]) ;
+
+ /* size of relaxed front (after pivot row column removed): */
+ fnrows_new [IN][IN] = (fnrows-1) + nr_in ;
+ fncols_new [IN][IN] = (fncols-1) + nc ;
+ /* relaxed_front = fnrows_new [IN][IN] * fncols_new [IN][IN] ; */
+
+ do_extend = TRUE ;
+
+ DEBUG2 (("Evaluating option IN-IN:\n")) ;
+ DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_in, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update should be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* There are fnpiv pivots currently in the front. This one
+ * will be the (fnpiv+1)st pivot, if it is extended. */
+
+ /* RELAX2 parameter uses a double relop, but ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX2 ;
+
+ DEBUG2 (("do_update "ID"\n", do_update))
+
+ DEBUG2 (("option IN IN : nr "ID" nc "ID" cost "ID"(0) relax "ID
+ "\n", nr_in, nc, thiscost, do_extend)) ;
+
+ /* this is the best option seen so far */
+ Work->pivot_case = IN_IN ;
+ bestcost = thiscost ;
+
+ /* do the amalgamation and extend the front */
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate IN_OUT option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [IN][OUT] != EMPTY)
+ {
+ /* The current front would become a Uson of the new front.
+ * Candidate pivot column is in the current front, but the
+ * candidate pivot row is not. */
+
+ ASSERT (fnrows >= 0 && fncols > 0) ;
+ ASSERT (cdeg_in > 0) ;
+
+ /* must be at least one row outside the front */
+ /* (the pivrow [IN][OUT] itself) */
+ ASSERT (nr_in >= 1) ;
+
+ /* count columns not in current front */
+ nc = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < rdeg [IN][OUT] ; i++)
+ {
+ col = Wio [i] ;
+ DEBUG4 (("counting col "ID" Fcpos[] = "ID"\n", col,
+ Fcpos [col])) ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (Fcpos [col] < 0) nc++ ;
+#ifndef NDEBUG
+ /* we must see the pivot column somewhere */
+ if (col == pivcol [IN])
+ {
+ ASSERT (Fcpos [col] >= 0) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+
+ thiscost =
+ /* each row in front grows by nc: */
+ (nc * fnrows) +
+ /* new rows not affected by front: */
+ ((nr_in-1) * (rdeg [IN][OUT]-1)) ;
+
+ /* check the cost of relaxed IN_OUT amalgamation */
+
+ extra_cols = ((fncols-1) + nc ) - (rdeg [IN][OUT] - 1) ;
+ ASSERT (extra_cols >= 0) ;
+ ASSERT (fncols + nc == extra_cols + rdeg [IN][OUT]) ;
+ extra_zeros = (nr_in-1) * extra_cols ; /* symbolic fill-in */
+
+ ASSERT (fnrows + nr_in == cdeg_in) ;
+ ASSERT (fncols + nc == rdeg [IN][OUT] + extra_cols) ;
+
+ /* size of relaxed front (after pivot column removed): */
+ fnrows_new [IN][OUT] = fnrows + (nr_in-1) ;
+ fncols_new [IN][OUT] = (fncols-1) + nc ;
+ relaxed_front = fnrows_new [IN][OUT] * fncols_new [IN][OUT] ;
+
+ /* do relaxed amalgamation if the extra zeros are no more */
+ /* than a fraction (default 0.25) of the relaxed front */
+ /* if relax = 0: no extra zeros allowed */
+ /* if relax = +inf: always amalgamate */
+
+ /* relax parameter uses a double relop, but ignore NaN case: */
+ if (extra_zeros == 0)
+ {
+ do_extend = TRUE ;
+ }
+ else
+ {
+ do_extend = ((double) extra_zeros) <
+ (relax1 * (double) relaxed_front) ;
+ }
+
+ if (do_extend)
+ {
+ /* count the cost of relaxed amalgamation */
+ thiscost += extra_zeros ;
+
+ DEBUG2 (("Evaluating option IN-OUT:\n")) ;
+ DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_in, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update to be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* RELAX3 parameter uses a double relop, ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
+ DEBUG2 (("do_update "ID"\n", do_update))
+
+ }
+ else
+ {
+ /* the current front would not be extended */
+ do_update = fnpiv > 0 ;
+ fnzeros = 0 ;
+ DEBUG2 (("IN-OUT do_update forced true: "ID"\n", do_update)) ;
+
+ /* The new front would be just big enough to hold the new
+ * pivot row and column. */
+ fnrows_new [IN][OUT] = cdeg_in - 1 ;
+ fncols_new [IN][OUT] = rdeg [IN][OUT] - 1 ;
+
+ }
+
+ DEBUG2 (("option IN OUT: nr "ID" nc "ID" cost "ID"("ID") relax "ID
+ "\n", nr_in, nc, thiscost, extra_zeros, do_extend)) ;
+
+ if (bestcost == EMPTY || thiscost < bestcost)
+ {
+ /* this is the best option seen so far */
+ Work->pivot_case = IN_OUT ;
+ bestcost = thiscost ;
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct candidate column not in front, and search for pivot rows */
+ /* ---------------------------------------------------------------------- */
+
+ search_pivcol_out = (bestcost != 0 && pivcol [OUT] != EMPTY) ;
+ if (Symbolic->prefer_diagonal)
+ {
+ search_pivcol_out = search_pivcol_out && (pivrow [IN][IN] == EMPTY) ;
+ }
+
+ if (search_pivcol_out)
+ {
+
+#ifndef NDEBUG
+ DEBUG2 (("out_col column "ID" NOT in front at position = "ID"\n",
+ pivcol [OUT], Fcpos [pivcol [OUT]])) ;
+ UMF_dump_rowcol (1, Numeric, Work, pivcol [OUT], !Symbolic->fixQ) ;
+ DEBUG2 (("fncols "ID" fncols_max "ID"\n", fncols, Work->fncols_max)) ;
+ ASSERT (fncols < Work->fncols_max) ;
+#endif
+
+ /* Use Wx as temporary workspace to construct the pivcol [OUT] */
+
+
+ /* ------------------------------------------------------------------ */
+ /* construct the candidate column (currently not in the front) */
+ /* ------------------------------------------------------------------ */
+
+ /* Construct the column in Wx, Wm, using Wp for the positions: */
+ /* Wm [0..cdeg_out-1] list of row indices in the column */
+ /* Wx [0..cdeg_out-1] list of corresponding numerical values */
+ /* Wp [0..n-1] starts as all negative, and ends that way too. */
+
+ cdeg_out = 0 ;
+
+#ifndef NDEBUG
+ /* check Wp */
+ DEBUG4 (("COL ASSEMBLE: cdeg 0\nREDUCE COL out "ID"\n", pivcol [OUT])) ;
+ if (UMF_debug > 0 || MAX (n_row, n_col) < 1000)
+ {
+ for (i = 0 ; i < MAX (n_row, n_col) ; i++)
+ {
+ ASSERT (Wp [i] < 0) ;
+ }
+ }
+ DEBUG4 (("max_cdeg: "ID"\n", max_cdeg)) ;
+#endif
+
+ ASSERT (pivcol [OUT] >= 0 && pivcol [OUT] < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol [OUT])) ;
+
+ tpi = Col_tuples [pivcol [OUT]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [pivcol [OUT]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (pivcol [OUT] == Cols [f]) ;
+
+ Rows = Cols + ep->ncols ;
+ nrows = ep->nrows ;
+ p += UNITS (Int, ep->ncols + nrows) ;
+ C = ((Entry *) p) + f * nrows ;
+
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0) /* skip this if already gone from element */
+ {
+ ASSERT (row < n_row) ;
+ pos = Wp [row] ;
+ if (pos < 0)
+ {
+ /* new entry in the pattern - save Wp */
+ ASSERT (cdeg_out < n_row) ;
+ if (cdeg_out >= max_cdeg)
+ {
+ /* :: pattern change (cdeg out failure) :: */
+ DEBUGm4 (("cdeg out failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wp [row] = cdeg_out ;
+ Wm [cdeg_out] = row ;
+ Wx [cdeg_out++] = C [i] ;
+ }
+ else
+ {
+ /* entry already in pattern - sum the values */
+ /* Wx [pos] += C [i] ; */
+ ASSEMBLE (Wx [pos], C [i]) ;
+ }
+ }
+ }
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Col_tlen [pivcol [OUT]] = tp2 - tp1 ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced column: cdeg out "ID"\n", cdeg_out)) ;
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ DEBUG4 ((" "ID" "ID" "ID, i, Wm [i], Wp [Wm [i]])) ;
+ EDEBUG4 (Wx [i]) ;
+ DEBUG4 (("\n")) ;
+ ASSERT (i == Wp [Wm [i]]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* new degree of pivcol [OUT] is cdeg_out */
+ /* ------------------------------------------------------------------ */
+
+ /* search for two candidate pivot rows */
+ status = UMF_row_search (Numeric, Work, Symbolic,
+ 0, cdeg_out, Wm, Wp, /* pattern of column to search */
+ pivrow [OUT], rdeg [OUT], Woi, Woo, pivrow [IN], Wx,
+ pivcol [OUT], freebie) ;
+
+ /* ------------------------------------------------------------------ */
+ /* fatal error if matrix pattern has changed since symbolic analysis */
+ /* ------------------------------------------------------------------ */
+
+ if (status == UMFPACK_ERROR_different_pattern)
+ {
+ /* :: pattern change detected in umf_local_search :: */
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* Clear Wp */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ Wp [Wm [i]] = EMPTY ; /* clear Wp */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* check for rectangular, singular matrix */
+ /* ------------------------------------------------------------------ */
+
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ /* Pivot column is empty, and row-merge set is empty too. The
+ * matrix is structurally singular. The current frontal matrix must
+ * be empty, too. It it weren't, and pivcol [OUT] exists, then
+ * there would be at least one row that could be selected. Since
+ * the current front is empty, pivcol [IN] must also be EMPTY.
+ */
+
+ DEBUGm4 (("Note: pivcol [OUT]: "ID" discard\n", pivcol [OUT])) ;
+ ASSERT ((Work->fnrows == 0 && Work->fncols == 0)) ;
+ ASSERT (pivcol [IN] == EMPTY) ;
+
+ /* remove the failed pivcol [OUT] from candidate set */
+ ASSERT (pivcol [OUT] == Work->Candidates [jcand [OUT]]) ;
+ remove_candidate (jcand [OUT], Work, Symbolic) ;
+ Work->ndiscard++ ;
+
+ /* delete all of the tuples, and all contributions to this column */
+ DEBUG1 (("Prune tuples of dead outcol: "ID"\n", pivcol [OUT])) ;
+ Col_tlen [pivcol [OUT]] = 0 ;
+ UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol [OUT]]) ;
+ Col_tuples [pivcol [OUT]] = 0 ;
+
+ /* no pivot found at all */
+ return (UMFPACK_WARNING_singular_matrix) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ if (freebie [IN])
+ {
+ /* the "in" row is the same as the "in" row for the "in" column */
+ Woi = Fcols ;
+ rdeg [OUT][IN] = rdeg [IN][IN] ;
+ DEBUG4 (("Freebie in, row "ID"\n", pivrow [IN][IN])) ;
+ }
+
+ if (freebie [OUT])
+ {
+ /* the "out" row is the same as the "out" row for the "in" column */
+ Woo = Wio ;
+ rdeg [OUT][OUT] = rdeg [IN][OUT] ;
+ DEBUG4 (("Freebie out, row "ID"\n", pivrow [IN][OUT])) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate OUT_IN option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [OUT][IN] != EMPTY)
+ {
+ /* The current front would become an Lson of the new front.
+ * The candidate pivot row is in the current front, but the
+ * candidate pivot column is not. */
+
+ ASSERT (fnrows > 0 && fncols >= 0) ;
+
+ did_rowmerge = (cdeg_out == 0) ;
+ if (did_rowmerge)
+ {
+ /* pivrow [OUT][IN] was found via row merge search */
+ /* it is not (yet) in the pivot column pattern (add it now) */
+ DEBUGm4 (("did row merge OUT col, IN row\n")) ;
+ Wm [0] = pivrow [OUT][IN] ;
+ CLEAR (Wx [0]) ;
+ cdeg_out = 1 ;
+ ASSERT (nr_out == EMPTY) ;
+ }
+
+ nc = rdeg [OUT][IN] - fncols ;
+ ASSERT (nc >= 1) ;
+
+ /* count rows not in current front */
+ nr_out = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ;
+#ifndef NDEBUG
+ /* we must see the pivot row somewhere */
+ if (row == pivrow [OUT][IN])
+ {
+ ASSERT (Frpos [row] >= 0) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+
+ thiscost =
+ /* each column in front grows by nr_out: */
+ (nr_out * fncols) +
+ /* new cols not affected by front: */
+ ((nc-1) * (cdeg_out-1)) ;
+
+ /* check the cost of relaxed OUT_IN amalgamation */
+
+ extra_rows = ((fnrows-1) + nr_out) - (cdeg_out - 1) ;
+ ASSERT (extra_rows >= 0) ;
+ ASSERT (fnrows + nr_out == extra_rows + cdeg_out) ;
+ extra_zeros = (nc-1) * extra_rows ; /* symbolic fill-in */
+
+ ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ;
+ ASSERT (fncols + nc == rdeg [OUT][IN]) ;
+
+ /* size of relaxed front (after pivot row removed): */
+ fnrows_new [OUT][IN] = (fnrows-1) + nr_out ;
+ fncols_new [OUT][IN] = fncols + (nc-1) ;
+ relaxed_front = fnrows_new [OUT][IN] * fncols_new [OUT][IN] ;
+
+ /* do relaxed amalgamation if the extra zeros are no more */
+ /* than a fraction (default 0.25) of the relaxed front */
+ /* if relax = 0: no extra zeros allowed */
+ /* if relax = +inf: always amalgamate */
+ if (did_rowmerge)
+ {
+ do_extend = FALSE ;
+ }
+ else
+ {
+ /* relax parameter uses a double relop, but ignore NaN case: */
+ if (extra_zeros == 0)
+ {
+ do_extend = TRUE ;
+ }
+ else
+ {
+ do_extend = ((double) extra_zeros) <
+ (relax1 * (double) relaxed_front) ;
+ }
+ }
+
+ if (do_extend)
+ {
+ /* count the cost of relaxed amalgamation */
+ thiscost += extra_zeros ;
+
+ DEBUG2 (("Evaluating option OUT-IN:\n")) ;
+ DEBUG2 ((" Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_out, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update to be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* RELAX3 parameter uses a double relop, ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
+ DEBUG2 (("do_update "ID"\n", do_update))
+ }
+ else
+ {
+ /* the current front would not be extended */
+ do_update = fnpiv > 0 ;
+ fnzeros = 0 ;
+ DEBUG2 (("OUT-IN do_update forced true: "ID"\n", do_update)) ;
+
+ /* The new front would be just big enough to hold the new
+ * pivot row and column. */
+ fnrows_new [OUT][IN] = cdeg_out - 1 ;
+ fncols_new [OUT][IN] = rdeg [OUT][IN] - 1 ;
+ }
+
+ DEBUG2 (("option OUT IN : nr "ID" nc "ID" cost "ID"("ID") relax "ID
+ "\n", nr_out, nc, thiscost, extra_zeros, do_extend)) ;
+
+ if (bestcost == EMPTY || thiscost < bestcost)
+ {
+ /* this is the best option seen so far */
+ Work->pivot_case = OUT_IN ;
+ bestcost = thiscost ;
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate OUT_OUT option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [OUT][OUT] != EMPTY)
+ {
+ /* Neither the candidate pivot row nor the candidate pivot column
+ * are in the current front. */
+
+ ASSERT (fnrows >= 0 && fncols >= 0) ;
+
+ did_rowmerge = (cdeg_out == 0) ;
+ if (did_rowmerge)
+ {
+ /* pivrow [OUT][OUT] was found via row merge search */
+ /* it is not (yet) in the pivot column pattern (add it now) */
+ DEBUGm4 (("did row merge OUT col, OUT row\n")) ;
+ Wm [0] = pivrow [OUT][OUT] ;
+ CLEAR (Wx [0]) ;
+ cdeg_out = 1 ;
+ ASSERT (nr_out == EMPTY) ;
+ nr_out = 1 ;
+ }
+
+ if (fnrows == 0 && fncols == 0)
+ {
+ /* the current front is completely empty */
+ ASSERT (fnpiv == 0) ;
+ nc = rdeg [OUT][OUT] ;
+ extra_cols = 0 ;
+ nr_out = cdeg_out ;
+ extra_rows = 0 ;
+ extra_zeros = 0 ;
+
+ thiscost = (nc-1) * (cdeg_out-1) ; /* new columns only */
+
+ /* size of new front: */
+ fnrows_new [OUT][OUT] = nr_out-1 ;
+ fncols_new [OUT][OUT] = nc-1 ;
+ relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ;
+ }
+ else
+ {
+
+ /* count rows not in current front */
+ if (nr_out == EMPTY)
+ {
+ nr_out = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ;
+#ifndef NDEBUG
+ /* we must see the pivot row somewhere */
+ if (row == pivrow [OUT][OUT])
+ {
+ ASSERT (Frpos [row] < 0 || Frpos [row] >= fnrows) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+ }
+
+ /* count columns not in current front */
+ nc = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < rdeg [OUT][OUT] ; i++)
+ {
+ col = Woo [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (Fcpos [col] < 0) nc++ ;
+#ifndef NDEBUG
+ /* we must see the pivot column somewhere */
+ if (col == pivcol [OUT])
+ {
+ ASSERT (Fcpos [col] < 0) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+
+ extra_cols = (fncols + (nc-1)) - (rdeg [OUT][OUT] - 1) ;
+ extra_rows = (fnrows + (nr_out-1)) - (cdeg_out - 1) ;
+ ASSERT (extra_rows >= 0) ;
+ ASSERT (extra_cols >= 0) ;
+ extra_zeros = ((nc-1) * extra_rows) + ((nr_out-1) * extra_cols);
+
+ ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ;
+ ASSERT (fncols + nc == rdeg [OUT][OUT] + extra_cols) ;
+
+ thiscost =
+ /* new columns: */
+ ((nc-1) * (cdeg_out-1)) +
+ /* old columns in front grow by nr_out-1: */
+ ((nr_out-1) * (fncols - extra_cols)) ;
+
+ /* size of relaxed front: */
+ fnrows_new [OUT][OUT] = fnrows + (nr_out-1) ;
+ fncols_new [OUT][OUT] = fncols + (nc-1) ;
+ relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ;
+
+ }
+
+ /* do relaxed amalgamation if the extra zeros are no more */
+ /* than a fraction (default 0.25) of the relaxed front */
+ /* if relax = 0: no extra zeros allowed */
+ /* if relax = +inf: always amalgamate */
+ if (did_rowmerge)
+ {
+ do_extend = FALSE ;
+ }
+ else
+ {
+ /* relax parameter uses a double relop, but ignore NaN case: */
+ if (extra_zeros == 0)
+ {
+ do_extend = TRUE ;
+ }
+ else
+ {
+ do_extend = ((double) extra_zeros) <
+ (relax1 * (double) relaxed_front) ;
+ }
+ }
+
+ if (do_extend)
+ {
+ /* count the cost of relaxed amalgamation */
+ thiscost += extra_zeros ;
+
+ DEBUG2 (("Evaluating option OUT-OUT:\n")) ;
+ DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_out, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update to be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* RELAX3 parameter uses a double relop, ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
+ DEBUG2 (("do_update "ID"\n", do_update))
+ }
+ else
+ {
+ /* the current front would not be extended */
+ do_update = fnpiv > 0 ;
+ fnzeros = 0 ;
+ DEBUG2 (("OUT-OUT do_update forced true: "ID"\n", do_update)) ;
+
+ /* The new front would be just big enough to hold the new
+ * pivot row and column. */
+ fnrows_new [OUT][OUT] = cdeg_out - 1 ;
+ fncols_new [OUT][OUT] = rdeg [OUT][OUT] - 1 ;
+ }
+
+ DEBUG2 (("option OUT OUT: nr "ID" nc "ID" cost "ID"\n",
+ rdeg [OUT][OUT], cdeg_out, thiscost)) ;
+
+ if (bestcost == EMPTY || thiscost < bestcost)
+ {
+ /* this is the best option seen so far */
+ Work->pivot_case = OUT_OUT ;
+ bestcost = thiscost ;
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+ }
+ }
+ }
+
+ /* At this point, a structural pivot has been found. */
+ /* It may be numerically zero, however. */
+ ASSERT (Work->pivot_case != EMPTY) ;
+ DEBUG2 (("local search, best option "ID", best cost "ID"\n",
+ Work->pivot_case, bestcost)) ;
+
+ /* ====================================================================== */
+ /* Pivot row and column, and extension, now determined */
+ /* ====================================================================== */
+
+ Work->fnzeros = new_fnzeros ;
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize the pivot row and column */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Work->pivot_case)
+ {
+ case IN_IN:
+ DEBUG2 (("IN-IN option selected\n")) ;
+ ASSERT (fnrows > 0 && fncols > 0) ;
+ Work->pivcol_in_front = TRUE ;
+ Work->pivrow_in_front = TRUE ;
+ Work->pivcol = pivcol [IN] ;
+ Work->pivrow = pivrow [IN][IN] ;
+ Work->ccdeg = nr_in ;
+ Work->Wrow = Fcols ;
+ Work->rrdeg = rdeg [IN][IN] ;
+ jj = jcand [IN] ;
+ Work->fnrows_new = fnrows_new [IN][IN] ;
+ Work->fncols_new = fncols_new [IN][IN] ;
+ break ;
+
+ case IN_OUT:
+ DEBUG2 (("IN-OUT option selected\n")) ;
+ ASSERT (fnrows >= 0 && fncols > 0) ;
+ Work->pivcol_in_front = TRUE ;
+ Work->pivrow_in_front = FALSE ;
+ Work->pivcol = pivcol [IN] ;
+ Work->pivrow = pivrow [IN][OUT] ;
+ Work->ccdeg = nr_in ;
+ Work->Wrow = Wio ;
+ Work->rrdeg = rdeg [IN][OUT] ;
+ jj = jcand [IN] ;
+ Work->fnrows_new = fnrows_new [IN][OUT] ;
+ Work->fncols_new = fncols_new [IN][OUT] ;
+ break ;
+
+ case OUT_IN:
+ DEBUG2 (("OUT-IN option selected\n")) ;
+ ASSERT (fnrows > 0 && fncols >= 0) ;
+ Work->pivcol_in_front = FALSE ;
+ Work->pivrow_in_front = TRUE ;
+ Work->pivcol = pivcol [OUT] ;
+ Work->pivrow = pivrow [OUT][IN] ;
+ Work->ccdeg = cdeg_out ;
+ /* Wrow might be equivalenced to Fcols (Freebie in): */
+ Work->Wrow = Woi ;
+ Work->rrdeg = rdeg [OUT][IN] ;
+ /* Work->Wrow[0..fncols-1] is not there. See Fcols instead */
+ jj = jcand [OUT] ;
+ Work->fnrows_new = fnrows_new [OUT][IN] ;
+ Work->fncols_new = fncols_new [OUT][IN] ;
+ break ;
+
+ case OUT_OUT:
+ DEBUG2 (("OUT-OUT option selected\n")) ;
+ ASSERT (fnrows >= 0 && fncols >= 0) ;
+ Work->pivcol_in_front = FALSE ;
+ Work->pivrow_in_front = FALSE ;
+ Work->pivcol = pivcol [OUT] ;
+ Work->pivrow = pivrow [OUT][OUT] ;
+ Work->ccdeg = cdeg_out ;
+ /* Wrow might be equivalenced to Wio (Freebie out): */
+ Work->Wrow = Woo ;
+ Work->rrdeg = rdeg [OUT][OUT] ;
+ jj = jcand [OUT] ;
+ Work->fnrows_new = fnrows_new [OUT][OUT] ;
+ Work->fncols_new = fncols_new [OUT][OUT] ;
+ break ;
+
+ }
+
+ ASSERT (IMPLIES (fnrows == 0 && fncols == 0, Work->pivot_case == OUT_OUT)) ;
+
+ if (!Work->pivcol_in_front && pivcol [IN] != EMPTY)
+ {
+ /* clear Frpos if pivcol [IN] was searched, but not selected */
+ for (i = fnrows ; i < cdeg_in ; i++)
+ {
+ Frpos [Frows [i]] = EMPTY;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Pivot row and column have been found */
+ /* ---------------------------------------------------------------------- */
+
+ /* ---------------------------------------------------------------------- */
+ /* remove pivot column from candidate pivot column set */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (jj >= 0 && jj < Work->nCandidates) ;
+ ASSERT (Work->pivcol == Work->Candidates [jj]) ;
+ remove_candidate (jj, Work, Symbolic) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for frontal matrix growth */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("Check frontal growth:\n")) ;
+ DEBUG1 (("fnrows_new "ID" + 1 = "ID", fnr_curr "ID"\n",
+ Work->fnrows_new, Work->fnrows_new + 1, fnr_curr)) ;
+ DEBUG1 (("fncols_new "ID" + 1 = "ID", fnc_curr "ID"\n",
+ Work->fncols_new, Work->fncols_new + 1, fnc_curr)) ;
+
+ Work->do_grow = (Work->fnrows_new + 1 > fnr_curr
+ || Work->fncols_new + 1 > fnc_curr) ;
+ if (Work->do_grow)
+ {
+ DEBUG0 (("\nNeed to grow frontal matrix, force do_update true\n")) ;
+ /* If the front must grow, then apply the pending updates and remove
+ * the current pivot rows/columns from the front prior to growing the
+ * front. This frees up as much space as possible for the new front. */
+ if (!Work->do_update && fnpiv > 0)
+ {
+ /* This update would not have to be done if the current front
+ * was big enough. */
+ Work->nforced++ ;
+ Work->do_update = TRUE ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* current pivot column */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ c1) If pivot column index is in the current front:
+
+ The pivot column pattern is in Frows [0 .. fnrows-1] and
+ the extension is in Frows [fnrows ... fnrows+ccdeg-1].
+
+ Frpos [Frows [0 .. fnrows+ccdeg-1]] is
+ equal to 0 .. fnrows+ccdeg-1. Wm is not needed.
+
+ The values are in Wy [0 .. fnrows+ccdeg-1].
+
+ c2) Otherwise, if the pivot column index is not in the current front:
+
+ c2a) If the front is being extended, old row indices in the the
+ pivot column pattern are in Frows [0 .. fnrows-1].
+
+ All entries are in Wm [0 ... ccdeg-1], with values in
+ Wx [0 .. ccdeg-1]. These may include entries already in
+ Frows [0 .. fnrows-1].
+
+ Frpos [Frows [0 .. fnrows-1]] is equal to 0 .. fnrows-1.
+ Frpos [Wm [0 .. ccdeg-1]] for new entries is < 0.
+
+ c2b) If the front is not being extended, then the entire pivot
+ column pattern is in Wm [0 .. ccdeg-1]. It includes
+ the pivot row index. It is does not contain the pattern
+ Frows [0..fnrows-1]. The intersection of these two
+ sets may or may not be empty. The values are in Wx [0..ccdeg-1]
+
+ In both cases c1 and c2, Frpos [Frows [0 .. fnrows-1]] is equal
+ to 0 .. fnrows-1, which is the pattern of the current front.
+ Any entry of Frpos that is not specified above is < 0.
+ */
+
+
+#ifndef NDEBUG
+ DEBUG2 (("\n\nSEARCH DONE: Pivot col "ID" in: ("ID") pivot row "ID" in: ("ID
+ ") extend: "ID"\n\n", Work->pivcol, Work->pivcol_in_front,
+ Work->pivrow, Work->pivrow_in_front, Work->do_extend)) ;
+ UMF_dump_rowcol (1, Numeric, Work, Work->pivcol, !Symbolic->fixQ) ;
+ DEBUG2 (("Pivot col "ID": fnrows "ID" ccdeg "ID"\n", Work->pivcol, fnrows,
+ Work->ccdeg)) ;
+ if (Work->pivcol_in_front) /* case c1 */
+ {
+ Int found = FALSE ;
+ DEBUG3 (("Pivcol in front\n")) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG3 ((ID": row:: "ID" in front ", i, row)) ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Frpos [row] == i) ;
+ EDEBUG3 (Wy [i]) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found == Work->pivrow_in_front) ;
+ found = FALSE ;
+ for (i = fnrows ; i < fnrows + Work->ccdeg ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG3 ((ID": row:: "ID" (new)", i, row)) ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Frpos [row] == i) ;
+ EDEBUG3 (Wy [i]) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found == !Work->pivrow_in_front) ;
+ }
+ else
+ {
+ if (Work->do_extend)
+ {
+ Int found = FALSE ;
+ DEBUG3 (("Pivcol not in front (extend)\n")) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG3 ((ID": row:: "ID" in front ", i, row)) ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Frpos [row] == i) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found == Work->pivrow_in_front) ;
+ found = FALSE ;
+ DEBUG3 (("----\n")) ;
+ for (i = 0 ; i < Work->ccdeg ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ DEBUG3 ((ID": row:: "ID" ", i, row)) ;
+ EDEBUG3 (Wx [i]) ;
+ if (Frpos [row] < 0)
+ {
+ DEBUG3 ((" (new) ")) ;
+ }
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ /* ... */
+ if (Work->pivrow_in_front) ASSERT (Frpos [row] >= 0) ;
+ else ASSERT (Frpos [row] < 0) ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found) ;
+ }
+ else
+ {
+ Int found = FALSE ;
+ DEBUG3 (("Pivcol not in front (no extend)\n")) ;
+ for (i = 0 ; i < Work->ccdeg ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ DEBUG3 ((ID": row:: "ID" ", i, row)) ;
+ EDEBUG3 (Wx [i]) ;
+ DEBUG3 ((" (new) ")) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* current pivot row */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ r1) If the pivot row index is in the current front:
+
+ The pivot row pattern is in Fcols [0..fncols-1] and the extenson is
+ in Wrow [fncols .. rrdeg-1]. If the pivot column is in the current
+ front, then Fcols and Wrow are equivalenced.
+
+ r2) If the pivot row index is not in the current front:
+
+ r2a) If the front is being extended, the pivot row pattern is in
+ Fcols [0 .. fncols-1]. New entries are in Wrow [0 .. rrdeg-1],
+ but these may include entries already in Fcols [0 .. fncols-1].
+
+ r2b) Otherwise, the pivot row pattern is Wrow [0 .. rrdeg-1].
+
+ Fcpos [Fcols [0..fncols-1]] is (0..fncols-1) * fnr_curr.
+ All other entries in Fcpos are < 0.
+
+ These conditions are asserted below.
+
+ ------------------------------------------------------------------------
+ Other items in Work structure that are relevant:
+
+ pivcol: the pivot column index
+ pivrow: the pivot column index
+
+ rrdeg:
+ ccdeg:
+
+ fnrows: the number of rows in the currnt contribution block
+ fncols: the number of columns in the current contribution block
+
+ fnrows_new: the number of rows in the new contribution block
+ fncols_new: the number of rows in the new contribution block
+
+ ------------------------------------------------------------------------
+ */
+
+
+#ifndef NDEBUG
+ UMF_dump_rowcol (0, Numeric, Work, Work->pivrow, TRUE) ;
+ DEBUG2 (("Pivot row "ID":\n", Work->pivrow)) ;
+ if (Work->pivrow_in_front)
+ {
+ Int found = FALSE ;
+ for (i = 0 ; i < fncols ; i++)
+ {
+ col = Fcols [i] ;
+ DEBUG3 ((" col:: "ID" in front\n", col)) ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ ASSERT (Fcpos [col] == i * fnr_curr) ;
+ if (col == Work->pivcol) found = TRUE ;
+ }
+ ASSERT (found == Work->pivcol_in_front) ;
+ found = FALSE ;
+ ASSERT (IMPLIES (Work->pivcol_in_front, Fcols == Work->Wrow)) ;
+ for (i = fncols ; i < Work->rrdeg ; i++)
+ {
+ col = Work->Wrow [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ ASSERT (Fcpos [col] < 0) ;
+ if (col == Work->pivcol) found = TRUE ;
+ else DEBUG3 ((" col:: "ID" (new)\n", col)) ;
+ }
+ ASSERT (found == !Work->pivcol_in_front) ;
+ }
+ else
+ {
+ if (Work->do_extend)
+ {
+ Int found = FALSE ;
+ for (i = 0 ; i < fncols ; i++)
+ {
+ col = Fcols [i] ;
+ DEBUG3 ((" col:: "ID" in front\n", col)) ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ ASSERT (Fcpos [col] == i * fnr_curr) ;
+ if (col == Work->pivcol) found = TRUE ;
+ }
+ ASSERT (found == Work->pivcol_in_front) ;
+ found = FALSE ;
+ for (i = 0 ; i < Work->rrdeg ; i++)
+ {
+ col = Work->Wrow [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (Fcpos [col] >= 0) continue ;
+ if (col == Work->pivcol) found = TRUE ;
+ else DEBUG3 ((" col:: "ID" (new, extend)\n", col)) ;
+ }
+ ASSERT (found == !Work->pivcol_in_front) ;
+ }
+ else
+ {
+ Int found = FALSE ;
+ for (i = 0 ; i < Work->rrdeg ; i++)
+ {
+ col = Work->Wrow [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (col == Work->pivcol) found = TRUE ;
+ else DEBUG3 ((" col:: "ID" (all new)\n", col)) ;
+ }
+ ASSERT (found) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine whether to do scan2-row and scan2-col */
+ /* ---------------------------------------------------------------------- */
+
+ if (Work->do_extend)
+ {
+ Work->do_scan2row = (fncols > 0) ;
+ Work->do_scan2col = (fnrows > 0) ;
+ }
+ else
+ {
+ Work->do_scan2row = (fncols > 0) && Work->pivrow_in_front ;
+ Work->do_scan2col = (fnrows > 0) && Work->pivcol_in_front ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG2 (("LOCAL SEARCH DONE: pivot column "ID" pivot row: "ID"\n",
+ Work->pivcol, Work->pivrow)) ;
+ DEBUG2 (("do_extend: "ID"\n", Work->do_extend)) ;
+ DEBUG2 (("do_update: "ID"\n", Work->do_update)) ;
+ DEBUG2 (("do_grow: "ID"\n", Work->do_grow)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* keep track of the diagonal */
+ /* ---------------------------------------------------------------------- */
+
+ if (Symbolic->prefer_diagonal
+ && Work->pivcol < Work->n_col - Symbolic->nempty_col)
+ {
+ Diagonal_map = Work->Diagonal_map ;
+ Diagonal_imap = Work->Diagonal_imap ;
+ ASSERT (Diagonal_map != (Int *) NULL) ;
+ ASSERT (Diagonal_imap != (Int *) NULL) ;
+
+ row2 = Diagonal_map [Work->pivcol] ;
+ col2 = Diagonal_imap [Work->pivrow] ;
+
+ if (row2 < 0)
+ {
+ /* this was an off-diagonal pivot row */
+ Work->noff_diagonal++ ;
+ row2 = UNFLIP (row2) ;
+ }
+
+ ASSERT (Diagonal_imap [row2] == Work->pivcol) ;
+ ASSERT (UNFLIP (Diagonal_map [col2]) == Work->pivrow) ;
+
+ if (row2 != Work->pivrow)
+ {
+ /* swap the diagonal map to attempt to maintain symmetry later on.
+ * Also mark the map for col2 (via FLIP) to denote that the entry
+ * now on the diagonal is not the original entry on the diagonal. */
+
+ DEBUG0 (("Unsymmetric pivot\n")) ;
+ Diagonal_map [Work->pivcol] = FLIP (Work->pivrow) ;
+ Diagonal_imap [Work->pivrow] = Work->pivcol ;
+
+ Diagonal_map [col2] = FLIP (row2) ;
+ Diagonal_imap [row2] = col2 ;
+
+ }
+ ASSERT (n_row == n_col) ;
+#ifndef NDEBUG
+ UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, Symbolic->n1,
+ Symbolic->n_col, Symbolic->nempty_col) ;
+#endif
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_local_search.h b/src/C/SuiteSparse/UMFPACK/Source/umf_local_search.h
new file mode 100644
index 0000000..bd039f4
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_local_search.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_local_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.c b/src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.c
new file mode 100644
index 0000000..a8c0c2d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.c
@@ -0,0 +1,151 @@
+/* ========================================================================== */
+/* === UMF_lsolve =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* solves Lx = b, where L is the lower triangular factor of a matrix */
+/* B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+
+GLOBAL double UMF_lsolve
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ Entry xk ;
+ Entry *xp, *Lval ;
+ Int k, deg, *ip, j, row, *Lpos, *Lilen, *Lip, llen, lp, newLchain,
+ pos, npiv, n1, *Li ;
+
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ npiv = Numeric->npiv ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Lsolve start:\n")) ;
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Lsolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ xk = X [k] ;
+ deg = Lilen [k] ;
+ if (deg > 0 && IS_NONZERO (xk))
+ {
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ;
+ EDEBUG4 (Lval [j]) ;
+ DEBUG4 (("\n")) ;
+ /* X [Li [j]] -= xk * Lval [j] ; */
+ MULT_SUB (X [Li [j]], xk, Lval [j]) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* rest of L */
+ /* ---------------------------------------------------------------------- */
+
+ deg = 0 ;
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ }
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (!newLchain) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k) ;
+ Pattern [deg++] = row ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* use column k of L */
+ /* ------------------------------------------------------------------ */
+
+ xk = X [k] ;
+ if (IS_NONZERO (xk))
+ {
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+ /* X [Pattern [j]] -= xk * (*xp) ; */
+ MULT_SUB (X [Pattern [j]], xk, *xp) ;
+ xp++ ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Lsolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Lsolve done.\n")) ;
+#endif
+
+ return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.h b/src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.h
new file mode 100644
index 0000000..187b950
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_lsolve.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_lsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.c b/src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.c
new file mode 100644
index 0000000..383cf9b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.c
@@ -0,0 +1,225 @@
+/* ========================================================================== */
+/* === UMF_ltsolve ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Solves L'x = b or L.'x=b, where L is the lower triangular factor of a */
+/* matrix. B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+
+GLOBAL double
+#ifdef CONJUGATE_SOLVE
+UMF_lhsolve /* solve L'x=b (complex conjugate transpose) */
+#else
+UMF_ltsolve /* solve L.'x=b (array transpose) */
+#endif
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ Entry xk ;
+ Entry *xp, *Lval ;
+ Int k, deg, *ip, j, row, *Lpos, *Lilen, kstart, kend, *Lip, llen,
+ lp, pos, npiv, n1, *Li ;
+
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ npiv = Numeric->npiv ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ kstart = npiv ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Ltsolve start:\n")) ;
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Ltsolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* non-singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (kend = npiv-1 ; kend >= n1 ; kend = kstart-1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* find the start of this Lchain */
+ /* ------------------------------------------------------------------ */
+
+ /* for (kstart = kend ; kstart >= 0 && Lip [kstart] > 0 ; kstart--) ; */
+ kstart = kend ;
+ while (kstart >= 0 && Lip [kstart] > 0)
+ {
+ kstart-- ;
+ }
+
+ /* the Lchain goes from kstart to kend */
+
+ /* ------------------------------------------------------------------ */
+ /* scan the whole chain to find the pattern of the last column of L */
+ /* ------------------------------------------------------------------ */
+
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ for (k = kstart ; k <= kend ; k++)
+ {
+ ASSERT (k >= 0 && k < npiv) ;
+
+ /* -------------------------------------------------------------- */
+ /* make column k of L in Pattern [0..deg-1] */
+ /* -------------------------------------------------------------- */
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (k != kstart) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ lp = Lip [k] ;
+ if (k == kstart)
+ {
+ lp = -lp ;
+ }
+ ASSERT (lp > 0) ;
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k) ;
+ Pattern [deg++] = row ;
+ }
+
+ }
+ /* Pattern [0..deg-1] is now the pattern of column kend */
+
+ /* ------------------------------------------------------------------ */
+ /* solve using this chain, in reverse order */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG4 (("Unwinding Lchain\n")) ;
+ for (k = kend ; k >= kstart ; k--)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use column k of L */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (k >= 0 && k < npiv) ;
+ lp = Lip [k] ;
+ if (k == kstart)
+ {
+ lp = -lp ;
+ }
+ ASSERT (lp > 0) ;
+ llen = Lilen [k] ;
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+ xk = X [k] ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+
+#ifdef CONJUGATE_SOLVE
+ /* xk -= X [Pattern [j]] * conjugate (*xp) ; */
+ MULT_SUB_CONJ (xk, X [Pattern [j]], *xp) ;
+#else
+ /* xk -= X [Pattern [j]] * (*xp) ; */
+ MULT_SUB (xk, X [Pattern [j]], *xp) ;
+#endif
+
+ xp++ ;
+ }
+ X [k] = xk ;
+
+ /* -------------------------------------------------------------- */
+ /* construct column k-1 of L */
+ /* -------------------------------------------------------------- */
+
+ /* un-concatenate the pattern */
+ deg -= llen ;
+
+ /* add pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" adding row "ID" at position "ID"\n",
+ k, k, pos)) ;
+ ASSERT (k != kstart) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ deg = Lilen [k] ;
+ if (deg > 0)
+ {
+ xk = X [k] ;
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ;
+ EDEBUG4 (Lval [j]) ;
+ DEBUG4 (("\n")) ;
+#ifdef CONJUGATE_SOLVE
+ /* xk -= X [Li [j]] * conjugate (Lval [j]) ; */
+ MULT_SUB_CONJ (xk, X [Li [j]], Lval [j]) ;
+#else
+ /* xk -= X [Li [j]] * Lval [j] ; */
+ MULT_SUB (xk, X [Li [j]], Lval [j]) ;
+#endif
+ }
+ X [k] = xk ;
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Ltsolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Ltsolve done.\n")) ;
+#endif
+
+ return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.h b/src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.h
new file mode 100644
index 0000000..ba5995a
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_ltsolve.h
@@ -0,0 +1,19 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_ltsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
+
+GLOBAL double UMF_lhsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_malloc.c b/src/C/SuiteSparse/UMFPACK/Source/umf_malloc.c
new file mode 100644
index 0000000..97c43fd
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_malloc.c
@@ -0,0 +1,91 @@
+/* ========================================================================== */
+/* === UMF_malloc =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Allocate a block of n objects, each of a given size. This routine does not
+ handle the case when the size is 1 (allocating char's) because of potential
+ integer overflow. UMFPACK never does that.
+ Also maintains the UMFPACK malloc count.
+*/
+
+#include "umf_internal.h"
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+
+/*
+ UMF_malloc_count is a count of the objects malloc'd by UMFPACK. If you
+ suspect a memory leak in your program (caused by not properly destroying
+ the Symbolic and Numeric objects) then compile with -DUMF_MALLOC_COUNT and
+ check value of UMF_malloc_count. By default, UMF_MALLOC_COUNT is not
+ defined, and thus UMFPACK has no global variables.
+*/
+
+GLOBAL Int UMF_malloc_count = 0 ;
+
+#endif
+
+#ifdef UMF_TCOV_TEST
+/* For exhaustive statement coverage testing only! */
+GLOBAL int umf_fail, umf_fail_lo, umf_fail_hi ;
+GLOBAL int umf_realloc_fail, umf_realloc_lo, umf_realloc_hi ;
+#endif
+
+GLOBAL void *UMF_malloc
+(
+ Int n_objects,
+ size_t size_of_object
+)
+{
+ size_t size ;
+ void *p ;
+
+#ifdef UMF_TCOV_TEST
+ /* For exhaustive statement coverage testing only! */
+ /* Pretend to fail, to test out-of-memory conditions. */
+ umf_fail-- ;
+ if (umf_fail <= umf_fail_hi && umf_fail >= umf_fail_lo)
+ {
+ DEBUG0 (("umf_malloc: Pretend to fail %d %d %d\n",
+ umf_fail, umf_fail_hi, umf_fail_lo)) ;
+ return ((void *) NULL) ;
+ }
+#endif
+
+ DEBUG0 (("UMF_malloc: ")) ;
+
+ /* make sure that we allocate something */
+ n_objects = MAX (1, n_objects) ;
+
+ size = (size_t) n_objects ;
+ ASSERT (size_of_object > 1) ;
+ if (size > Int_MAX / size_of_object)
+ {
+ /* object is too big for integer pointer arithmetic */
+ return ((void *) NULL) ;
+ }
+ size *= size_of_object ;
+
+ /* see AMD/Source/amd_global.c for the memory allocator selection */
+ p = amd_malloc (size) ;
+
+ DEBUG0 ((ID"\n", (Int) p)) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (p)
+ {
+ /* One more object has been malloc'ed. Keep track of the count. */
+ /* (purely for sanity checks). */
+ UMF_malloc_count++ ;
+ DEBUG0 ((" successful, new malloc count: "ID"\n", UMF_malloc_count)) ;
+ }
+#endif
+
+ return (p) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_malloc.h b/src/C/SuiteSparse/UMFPACK/Source/umf_malloc.h
new file mode 100644
index 0000000..486a491
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_malloc.h
@@ -0,0 +1,25 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#ifndef _UMF_MALLOC
+#define _UMF_MALLOC
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+GLOBAL EXTERN Int UMF_malloc_count ;
+#endif
+
+GLOBAL void *UMF_malloc
+(
+ Int n_objects,
+ size_t size_of_object
+) ;
+
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c
new file mode 100644
index 0000000..73553bd
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c
@@ -0,0 +1,82 @@
+/* ========================================================================== */
+/* === UMF_mem_alloc_element ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+/* Allocate a nrows-by-ncols element, and initialize it. */
+/* Returns the index into Numeric->Memory if successful, or 0 on failure. */
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_tail_block.h"
+
+GLOBAL Int UMF_mem_alloc_element
+(
+ NumericType *Numeric,
+ Int nrows,
+ Int ncols,
+ Int **Rows,
+ Int **Cols,
+ Entry **C,
+ Int *size,
+ Element **epout
+)
+{
+
+ Element *ep ;
+ Unit *p ;
+ Int i ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+
+ *size = GET_ELEMENT_SIZE (nrows, ncols) ;
+ if (INT_OVERFLOW (DGET_ELEMENT_SIZE (nrows, ncols) + 1))
+ {
+ /* :: allocate element, int overflow :: */
+ return (0) ; /* problem is too large */
+ }
+
+ i = UMF_mem_alloc_tail_block (Numeric, *size) ;
+ (*size)++ ;
+ if (!i)
+ {
+ DEBUG0 (("alloc element failed - out of memory\n")) ;
+ return (0) ; /* out of memory */
+ }
+ p = Numeric->Memory + i ;
+
+ ep = (Element *) p ;
+
+ DEBUG2 (("alloc_element done ("ID" x "ID"): p: "ID" i "ID"\n",
+ nrows, ncols, (Int) (p-Numeric->Memory), i)) ;
+
+ /* Element data structure, in order: */
+ p += UNITS (Element, 1) ; /* (1) Element header */
+ *Cols = (Int *) p ; /* (2) col [0..ncols-1] indices */
+ *Rows = *Cols + ncols ; /* (3) row [0..nrows-1] indices */
+ p += UNITS (Int, ncols + nrows) ;
+ *C = (Entry *) p ; /* (4) C [0..nrows-1, 0..ncols-1] */
+
+ ep->nrows = nrows ; /* initialize the header information */
+ ep->ncols = ncols ;
+ ep->nrowsleft = nrows ;
+ ep->ncolsleft = ncols ;
+ ep->cdeg = 0 ;
+ ep->rdeg = 0 ;
+ ep->next = EMPTY ;
+
+ DEBUG2 (("new block size: "ID" ", GET_BLOCK_SIZE (Numeric->Memory + i))) ;
+ DEBUG2 (("Element size needed "ID"\n", GET_ELEMENT_SIZE (nrows, ncols))) ;
+
+ *epout = ep ;
+
+ /* return the offset into Numeric->Memory */
+ return (i) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.h b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.h
new file mode 100644
index 0000000..4463071
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.h
@@ -0,0 +1,17 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_mem_alloc_element
+(
+ NumericType *Numeric,
+ Int nrows,
+ Int ncols,
+ Int **Rows,
+ Int **Cols,
+ Entry **C,
+ Int *size,
+ Element **epout
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c
new file mode 100644
index 0000000..bc9cd22
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c
@@ -0,0 +1,54 @@
+/* ========================================================================== */
+/* === UMF_mem_alloc_head_block ============================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+/* allocate nunits from head of Numeric->Memory. No header allocated. */
+/* Returns the index into Numeric->Memory if successful, or 0 on failure. */
+
+#include "umf_internal.h"
+
+GLOBAL Int UMF_mem_alloc_head_block
+(
+ NumericType *Numeric,
+ Int nunits
+)
+{
+ Int p, usage ;
+ DEBUG2 (("GET BLOCK: from head, size "ID" ", nunits)) ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+
+#ifndef NDEBUG
+ if (UMF_allocfail)
+ {
+ /* pretend to fail, to test garbage_collection */
+ DEBUGm2 (("UMF_mem_alloc_head_block: pretend to fail\n")) ;
+ UMF_allocfail = FALSE ; /* don't fail the next time */
+ return (0) ;
+ }
+#endif
+
+ if (nunits > (Numeric->itail - Numeric->ihead))
+ {
+ DEBUG2 ((" failed\n")) ;
+ return (0) ;
+ }
+
+ /* return p as an offset from Numeric->Memory */
+ p = Numeric->ihead ;
+ Numeric->ihead += nunits ;
+
+ DEBUG2 (("p: "ID"\n", p)) ;
+ usage = Numeric->ihead + Numeric->tail_usage ;
+ Numeric->max_usage = MAX (Numeric->max_usage, usage) ;
+ return (p) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.h b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.h
new file mode 100644
index 0000000..d861330
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_mem_alloc_head_block
+(
+ NumericType *Numeric,
+ Int nunits
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c
new file mode 100644
index 0000000..afe8ee1
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c
@@ -0,0 +1,133 @@
+/* ========================================================================== */
+/* === UMF_mem_alloc_tail_block ============================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+#include "umf_internal.h"
+
+/* allocate nunits from tail of Numeric->Memory */
+/* (requires nunits+1, for header). */
+/* Returns the index into Numeric->Memory if successful, or 0 on failure. */
+
+GLOBAL Int UMF_mem_alloc_tail_block
+(
+ NumericType *Numeric,
+ Int nunits
+)
+{
+ Int bigsize, usage ;
+ Unit *p, *pnext, *pbig ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+
+#ifndef NDEBUG
+ if (UMF_allocfail)
+ {
+ /* pretend to fail, to test garbage_collection */
+ DEBUGm2 (("UMF_mem_alloc_tail_block: pretend to fail\n")) ;
+ UMF_allocfail = FALSE ; /* don't fail the next time */
+ return (0) ;
+ }
+ DEBUG2 (("UMF_mem_alloc_tail_block, size: "ID" + 1 = "ID": ",
+ nunits, nunits+1)) ;
+#endif
+
+ bigsize = 0 ;
+ pbig = (Unit *) NULL ;
+
+ ASSERT (nunits > 0) ; /* size must be positive */
+ if (Numeric->ibig != EMPTY)
+ {
+ ASSERT (Numeric->ibig > Numeric->itail) ;
+ ASSERT (Numeric->ibig < Numeric->size) ;
+ pbig = Numeric->Memory + Numeric->ibig ;
+ bigsize = -pbig->header.size ;
+ ASSERT (bigsize > 0) ; /* Numeric->ibig is free */
+ ASSERT (pbig->header.prevsize >= 0) ; /* prev. is not free */
+ }
+
+ if (pbig && bigsize >= nunits)
+ {
+
+ /* use the biggest block, somewhere in middle of memory */
+ p = pbig ;
+ pnext = p + 1 + bigsize ;
+ /* next is in range */
+ ASSERT (pnext < Numeric->Memory + Numeric->size) ;
+ /* prevsize of next = this size */
+ ASSERT (pnext->header.prevsize == bigsize) ;
+ /* next is not free */
+ ASSERT (pnext->header.size > 0) ;
+ bigsize -= nunits + 1 ;
+
+ if (bigsize < 4)
+ {
+ /* internal fragmentation would be too small */
+ /* allocate the entire free block */
+ p->header.size = -p->header.size ;
+ DEBUG2 (("GET BLOCK: p: "ID" size: "ID", all of big: "ID" size: "
+ ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->ibig,
+ p->header.size)) ;
+ /* no more biggest block */
+ Numeric->ibig = EMPTY ;
+
+ }
+ else
+ {
+
+ /* allocate just the first nunits Units of the free block */
+ p->header.size = nunits ;
+ /* make a new free block */
+ Numeric->ibig += nunits + 1 ;
+ pbig = Numeric->Memory + Numeric->ibig ;
+ pbig->header.size = -bigsize ;
+ pbig->header.prevsize = nunits ;
+ pnext->header.prevsize = bigsize ;
+ DEBUG2 (("GET BLOCK: p: "ID" size: "ID", some of big: "ID" left: "
+ ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->ibig,
+ bigsize)) ;
+ }
+
+ }
+ else
+ {
+
+ /* allocate from the top of tail */
+ pnext = Numeric->Memory + Numeric->itail ;
+ DEBUG2 (("GET BLOCK: from tail ")) ;
+ if ((nunits + 1) > (Numeric->itail - Numeric->ihead))
+ {
+ DEBUG2 (("\n")) ;
+ return (0) ;
+ }
+ Numeric->itail -= (nunits + 1) ;
+ p = Numeric->Memory + Numeric->itail ;
+ p->header.size = nunits ;
+ p->header.prevsize = 0 ;
+ pnext->header.prevsize = nunits ;
+ DEBUG2 (("p: "ID" size: "ID", new tail "ID"\n",
+ (Int) (p-Numeric->Memory), nunits, Numeric->itail)) ;
+ }
+
+ Numeric->tail_usage += p->header.size + 1 ;
+ usage = Numeric->ihead + Numeric->tail_usage ;
+ Numeric->max_usage = MAX (Numeric->max_usage, usage) ;
+
+#ifndef NDEBUG
+ UMF_debug -= 10 ;
+ UMF_dump_memory (Numeric) ;
+ UMF_debug += 10 ;
+#endif
+
+ /* p points to the header. Add one to point to the usable block itself. */
+ /* return the offset into Numeric->Memory */
+ return ((p - Numeric->Memory) + 1) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.h b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.h
new file mode 100644
index 0000000..91ae285
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_mem_alloc_tail_block
+(
+ NumericType *Numeric,
+ Int nunits
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c
new file mode 100644
index 0000000..6aea23a
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c
@@ -0,0 +1,142 @@
+/* ========================================================================== */
+/* === UMF_mem_free_tail_block ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+/* free a block from the tail of Numeric->memory */
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_mem_free_tail_block
+(
+ NumericType *Numeric,
+ Int i
+)
+{
+ Unit *pprev, *pnext, *p, *pbig ;
+ Int sprev ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+ if (i == EMPTY || i == 0) return ; /* already deallocated */
+
+ /* ---------------------------------------------------------------------- */
+ /* get the block */
+ /* ---------------------------------------------------------------------- */
+
+ p = Numeric->Memory + i ;
+
+ p-- ; /* get the corresponding header */
+ DEBUG2 (("free block: p: "ID, (Int) (p-Numeric->Memory))) ;
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+ ASSERT (p->header.size > 0) ; /* block not already free */
+ ASSERT (p->header.prevsize >= 0) ;
+
+ Numeric->tail_usage -= p->header.size + 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* merge with next free block, if any */
+ /* ---------------------------------------------------------------------- */
+
+ pnext = p + 1 + p->header.size ;
+ DEBUG2 (("size: "ID" next: "ID" ", p->header.size,
+ (Int) (pnext-Numeric->Memory))) ;
+ ASSERT (pnext < Numeric->Memory + Numeric->size) ;
+ ASSERT (pnext->header.prevsize == p->header.size) ;
+ ASSERT (pnext->header.size != 0) ;
+
+ if (pnext->header.size < 0)
+ {
+ /* next block is also free - merge with current block */
+ p->header.size += (-(pnext->header.size)) + 1 ;
+ DEBUG2 ((" NEXT FREE ")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* merge with previous free block, if any */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ DEBUG2 ((" at top of tail ")) ;
+ ASSERT (p->header.prevsize == 0) ;
+ }
+#endif
+
+ if (p > Numeric->Memory + Numeric->itail)
+ {
+ ASSERT (p->header.prevsize > 0) ;
+ pprev = p - 1 - p->header.prevsize ;
+ DEBUG2 ((" prev: "ID" ", (Int) (pprev-Numeric->Memory))) ;
+ ASSERT (pprev >= Numeric->Memory + Numeric->itail) ;
+ sprev = pprev->header.size ;
+ if (sprev < 0)
+ {
+ /* previous block is also free - merge it with current block */
+ ASSERT (p->header.prevsize == -sprev) ;
+ pprev->header.size = p->header.size + (-sprev) + 1 ;
+ p = pprev ;
+ DEBUG2 ((" PREV FREE ")) ;
+ /* note that p may now point to Numeric->itail */
+ }
+#ifndef NDEBUG
+ else
+ {
+ ASSERT (p->header.prevsize == sprev) ;
+ }
+#endif
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the block, p */
+ /* ---------------------------------------------------------------------- */
+
+ pnext = p + 1 + p->header.size ;
+ ASSERT (pnext < Numeric->Memory + Numeric->size) ;
+
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ /* top block in list is freed */
+ Numeric->itail = pnext - Numeric->Memory ;
+ pnext->header.prevsize = 0 ;
+ DEBUG2 ((" NEW TAIL : "ID" ", Numeric->itail)) ;
+ ASSERT (pnext->header.size > 0) ;
+ if (Numeric->ibig != EMPTY && Numeric->ibig <= Numeric->itail)
+ {
+ /* the big free block is now above the tail */
+ Numeric->ibig = EMPTY ;
+ }
+ }
+ else
+ {
+ /* keep track of the biggest free block seen */
+ if (Numeric->ibig == EMPTY)
+ {
+ Numeric->ibig = p - Numeric->Memory ;
+ }
+ else
+ {
+ pbig = Numeric->Memory + Numeric->ibig ;
+ if (-(pbig->header.size) < p->header.size)
+ {
+ Numeric->ibig = p - Numeric->Memory ;
+ }
+ }
+ /* flag the block as free, somewhere in the middle of the tail */
+ pnext->header.prevsize = p->header.size ;
+ p->header.size = -(p->header.size) ;
+ }
+
+ DEBUG2 (("new p: "ID" freesize: "ID"\n", (Int) (p-Numeric->Memory),
+ -(p->header.size))) ;
+
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.h b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.h
new file mode 100644
index 0000000..15c4c3b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_mem_free_tail_block
+(
+ NumericType *Numeric,
+ Int i
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c
new file mode 100644
index 0000000..3b4e0c0
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c
@@ -0,0 +1,64 @@
+/* ========================================================================== */
+/* === UMF_mem_init_memoryspace ============================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+#include "umf_internal.h"
+
+/* initialize the LU and element workspace (Numeric->Memory) */
+
+GLOBAL void UMF_mem_init_memoryspace
+(
+ NumericType *Numeric
+)
+{
+ Unit *p ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+ ASSERT (Numeric->size >= 3) ;
+ DEBUG0 (("Init memory space, size "ID"\n", Numeric->size)) ;
+
+ Numeric->ngarbage = 0 ;
+ Numeric->nrealloc = 0 ;
+ Numeric->ncostly = 0 ;
+ Numeric->ibig = EMPTY ;
+ Numeric->ihead = 0 ;
+ Numeric->itail = Numeric->size ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+#endif
+
+ /* allocate the 2-unit tail marker block and initialize it */
+ Numeric->itail -= 2 ;
+ p = Numeric->Memory + Numeric->itail ;
+ DEBUG2 (("p "ID" tail "ID"\n", (Int) (p-Numeric->Memory), Numeric->itail)) ;
+ Numeric->tail_usage = 2 ;
+ p->header.prevsize = 0 ;
+ p->header.size = 1 ;
+
+ /* allocate a 1-unit head marker block at the head of memory */
+ /* this is done so that an offset of zero is treated as a NULL pointer */
+ Numeric->ihead++ ;
+
+ /* initial usage in Numeric->Memory */
+ Numeric->max_usage = 3 ;
+ Numeric->init_usage = Numeric->max_usage ;
+
+ /* Note that UMFPACK_*symbolic ensures that Numeric->Memory is of size */
+ /* at least 3, so this initialization will always succeed. */
+
+#ifndef NDEBUG
+ DEBUG2 (("init_memoryspace, all free (except one unit at head\n")) ;
+ UMF_dump_memory (Numeric) ;
+#endif
+
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.h b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.h
new file mode 100644
index 0000000..30a09b8
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_mem_init_memoryspace
+(
+ NumericType *Numeric
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_multicompile.c b/src/C/SuiteSparse/UMFPACK/Source/umf_multicompile.c
new file mode 100644
index 0000000..ffafef3
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_multicompile.c
@@ -0,0 +1,58 @@
+/* ========================================================================== */
+/* === UMF_multicompile ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* This file is not needed if you have the Unix/Linux "make" command for
+ * compiling UMFPACK. Microsoft Visual Studio cannot be configured to compile
+ * one file multiple times, with different -D flags. In this case, you can
+ * use this file instead. To use this file, see the Demo/simple_compile file.
+ *
+ * This file includes the following source files:
+ *
+ * umf_ltsolve.c
+ * umf_utsolve.c
+ * umf_triplet.c
+ * umf_assemble.c
+ * umf_store_lu.c
+ * umfpack_solve.c
+ *
+ * This file simply compiles the above files with different pre-#define'd flags,
+ * by defining the flags and then #include'ing the source files themselves.
+ * This is a rather unconventional approach, since by convention #include is
+ * supposed to be used with *.h files not *.c. However, it is one way of
+ * working around the limitations of Microsoft Visual Studio.
+ *
+ * You still need to compile all files separately as well, with none of the
+ * pre-#define'd terms listed below.
+ */
+
+/* compile the complex conjugate forward/backsolves */
+#define CONJUGATE_SOLVE
+#include "umf_ltsolve.c"
+#include "umf_utsolve.c"
+
+/* compile umf_triplet with DO_MAP, DO_VALUES and DO_MAP, and just DO_VALUES */
+#define DO_MAP
+#include "umf_triplet.c"
+#define DO_VALUES
+#include "umf_triplet.c"
+#undef DO_MAP
+#include "umf_triplet.c"
+
+/* compile the FIXQ version of umf_assemble */
+#define FIXQ
+#include "umf_assemble.c"
+
+/* compile the DROP version of umf_store_lu */
+#define DROP
+#include "umf_store_lu.c"
+
+/* compile umfpack_wsolve */
+#define WSOLVE
+#include "umfpack_solve.c"
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_realloc.c b/src/C/SuiteSparse/UMFPACK/Source/umf_realloc.c
new file mode 100644
index 0000000..8504d0b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_realloc.c
@@ -0,0 +1,75 @@
+/* ========================================================================== */
+/* === UMF_realloc ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Realloc a block previously allocated by UMF_malloc.
+ Return NULL on failure (in which case the block is still allocated, and will
+ be kept at is present size). This routine is only used for Numeric->Memory.
+*/
+
+#include "umf_internal.h"
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+#include "umf_malloc.h"
+#endif
+
+GLOBAL void *UMF_realloc
+(
+ void *p,
+ Int n_objects,
+ size_t size_of_object
+)
+{
+ size_t size ;
+ void *p2 ;
+
+#ifdef UMF_TCOV_TEST
+ /* For exhaustive statement coverage testing only! */
+ /* Pretend to fail, to test out-of-memory conditions. */
+ umf_realloc_fail-- ;
+ if (umf_realloc_fail <= umf_realloc_hi &&
+ umf_realloc_fail >= umf_realloc_lo)
+ {
+ return ((void *) NULL) ;
+ }
+#endif
+
+ /* make sure that we allocate something */
+ n_objects = MAX (1, n_objects) ;
+
+ size = (size_t) n_objects ;
+ ASSERT (size_of_object > 1) ;
+ if (size > Int_MAX / size_of_object)
+ {
+ /* :: int overflow in umf_realloc :: */
+ return ((void *) NULL) ;
+ }
+ size *= size_of_object ;
+
+ DEBUG0 (("UMF_realloc: "ID" n_objects "ID" size_of_object "ID"\n",
+ (Int) p, n_objects, (Int) size_of_object)) ;
+
+ /* see AMD/Source/amd_global.c for the memory allocator selection */
+ p2 = amd_realloc (p, size) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ /* If p didn't exist on input, and p2 exists, then a new object has been
+ * allocated. */
+ if (p == (void *) NULL && p2 != (void *) NULL)
+ {
+ UMF_malloc_count++ ;
+ }
+#endif
+
+ DEBUG0 (("UMF_realloc: "ID" new malloc count "ID"\n",
+ (Int) p2, UMF_malloc_count)) ;
+
+ return (p2) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_realloc.h b/src/C/SuiteSparse/UMFPACK/Source/umf_realloc.h
new file mode 100644
index 0000000..b55c30e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_realloc.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void *UMF_realloc
+(
+ void *p,
+ Int n_objects,
+ size_t size_of_object
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.c b/src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.c
new file mode 100644
index 0000000..bc25faa
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.c
@@ -0,0 +1,85 @@
+/* ========================================================================== */
+/* === UMF_report_perm ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+
+#define PRINTF4U(params) { if (user || prl >= 4) PRINTF (params) ; }
+
+GLOBAL Int UMF_report_perm
+(
+ Int n,
+ const Int P [ ],
+ Int W [ ], /* workspace of size n */
+ Int prl,
+ Int user
+)
+{
+ Int i, k, valid, prl1 ;
+
+ ASSERT (prl >= 3) ;
+
+ PRINTF4U (("permutation vector, n = "ID". ", n)) ;
+
+ if (n <= 0)
+ {
+ PRINTF (("ERROR: length of permutation is <= 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (!P)
+ {
+ /* if P is (Int *) NULL, this is the identity permutation */
+ PRINTF (("(not present)\n\n")) ;
+ return (UMFPACK_OK) ;
+ }
+
+ if (!W)
+ {
+ PRINTF (("ERROR: out of memory\n\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ PRINTF4 (("\n")) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = TRUE ;
+ }
+
+ prl1 = prl ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P [k] ;
+ PRINTF4 ((" "ID" : "ID" ", INDEX (k), INDEX (i))) ;
+ valid = (i >= 0 && i < n) ;
+ if (valid)
+ {
+ valid = W [i] ;
+ W [i] = FALSE ;
+ }
+ if (!valid)
+ {
+ /* out of range or duplicate entry */
+ PRINTF (("ERROR: invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_permutation) ;
+ }
+ PRINTF4 (("\n")) ;
+ if (prl == 4 && k == 9 && n > 10)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ }
+ prl = prl1 ;
+
+ PRINTF4 ((" permutation vector ")) ;
+ PRINTF4U (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.h b/src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.h
new file mode 100644
index 0000000..dd81936
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_report_perm.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_report_perm
+(
+ Int n,
+ const Int P [ ],
+ Int W [ ],
+ Int prl,
+ Int user
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_report_vector.c b/src/C/SuiteSparse/UMFPACK/Source/umf_report_vector.c
new file mode 100644
index 0000000..7587204
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_report_vector.c
@@ -0,0 +1,110 @@
+/* ========================================================================== */
+/* === UMF_report_vector ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+
+/* ========================================================================== */
+/* === print_value ========================================================== */
+/* ========================================================================== */
+
+PRIVATE void print_value
+(
+ Int i,
+ const double Xx [ ],
+ const double Xz [ ], /* used for complex case only */
+ Int scalar /* if true, then print real part only */
+)
+{
+ Entry xi ;
+ /* if Xz is null, then X is in "merged" format (compatible with Entry, */
+ /* and ANSI C99 double _Complex type). */
+ PRINTF ((" "ID" :", INDEX (i))) ;
+ if (scalar)
+ {
+ PRINT_SCALAR (Xx [i]) ;
+ }
+ else
+ {
+ ASSIGN (xi, Xx, Xz, i, SPLIT (Xz)) ;
+ PRINT_ENTRY (xi) ;
+ }
+ PRINTF (("\n")) ;
+}
+
+/* ========================================================================== */
+/* === UMF_report_vector ==================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_report_vector
+(
+ Int n,
+ const double Xx [ ],
+ const double Xz [ ],
+ Int prl,
+ Int user,
+ Int scalar
+)
+{
+ Int n2, i ;
+
+ if (user || prl >= 4)
+ {
+ PRINTF (("dense vector, n = "ID". ", n)) ;
+ }
+
+ if (user)
+ {
+ if (!Xx)
+ {
+ PRINTF (("ERROR: vector not present\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ if (n < 0)
+ {
+ PRINTF (("ERROR: length of vector is < 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+ }
+
+ if (user || prl >= 4)
+ {
+ PRINTF4 (("\n")) ;
+ }
+
+ if (prl == 4)
+ {
+ /* print level of 4 */
+ n2 = MIN (10, n) ;
+ for (i = 0 ; i < n2 ; i++)
+ {
+ print_value (i, Xx, Xz, scalar) ;
+ }
+ if (n2 < n)
+ {
+ PRINTF ((" ...\n")) ;
+ print_value (n-1, Xx, Xz, scalar) ;
+ }
+ }
+ else if (prl > 4)
+ {
+ /* print level 4 or more */
+ for (i = 0 ; i < n ; i++)
+ {
+ print_value (i, Xx, Xz, scalar) ;
+ }
+ }
+
+ PRINTF4 ((" dense vector ")) ;
+ if (user || prl >= 4)
+ {
+ PRINTF (("OK\n\n")) ;
+ }
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_report_vector.h b/src/C/SuiteSparse/UMFPACK/Source/umf_report_vector.h
new file mode 100644
index 0000000..665a8d4
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_report_vector.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_report_vector
+(
+ Int n,
+ const double Xx [ ],
+ const double Xz [ ],
+ Int prl,
+ Int user,
+ Int scalar
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_row_search.c b/src/C/SuiteSparse/UMFPACK/Source/umf_row_search.c
new file mode 100644
index 0000000..aefb36d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_row_search.c
@@ -0,0 +1,837 @@
+/* ========================================================================== */
+/* === UMF_row_search ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Find two candidate pivot rows in a column: the best one in the front,
+ and the best one not in the front. Return the two pivot row patterns and
+ their exact degrees. Called by UMF_local_search.
+
+ Returns UMFPACK_OK if successful, or UMFPACK_WARNING_singular_matrix or
+ UMFPACK_ERROR_different_pattern if not.
+
+*/
+
+#include "umf_internal.h"
+#include "umf_row_search.h"
+
+GLOBAL Int UMF_row_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic,
+ Int cdeg0, /* length of column in Front */
+ Int cdeg1, /* length of column outside Front */
+ const Int Pattern [ ], /* pattern of column, Pattern [0..cdeg1 -1] */
+ const Int Pos [ ], /* Pos [Pattern [0..cdeg1 -1]] = 0..cdeg1 -1 */
+ Int pivrow [2], /* pivrow [IN] and pivrow [OUT] */
+ Int rdeg [2], /* rdeg [IN] and rdeg [OUT] */
+ Int W_i [ ], /* pattern of pivrow [IN], */
+ /* either Fcols or Woi */
+ Int W_o [ ], /* pattern of pivrow [OUT], */
+ /* either Wio or Woo */
+ Int prior_pivrow [2], /* the two other rows just scanned, if any */
+ const Entry Wxy [ ], /* numerical values Wxy [0..cdeg1-1],
+ either Wx or Wy */
+
+ Int pivcol, /* the candidate column being searched */
+ Int freebie [ ]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double maxval, toler, toler2, value, pivot [2] ;
+ Int i, row, deg, col, *Frpos, fnrows, *E, j, ncols, *Cols, *Rows,
+ e, f, Wrpflag, *Fcpos, fncols, tpi, max_rdeg, nans_in_col, was_offdiag,
+ diag_row, prefer_diagonal, *Wrp, found, *Diagonal_map ;
+ Tuple *tp, *tpend, *tp1, *tp2 ;
+ Unit *Memory, *p ;
+ Element *ep ;
+ Int *Row_tuples, *Row_degree, *Row_tlen ;
+
+#ifndef NDEBUG
+ Int *Col_degree ;
+ DEBUG2 (("Row_search:\n")) ;
+ for (i = 0 ; i < cdeg1 ; i++)
+ {
+ row = Pattern [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < Numeric->n_row) ;
+ ASSERT (i == Pos [row]) ;
+ }
+ /* If row is not in Pattern [0..cdeg1-1], then Pos [row] == EMPTY */
+ if (UMF_debug > 0 || Numeric->n_row < 1000)
+ {
+ Int cnt = cdeg1 ;
+ DEBUG4 (("Scan all rows:\n")) ;
+ for (row = 0 ; row < Numeric->n_row ; row++)
+ {
+ if (Pos [row] < 0)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Pos [row])) ;
+ }
+ }
+ ASSERT (cnt == Numeric->n_row) ;
+ }
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro only */
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol)) ;
+#endif
+
+ pivot [IN] = 0. ;
+ pivot [OUT] = 0. ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Row_degree = Numeric->Rperm ;
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Wrp = Work->Wrp ;
+ Frpos = Work->Frpos ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ fnrows = Work->fnrows ;
+
+ prefer_diagonal = Symbolic->prefer_diagonal ;
+ Diagonal_map = Work->Diagonal_map ;
+
+ if (Diagonal_map)
+ {
+ diag_row = Diagonal_map [pivcol] ;
+ was_offdiag = diag_row < 0 ;
+ if (was_offdiag)
+ {
+ /* the "diagonal" entry in this column was permuted here by an
+ * earlier pivot choice. The tighter off-diagonal tolerance will
+ * be used instead of the symmetric tolerance. */
+ diag_row = FLIP (diag_row) ;
+ }
+ ASSERT (diag_row >= 0 && diag_row < Numeric->n_row) ;
+ }
+ else
+ {
+ diag_row = EMPTY ; /* unused */
+ was_offdiag = EMPTY ; /* unused */
+ }
+
+ /* pivot row degree cannot exceed max_rdeg */
+ max_rdeg = Work->fncols_max ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scan pivot column for candidate rows */
+ /* ---------------------------------------------------------------------- */
+
+ maxval = 0.0 ;
+ nans_in_col = FALSE ;
+
+ for (i = 0 ; i < cdeg1 ; i++)
+ {
+ APPROX_ABS (value, Wxy [i]) ;
+ if (SCALAR_IS_NAN (value))
+ {
+ nans_in_col = TRUE ;
+ maxval = value ;
+ break ;
+ }
+ /* This test can now ignore the NaN case: */
+ maxval = MAX (maxval, value) ;
+ }
+
+ /* if maxval is zero, the matrix is numerically singular */
+
+ toler = Numeric->relpt * maxval ;
+ toler2 = Numeric->relpt2 * maxval ;
+ toler2 = was_offdiag ? toler : toler2 ;
+
+ DEBUG5 (("Row_search begins [ maxval %g toler %g %g\n",
+ maxval, toler, toler2)) ;
+ if (SCALAR_IS_NAN (toler) || SCALAR_IS_NAN (toler2))
+ {
+ nans_in_col = TRUE ;
+ }
+
+ if (!nans_in_col)
+ {
+
+ /* look for the diagonal entry, if it exists */
+ found = FALSE ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+
+ if (prefer_diagonal)
+ {
+ ASSERT (diag_row != EMPTY) ;
+ i = Pos [diag_row] ;
+ if (i >= 0)
+ {
+ double a ;
+ ASSERT (i < cdeg1) ;
+ ASSERT (diag_row == Pattern [i]) ;
+
+ APPROX_ABS (a, Wxy [i]) ;
+
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler2)) ;
+
+ if (SCALAR_IS_NONZERO (a) && a >= toler2)
+ {
+ /* found it! */
+ DEBUG3 (("Symmetric pivot: "ID" "ID"\n", pivcol, diag_row));
+ found = TRUE ;
+ if (Frpos [diag_row] >= 0 && Frpos [diag_row] < fnrows)
+ {
+ pivrow [IN] = diag_row ;
+ pivrow [OUT] = EMPTY ;
+ }
+ else
+ {
+ pivrow [IN] = EMPTY ;
+ pivrow [OUT] = diag_row ;
+ }
+ }
+ }
+ }
+
+ /* either no diagonal found, or we didn't look for it */
+ if (!found)
+ {
+ if (cdeg0 > 0)
+ {
+
+ /* this is a column in the front */
+ for (i = 0 ; i < cdeg0 ; i++)
+ {
+ double a ;
+ APPROX_ABS (a, Wxy [i]) ;
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+ if (SCALAR_IS_NONZERO (a) && a >= toler)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+#ifndef NDEBUG
+ DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n",
+ i, row, deg, a)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+#endif
+ ASSERT (Frpos [row] >= 0 && Frpos [row] < fnrows) ;
+ ASSERT (Frpos [row] == i) ;
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ if (deg < rdeg [IN]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg [IN] && a > pivot [IN])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg [IN] && row == diag_row) */
+ )
+ {
+ /* best row in front, so far */
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ pivot [IN] = a ;
+ }
+ }
+ }
+ for ( ; i < cdeg1 ; i++)
+ {
+ double a ;
+ APPROX_ABS (a, Wxy [i]) ;
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+ if (SCALAR_IS_NONZERO (a) && a >= toler)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+#ifndef NDEBUG
+ DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n",
+ i, row, deg, a)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+#endif
+ ASSERT (Frpos [row] == i) ;
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ if (deg < rdeg [OUT]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg [OUT] && a > pivot [OUT])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg [OUT] && row == diag_row) */
+ )
+ {
+ /* best row not in front, so far */
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ pivot [OUT] = a ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* this column is not in the front */
+ for (i = 0 ; i < cdeg1 ; i++)
+ {
+ double a ;
+ APPROX_ABS (a, Wxy [i]) ;
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+ if (SCALAR_IS_NONZERO (a) && a >= toler)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+#ifndef NDEBUG
+ DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n",
+ i, row, deg, a)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+#endif
+ if (Frpos [row] >= 0 && Frpos [row] < fnrows)
+ {
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ if (deg < rdeg [IN]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg [IN] && a > pivot [IN])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg [IN] && row == diag_row) */
+ )
+ {
+ /* best row in front, so far */
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ pivot [IN] = a ;
+ }
+ }
+ else
+ {
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ if (deg < rdeg [OUT]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg[OUT] && a > pivot [OUT])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg[OUT] && row == diag_row) */
+ )
+ {
+ /* best row not in front, so far */
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ pivot [OUT] = a ;
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* NaN handling */
+ /* ---------------------------------------------------------------------- */
+
+ /* if cdeg1 > 0 then we must have found a pivot row ... unless NaN's */
+ /* exist. Try with no numerical tests if no pivot found. */
+
+ if (cdeg1 > 0 && pivrow [IN] == EMPTY && pivrow [OUT] == EMPTY)
+ {
+ /* cleanup for the NaN case */
+ DEBUG0 (("Found a NaN in pivot column!\n")) ;
+
+ /* grab the first entry in the pivot column, ignoring degree, */
+ /* numerical stability, and symmetric preference */
+ row = Pattern [0] ;
+ deg = Row_degree [row] ;
+ if (Frpos [row] >= 0 && Frpos [row] < fnrows)
+ {
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ }
+ else
+ {
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ }
+
+ /* We are now guaranteed to have a pivot, no matter how broken */
+ /* (non-IEEE compliant) the underlying numerical operators are. */
+ /* This is particularly a problem for Microsoft compilers (they do */
+ /* not handle NaN's properly). Now try to find a sparser pivot, if */
+ /* possible. */
+
+ for (i = 1 ; i < cdeg1 ; i++)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+
+ if (Frpos [row] >= 0 && Frpos [row] < fnrows)
+ {
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ if (deg < rdeg [IN] || (deg == rdeg [IN] && row == diag_row))
+ {
+ /* best row in front, so far */
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ }
+ }
+ else
+ {
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ if (deg < rdeg [OUT] || (deg == rdeg [OUT] && row == diag_row))
+ {
+ /* best row not in front, so far */
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ }
+ }
+ }
+ }
+
+ /* We found a pivot if there are entries (even zero ones) in pivot col */
+ ASSERT (IMPLIES (cdeg1 > 0, pivrow[IN] != EMPTY || pivrow[OUT] != EMPTY)) ;
+
+ /* If there are no entries in the pivot column, then no pivot is found */
+ ASSERT (IMPLIES (cdeg1 == 0, pivrow[IN] == EMPTY && pivrow[OUT] == EMPTY)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for singular matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (cdeg1 == 0)
+ {
+ if (fnrows > 0)
+ {
+ /*
+ Get the pivrow [OUT][IN] from the current front.
+ The frontal matrix looks like this:
+
+ pivcol[OUT]
+ |
+ v
+ x x x x 0 <- so grab this row as the pivrow [OUT][IN].
+ x x x x 0
+ x x x x 0
+ 0 0 0 0 0
+
+ The current frontal matrix has some rows in it. The degree
+ of the pivcol[OUT] is zero. The column is empty, and the
+ current front does not contribute to it.
+
+ */
+ pivrow [IN] = Work->Frows [0] ;
+ DEBUGm4 (("Got zero pivrow[OUT][IN] "ID" from current front\n",
+ pivrow [IN])) ;
+ }
+ else
+ {
+
+ /*
+ Get a pivot row from the row-merge tree, use as
+ pivrow [OUT][OUT]. pivrow [IN] remains EMPTY.
+ This can only happen if the current front is 0-by-0.
+ */
+
+ Int *Front_leftmostdesc, *Front_1strow, *Front_new1strow, row1,
+ row2, fleftmost, nfr, n_row, frontid ;
+
+ ASSERT (Work->fncols == 0) ;
+
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_new1strow = Work->Front_new1strow ;
+ nfr = Symbolic->nfr ;
+ n_row = Numeric->n_row ;
+ frontid = Work->frontid ;
+
+ DEBUGm4 (("Note: pivcol: "ID" is empty front "ID"\n",
+ pivcol, frontid)) ;
+#ifndef NDEBUG
+ DEBUG1 (("Calling dump rowmerge\n")) ;
+ UMF_dump_rowmerge (Numeric, Symbolic, Work) ;
+#endif
+
+ /* Row-merge set is the non-pivotal rows in the range */
+ /* Front_new1strow [Front_leftmostdesc [frontid]] to */
+ /* Front_1strow [frontid+1] - 1. */
+ /* If this is empty, then use the empty rows, in the range */
+ /* Front_new1strow [nfr] to n_row-1. */
+ /* If this too is empty, then pivrow [OUT] will be empty. */
+ /* In both cases, update Front_new1strow [...]. */
+
+ fleftmost = Front_leftmostdesc [frontid] ;
+ row1 = Front_new1strow [fleftmost] ;
+ row2 = Front_1strow [frontid+1] - 1 ;
+ DEBUG1 (("Leftmost: "ID" Rows ["ID" to "ID"] srch ["ID" to "ID"]\n",
+ fleftmost, Front_1strow [frontid], row2, row1, row2)) ;
+
+ /* look in the range row1 ... row2 */
+ for (row = row1 ; row <= row2 ; row++)
+ {
+ DEBUG3 ((" Row: "ID"\n", row)) ;
+ if (NON_PIVOTAL_ROW (row))
+ {
+ /* found it */
+ DEBUG3 ((" Row: "ID" found\n", row)) ;
+ ASSERT (Frpos [row] == EMPTY) ;
+ pivrow [OUT] = row ;
+ DEBUGm4 (("got row merge pivrow %d\n", pivrow [OUT])) ;
+ break ;
+ }
+ }
+ Front_new1strow [fleftmost] = row ;
+
+ if (pivrow [OUT] == EMPTY)
+ {
+ /* not found, look in empty row set in "dummy" front */
+ row1 = Front_new1strow [nfr] ;
+ row2 = n_row-1 ;
+ DEBUG3 (("Empty: "ID" Rows ["ID" to "ID"] srch["ID" to "ID"]\n",
+ nfr, Front_1strow [nfr], row2, row1, row2)) ;
+
+ /* look in the range row1 ... row2 */
+ for (row = row1 ; row <= row2 ; row++)
+ {
+ DEBUG3 ((" Empty Row: "ID"\n", row)) ;
+ if (NON_PIVOTAL_ROW (row))
+ {
+ /* found it */
+ DEBUG3 ((" Empty Row: "ID" found\n", row)) ;
+ ASSERT (Frpos [row] == EMPTY) ;
+ pivrow [OUT] = row ;
+ DEBUGm4 (("got dummy row pivrow %d\n", pivrow [OUT])) ;
+ break ;
+ }
+ }
+ Front_new1strow [nfr] = row ;
+ }
+
+ if (pivrow [OUT] == EMPTY)
+ {
+ /* Row-merge set is empty. We can just discard */
+ /* the candidate pivot column. */
+ DEBUG0 (("Note: row-merge set empty\n")) ;
+ DEBUGm4 (("got no pivrow \n")) ;
+ return (UMFPACK_WARNING_singular_matrix) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the candidate row in the front, if any */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ /* check Wrp */
+ ASSERT (Work->Wrpflag > 0) ;
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ for (i = 0 ; i < Work->n_col ; i++)
+ {
+ ASSERT (Wrp [i] < Work->Wrpflag) ;
+ }
+ }
+#endif
+
+#ifndef NDEBUG
+ DEBUG4 (("pivrow [IN]: "ID"\n", pivrow [IN])) ;
+ UMF_dump_rowcol (0, Numeric, Work, pivrow [IN], TRUE) ;
+#endif
+
+ if (pivrow [IN] != EMPTY)
+ {
+
+ /* the row merge candidate row is not pivrow [IN] */
+ freebie [IN] = (pivrow [IN] == prior_pivrow [IN]) && (cdeg1 > 0) ;
+ ASSERT (cdeg1 >= 0) ;
+
+ if (!freebie [IN])
+ {
+ /* include current front in the degree of this row */
+
+ Fcpos = Work->Fcpos ;
+ fncols = Work->fncols ;
+
+ Wrpflag = Work->Wrpflag ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the pattern of the IN row */
+ /* -------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ /* check Fcols */
+ DEBUG5 (("ROW ASSEMBLE: rdeg "ID"\nREDUCE ROW "ID"\n",
+ fncols, pivrow [IN])) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Work->Fcols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] >= 0) ;
+ }
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ Int cnt = fncols ;
+ for (col = 0 ; col < Work->n_col ; col++)
+ {
+ if (Fcpos [col] < 0) cnt++ ;
+ }
+ ASSERT (cnt == Work->n_col) ;
+ }
+#endif
+
+ rdeg [IN] = fncols ;
+
+ ASSERT (pivrow [IN] >= 0 && pivrow [IN] < Work->n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (pivrow [IN])) ;
+
+ /* add the pivot column itself */
+ ASSERT (Wrp [pivcol] != Wrpflag) ;
+ if (Fcpos [pivcol] < 0)
+ {
+ DEBUG3 (("Adding pivot col to pivrow [IN] pattern\n")) ;
+ if (rdeg [IN] >= max_rdeg)
+ {
+ /* :: pattern change (in) :: */
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [pivcol] = Wrpflag ;
+ W_i [rdeg [IN]++] = pivcol ;
+ }
+
+ tpi = Row_tuples [pivrow [IN]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [pivrow [IN]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e])
+ {
+ continue ; /* element already deallocated */
+ }
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ ncols = ep->ncols ;
+ Rows = Cols + ncols ;
+ if (Rows [f] == EMPTY)
+ {
+ continue ; /* row already assembled */
+ }
+ ASSERT (pivrow [IN] == Rows [f]) ;
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= EMPTY && col < Work->n_col) ;
+ if ((col >= 0) && (Wrp [col] != Wrpflag)
+ && Fcpos [col] <0)
+ {
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ if (rdeg [IN] >= max_rdeg)
+ {
+ /* :: pattern change (rdeg in failure) :: */
+ DEBUGm4 (("rdeg [IN] >= max_rdeg failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [col] = Wrpflag ;
+ W_i [rdeg [IN]++] = col ;
+ }
+ }
+
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Row_tlen [pivrow [IN]] = tp2 - tp1 ;
+ }
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced IN row:\n")) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG6 ((" "ID" "ID" "ID"\n",
+ j, Work->Fcols [j], Fcpos [Work->Fcols [j]])) ;
+ ASSERT (Fcpos [Work->Fcols [j]] >= 0) ;
+ }
+ for (j = fncols ; j < rdeg [IN] ; j++)
+ {
+ DEBUG6 ((" "ID" "ID" "ID"\n", j, W_i [j], Wrp [W_i [j]]));
+ ASSERT (W_i [j] >= 0 && W_i [j] < Work->n_col) ;
+ ASSERT (Wrp [W_i [j]] == Wrpflag) ;
+ }
+ /* mark the end of the pattern in case we scan it by mistake */
+ /* Note that this means W_i must be of size >= fncols_max + 1 */
+ W_i [rdeg [IN]] = EMPTY ;
+#endif
+
+ /* rdeg [IN] is now the exact degree of the IN row */
+
+ /* clear Work->Wrp. */
+ Work->Wrpflag++ ;
+ /* All Wrp [0..n_col] is now < Wrpflag */
+ }
+ }
+
+#ifndef NDEBUG
+ /* check Wrp */
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ for (i = 0 ; i < Work->n_col ; i++)
+ {
+ ASSERT (Wrp [i] < Work->Wrpflag) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the candidate row not in the front, if any */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG4 (("pivrow [OUT]: "ID"\n", pivrow [OUT])) ;
+ UMF_dump_rowcol (0, Numeric, Work, pivrow [OUT], TRUE) ;
+#endif
+
+ /* If this is a candidate row from the row merge set, force it to be */
+ /* scanned (ignore prior_pivrow [OUT]). */
+
+ if (pivrow [OUT] != EMPTY)
+ {
+ freebie [OUT] = (pivrow [OUT] == prior_pivrow [OUT]) && cdeg1 > 0 ;
+ ASSERT (cdeg1 >= 0) ;
+
+ if (!freebie [OUT])
+ {
+
+ Wrpflag = Work->Wrpflag ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the pattern of the row */
+ /* -------------------------------------------------------------- */
+
+ rdeg [OUT] = 0 ;
+
+ ASSERT (pivrow [OUT] >= 0 && pivrow [OUT] < Work->n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (pivrow [OUT])) ;
+
+ /* add the pivot column itself */
+ ASSERT (Wrp [pivcol] != Wrpflag) ;
+ DEBUG3 (("Adding pivot col to pivrow [OUT] pattern\n")) ;
+ if (rdeg [OUT] >= max_rdeg)
+ {
+ /* :: pattern change (out) :: */
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [pivcol] = Wrpflag ;
+ W_o [rdeg [OUT]++] = pivcol ;
+
+ tpi = Row_tuples [pivrow [OUT]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [pivrow [OUT]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e])
+ {
+ continue ; /* element already deallocated */
+ }
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ ncols = ep->ncols ;
+ Rows = Cols + ncols ;
+ if (Rows [f] == EMPTY)
+ {
+ continue ; /* row already assembled */
+ }
+ ASSERT (pivrow [OUT] == Rows [f]) ;
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= EMPTY && col < Work->n_col) ;
+ if ((col >= 0) && (Wrp [col] != Wrpflag))
+ {
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ if (rdeg [OUT] >= max_rdeg)
+ {
+ /* :: pattern change (rdeg out failure) :: */
+ DEBUGm4 (("rdeg [OUT] failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [col] = Wrpflag ;
+ W_o [rdeg [OUT]++] = col ;
+ }
+ }
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Row_tlen [pivrow [OUT]] = tp2 - tp1 ;
+ }
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced row OUT:\n")) ;
+ for (j = 0 ; j < rdeg [OUT] ; j++)
+ {
+ DEBUG6 ((" "ID" "ID" "ID"\n", j, W_o [j], Wrp [W_o [j]])) ;
+ ASSERT (W_o [j] >= 0 && W_o [j] < Work->n_col) ;
+ ASSERT (Wrp [W_o [j]] == Wrpflag) ;
+ }
+ /* mark the end of the pattern in case we scan it by mistake */
+ /* Note that this means W_o must be of size >= fncols_max + 1 */
+ W_o [rdeg [OUT]] = EMPTY ;
+#endif
+
+ /* rdeg [OUT] is now the exact degree of the row */
+
+ /* clear Work->Wrp. */
+ Work->Wrpflag++ ;
+ /* All Wrp [0..n] is now < Wrpflag */
+
+ }
+
+ }
+ DEBUG5 (("Row_search end ] \n")) ;
+
+#ifndef NDEBUG
+ /* check Wrp */
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ for (i = 0 ; i < Work->n_col ; i++)
+ {
+ ASSERT (Wrp [i] < Work->Wrpflag) ;
+ }
+ }
+#endif
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_row_search.h b/src/C/SuiteSparse/UMFPACK/Source/umf_row_search.h
new file mode 100644
index 0000000..8a9dac0
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_row_search.h
@@ -0,0 +1,32 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_row_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic,
+ Int cdeg0,
+ Int cdeg1,
+ const Int Pattern [ ],
+ const Int Pos [ ],
+ Int pivrow [2],
+ Int rdeg [2],
+ Int W_i [ ],
+ Int W_o [ ],
+ Int prior_pivrow [2],
+ const Entry Wxy [ ],
+ Int pivcol,
+ Int freebie [2]
+) ;
+
+#define IN 0
+#define OUT 1
+
+#define IN_IN 0
+#define IN_OUT 1
+#define OUT_IN 2
+#define OUT_OUT 3
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_scale.c b/src/C/SuiteSparse/UMFPACK/Source/umf_scale.c
new file mode 100644
index 0000000..c716bee
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_scale.c
@@ -0,0 +1,81 @@
+/* ========================================================================== */
+/* === UMF_scale ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Divide a vector of stride 1 by the pivot value. */
+
+#include "umf_internal.h"
+
+GLOBAL void UMF_scale
+(
+ Int n,
+ Entry pivot,
+ Entry X [ ]
+)
+{
+ Entry x ;
+ double s ;
+ Int i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the approximate absolute value of the pivot, and select method */
+ /* ---------------------------------------------------------------------- */
+
+ APPROX_ABS (s, pivot) ;
+
+ if (s < RECIPROCAL_TOLERANCE || IS_NAN (pivot))
+ {
+ /* ------------------------------------------------------------------ */
+ /* tiny, or zero, pivot case */
+ /* ------------------------------------------------------------------ */
+
+ /* The pivot is tiny, or NaN. Do not divide zero by the pivot value,
+ * and do not multiply by 1/pivot, either. */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] /= pivot ; */
+ x = X [i] ;
+
+#ifndef NO_DIVIDE_BY_ZERO
+ if (IS_NONZERO (x))
+ {
+ DIV (X [i], x, pivot) ;
+ }
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (x) && IS_NONZERO (pivot))
+ {
+ DIV (X [i], x, pivot) ;
+ }
+#endif
+
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* normal case */
+ /* ------------------------------------------------------------------ */
+
+ /* The pivot is not tiny, and is not NaN. Don't bother to check for
+ * zeros in the pivot column, X. This is slightly more accurate than
+ * multiplying by 1/pivot (but slightly slower), particularly if the
+ * pivot column consists of only IEEE subnormals. */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] /= pivot ; */
+ x = X [i] ;
+ DIV (X [i], x, pivot) ;
+ }
+ }
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_scale.h b/src/C/SuiteSparse/UMFPACK/Source/umf_scale.h
new file mode 100644
index 0000000..5b24afb
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_scale.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_scale
+(
+ Int n,
+ Entry alpha,
+ Entry X [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_scale_column.c b/src/C/SuiteSparse/UMFPACK/Source/umf_scale_column.c
new file mode 100644
index 0000000..ace38bc
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_scale_column.c
@@ -0,0 +1,433 @@
+/* ========================================================================== */
+/* === UMF_scale_column ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Scale the current pivot column, move the pivot row and column into place,
+ and log the permutation.
+*/
+
+#include "umf_internal.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_scale.h"
+
+/* ========================================================================== */
+/* === shift_pivot_row ====================================================== */
+/* ========================================================================== */
+
+/* Except for the BLAS, most of the time is typically spent in the following
+ * shift_pivot_row routine. It copies the pivot row into the U block, and
+ * then fills in the whole in the C block by shifting the last row of C into
+ * the row vacated by the pivot row.
+ */
+
+PRIVATE void shift_pivot_row (Entry *Fd, Entry *Fs, Entry *Fe, Int len, Int d)
+{
+ Int j ;
+#pragma ivdep
+ for (j = 0 ; j < len ; j++)
+ {
+ Fd [j] = Fs [j*d] ;
+ Fs [j*d] = Fe [j*d] ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_scale_column ===================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_scale_column
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry pivot_value ;
+ Entry *Fcol, *Flublock, *Flblock, *Fublock, *Fcblock ;
+ Int k, k1, fnr_curr, fnrows, fncols, *Frpos, *Fcpos, pivrow, pivcol,
+ *Frows, *Fcols, fnc_curr, fnpiv, *Row_tuples, nb,
+ *Col_tuples, *Rperm, *Cperm, fspos, col2, row2 ;
+#ifndef NDEBUG
+ Int *Col_degree, *Row_degree ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ fnpiv = Work->fnpiv ;
+
+ /* ---------------------------------------------------------------------- */
+
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+
+ /* ---------------------------------------------------------------------- */
+
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fcblock = Work->Fcblock ;
+
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ pivrow = Work->pivrow ;
+ pivcol = Work->pivcol ;
+
+ ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+
+#ifndef NDEBUG
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+#endif
+
+ Row_tuples = Numeric->Uip ;
+ Col_tuples = Numeric->Lip ;
+ nb = Work->nb ;
+
+#ifndef NDEBUG
+ ASSERT (fnrows == Work->fnrows_new + 1) ;
+ ASSERT (fncols == Work->fncols_new + 1) ;
+ DEBUG1 (("SCALE COL: fnrows "ID" fncols "ID"\n", fnrows, fncols)) ;
+ DEBUG2 (("\nFrontal matrix, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ;
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, nb, fnpiv, fnpiv) ;
+#endif
+
+ /* ====================================================================== */
+ /* === Shift pivot row and column ======================================= */
+ /* ====================================================================== */
+
+ /* ---------------------------------------------------------------------- */
+ /* move pivot column into place */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that the pivot column is already in place. Just shift the last
+ * column into the position vacated by the pivot column. */
+
+ fspos = Fcpos [pivcol] ;
+
+ /* one less column in the contribution block */
+ fncols = --(Work->fncols) ;
+
+ if (fspos != fncols * fnr_curr)
+ {
+
+ Int fs = fspos / fnr_curr ;
+
+ DEBUG6 (("Shift pivot column in front\n")) ;
+ DEBUG6 (("fspos: "ID" flpos: "ID"\n", fspos, fncols * fnr_curr)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* move Fe => Fs */
+ /* ------------------------------------------------------------------ */
+
+ /* column of the contribution block: */
+ {
+ /* Fs: current position of pivot column in contribution block */
+ /* Fe: position of last column in contribution block */
+ Int i ;
+ Entry *Fs, *Fe ;
+ Fs = Fcblock + fspos ;
+ Fe = Fcblock + fncols * fnr_curr ;
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Fs [i] = Fe [i] ;
+ }
+ }
+
+ /* column of the U2 block */
+ {
+ /* Fs: current position of pivot column in U block */
+ /* Fe: last column in U block */
+ Int i ;
+ Entry *Fs, *Fe ;
+ Fs = Fublock + fs ;
+ Fe = Fublock + fncols ;
+#pragma ivdep
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ Fs [i * fnc_curr] = Fe [i * fnc_curr] ;
+ }
+ }
+
+ /* move column Fe to Fs in the Fcols pattern */
+ col2 = Fcols [fncols] ;
+ Fcols [fs] = col2 ;
+ Fcpos [col2] = fspos ;
+ }
+
+ /* pivot column is no longer in the frontal matrix */
+ Fcpos [pivcol] = EMPTY ;
+
+#ifndef NDEBUG
+ DEBUG2 (("\nFrontal matrix after col swap, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ fnr_curr, fnc_curr, nb,
+ fnrows, fncols, fnpiv)) ;
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, nb, fnpiv, fnpiv+1) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* move pivot row into place */
+ /* ---------------------------------------------------------------------- */
+
+ fspos = Frpos [pivrow] ;
+
+ /* one less row in the contribution block */
+ fnrows = --(Work->fnrows) ;
+
+ DEBUG6 (("Swap/shift pivot row in front:\n")) ;
+ DEBUG6 (("fspos: "ID" flpos: "ID"\n", fspos, fnrows)) ;
+
+ if (fspos == fnrows)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* move Fs => Fd */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG6 (("row case 1\n")) ;
+
+ /* row of the contribution block: */
+ {
+ Int j ;
+ Entry *Fd, *Fs ;
+ Fd = Fublock + fnpiv * fnc_curr ;
+ Fs = Fcblock + fspos ;
+#pragma ivdep
+ for (j = 0 ; j < fncols ; j++)
+ {
+ Fd [j] = Fs [j * fnr_curr] ;
+ }
+ }
+
+ /* row of the L2 block: */
+ if (Work->pivrow_in_front)
+ {
+ Int j ;
+ Entry *Fd, *Fs ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+#pragma ivdep
+ for (j = 0 ; j <= fnpiv ; j++)
+ {
+ Fd [j * nb] = Fs [j * fnr_curr] ;
+ }
+ }
+ else
+ {
+ Int j ;
+ Entry *Fd, *Fs ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+#pragma ivdep
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ ASSERT (IS_ZERO (Fs [j * fnr_curr])) ;
+ CLEAR (Fd [j * nb]) ;
+ }
+ Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ;
+ }
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* move Fs => Fd */
+ /* move Fe => Fs */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG6 (("row case 2\n")) ;
+ /* this is the most common case, by far */
+
+ /* row of the contribution block: */
+ {
+ /* Fd: destination of pivot row on U block */
+ /* Fs: current position of pivot row in contribution block */
+ /* Fe: position of last row in contribution block */
+ Entry *Fd, *Fs, *Fe ;
+ Fd = Fublock + fnpiv * fnc_curr ;
+ Fs = Fcblock + fspos ;
+ Fe = Fcblock + fnrows ;
+ shift_pivot_row (Fd, Fs, Fe, fncols, fnr_curr) ;
+ }
+
+ /* row of the L2 block: */
+ if (Work->pivrow_in_front)
+ {
+ /* Fd: destination of pivot row in LU block */
+ /* Fs: current position of pivot row in L block */
+ /* Fe: last row in L block */
+ Int j ;
+ Entry *Fd, *Fs, *Fe ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+ Fe = Flblock + fnrows ;
+#pragma ivdep
+ for (j = 0 ; j <= fnpiv ; j++)
+ {
+ Fd [j * nb] = Fs [j * fnr_curr] ;
+ Fs [j * fnr_curr] = Fe [j * fnr_curr] ;
+ }
+ }
+ else
+ {
+ Int j ;
+ Entry *Fd, *Fs, *Fe ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+ Fe = Flblock + fnrows ;
+#pragma ivdep
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ ASSERT (IS_ZERO (Fs [j * fnr_curr])) ;
+ CLEAR (Fd [j * nb]) ;
+ Fs [j * fnr_curr] = Fe [j * fnr_curr] ;
+ }
+ Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ;
+ Fs [fnpiv * fnr_curr] = Fe [fnpiv * fnr_curr] ;
+ }
+
+ /* move row Fe to Fs in the Frows pattern */
+ row2 = Frows [fnrows] ;
+ Frows [fspos] = row2 ;
+ Frpos [row2] = fspos ;
+
+ }
+ /* pivot row is no longer in the frontal matrix */
+ Frpos [pivrow] = EMPTY ;
+
+#ifndef NDEBUG
+ DEBUG2 (("\nFrontal matrix after row swap, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ Work->fnr_curr, Work->fnc_curr, Work->nb,
+ Work->fnrows, Work->fncols, Work->fnpiv)) ;
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv+1) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, nb, fnpiv+1, fnpiv+1) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* Frpos [row] >= 0 for each row in pivot column pattern. */
+ /* offset into pattern is given by: */
+ /* Frpos [row] == offset - 1 */
+ /* Frpos [pivrow] is EMPTY */
+
+ /* Fcpos [col] >= 0 for each col in pivot row pattern. */
+ /* Fcpos [col] == (offset - 1) * fnr_curr */
+ /* Fcpos [pivcol] is EMPTY */
+
+ /* Fcols [0..fncols-1] is the pivot row pattern (excl pivot cols) */
+ /* Frows [0..fnrows-1] is the pivot col pattern (excl pivot rows) */
+
+ /* ====================================================================== */
+ /* === scale pivot column =============================================== */
+ /* ====================================================================== */
+
+ /* pivot column (except for pivot entry itself) */
+ Fcol = Flblock + fnpiv * fnr_curr ;
+ /* fnpiv-th pivot in frontal matrix located in Flublock (fnpiv, fnpiv) */
+ pivot_value = Flublock [fnpiv + fnpiv * nb] ;
+
+ /* this is the kth global pivot */
+ k = Work->npiv + fnpiv ;
+
+ DEBUG4 (("Pivot value: ")) ;
+ EDEBUG4 (pivot_value) ;
+ DEBUG4 (("\n")) ;
+
+ UMF_scale (fnrows, pivot_value, Fcol) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* deallocate the pivot row and pivot column tuples */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_mem_free_tail_block (Numeric, Row_tuples [pivrow]) ;
+ UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol]) ;
+
+ Row_tuples [pivrow] = 0 ;
+ Col_tuples [pivcol] = 0 ;
+
+ DEBUG5 (("number of pivots prior to this one: "ID"\n", k)) ;
+ ASSERT (NON_PIVOTAL_ROW (pivrow)) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol)) ;
+
+ /* save row and column inverse permutation */
+ k1 = ONES_COMPLEMENT (k) ;
+ Rperm [pivrow] = k1 ; /* aliased with Row_degree */
+ Cperm [pivcol] = k1 ; /* aliased with Col_degree */
+
+ ASSERT (!NON_PIVOTAL_ROW (pivrow)) ;
+ ASSERT (!NON_PIVOTAL_COL (pivcol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Keep track of the pivot order. This is the kth pivot row and column. */
+ /* ---------------------------------------------------------------------- */
+
+ /* keep track of pivot rows and columns in the LU, L, and U blocks */
+ ASSERT (fnpiv < MAXNB) ;
+ Work->Pivrow [fnpiv] = pivrow ;
+ Work->Pivcol [fnpiv] = pivcol ;
+
+ /* ====================================================================== */
+ /* === one step in the factorization is done ============================ */
+ /* ====================================================================== */
+
+ /* One more step is done, except for pending updates to the U and C blocks
+ * of this frontal matrix. Those are saved up, and applied by
+ * UMF_blas3_update when enough pivots have accumulated. Also, the
+ * LU factors for these pending pivots have not yet been stored. */
+
+ Work->fnpiv++ ;
+
+#ifndef NDEBUG
+ DEBUG7 (("Current frontal matrix: (after pivcol scale)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_scale_column.h b/src/C/SuiteSparse/UMFPACK/Source/umf_scale_column.h
new file mode 100644
index 0000000..166a4e5
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_scale_column.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_scale_column
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.c b/src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.c
new file mode 100644
index 0000000..1458763
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.c
@@ -0,0 +1,133 @@
+/* ========================================================================== */
+/* === UMF_set_stats ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Sets statistics in Info array. Calculates everything in double precision,
+ rather than Int or size_t, so that usage estimates can be computed even if
+ the problem is so large that it would cause integer overflow.
+
+ This routine has many double relop's, but the NaN case is ignored.
+*/
+
+#include "umf_internal.h"
+#include "umf_symbolic_usage.h"
+
+GLOBAL void UMF_set_stats
+(
+ double Info [ ],
+ SymbolicType *Symbolic,
+ double max_usage, /* peak size of Numeric->Memory, in Units */
+ double num_mem_size, /* final size of Numeric->Memory, in Units */
+ double flops, /* "true flops" */
+ double lnz, /* nz in L */
+ double unz, /* nz in U */
+ double maxfrsize, /* largest front size */
+ double ulen, /* size of Numeric->Upattern */
+ double npiv, /* number of pivots found */
+ double maxnrows, /* largest #rows in front */
+ double maxncols, /* largest #cols in front */
+ Int scale, /* true if scaling the rows of A */
+ Int prefer_diagonal, /* true if diagonal pivoting (only square A) */
+ Int what /* ESTIMATE or ACTUAL */
+)
+{
+
+ double sym_size, work_usage, nn, n_row, n_col, n_inner, num_On_size1,
+ num_On_size2, num_usage, sym_maxncols, sym_maxnrows, elen, n1 ;
+
+ n_col = Symbolic->n_col ;
+ n_row = Symbolic->n_row ;
+ n1 = Symbolic->n1 ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ sym_maxncols = MIN (Symbolic->maxncols + Symbolic->nb, n_col) ;
+ sym_maxnrows = MIN (Symbolic->maxnrows + Symbolic->nb, n_row) ;
+ elen = (n_col - n1) + (n_row - n1) + MIN (n_col - n1, n_row - n1) + 1 ;
+
+ /* final Symbolic object size */
+ sym_size = UMF_symbolic_usage (Symbolic->n_row, Symbolic->n_col,
+ Symbolic->nchains, Symbolic->nfr, Symbolic->esize, prefer_diagonal) ;
+
+ /* size of O(n) part of Numeric object during factorization, */
+ /* except Numeric->Memory and Numeric->Upattern */
+ num_On_size1 =
+ DUNITS (NumericType, 1) /* Numeric structure */
+ + DUNITS (Entry, n_inner+1) /* D */
+ + 4 * DUNITS (Int, n_row+1) /* Rperm, Lpos, Uilen, Uip */
+ + 4 * DUNITS (Int, n_col+1) /* Cperm, Upos, Lilen, Lip */
+ + (scale ? DUNITS (Entry, n_row) : 0) ; /* Rs, row scale factors */
+
+ /* size of O(n) part of Numeric object after factorization, */
+ /* except Numeric->Memory and Numeric->Upattern */
+ num_On_size2 =
+ DUNITS (NumericType, 1) /* Numeric structure */
+ + DUNITS (Entry, n_inner+1) /* D */
+ + DUNITS (Int, n_row+1) /* Rperm */
+ + DUNITS (Int, n_col+1) /* Cperm */
+ + 6 * DUNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */
+ + (scale ? DUNITS (Entry, n_row) : 0) ; /* Rs, row scale factors */
+
+ DEBUG1 (("num O(n) size2: %g\n", num_On_size2)) ;
+
+ /* peak size of Numeric->Memory, including LU factors, current frontal
+ * matrix, elements, and tuple lists. */
+ Info [UMFPACK_VARIABLE_PEAK + what] = max_usage ;
+
+ /* final size of Numeric->Memory (LU factors only) */
+ Info [UMFPACK_VARIABLE_FINAL + what] = num_mem_size ;
+
+ /* final size of Numeric object, including Numeric->Memory and ->Upattern */
+ Info [UMFPACK_NUMERIC_SIZE + what] =
+ num_On_size2
+ + num_mem_size /* final Numeric->Memory size */
+ + DUNITS (Int, ulen+1) ;/* Numeric->Upattern (from Work->Upattern) */
+
+ DEBUG1 (("num mem size: %g\n", num_mem_size)) ;
+ DEBUG1 (("ulen units %g\n", DUNITS (Int, ulen))) ;
+ DEBUG1 (("numeric size %g\n", Info [UMFPACK_NUMERIC_SIZE + what])) ;
+
+ /* largest front size (working array size, or actual size used) */
+ Info [UMFPACK_MAX_FRONT_SIZE + what] = maxfrsize ;
+ Info [UMFPACK_MAX_FRONT_NROWS + what] = maxnrows ;
+ Info [UMFPACK_MAX_FRONT_NCOLS + what] = maxncols ;
+ DEBUGm4 (("maxnrows %g maxncols %g\n", maxnrows, maxncols)) ;
+ DEBUGm4 (("maxfrsize %g\n", maxfrsize)) ;
+
+ /* UMF_kernel usage, from work_alloc routine in umf_kernel.c */
+ work_usage =
+ /* Work-> arrays, except for current frontal matrix which is allocated
+ * inside Numeric->Memory. */
+ 2 * DUNITS (Entry, sym_maxnrows + 1) /* Wx, Wy */
+ + 2 * DUNITS (Int, n_row+1) /* Frpos, Lpattern */
+ + 2 * DUNITS (Int, n_col+1) /* Fcpos, Upattern */
+ + DUNITS (Int, nn + 1) /* Wp */
+ + DUNITS (Int, MAX (n_col, sym_maxnrows) + 1) /* Wrp */
+ + 2 * DUNITS (Int, sym_maxnrows + 1) /* Frows, Wm */
+ + 3 * DUNITS (Int, sym_maxncols + 1) /* Fcols, Wio, Woi */
+ + DUNITS (Int, MAX (sym_maxnrows, sym_maxncols) + 1) /* Woo */
+ + DUNITS (Int, elen) /* E */
+ + DUNITS (Int, Symbolic->nfr + 1) /* Front_new1strow */
+ + ((n_row == n_col) ? (2 * DUNITS (Int, nn)) : 0) ; /* Diag map,imap */
+
+ /* Peak memory for just UMFPACK_numeric. */
+ num_usage =
+ sym_size /* size of Symbolic object */
+ + num_On_size1 /* O(n) part of Numeric object (excl. Upattern) */
+ + work_usage /* Work-> arrays (including Upattern) */
+ + max_usage ; /* peak size of Numeric->Memory */
+
+ /* peak memory usage for both UMFPACK_*symbolic and UMFPACK_numeric. */
+ Info [UMFPACK_PEAK_MEMORY + what] =
+ MAX (Symbolic->peak_sym_usage, num_usage) ;
+
+ Info [UMFPACK_FLOPS + what] = flops ;
+ Info [UMFPACK_LNZ + what] = lnz ;
+ Info [UMFPACK_UNZ + what] = unz ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.h b/src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.h
new file mode 100644
index 0000000..deb654d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_set_stats.h
@@ -0,0 +1,24 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_set_stats
+(
+ double Info [ ],
+ SymbolicType *Symbolic,
+ double max_usage,
+ double num_mem_size,
+ double flops,
+ double lnz,
+ double unz,
+ double maxfrsize,
+ double ulen,
+ double npiv,
+ double maxnrows,
+ double maxncols,
+ Int scale,
+ Int prefer_diagonal,
+ Int what
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_singletons.c b/src/C/SuiteSparse/UMFPACK/Source/umf_singletons.c
new file mode 100644
index 0000000..88b12db
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_singletons.c
@@ -0,0 +1,915 @@
+/* ========================================================================== */
+/* === UMF_singletons ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Find and order the row and column singletons of a matrix A. If there are
+ * row and column singletons, the output is a row and column permutation such
+ * that the matrix is in the following form:
+ *
+ * x x x x x x x x x
+ * 0 x x x x x x x x
+ * 0 0 x x x x x x x
+ * 0 0 0 x 0 0 0 0 0
+ * 0 0 0 x x 0 0 0 0
+ * 0 0 0 x x s s s s
+ * 0 0 0 x x s s s s
+ * 0 0 0 x x s s s s
+ * 0 0 0 x x s s s s
+ *
+ * The above example has 3 column singletons (the first three columns and
+ * their corresponding pivot rows) and 2 row singletons. The singletons are
+ * ordered first, because they have zero Markowitz cost. The LU factorization
+ * for these first five rows and columns is free - there is no work to do
+ * (except to scale the pivot columns for the 2 row singletons), and no
+ * fill-in occurs. * The remaining * submatrix (4-by-4 in the above example)
+ * has no rows or columns with degree one. It may have empty rows or columns.
+ *
+ * This algorithm does not perform a full permutation to block triangular
+ * form. If there are one or more singletons, then the matrix can be
+ * permuted to block triangular form, but UMFPACK does not perform the full
+ * BTF permutation (see also "dmperm" in MATLAB).
+ */
+
+#include "umf_internal.h"
+
+#ifndef NDEBUG
+
+/* ========================================================================== */
+/* === debug routines ======================================================= */
+/* ========================================================================== */
+
+/* Dump the singleton queue */
+
+PRIVATE void dump_singletons
+(
+ Int head, /* head of the queue */
+ Int tail, /* tail of the queue */
+ Int Next [ ], /* Next [i] is the next object after i */
+ char *name, /* "row" or "col" */
+ Int Deg [ ], /* Deg [i] is the degree of object i */
+ Int n /* objects are in the range 0 to n-1 */
+)
+{
+ Int i, next, cnt ;
+ DEBUG6 (("%s Singleton list: head "ID" tail "ID"\n", name, head, tail)) ;
+ i = head ;
+ ASSERT (head >= EMPTY && head < n) ;
+ ASSERT (tail >= EMPTY && tail < n) ;
+ cnt = 0 ;
+ while (i != EMPTY)
+ {
+ DEBUG7 ((" "ID": "ID" deg: "ID"\n", cnt, i, Deg [i])) ;
+ ASSERT (i >= 0 && i < n) ;
+ next = Next [i] ;
+ if (i == tail) ASSERT (next == EMPTY) ;
+ i = next ;
+ cnt++ ;
+ ASSERT (cnt <= n) ;
+ }
+}
+
+PRIVATE void dump_mat
+(
+ char *xname,
+ char *yname,
+ Int nx,
+ Int ny,
+ const Int Xp [ ],
+ const Int Xi [ ],
+ Int Xdeg [ ],
+ Int Ydeg [ ]
+)
+{
+ Int x, y, p, p1, p2, xdeg, do_xdeg, ydeg ;
+ DEBUG6 (("\n ==== Dump %s mat:\n", xname)) ;
+ for (x = 0 ; x < nx ; x++)
+ {
+ p1 = Xp [x] ;
+ p2 = Xp [x+1] ;
+ xdeg = Xdeg [x] ;
+ DEBUG6 (("Dump %s "ID" p1 "ID" p2 "ID" deg "ID"\n",
+ xname, x, p1, p2, xdeg)) ;
+ do_xdeg = (xdeg >= 0) ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ y = Xi [p] ;
+ DEBUG7 ((" %s "ID" deg: ", yname, y)) ;
+ ASSERT (y >= 0 && y < ny) ;
+ ydeg = Ydeg [y] ;
+ DEBUG7 ((ID"\n", ydeg)) ;
+ if (do_xdeg && ydeg >= 0)
+ {
+ xdeg-- ;
+ }
+ }
+ ASSERT (IMPLIES (do_xdeg, xdeg == 0)) ;
+ }
+}
+#endif
+
+/* ========================================================================== */
+/* === create_row_form ====================================================== */
+/* ========================================================================== */
+
+/* Create the row-form R of the column-form input matrix A. This could be done
+ * by UMF_transpose, except that Rdeg has already been computed.
+ */
+
+PRIVATE void create_row_form
+(
+ /* input, not modified: */
+ Int n_row, /* A is n_row-by-n_col, nz = Ap [n_col] */
+ Int n_col,
+ const Int Ap [ ], /* Ap [0..n_col]: column pointers for A */
+ const Int Ai [ ], /* Ai [0..nz-1]: row indices for A */
+ Int Rdeg [ ], /* Rdeg [0..n_row-1]: row degrees */
+
+ /* output, not defined on input: */
+ Int Rp [ ], /* Rp [0..n_row]: row pointers for R */
+ Int Ri [ ], /* Ri [0..nz-1]: column indices for R */
+
+ /* workspace, not defined on input or output */
+ Int W [ ] /* size n_row */
+)
+{
+ Int row, col, p, p2 ;
+
+ /* create the row pointers */
+ Rp [0] = 0 ;
+ W [0] = 0 ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rp [row+1] = Rp [row] + Rdeg [row] ;
+ W [row] = Rp [row] ;
+ }
+
+ /* create the indices for the row-form */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p2 = Ap [col+1] ;
+ for (p = Ap [col] ; p < p2 ; p++)
+ {
+ Ri [W [Ai [p]]++] = col ;
+ }
+ }
+}
+
+/* ========================================================================== */
+/* === order_singletons ===================================================== */
+/* ========================================================================== */
+
+PRIVATE int order_singletons /* return new number of singletons */
+(
+ Int k, /* the number of singletons so far */
+ Int head,
+ Int tail,
+ Int Next [ ],
+ Int Xdeg [ ], Int Xperm [ ], const Int Xp [ ], const Int Xi [ ],
+ Int Ydeg [ ], Int Yperm [ ], const Int Yp [ ], const Int Yi [ ]
+#ifndef NDEBUG
+ , char *xname, char *yname, Int nx, Int ny
+#endif
+)
+{
+ Int xpivot, x, y, ypivot, p, p2, deg ;
+
+#ifndef NDEBUG
+ Int i, k1 = k ;
+ dump_singletons (head, tail, Next, xname, Xdeg, nx) ;
+ dump_mat (xname, yname, nx, ny, Xp, Xi, Xdeg, Ydeg) ;
+ dump_mat (yname, xname, ny, nx, Yp, Yi, Ydeg, Xdeg) ;
+#endif
+
+ while (head != EMPTY)
+ {
+ /* remove the singleton at the head of the queue */
+ xpivot = head ;
+ DEBUG1 (("------ Order %s singleton: "ID"\n", xname, xpivot)) ;
+ head = Next [xpivot] ;
+ if (head == EMPTY) tail = EMPTY ;
+
+#ifndef NDEBUG
+ if (k % 100 == 0) dump_singletons (head, tail, Next, xname, Xdeg, nx) ;
+#endif
+
+ ASSERT (Xdeg [xpivot] >= 0) ;
+ if (Xdeg [xpivot] != 1)
+ {
+ /* This row/column x is empty. The matrix is singular.
+ * x will be ordered last in Xperm. */
+ DEBUG1 (("empty %s, after singletons removed\n", xname)) ;
+ continue ;
+ }
+
+ /* find the ypivot to match with this xpivot */
+#ifndef NDEBUG
+ /* there can only be one ypivot, since the degree of x is 1 */
+ deg = 0 ;
+ p2 = Xp [xpivot+1] ;
+ for (p = Xp [xpivot] ; p < p2 ; p++)
+ {
+ y = Xi [p] ;
+ DEBUG1 (("%s: "ID"\n", yname, y)) ;
+ if (Ydeg [y] >= 0)
+ {
+ /* this is a live index in this xpivot vector */
+ deg++ ;
+ }
+ }
+ ASSERT (deg == 1) ;
+#endif
+
+ ypivot = EMPTY ;
+ p2 = Xp [xpivot+1] ;
+ for (p = Xp [xpivot] ; p < p2 ; p++)
+ {
+ y = Xi [p] ;
+ DEBUG1 (("%s: "ID"\n", yname, y)) ;
+ if (Ydeg [y] >= 0)
+ {
+ /* this is a live index in this xpivot vector */
+ ypivot = y ;
+ break ;
+ }
+ }
+
+ DEBUG1 (("Pivot %s: "ID"\n", yname, ypivot)) ;
+ ASSERT (ypivot != EMPTY) ;
+ DEBUG1 (("deg "ID"\n", Ydeg [ypivot])) ;
+ ASSERT (Ydeg [ypivot] >= 0) ;
+
+ /* decrement the degrees after removing this singleton */
+ DEBUG1 (("p1 "ID"\n", Yp [ypivot])) ;
+ DEBUG1 (("p2 "ID"\n", Yp [ypivot+1])) ;
+ p2 = Yp [ypivot+1] ;
+ for (p = Yp [ypivot] ; p < p2 ; p++)
+ {
+ x = Yi [p] ;
+ DEBUG1 ((" %s: "ID" deg: "ID"\n", xname, x, Xdeg [x])) ;
+ if (Xdeg [x] < 0) continue ;
+ ASSERT (Xdeg [x] > 0) ;
+ if (x == xpivot) continue ;
+ deg = --(Xdeg [x]) ;
+ ASSERT (Xdeg [x] >= 0) ;
+ if (deg == 1)
+ {
+ /* this is a new singleton, put at the end of the queue */
+ Next [x] = EMPTY ;
+ if (head == EMPTY)
+ {
+ head = x ;
+ }
+ else
+ {
+ ASSERT (tail != EMPTY) ;
+ Next [tail] = x ;
+ }
+ tail = x ;
+ DEBUG1 ((" New %s singleton: "ID"\n", xname, x)) ;
+#ifndef NDEBUG
+ if (k % 100 == 0)
+ {
+ dump_singletons (head, tail, Next, xname, Xdeg, nx) ;
+ }
+#endif
+ }
+ }
+
+ /* flag the xpivot and ypivot by FLIP'ing the degrees */
+ Xdeg [xpivot] = FLIP (1) ;
+ Ydeg [ypivot] = FLIP (Ydeg [ypivot]) ;
+
+ /* keep track of the pivot row and column */
+ Xperm [k] = xpivot ;
+ Yperm [k] = ypivot ;
+ k++ ;
+
+#ifndef NDEBUG
+ if (k % 1000 == 0)
+ {
+ dump_mat (xname, yname, nx, ny, Xp, Xi, Xdeg, Ydeg) ;
+ dump_mat (yname, xname, ny, nx, Yp, Yi, Ydeg, Xdeg) ;
+ }
+#endif
+ }
+
+#ifndef NDEBUG
+ DEBUGm4 (("%s singletons: k = "ID"\n", xname, k)) ;
+ for (i = k1 ; i < k ; i++)
+ {
+ DEBUG1 ((" %s: "ID" %s: "ID"\n", xname, Xperm [i], yname, Yperm [i])) ;
+ }
+ ASSERT (k > 0) ;
+#endif
+
+ return (k) ;
+}
+
+/* ========================================================================== */
+/* === find_any_singletons ================================================== */
+/* ========================================================================== */
+
+PRIVATE Int find_any_singletons /* returns # of singletons found */
+(
+ /* input, not modified: */
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+
+ /* input, modified on output: */
+ Int Cdeg [ ], /* size n_col */
+ Int Rdeg [ ], /* size n_row */
+
+ /* output, not defined on input: */
+ Int Cperm [ ], /* size n_col */
+ Int Rperm [ ], /* size n_row */
+ Int *p_n1r, /* # of row singletons */
+ Int *p_n1c, /* # of col singletons */
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ Int W [ ], /* size n_row */
+ Int Next [ ] /* size MAX (n_row, n_col) */
+)
+{
+ Int n1, col, row, row_form, head, tail, n1r, n1c ;
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate column singletons */
+ /* ---------------------------------------------------------------------- */
+
+ n1 = 0 ;
+ n1r = 0 ;
+ n1c = 0 ;
+ row_form = FALSE ;
+
+ head = EMPTY ;
+ tail = EMPTY ;
+ for (col = n_col-1 ; col >= 0 ; col--)
+ {
+ if (Cdeg [col] == 1)
+ {
+ /* put the column singleton in the queue */
+ if (head == EMPTY) tail = col ;
+ Next [col] = head ;
+ head = col ;
+ DEBUG1 (("Column singleton: "ID"\n", col)) ;
+ }
+ }
+
+ if (head != EMPTY)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create the row-form of A */
+ /* ------------------------------------------------------------------ */
+
+ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ;
+ row_form = TRUE ;
+
+ /* ------------------------------------------------------------------ */
+ /* find and order the column singletons */
+ /* ------------------------------------------------------------------ */
+
+ n1 = order_singletons (0, head, tail, Next,
+ Cdeg, Cperm, Ap, Ai,
+ Rdeg, Rperm, Rp, Ri
+#ifndef NDEBUG
+ , "col", "row", n_col, n_row
+#endif
+ ) ;
+ n1c = n1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate row singletons */
+ /* ---------------------------------------------------------------------- */
+
+ head = EMPTY ;
+ tail = EMPTY ;
+ for (row = n_row-1 ; row >= 0 ; row--)
+ {
+ if (Rdeg [row] == 1)
+ {
+ /* put the row singleton in the queue */
+ if (head == EMPTY) tail = row ;
+ Next [row] = head ;
+ head = row ;
+ DEBUG1 (("Row singleton: "ID"\n", row)) ;
+ }
+ }
+
+ if (head != EMPTY)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create the row-form of A, if not already created */
+ /* ------------------------------------------------------------------ */
+
+ if (!row_form)
+ {
+ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* find and order the row singletons */
+ /* ------------------------------------------------------------------ */
+
+ n1 = order_singletons (n1, head, tail, Next,
+ Rdeg, Rperm, Rp, Ri,
+ Cdeg, Cperm, Ap, Ai
+#ifndef NDEBUG
+ , "row", "col", n_row, n_col
+#endif
+ ) ;
+ n1r = n1 - n1c ;
+ }
+
+ DEBUG0 (("n1 "ID"\n", n1)) ;
+ *p_n1r = n1r ;
+ *p_n1c = n1c ;
+ return (n1) ;
+}
+
+/* ========================================================================== */
+/* === find_user_singletons ================================================= */
+/* ========================================================================== */
+
+PRIVATE Int find_user_singletons /* returns # singletons found */
+(
+ /* input, not modified: */
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const Int Quser [ ], /* size n_col if present */
+
+ /* input, modified on output: */
+ Int Cdeg [ ], /* size n_col */
+ Int Rdeg [ ], /* size n_row */
+
+ /* output, not defined on input */
+ Int Cperm [ ], /* size n_col */
+ Int Rperm [ ], /* size n_row */
+ Int *p_n1r, /* # of row singletons */
+ Int *p_n1c, /* # of col singletons */
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ Int W [ ] /* size n_row */
+)
+{
+ Int n1, col, row, p, p2, pivcol, pivrow, found, k, n1r, n1c ;
+
+ n1 = 0 ;
+ n1r = 0 ;
+ n1c = 0 ;
+ *p_n1r = 0 ;
+ *p_n1c = 0 ;
+
+ /* find singletons in the user column permutation, Quser */
+ pivcol = Quser [0] ;
+ found = (Cdeg [pivcol] == 1) ;
+ DEBUG0 (("Is first col: "ID" a col singleton?: "ID"\n", pivcol, found)) ;
+ if (!found)
+ {
+ /* the first column is not a column singleton, check for a row
+ * singleton in the first column. */
+ for (p = Ap [pivcol] ; p < Ap [pivcol+1] ; p++)
+ {
+ if (Rdeg [Ai [p]] == 1)
+ {
+ DEBUG0 (("Row singleton in first col: "ID" row: "ID"\n",
+ pivcol, Ai [p])) ;
+ found = TRUE ;
+ break ;
+ }
+ }
+ }
+
+ if (!found)
+ {
+ /* no singletons in the leading part of A (:,Quser) */
+ return (0) ;
+ }
+
+ /* there is at least one row or column singleton. Look for more. */
+ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ;
+
+ n1 = 0 ;
+
+ for (k = 0 ; k < n_col ; k++)
+ {
+ pivcol = Quser [k] ;
+ pivrow = EMPTY ;
+
+ /* ------------------------------------------------------------------ */
+ /* check if col is a column singleton, or contains a row singleton */
+ /* ------------------------------------------------------------------ */
+
+ found = (Cdeg [pivcol] == 1) ;
+
+ if (found)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pivcol is a column singleton */
+ /* -------------------------------------------------------------- */
+
+ DEBUG0 (("Found a col singleton: k "ID" pivcol "ID"\n", k, pivcol));
+
+ /* find the pivrow to match with this pivcol */
+#ifndef NDEBUG
+ /* there can only be one pivrow, since the degree of pivcol is 1 */
+ {
+ Int deg = 0 ;
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG1 (("row: "ID"\n", row)) ;
+ if (Rdeg [row] >= 0)
+ {
+ /* this is a live index in this column vector */
+ deg++ ;
+ }
+ }
+ ASSERT (deg == 1) ;
+ }
+#endif
+
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG1 (("row: "ID"\n", row)) ;
+ if (Rdeg [row] >= 0)
+ {
+ /* this is a live index in this pivcol vector */
+ pivrow = row ;
+ break ;
+ }
+ }
+
+ DEBUG1 (("Pivot row: "ID"\n", pivrow)) ;
+ ASSERT (pivrow != EMPTY) ;
+ DEBUG1 (("deg "ID"\n", Rdeg [pivrow])) ;
+ ASSERT (Rdeg [pivrow] >= 0) ;
+
+ /* decrement the degrees after removing this col singleton */
+ DEBUG1 (("p1 "ID"\n", Rp [pivrow])) ;
+ DEBUG1 (("p2 "ID"\n", Rp [pivrow+1])) ;
+ p2 = Rp [pivrow+1] ;
+ for (p = Rp [pivrow] ; p < p2 ; p++)
+ {
+ col = Ri [p] ;
+ DEBUG1 ((" col: "ID" deg: "ID"\n", col, Cdeg [col])) ;
+ if (Cdeg [col] < 0) continue ;
+ ASSERT (Cdeg [col] > 0) ;
+ Cdeg [col]-- ;
+ ASSERT (Cdeg [col] >= 0) ;
+ }
+
+ /* flag the pivcol and pivrow by FLIP'ing the degrees */
+ Cdeg [pivcol] = FLIP (1) ;
+ Rdeg [pivrow] = FLIP (Rdeg [pivrow]) ;
+ n1c++ ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pivcol may contain a row singleton */
+ /* -------------------------------------------------------------- */
+
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ pivrow = Ai [p] ;
+ if (Rdeg [pivrow] == 1)
+ {
+ DEBUG0 (("Row singleton in pivcol: "ID" row: "ID"\n",
+ pivcol, pivrow)) ;
+ found = TRUE ;
+ break ;
+ }
+ }
+
+ if (!found)
+ {
+ DEBUG0 (("End of user singletons\n")) ;
+ break ;
+ }
+
+#ifndef NDEBUG
+ /* there can only be one pivrow, since the degree of pivcol is 1 */
+ {
+ Int deg = 0 ;
+ p2 = Rp [pivrow+1] ;
+ for (p = Rp [pivrow] ; p < p2 ; p++)
+ {
+ col = Ri [p] ;
+ DEBUG1 (("col: "ID" cdeg::: "ID"\n", col, Cdeg [col])) ;
+ if (Cdeg [col] >= 0)
+ {
+ /* this is a live index in this column vector */
+ ASSERT (col == pivcol) ;
+ deg++ ;
+ }
+ }
+ ASSERT (deg == 1) ;
+ }
+#endif
+
+ DEBUG1 (("Pivot row: "ID"\n", pivrow)) ;
+ DEBUG1 (("pivcol deg "ID"\n", Cdeg [pivcol])) ;
+ ASSERT (Cdeg [pivcol] > 1) ;
+
+ /* decrement the degrees after removing this row singleton */
+ DEBUG1 (("p1 "ID"\n", Ap [pivcol])) ;
+ DEBUG1 (("p2 "ID"\n", Ap [pivcol+1])) ;
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG1 ((" row: "ID" deg: "ID"\n", row, Rdeg [row])) ;
+ if (Rdeg [row] < 0) continue ;
+ ASSERT (Rdeg [row] > 0) ;
+ Rdeg [row]-- ;
+ ASSERT (Rdeg [row] >= 0) ;
+ }
+
+ /* flag the pivcol and pivrow by FLIP'ing the degrees */
+ Cdeg [pivcol] = FLIP (Cdeg [pivcol]) ;
+ Rdeg [pivrow] = FLIP (1) ;
+ n1r++ ;
+ }
+
+ /* keep track of the pivot row and column */
+ Cperm [k] = pivcol ;
+ Rperm [k] = pivrow ;
+ n1++ ;
+
+#ifndef NDEBUG
+ dump_mat ("col", "row", n_col, n_row, Ap, Ai, Cdeg, Rdeg) ;
+ dump_mat ("row", "col", n_row, n_col, Rp, Ri, Rdeg, Cdeg) ;
+#endif
+
+ }
+
+ DEBUGm4 (("User singletons found: "ID"\n", n1)) ;
+ ASSERT (n1 > 0) ;
+
+ *p_n1r = n1r ;
+ *p_n1c = n1c ;
+ return (n1) ;
+}
+
+/* ========================================================================== */
+/* === finish_permutation =================================================== */
+/* ========================================================================== */
+
+/* Complete the permutation for the pruned submatrix. The singletons are
+ * already ordered, but remove their flags. Place rows/columns that are empty
+ * in the pruned submatrix at the end of the output permutation. This can only
+ * occur if the matrix is singular.
+ */
+
+PRIVATE Int finish_permutation
+(
+ Int n1,
+ Int nx,
+ Int Xdeg [ ],
+ const Int Xuser [ ],
+ Int Xperm [ ],
+ Int *p_max_deg
+)
+{
+ Int nempty, x, deg, s, max_deg, k ;
+ nempty = 0 ;
+ s = n1 ;
+ max_deg = 0 ;
+ DEBUG0 (("n1 "ID" nempty "ID"\n", n1, nempty)) ;
+ for (k = 0 ; k < nx ; k++)
+ {
+ x = (Xuser != (Int *) NULL) ? Xuser [k] : k ;
+ DEBUG0 (("finish perm k "ID" x "ID" nx "ID"\n", k, x, nx)) ;
+ deg = Xdeg [x] ;
+ if (deg == 0)
+ {
+ /* this row/col is empty in the pruned submatrix */
+ ASSERT (s < nx - nempty) ;
+ DEBUG0 (("empty k "ID"\n", k)) ;
+ nempty++ ;
+ Xperm [nx - nempty] = x ;
+ }
+ else if (deg > 0)
+ {
+ /* this row/col is nonempty in the pruned submatrix */
+ ASSERT (s < nx - nempty) ;
+ Xperm [s++] = x ;
+ max_deg = MAX (max_deg, deg) ;
+ }
+ else
+ {
+ /* This is a singleton row/column - it is already ordered.
+ * Just clear the flag. */
+ Xdeg [x] = FLIP (deg) ;
+ }
+ }
+ ASSERT (s == nx - nempty) ;
+ *p_max_deg = max_deg ;
+ return (nempty) ;
+}
+
+/* ========================================================================== */
+/* === UMF_singletons ======================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMF_singletons
+(
+
+ /* input, not modified: */
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const Int Quser [ ], /* size n_col if present */
+ Int strategy, /* strategy requested by user */
+
+ /* output, not defined on input: */
+ Int Cdeg [ ], /* size n_col */
+ Int Cperm [ ], /* size n_col */
+ Int Rdeg [ ], /* size n_row */
+ Int Rperm [ ], /* size n_row */
+ Int InvRperm [ ], /* size n_row, the inverse of Rperm */
+ Int *p_n1, /* # of col and row singletons */
+ Int *p_n1c, /* # of col singletons */
+ Int *p_n1r, /* # of row singletons */
+ Int *p_nempty_col, /* # of empty columns in pruned submatrix */
+ Int *p_nempty_row, /* # of empty columns in pruned submatrix */
+ Int *p_is_sym, /* TRUE if pruned submatrix is square and has been
+ * symmetrically permuted by Cperm and Rperm */
+ Int *p_max_rdeg, /* maximum Rdeg in pruned submatrix */
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ Int W [ ], /* size n_row */
+ Int Next [ ] /* size MAX (n_row, n_col) */
+)
+{
+ Int n1, s, col, row, p, p1, p2, cdeg, last_row, is_sym, k,
+ nempty_row, nempty_col, max_cdeg, max_rdeg, n1c, n1r ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ DEBUGm4 (("Starting umf_singletons\n")) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* scan the columns, check for errors and count row degrees */
+ /* ---------------------------------------------------------------------- */
+
+ if (Ap [0] != 0 || Ap [n_col] < 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rdeg [row] = 0 ;
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p1 = Ap [col] ;
+ p2 = Ap [col+1] ;
+ cdeg = p2 - p1 ;
+ if (cdeg < 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ last_row = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ if (row <= last_row || row >= n_row)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ Rdeg [row]++ ;
+ last_row = row ;
+ }
+ Cdeg [col] = cdeg ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find singletons */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL)
+ {
+ /* user has provided an input column ordering */
+ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ /* look for singletons, but respect the user's input permutation */
+ n1 = find_user_singletons (n_row, n_col, Ap, Ai, Quser,
+ Cdeg, Rdeg, Cperm, Rperm, &n1r, &n1c, Rp, Ri, W) ;
+ }
+ else
+ {
+ /* do not look for singletons if Quser given and strategy is
+ * not unsymmetric */
+ n1 = 0 ;
+ n1r = 0 ;
+ n1c = 0 ;
+ }
+ }
+ else
+ {
+ /* look for singletons anywhere */
+ n1 = find_any_singletons (n_row, n_col, Ap, Ai,
+ Cdeg, Rdeg, Cperm, Rperm, &n1r, &n1c, Rp, Ri, W, Next) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate empty columns and complete the column permutation */
+ /* ---------------------------------------------------------------------- */
+
+ nempty_col = finish_permutation (n1, n_col, Cdeg, Quser, Cperm, &max_cdeg) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate empty rows and complete the row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL && strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ /* rows should be symmetrically permuted according to Quser */
+ ASSERT (n_row == n_col) ;
+ nempty_row = finish_permutation (n1, n_row, Rdeg, Quser, Rperm,
+ &max_rdeg) ;
+ }
+ else
+ {
+ /* rows should not be symmetrically permuted according to Quser */
+ nempty_row = finish_permutation (n1, n_row, Rdeg, (Int *) NULL, Rperm,
+ &max_rdeg) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the inverse of Rperm */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n_row ; k++)
+ {
+ ASSERT (Rperm [k] >= 0 && Rperm [k] < n_row) ;
+ InvRperm [Rperm [k]] = k ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* see if pruned submatrix is square and has been symmetrically permuted */
+ /* ---------------------------------------------------------------------- */
+
+ if (n_row == n_col && nempty_row == nempty_col)
+ {
+ /* is_sym is true if the submatrix is square, and
+ * Rperm [n1..n_row-nempty_row-1] = Cperm [n1..n_col-nempty_col-1] */
+ is_sym = TRUE ;
+ for (s = n1 ; s < n_col - nempty_col ; s++)
+ {
+ if (Cperm [s] != Rperm [s])
+ {
+ is_sym = FALSE ;
+ break ;
+ }
+ }
+ }
+ else
+ {
+ is_sym = FALSE ;
+ }
+ DEBUGm4 (("Submatrix square and symmetrically permuted? "ID"\n", is_sym)) ;
+ DEBUGm4 (("singletons "ID" row "ID" col "ID"\n", n1, n1r, n1c)) ;
+ DEBUGm4 (("Empty cols "ID" rows "ID"\n", nempty_col, nempty_row)) ;
+ *p_n1 = n1 ;
+ *p_n1r = n1r ;
+ *p_n1c = n1c ;
+ *p_is_sym = is_sym ;
+ *p_nempty_col = nempty_col ;
+ *p_nempty_row = nempty_row ;
+ *p_max_rdeg = max_rdeg ;
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_singletons.h b/src/C/SuiteSparse/UMFPACK/Source/umf_singletons.h
new file mode 100644
index 0000000..1d3316f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_singletons.h
@@ -0,0 +1,31 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_singletons
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const Int Quser [ ],
+ Int strategy,
+ Int Cdeg [ ],
+ Int Cperm [ ],
+ Int Rdeg [ ],
+ Int Rperm [ ],
+ Int InvRperm [ ],
+ Int *n1,
+ Int *n1c,
+ Int *n1r,
+ Int *nempty_col,
+ Int *nempty_row,
+ Int *is_sym,
+ Int *max_rdeg,
+ Int Rp [ ],
+ Int Ri [ ],
+ Int W [ ],
+ Int Next [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_solve.c b/src/C/SuiteSparse/UMFPACK/Source/umf_solve.c
new file mode 100644
index 0000000..8f37ec0
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_solve.c
@@ -0,0 +1,1395 @@
+/* ========================================================================== */
+/* === UMF_solve ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Not user-callable. Solves a linear system using the numerical factorization
+ computed by UMFPACK_numeric. No workspace is dynamically allocated. Counts
+ flops, but excludes floating-point comparisons (thus real abs (...) are
+ zero flops, but complex abs (...) takes 6 flops).
+
+ Returns UMFPACK_OK if successful, UMFPACK_ERROR_argument_missing if
+ required arguments are missing, UMFPACK_ERROR_invalid_system if the sys
+ string is not valid or if the matrix A is not square.
+
+ Uses the sparse backward error method of Arioli, Demmel, and Duff
+ (Solving sparse linear systems with sparse backward error, SIAM J. Matrix
+ Analysis and Applic., vol 10, pp. 165-190).
+
+ Added on option that allows the complex A and X to be split differently
+ than B, Oct 10, 2005. Contributed by David Bateman.
+*/
+
+#include "umf_internal.h"
+#include "umf_lsolve.h"
+#include "umf_usolve.h"
+#include "umf_ltsolve.h"
+#include "umf_utsolve.h"
+#include "umf_report_vector.h"
+
+PRIVATE Int do_step
+(
+ double omega [3],
+ Int step,
+ const double B2 [ ],
+ Entry X [ ],
+ const Entry W [ ],
+ const double Y [ ],
+ const double Z2 [ ],
+ Entry S [ ],
+ Int n,
+ double Info [UMFPACK_INFO]
+) ;
+
+/* ========================================================================== */
+/* === UMF_solve ============================================================ */
+/* ========================================================================== */
+
+GLOBAL Int UMF_solve
+(
+ Int sys,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+ double Xx [ ],
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+ double Xz [ ],
+ const double Bz [ ],
+#endif
+ NumericType *Numeric,
+ Int irstep,
+ double Info [UMFPACK_INFO],
+ Int Pattern [ ], /* size n */
+ double SolveWork [ ] /* if irstep>0 real: size 5*n. complex:10*n */
+ /* otherwise real: size n. complex: 4*n */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry axx, wi, xj, zi, xi, aij, bi ;
+ double omega [3], d, z2i, yi, flops ;
+ Entry *W, *Z, *S, *X ;
+ double *Z2, *Y, *B2, *Rs ;
+ Int *Rperm, *Cperm, i, n, p, step, j, nz, status, p2, do_scale ;
+#ifdef COMPLEX
+ Int AXsplit ;
+ Int Bsplit ;
+#endif
+#ifndef NRECIPROCAL
+ Int do_recip = Numeric->do_recip ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_lu (Numeric) ;
+ ASSERT (Numeric && Xx && Bx && Pattern && SolveWork && Info) ;
+#endif
+
+ nz = 0 ;
+ omega [0] = 0. ;
+ omega [1] = 0. ;
+ omega [2] = 0. ;
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+ Rs = Numeric->Rs ; /* row scale factors */
+ do_scale = (Rs != (double *) NULL) ;
+ flops = 0 ;
+ Info [UMFPACK_SOLVE_FLOPS] = 0 ;
+ Info [UMFPACK_IR_TAKEN] = 0 ;
+ Info [UMFPACK_IR_ATTEMPTED] = 0 ;
+
+ /* UMFPACK_solve does not call this routine if A is rectangular */
+ ASSERT (Numeric->n_row == Numeric->n_col) ;
+ n = Numeric->n_row ;
+ if (Numeric->nnzpiv < n
+ || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
+ {
+ /* Note that systems involving just L return UMFPACK_OK, even if */
+ /* A is singular (L is always has a unit diagonal). */
+ DEBUGm4 (("Note, matrix is singular in umf_solve\n")) ;
+ status = UMFPACK_WARNING_singular_matrix ;
+ irstep = 0 ;
+ }
+ else
+ {
+ status = UMFPACK_OK ;
+ }
+ irstep = MAX (0, irstep) ; /* make sure irstep is >= 0 */
+
+ W = (Entry *) SolveWork ; /* Entry W [0..n-1] */
+
+ Z = (Entry *) NULL ; /* unused if no iterative refinement */
+ S = (Entry *) NULL ;
+ Y = (double *) NULL ;
+ Z2 = (double *) NULL ;
+ B2 = (double *) NULL ;
+
+#ifdef COMPLEX
+ if (irstep > 0)
+ {
+ if (!Ap || !Ai || !Ax)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ /* A, B, and X in split format if Az, Bz, and Xz present */
+ AXsplit = SPLIT (Az) || SPLIT(Xz);
+ Z = (Entry *) (SolveWork + 4*n) ; /* Entry Z [0..n-1] */
+ S = (Entry *) (SolveWork + 6*n) ; /* Entry S [0..n-1] */
+ Y = (double *) (SolveWork + 8*n) ; /* double Y [0..n-1] */
+ B2 = (double *) (SolveWork + 9*n) ; /* double B2 [0..n-1] */
+ Z2 = (double *) Z ; /* double Z2 [0..n-1], equiv. to Z */
+ }
+ else
+ {
+ /* A is ignored, only look at X for split/packed cases */
+ AXsplit = SPLIT(Xz);
+ }
+ Bsplit = SPLIT (Bz);
+
+ if (AXsplit)
+ {
+ X = (Entry *) (SolveWork + 2*n) ; /* Entry X [0..n-1] */
+ }
+ else
+ {
+ X = (Entry *) Xx ; /* Entry X [0..n-1] */
+ }
+#else
+ X = (Entry *) Xx ; /* Entry X [0..n-1] */
+ if (irstep > 0)
+ {
+ if (!Ap || !Ai || !Ax)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ Z = (Entry *) (SolveWork + n) ; /* Entry Z [0..n-1] */
+ S = (Entry *) (SolveWork + 2*n) ; /* Entry S [0..n-1] */
+ Y = (double *) (SolveWork + 3*n) ; /* double Y [0..n-1] */
+ B2 = (double *) (SolveWork + 4*n) ; /* double B2 [0..n-1] */
+ Z2 = (double *) Z ; /* double Z2 [0..n-1], equiv. to Z */
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine which system to solve */
+ /* ---------------------------------------------------------------------- */
+
+ if (sys == UMFPACK_A)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve A x = b with optional iterative refinement */
+ /* ------------------------------------------------------------------ */
+
+ if (irstep > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* using iterative refinement: compute Y and B2 */
+ /* -------------------------------------------------------------- */
+
+ nz = Ap [n] ;
+ Info [UMFPACK_NZ] = nz ;
+
+ /* A is stored by column */
+ /* Y (i) = ||R A_i||, 1-norm of row i of R A */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] = 0. ;
+ }
+ flops += (ABS_FLOPS + 1) * nz ;
+ p2 = Ap [n] ;
+ for (p = 0 ; p < p2 ; p++)
+ {
+ /* Y [Ai [p]] += ABS (Ax [p]) ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ Y [Ai [p]] += d ;
+ }
+
+ /* B2 = abs (B) */
+ flops += ABS_FLOPS * n ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* B2 [i] = ABS (B [i]) ; */
+ ASSIGN (bi, Bx, Bz, i, Bsplit) ;
+ ABS (B2 [i], bi) ;
+ }
+
+ /* scale Y and B2. */
+ if (do_scale)
+ {
+ /* Y = R Y */
+ /* B2 = R B2 */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] *= Rs [i] ;
+ B2 [i] *= Rs [i] ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] /= Rs [i] ;
+ B2 [i] /= Rs [i] ;
+ }
+ }
+
+ flops += 2 * n ;
+ }
+
+ }
+
+ for (step = 0 ; step <= irstep ; step++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Solve A x = b (step 0): */
+ /* x = Q (U \ (L \ (P R b))) */
+ /* and then perform iterative refinement (step > 0): */
+ /* x = x + Q (U \ (L \ (P R (b - A x)))) */
+ /* -------------------------------------------------------------- */
+
+ if (step == 0)
+ {
+ if (do_scale)
+ {
+ /* W = P R b, using X as workspace, since Z is not
+ * allocated if irstep = 0. */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ SCALE (X [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ SCALE_DIV (X [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = X [Rperm [i]] ;
+ }
+ }
+ else
+ {
+ /* W = P b, since the row scaling R = I */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [Rperm [i]] ; */
+ ASSIGN (W [i], Bx, Bz, Rperm [i], Bsplit) ;
+ }
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ /* Z [i] = B [i] ; */
+ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops += MULTSUB_FLOPS * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ xi = X [i] ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* Z [Ai [p]] -= Ax [p] * xi ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT_SUB (Z [Ai [p]], aij, xi) ;
+ }
+ }
+ /* scale, Z = R Z */
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (Z [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (Z [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Z [Rperm [i]] ;
+ }
+ }
+
+ flops += UMF_lsolve (Numeric, W, Pattern) ;
+ flops += UMF_usolve (Numeric, W, Pattern) ;
+
+ if (step == 0)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Cperm [i]] = W [i] ;
+ }
+ }
+ else
+ {
+ flops += ASSEMBLE_FLOPS * n ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [Cperm [i]] += W [i] ; */
+ ASSEMBLE (X [Cperm [i]], W [i]) ;
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* sparse backward error estimate */
+ /* -------------------------------------------------------------- */
+
+ if (irstep > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A is stored by column */
+ /* W (i) = R (b - A x)_i, residual */
+ /* Z2 (i) = R (|A||x|)_i */
+ /* ---------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ Z2 [i] = 0. ;
+ }
+ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ;
+ for (j = 0 ; j < n ; j++)
+ {
+ xj = X [j] ;
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+
+ /* axx = Ax [p] * xj ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT (axx, aij, xj) ;
+
+ /* W [i] -= axx ; */
+ DECREMENT (W [i], axx) ;
+
+ /* Z2 [i] += ABS (axx) ; */
+ ABS (d, axx) ;
+ Z2 [i] += d ;
+ }
+ }
+
+ /* scale W and Z2 */
+ if (do_scale)
+ {
+ /* Z2 = R Z2 */
+ /* W = R W */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (W [i], Rs [i]) ;
+ Z2 [i] *= Rs [i] ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (W [i], Rs [i]) ;
+ Z2 [i] /= Rs [i] ;
+ }
+ }
+ flops += (SCALE_FLOPS + 1) * n ;
+ }
+
+ flops += (2*ABS_FLOPS + 5) * n ;
+ if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info))
+ {
+ /* iterative refinement is done */
+ break ;
+ }
+
+ }
+
+ }
+
+ }
+ else if (sys == UMFPACK_At)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve A' x = b with optional iterative refinement */
+ /* ------------------------------------------------------------------ */
+
+ /* A' is the complex conjugate transpose */
+
+ if (irstep > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* using iterative refinement: compute Y */
+ /* -------------------------------------------------------------- */
+
+ nz = Ap [n] ;
+ Info [UMFPACK_NZ] = nz ;
+
+ /* A' is stored by row */
+ /* Y (i) = ||(A' R)_i||, 1-norm of row i of A' R */
+
+ if (do_scale)
+ {
+ flops += (ABS_FLOPS + 2) * nz ;
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) * Rs [Ai [p]] ; */
+ /* note that abs (aij) is the same as
+ * abs (conj (aij)) */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d * Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) / Rs [Ai [p]] ; */
+ /* note that abs (aij) is the same as
+ * abs (conj (aij)) */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d / Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ }
+ else
+ {
+ /* no scaling */
+ flops += (ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) ; */
+ /* note that abs (aij) is the same as
+ * abs (conj (aij)) */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += d ;
+ }
+ Y [i] = yi ;
+ }
+ }
+
+ /* B2 = abs (B) */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* B2 [i] = ABS (B [i]) ; */
+ ASSIGN (bi, Bx, Bz, i, Bsplit) ;
+ ABS (B2 [i], bi) ;
+ }
+
+ }
+
+ for (step = 0 ; step <= irstep ; step++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Solve A' x = b (step 0): */
+ /* x = R P' (L' \ (U' \ (Q' b))) */
+ /* and then perform iterative refinement (step > 0): */
+ /* x = x + R P' (L' \ (U' \ (Q' (b - A' x)))) */
+ /* -------------------------------------------------------------- */
+
+ if (step == 0)
+ {
+ /* W = Q' b */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [Cperm [i]] ; */
+ ASSIGN (W [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ }
+ else
+ {
+ /* Z = b - A' x */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* Z [i] = B [i] ; */
+ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops += MULTSUB_FLOPS * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ zi = Z [i] ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* zi -= conjugate (Ax [p]) * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, Bsplit) ;
+ MULT_SUB_CONJ (zi, X [Ai [p]], aij) ;
+ }
+ Z [i] = zi ;
+ }
+ /* W = Q' Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Z [Cperm [i]] ;
+ }
+ }
+
+ flops += UMF_uhsolve (Numeric, W, Pattern) ;
+ flops += UMF_lhsolve (Numeric, W, Pattern) ;
+
+ if (step == 0)
+ {
+
+ /* X = R P' W */
+ /* do not use Z, since it isn't allocated if irstep = 0 */
+
+ /* X = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* X = R X */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (X [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (X [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ }
+ else
+ {
+
+ /* Z = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ Z [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* Z = R Z */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (Z [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (Z [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ flops += ASSEMBLE_FLOPS * n ;
+ /* X += Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] += Z [i] ; was +=W[i] in v4.3, which is wrong */
+ ASSEMBLE (X [i], Z [i]) ; /* bug fix, v4.3.1 */
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* sparse backward error estimate */
+ /* -------------------------------------------------------------- */
+
+ if (irstep > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A' is stored by row */
+ /* W (i) = (b - A' x)_i, residual */
+ /* Z2 (i) = (|A'||x|)_i */
+ /* ---------------------------------------------------------- */
+
+ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* wi = B [i] ; */
+ ASSIGN (wi, Bx, Bz, i, Bsplit) ;
+ z2i = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* axx = conjugate (Ax [p]) * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT_CONJ (axx, X [Ai [p]], aij) ;
+
+ /* wi -= axx ; */
+ DECREMENT (wi, axx) ;
+
+ /* z2i += ABS (axx) ; */
+ ABS (d, axx) ;
+ z2i += d ;
+ }
+ W [i] = wi ;
+ Z2 [i] = z2i ;
+ }
+
+ flops += (2*ABS_FLOPS + 5) * n ;
+ if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info))
+ {
+ /* iterative refinement is done */
+ break ;
+ }
+
+ }
+
+ }
+
+ }
+ else if (sys == UMFPACK_Aat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve A.' x = b with optional iterative refinement */
+ /* ------------------------------------------------------------------ */
+
+ /* A' is the array transpose */
+
+ if (irstep > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* using iterative refinement: compute Y */
+ /* -------------------------------------------------------------- */
+
+ nz = Ap [n] ;
+ Info [UMFPACK_NZ] = nz ;
+
+ /* A.' is stored by row */
+ /* Y (i) = ||(A.' R)_i||, 1-norm of row i of A.' R */
+
+ if (do_scale)
+ {
+ flops += (ABS_FLOPS + 2) * nz ;
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) * Rs [Ai [p]] ; */
+ /* note that A.' is the array transpose,
+ * so no conjugate */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d * Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) / Rs [Ai [p]] ; */
+ /* note that A.' is the array transpose,
+ * so no conjugate */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d / Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ }
+ else
+ {
+ /* no scaling */
+ flops += (ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) */
+ /* note that A.' is the array transpose,
+ * so no conjugate */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += d ;
+ }
+ Y [i] = yi ;
+ }
+ }
+
+ /* B2 = abs (B) */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* B2 [i] = ABS (B [i]) ; */
+ ASSIGN (bi, Bx, Bz, i, Bsplit) ;
+ ABS (B2 [i], bi) ;
+ }
+
+ }
+
+ for (step = 0 ; step <= irstep ; step++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Solve A.' x = b (step 0): */
+ /* x = R P' (L.' \ (U.' \ (Q' b))) */
+ /* and then perform iterative refinement (step > 0): */
+ /* x = x + R P' (L.' \ (U.' \ (Q' (b - A.' x)))) */
+ /* -------------------------------------------------------------- */
+
+ if (step == 0)
+ {
+ /* W = Q' b */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [Cperm [i]] ; */
+ ASSIGN (W [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ }
+ else
+ {
+ /* Z = b - A.' x */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* Z [i] = B [i] ; */
+ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops += MULTSUB_FLOPS * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ zi = Z [i] ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* zi -= Ax [p] * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT_SUB (zi, aij, X [Ai [p]]) ;
+ }
+ Z [i] = zi ;
+ }
+ /* W = Q' Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Z [Cperm [i]] ;
+ }
+ }
+
+ flops += UMF_utsolve (Numeric, W, Pattern) ;
+ flops += UMF_ltsolve (Numeric, W, Pattern) ;
+
+ if (step == 0)
+ {
+
+ /* X = R P' W */
+ /* do not use Z, since it isn't allocated if irstep = 0 */
+
+ /* X = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* X = R X */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (X [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (X [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ }
+ else
+ {
+
+ /* Z = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ Z [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* Z = R Z */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (Z [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (Z [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ flops += ASSEMBLE_FLOPS * n ;
+ /* X += Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] += Z [i] ; was +=W[i] in v4.3, which is wrong */
+ ASSEMBLE (X [i], Z [i]) ; /* bug fix, v4.3.1 */
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* sparse backward error estimate */
+ /* -------------------------------------------------------------- */
+
+ if (irstep > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A.' is stored by row */
+ /* W (i) = (b - A.' x)_i, residual */
+ /* Z (i) = (|A.'||x|)_i */
+ /* ---------------------------------------------------------- */
+
+ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* wi = B [i] ; */
+ ASSIGN (wi, Bx, Bz, i, Bsplit) ;
+ z2i = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* axx = Ax [p] * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT (axx, aij, X [Ai [p]]) ;
+
+ /* wi -= axx ; */
+ DECREMENT (wi, axx) ;
+
+ /* z2i += ABS (axx) ; */
+ ABS (d, axx) ;
+ z2i += d ;
+ }
+ W [i] = wi ;
+ Z2 [i] = z2i ;
+ }
+
+ flops += (2*ABS_FLOPS + 5) * n ;
+ if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info))
+ {
+ /* iterative refinement is done */
+ break ;
+ }
+
+ }
+
+ }
+
+ }
+ else if (sys == UMFPACK_Pt_L)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve P'Lx=b: x = L \ Pb */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [Rperm [i]] ; */
+ ASSIGN (X [i], Bx, Bz, Rperm [i], Bsplit) ;
+ }
+ flops = UMF_lsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_L)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve Lx=b: x = L \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_lsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lt_P)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L'Px=b: x = P' (L' \ b) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_lhsolve (Numeric, W, Pattern) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lat_P)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L.'Px=b: x = P' (L.' \ b) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_ltsolve (Numeric, W, Pattern) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lt)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L'x=b: x = L' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_lhsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L.'x=b: x = L.' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_ltsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_U_Qt)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve UQ'x=b: x = Q (U \ b) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_usolve (Numeric, W, Pattern) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Cperm [i]] = W [i] ;
+ }
+
+ }
+ else if (sys == UMFPACK_U)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve Ux=b: x = U \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_usolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Q_Ut)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve QU'x=b: x = U' \ Q'b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [Cperm [i]] ; */
+ ASSIGN (X [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ flops = UMF_uhsolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Q_Uat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve QU.'x=b: x = U.' \ Q'b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [Cperm [i]] ; */
+ ASSIGN (X [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ flops = UMF_utsolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Ut)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve U'x=b: x = U' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_uhsolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Uat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve U'x=b: x = U' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_utsolve (Numeric, X, Pattern) ;
+
+ }
+ else
+ {
+ return (UMFPACK_ERROR_invalid_system) ;
+ }
+
+#ifdef COMPLEX
+ /* copy the solution back, from Entry X [ ] to double Xx [ ] and Xz [ ] */
+ if (AXsplit)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = REAL_COMPONENT (X [i]) ;
+ Xz [i] = IMAG_COMPONENT (X [i]) ;
+ }
+ }
+#endif
+
+ /* return UMFPACK_OK, or UMFPACK_WARNING_singular_matrix */
+ /* Note that systems involving just L will return UMFPACK_OK */
+ Info [UMFPACK_SOLVE_FLOPS] = flops ;
+ return (status) ;
+}
+
+
+/* ========================================================================== */
+/* === do_step ============================================================== */
+/* ========================================================================== */
+
+/* Perform one step of iterative refinement, for A x = b or A' x = b */
+
+PRIVATE Int do_step /* return TRUE if iterative refinement done */
+(
+ double omega [3],
+ Int step, /* which step of iterative refinement to do */
+ const double B2 [ ], /* abs (B) */
+ Entry X [ ],
+ const Entry W [ ],
+ const double Y [ ],
+ const double Z2 [ ],
+ Entry S [ ],
+ Int n,
+ double Info [UMFPACK_INFO]
+)
+{
+ double last_omega [3], tau, nctau, d1, wd1, d2, wd2, xi, yix, wi, xnorm ;
+ Int i ;
+
+ /* DBL_EPSILON is a standard ANSI C term defined in <float.h> */
+ /* It is the smallest positive x such that 1.0+x != 1.0 */
+
+ nctau = 1000 * n * DBL_EPSILON ;
+ DEBUG0 (("do_step start: nctau = %30.20e\n", nctau)) ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+
+ /* for approximate flop count, assume d1 > tau is always true */
+ /* flops += (2*ABS_FLOPS + 5) * n ; (done in UMF_solve, above) */
+
+ /* ---------------------------------------------------------------------- */
+ /* save the last iteration in case we need to reinstate it */
+ /* ---------------------------------------------------------------------- */
+
+ last_omega [0] = omega [0] ;
+ last_omega [1] = omega [1] ;
+ last_omega [2] = omega [2] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute sparse backward errors: omega [1] and omega [2] */
+ /* ---------------------------------------------------------------------- */
+
+ /* xnorm = ||x|| maxnorm */
+ xnorm = 0.0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* xi = ABS (X [i]) ; */
+ ABS (xi, X [i]) ;
+ if (SCALAR_IS_NAN (xi))
+ {
+ xnorm = xi ;
+ break ;
+ }
+ /* no NaN's to consider here: */
+ xnorm = MAX (xnorm, xi) ;
+ }
+
+ omega [1] = 0. ;
+ omega [2] = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ yix = Y [i] * xnorm ;
+ tau = (yix + B2 [i]) * nctau ;
+ d1 = Z2 [i] + B2 [i] ;
+ /* wi = ABS (W [i]) ; */
+ ABS (wi, W [i]) ;
+ if (SCALAR_IS_NAN (d1))
+ {
+ omega [1] = d1 ;
+ omega [2] = d1 ;
+ break ;
+ }
+ if (SCALAR_IS_NAN (tau))
+ {
+ omega [1] = tau ;
+ omega [2] = tau ;
+ break ;
+ }
+ if (d1 > tau) /* a double relop, but no NaN's here */
+ {
+ wd1 = wi / d1 ;
+ omega [1] = MAX (omega [1], wd1) ;
+ }
+ else if (tau > 0.0) /* a double relop, but no NaN's here */
+ {
+ d2 = Z2 [i] + yix ;
+ wd2 = wi / d2 ;
+ omega [2] = MAX (omega [2], wd2) ;
+ }
+ }
+
+ omega [0] = omega [1] + omega [2] ;
+ Info [UMFPACK_OMEGA1] = omega [1] ;
+ Info [UMFPACK_OMEGA2] = omega [2] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* stop the iterations if the backward error is small, or NaN */
+ /* ---------------------------------------------------------------------- */
+
+ Info [UMFPACK_IR_TAKEN] = step ;
+ Info [UMFPACK_IR_ATTEMPTED] = step ;
+
+ if (SCALAR_IS_NAN (omega [0]))
+ {
+ DEBUG0 (("omega[0] is NaN - done.\n")) ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (TRUE) ;
+ }
+
+ if (omega [0] < DBL_EPSILON) /* double relop, but no NaN case here */
+ {
+ DEBUG0 (("omega[0] too small - done.\n")) ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* stop if insufficient decrease in omega */
+ /* ---------------------------------------------------------------------- */
+
+ /* double relop, but no NaN case here: */
+ if (step > 0 && omega [0] > last_omega [0] / 2)
+ {
+ DEBUG0 (("stop refinement\n")) ;
+ if (omega [0] > last_omega [0])
+ {
+ /* last iteration better than this one, reinstate it */
+ DEBUG0 (("last iteration better\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [i] = S [i] ;
+ }
+ Info [UMFPACK_OMEGA1] = last_omega [1] ;
+ Info [UMFPACK_OMEGA2] = last_omega [2] ;
+ }
+ Info [UMFPACK_IR_TAKEN] = step - 1 ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* save current solution in case we need to reinstate */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ S [i] = X [i] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* iterative refinement continues */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (FALSE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_solve.h b/src/C/SuiteSparse/UMFPACK/Source/umf_solve.h
new file mode 100644
index 0000000..6eb1cf0
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_solve.h
@@ -0,0 +1,25 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_solve
+(
+ Int sys,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+ double Xx [ ],
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+ double Xz [ ],
+ const double Bz [ ],
+#endif
+ NumericType *Numeric,
+ Int irstep,
+ double Info [UMFPACK_INFO],
+ Int Pattern [ ],
+ double SolveWork [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_start_front.c b/src/C/SuiteSparse/UMFPACK/Source/umf_start_front.c
new file mode 100644
index 0000000..cff6ad4
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_start_front.c
@@ -0,0 +1,283 @@
+/* ========================================================================== */
+/* === UMF_start_front ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Allocate the initial frontal matrix working array for a single chain. The
+ * front does not have to be big enough, since if it's too small it will get
+ * reallocated. The size computed here is just an estimate. */
+
+#include "umf_internal.h"
+#include "umf_grow_front.h"
+
+GLOBAL Int UMF_start_front /* returns TRUE if successful, FALSE otherwise */
+(
+ Int chain,
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ double maxbytes ;
+ Int fnrows_max, fncols_max, fnr2, fnc2, fsize, fcurr_size, maxfrsize,
+ overflow, nb, f, cdeg ;
+
+ nb = Symbolic->nb ;
+ fnrows_max = Symbolic->Chain_maxrows [chain] ;
+ fncols_max = Symbolic->Chain_maxcols [chain] ;
+
+ DEBUGm2 (("Start Front for chain "ID". fnrows_max "ID" fncols_max "ID"\n",
+ chain, fnrows_max, fncols_max)) ;
+
+ Work->fnrows_max = fnrows_max ;
+ Work->fncols_max = fncols_max ;
+ Work->any_skip = FALSE ;
+
+ maxbytes = sizeof (Entry) *
+ (double) (fnrows_max + nb) * (double) (fncols_max + nb) ;
+ fcurr_size = Work->fcurr_size ;
+
+ if (Symbolic->prefer_diagonal)
+ {
+ /* Get a rough upper bound on the degree of the first pivot column in
+ * this front. Note that Col_degree is not maintained if diagonal
+ * pivoting is preferred. For most matrices, the first pivot column
+ * of the first frontal matrix of a new chain has only one tuple in
+ * it anyway, so this bound is exact in that case. */
+ Int col, tpi, e, *E, *Col_tuples, *Col_tlen, *Cols ;
+ Tuple *tp, *tpend ;
+ Unit *Memory, *p ;
+ Element *ep ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ col = Work->nextcand ;
+ tpi = Col_tuples [col] ;
+ tp = (Tuple *) Memory + tpi ;
+ tpend = tp + Col_tlen [col] ;
+ cdeg = 0 ;
+ DEBUGm3 (("\n=============== start front: col "ID" tlen "ID"\n",
+ col, Col_tlen [col])) ;
+ for ( ; tp < tpend ; tp++)
+ {
+ DEBUG1 (("Tuple ("ID","ID")\n", tp->e, tp->f)) ;
+ e = tp->e ;
+ if (!E [e]) continue ;
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ;
+ DEBUG1 ((" nrowsleft "ID"\n", ep->nrowsleft)) ;
+ cdeg += ep->nrowsleft ;
+ }
+#ifndef NDEBUG
+ DEBUGm3 (("start front cdeg: "ID" col "ID"\n", cdeg, col)) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ /* cdeg is now the rough upper bound on the degree of the next pivot
+ * column. */
+
+ /* If AMD was called, we know the maximum number of nonzeros in any
+ * column of L. Use this as an upper bound for cdeg, but add 2 to
+ * account for a small amount of off-diagonal pivoting. */
+ if (Symbolic->amd_dmax > 0)
+ {
+ cdeg = MIN (cdeg, Symbolic->amd_dmax) ;
+ }
+
+ /* Increase it to account for larger columns later on.
+ * Also ensure that it's larger than zero. */
+ cdeg += 2 ;
+
+ /* cdeg cannot be larger than fnrows_max */
+ cdeg = MIN (cdeg, fnrows_max) ;
+
+ }
+ else
+ {
+ /* don't do the above cdeg computation */
+ cdeg = 0 ;
+ }
+
+ DEBUGm2 (("fnrows max "ID" fncols_max "ID"\n", fnrows_max, fncols_max)) ;
+
+ /* the current frontal matrix is empty */
+ ASSERT (Work->fnrows == 0 && Work->fncols == 0 && Work->fnpiv == 0) ;
+
+ /* maximum row dimension is always odd, to avoid bad cache effects */
+ ASSERT (fnrows_max >= 0) ;
+ ASSERT (fnrows_max % 2 == 1) ;
+
+ /* ----------------------------------------------------------------------
+ * allocate working array for current frontal matrix:
+ * minimum size: 1-by-1
+ * maximum size: fnrows_max-by-fncols_max
+ * desired size:
+ *
+ * if Numeric->front_alloc_init >= 0:
+ *
+ * for unsymmetric matrices:
+ * Numeric->front_alloc_init * (fnrows_max-by-fncols_max)
+ *
+ * for symmetric matrices (diagonal pivoting preference, actually):
+ * Numeric->front_alloc_init * (fnrows_max-by-fncols_max), or
+ * cdeg*cdeg, whichever is smaller.
+ *
+ * if Numeric->front_alloc_init < 0:
+ * allocate a front of size -Numeric->front_alloc_init.
+ *
+ * Allocate the whole thing if it's small (less than 2*nb^2). Make sure the
+ * leading dimension of the frontal matrix is odd.
+ *
+ * Also allocate the nb-by-nb LU block, the dr-by-nb L block, and the
+ * nb-by-dc U block.
+ * ---------------------------------------------------------------------- */
+
+ /* get the maximum front size, avoiding integer overflow */
+ overflow = INT_OVERFLOW (maxbytes) ;
+ if (overflow)
+ {
+ /* :: int overflow, max front size :: */
+ maxfrsize = Int_MAX / sizeof (Entry) ;
+ }
+ else
+ {
+ maxfrsize = (fnrows_max + nb) * (fncols_max + nb) ;
+ }
+ ASSERT (!INT_OVERFLOW ((double) maxfrsize * sizeof (Entry))) ;
+
+ if (Numeric->front_alloc_init < 0)
+ {
+ /* allocate a front of -Numeric->front_alloc_init entries */
+ fsize = -Numeric->front_alloc_init ;
+ fsize = MAX (1, fsize) ;
+ }
+ else
+ {
+ if (INT_OVERFLOW (Numeric->front_alloc_init * maxbytes))
+ {
+ /* :: int overflow, requested front size :: */
+ fsize = Int_MAX / sizeof (Entry) ;
+ }
+ else
+ {
+ fsize = Numeric->front_alloc_init * maxfrsize ;
+ }
+
+ if (cdeg > 0)
+ {
+ /* diagonal pivoting is in use. cdeg was computed above */
+ Int fsize2 ;
+
+ /* add the L and U blocks */
+ cdeg += nb ;
+
+ if (INT_OVERFLOW (((double) cdeg * (double) cdeg) * sizeof (Entry)))
+ {
+ /* :: int overflow, symmetric front size :: */
+ fsize2 = Int_MAX / sizeof (Entry) ;
+ }
+ else
+ {
+ fsize2 = MAX (cdeg * cdeg, fcurr_size) ;
+ }
+ fsize = MIN (fsize, fsize2) ;
+ }
+ }
+
+ fsize = MAX (fsize, 2*nb*nb) ;
+
+ /* fsize and maxfrsize are now safe from integer overflow. They both
+ * include the size of the pivot blocks. */
+ ASSERT (!INT_OVERFLOW ((double) fsize * sizeof (Entry))) ;
+
+ Work->fnrows_new = 0 ;
+ Work->fncols_new = 0 ;
+
+ /* desired size is fnr2-by-fnc2 (includes L and U blocks): */
+ DEBUGm2 ((" fsize "ID" fcurr_size "ID"\n", fsize, fcurr_size)) ;
+ DEBUGm2 ((" maxfrsize "ID" fnr_curr "ID" fnc_curr "ID"\n", maxfrsize,
+ Work->fnr_curr, Work->fnc_curr)) ;
+
+ if (fsize >= maxfrsize && !overflow)
+ {
+ /* max working array is small, allocate all of it */
+ fnr2 = fnrows_max + nb ;
+ fnc2 = fncols_max + nb ;
+ fsize = maxfrsize ;
+ DEBUGm1 ((" sufficient for ("ID"+"ID")-by-("ID"+"ID")\n",
+ fnrows_max, nb, fncols_max, nb)) ;
+ }
+ else
+ {
+ /* allocate a smaller working array */
+ if (fnrows_max <= fncols_max)
+ {
+ fnr2 = (Int) sqrt ((double) fsize) ;
+ /* make sure fnr2 is odd */
+ fnr2 = MAX (fnr2, 1) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ fnr2 = MIN (fnr2, fnrows_max + nb) ;
+ fnc2 = fsize / fnr2 ;
+ }
+ else
+ {
+ fnc2 = (Int) sqrt ((double) fsize) ;
+ fnc2 = MIN (fnc2, fncols_max + nb) ;
+ fnr2 = fsize / fnc2 ;
+ /* make sure fnr2 is odd */
+ fnr2 = MAX (fnr2, 1) ;
+ if (fnr2 % 2 == 0)
+ {
+ fnr2++ ;
+ fnc2 = fsize / fnr2 ;
+ }
+ }
+ DEBUGm1 ((" smaller "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ }
+ fnr2 = MIN (fnr2, fnrows_max + nb) ;
+ fnc2 = MIN (fnc2, fncols_max + nb) ;
+ ASSERT (fnr2 % 2 == 1) ;
+ ASSERT (fnr2 * fnc2 <= fsize) ;
+
+ fnr2 -= nb ;
+ fnc2 -= nb ;
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnc2 >= 0) ;
+
+ if (fsize > fcurr_size)
+ {
+ DEBUGm1 ((" Grow front \n")) ;
+ Work->do_grow = TRUE ;
+ if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, -1))
+ {
+ /* since the minimum front size is 1-by-1, it would be nearly
+ * impossible to run out of memory here. */
+ DEBUGm4 (("out of memory: start front\n")) ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ /* use the existing front */
+ DEBUGm1 ((" existing front ok\n")) ;
+ Work->fnr_curr = fnr2 ;
+ Work->fnc_curr = fnc2 ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + nb * fnr2 ;
+ Work->Fcblock = Work->Fublock + nb * fnc2 ;
+ }
+ ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ;
+ ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ;
+ ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_start_front.h b/src/C/SuiteSparse/UMFPACK/Source/umf_start_front.h
new file mode 100644
index 0000000..d6d63b3
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_start_front.h
@@ -0,0 +1,13 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_start_front
+(
+ Int chain,
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.c b/src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.c
new file mode 100644
index 0000000..4235917
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.c
@@ -0,0 +1,1056 @@
+/* ========================================================================== */
+/* === UMF_store_lu ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Store the LU factors. Called by the kernel.
+ Returns TRUE if successful, FALSE if out of memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_head_block.h"
+#include "umf_get_memory.h"
+
+/* ========================================================================== */
+
+#ifdef DROP
+GLOBAL Int UMF_store_lu_drop
+#else
+GLOBAL Int UMF_store_lu
+#endif
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry pivot_value ;
+#ifdef DROP
+ double droptol ;
+#endif
+ Entry *D, *Lval, *Uval, *Fl1, *Fl2, *Fu1, *Fu2,
+ *Flublock, *Flblock, *Fublock ;
+ Int i, k, fnr_curr, fnrows, fncols, row, col, pivrow, pivcol, *Frows,
+ *Fcols, *Lpattern, *Upattern, *Lpos, *Upos, llen, ulen, fnc_curr, fnpiv,
+ uilen, lnz, unz, nb, *Lilen,
+ *Uilen, *Lip, *Uip, *Li, *Ui, pivcol_position, newLchain, newUchain,
+ pivrow_position, p, size, lip, uip, lnzi, lnzx, unzx, lnz2i, lnz2x,
+ unz2i, unz2x, zero_pivot, *Pivrow, *Pivcol, kk,
+ Lnz [MAXNB] ;
+
+#ifndef NDEBUG
+ Int *Col_degree, *Row_degree ;
+#endif
+
+#ifdef DROP
+ Int all_lnz, all_unz ;
+ droptol = Numeric->droptol ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ fnpiv = Work->fnpiv ;
+
+ Lpos = Numeric->Lpos ;
+ Upos = Numeric->Upos ;
+ Lilen = Numeric->Lilen ;
+ Uilen = Numeric->Uilen ;
+
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+
+#ifndef NDEBUG
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+#endif
+
+ Lpattern = Work->Lpattern ;
+ llen = Work->llen ;
+ Upattern = Work->Upattern ;
+ ulen = Work->ulen ;
+
+ nb = Work->nb ;
+
+#ifndef NDEBUG
+ DEBUG1 (("\nSTORE LU: fnrows "ID
+ " fncols "ID"\n", fnrows, fncols)) ;
+
+ DEBUG2 (("\nFrontal matrix, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ;
+
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, fnr_curr, fnrows, fnpiv);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, nb, fnpiv, fnpiv) ;
+ DEBUG7 (("Current frontal matrix: (prior to store LU)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ Pivrow = Work->Pivrow ;
+ Pivcol = Work->Pivcol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* store the columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ for (kk = 0 ; kk < fnpiv ; kk++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* one more pivot row and column is being stored into L and U */
+ /* ------------------------------------------------------------------ */
+
+ k = Work->npiv + kk ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the kth pivot row and pivot column */
+ /* ------------------------------------------------------------------ */
+
+ pivrow = Pivrow [kk] ;
+ pivcol = Pivcol [kk] ;
+
+#ifndef NDEBUG
+ ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+
+ DEBUGm4 ((
+ "\n -------------------------------------------------------------"
+ "Store LU: step " ID"\n", k)) ;
+ ASSERT (k < MIN (Work->n_row, Work->n_col)) ;
+ DEBUG2 (("Store column of L, k = "ID", llen "ID"\n", k, llen)) ;
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = Lpattern [i] ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+ DEBUG2 ((" Lpattern["ID"] "ID" Lpos "ID, i, row, Lpos [row])) ;
+ if (row == pivrow) DEBUG2 ((" <- pivot row")) ;
+ DEBUG2 (("\n")) ;
+ ASSERT (i == Lpos [row]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* remove pivot row from L */
+ /* ------------------------------------------------------------------ */
+
+ /* remove pivot row index from current column of L */
+ /* if a new Lchain starts, then all entries are removed later */
+ DEBUG2 (("Removing pivrow from Lpattern, k = "ID"\n", k)) ;
+ ASSERT (!NON_PIVOTAL_ROW (pivrow)) ;
+ pivrow_position = Lpos [pivrow] ;
+ if (pivrow_position != EMPTY)
+ {
+ /* place the last entry in the column in the */
+ /* position of the pivot row index */
+ ASSERT (pivrow == Lpattern [pivrow_position]) ;
+ row = Lpattern [--llen] ;
+ /* ASSERT (NON_PIVOTAL_ROW (row)) ; */
+ Lpattern [pivrow_position] = row ;
+ Lpos [row] = pivrow_position ;
+ Lpos [pivrow] = EMPTY ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* store the pivot value, for the diagonal matrix D */
+ /* ------------------------------------------------------------------ */
+
+ /* kk-th column of LU block */
+ Fl1 = Flublock + kk * nb ;
+
+ /* kk-th column of L in the L block */
+ Fl2 = Flblock + kk * fnr_curr ;
+
+ /* kk-th pivot in frontal matrix located in Flublock [kk, kk] */
+ pivot_value = Fl1 [kk] ;
+
+ D [k] = pivot_value ;
+ zero_pivot = IS_ZERO (pivot_value) ;
+
+ DEBUG4 (("Pivot D["ID"]=", k)) ;
+ EDEBUG4 (pivot_value) ;
+ DEBUG4 (("\n")) ;
+
+ /* ------------------------------------------------------------------ */
+ /* count nonzeros in kth column of L */
+ /* ------------------------------------------------------------------ */
+
+ lnz = 0 ;
+ lnz2i = 0 ;
+ lnz2x = llen ;
+
+#ifdef DROP
+ all_lnz = 0 ;
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fl1 [i] ;
+ if (IS_ZERO (x)) continue ;
+ all_lnz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ lnz++ ;
+ if (Lpos [Pivrow [i]] == EMPTY) lnz2i++ ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fl2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ all_lnz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ lnz++ ;
+ if (Lpos [Frows [i]] == EMPTY) lnz2i++ ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ if (IS_ZERO (Fl1 [i])) continue ;
+ lnz++ ;
+ if (Lpos [Pivrow [i]] == EMPTY) lnz2i++ ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ if (IS_ZERO (Fl2 [i])) continue ;
+ lnz++ ;
+ if (Lpos [Frows [i]] == EMPTY) lnz2i++ ;
+ }
+
+#endif
+
+ lnz2x += lnz2i ;
+
+ /* determine if we start a new Lchain or continue the old one */
+ if (llen == 0 || zero_pivot)
+ {
+ /* llen == 0 means there is no prior Lchain */
+ /* D [k] == 0 means the pivot column is empty */
+ newLchain = TRUE ;
+ }
+ else
+ {
+ newLchain =
+ /* storage for starting a new Lchain */
+ UNITS (Entry, lnz) + UNITS (Int, lnz)
+ <=
+ /* storage for continuing a prior Lchain */
+ UNITS (Entry, lnz2x) + UNITS (Int, lnz2i) ;
+ }
+
+ if (newLchain)
+ {
+ /* start a new chain for column k of L */
+ DEBUG2 (("Start new Lchain, k = "ID"\n", k)) ;
+
+ pivrow_position = EMPTY ;
+
+ /* clear the prior Lpattern */
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = Lpattern [i] ;
+ Lpos [row] = EMPTY ;
+ }
+ llen = 0 ;
+
+ lnzi = lnz ;
+ lnzx = lnz ;
+ }
+ else
+ {
+ /* continue the prior Lchain */
+ DEBUG2 (("Continue Lchain, k = "ID"\n", k)) ;
+ lnzi = lnz2i ;
+ lnzx = lnz2x ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* allocate space for the column of L */
+ /* ------------------------------------------------------------------ */
+
+ size = UNITS (Int, lnzi) + UNITS (Entry, lnzx) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0)
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage coll. (store LU)\n"));
+ }
+#endif
+
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ Int r2, c2 ;
+ /* Do garbage collection, realloc, and try again. */
+ /* Note that there are pivot rows/columns in current front. */
+ if (Work->do_grow)
+ {
+ /* full compaction of current frontal matrix, since
+ * UMF_grow_front will be called next anyway. */
+ r2 = fnrows ;
+ c2 = fncols ;
+ }
+ else
+ {
+ /* partial compaction. */
+ r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ c2 = MAX (fncols, Work->fncols_new + 1) ;
+ }
+ DEBUGm3 (("get_memory from umf_store_lu:\n")) ;
+ if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ {
+ DEBUGm4 (("out of memory: store LU (1)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ DEBUGm4 (("out of memory: store LU (2)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ /* garbage collection may have moved the current front */
+ fnc_curr = Work->fnc_curr ;
+ fnr_curr = Work->fnr_curr ;
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fl1 = Flublock + kk * nb ;
+ Fl2 = Flblock + kk * fnr_curr ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* store the column of L */
+ /* ------------------------------------------------------------------ */
+
+ lip = p ;
+
+ Li = (Int *) (Numeric->Memory + p) ;
+ p += UNITS (Int, lnzi) ;
+ Lval = (Entry *) (Numeric->Memory + p) ;
+ p += UNITS (Entry, lnzx) ;
+
+ for (i = 0 ; i < lnzx ; i++)
+ {
+ CLEAR (Lval [i]) ;
+ }
+
+ /* store the numerical entries */
+
+ if (newLchain)
+ {
+ /* flag the first column in the Lchain by negating Lip [k] */
+ lip = -lip ;
+
+ ASSERT (llen == 0) ;
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Pivrow [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Frows [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Pivrow [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Frows [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+#endif
+
+ }
+ else
+ {
+ ASSERT (llen > 0) ;
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Pivrow [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Frows [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Pivrow [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Frows [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+#endif
+
+ }
+ DEBUG4 (("llen "ID" lnzx "ID"\n", llen, lnzx)) ;
+ ASSERT (llen == lnzx) ;
+ ASSERT (lnz <= llen) ;
+ DEBUG4 (("lnz "ID" \n", lnz)) ;
+
+#ifdef DROP
+
+ DEBUG4 (("all_lnz "ID" \n", all_lnz)) ;
+ ASSERT (lnz <= all_lnz) ;
+ Numeric->lnz += lnz ;
+ Numeric->all_lnz += all_lnz ;
+ Lnz [kk] = all_lnz ;
+
+#else
+
+ Numeric->lnz += lnz ;
+ Numeric->all_lnz += lnz ;
+ Lnz [kk] = lnz ;
+#endif
+
+ Numeric->nLentries += lnzx ;
+ Work->llen = llen ;
+ Numeric->isize += lnzi ;
+
+ /* ------------------------------------------------------------------ */
+ /* the pivot column is fully assembled and scaled, and is now the */
+ /* k-th column of L */
+ /* ------------------------------------------------------------------ */
+
+ Lpos [pivrow] = pivrow_position ; /* not aliased */
+ Lip [pivcol] = lip ; /* aliased with Col_tuples */
+ Lilen [pivcol] = lnzi ; /* aliased with Col_tlen */
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* store the rows of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (kk = 0 ; kk < fnpiv ; kk++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* one more pivot row and column is being stored into L and U */
+ /* ------------------------------------------------------------------ */
+
+ k = Work->npiv + kk ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the kth pivot row and pivot column */
+ /* ------------------------------------------------------------------ */
+
+ pivrow = Pivrow [kk] ;
+ pivcol = Pivcol [kk] ;
+
+#ifndef NDEBUG
+ ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+
+ DEBUG2 (("Store row of U, k = "ID", ulen "ID"\n", k, ulen)) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = Upattern [i] ;
+ DEBUG2 ((" Upattern["ID"] "ID, i, col)) ;
+ if (col == pivcol) DEBUG2 ((" <- pivot col")) ;
+ DEBUG2 (("\n")) ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (i == Upos [col]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* get the pivot value, for the diagonal matrix D */
+ /* ------------------------------------------------------------------ */
+
+ zero_pivot = IS_ZERO (D [k]) ;
+
+ /* ------------------------------------------------------------------ */
+ /* count the nonzeros in the row of U */
+ /* ------------------------------------------------------------------ */
+
+ /* kk-th row of U in the LU block */
+ Fu1 = Flublock + kk ;
+
+ /* kk-th row of U in the U block */
+ Fu2 = Fublock + kk * fnc_curr ;
+
+ unz = 0 ;
+ unz2i = 0 ;
+ unz2x = ulen ;
+ DEBUG2 (("unz2x is "ID", lnzx "ID"\n", unz2x, lnzx)) ;
+
+ /* if row k does not end a Uchain, pivcol not included in ulen */
+ ASSERT (!NON_PIVOTAL_COL (pivcol)) ;
+ pivcol_position = Upos [pivcol] ;
+ if (pivcol_position != EMPTY)
+ {
+ unz2x-- ;
+ DEBUG2 (("(exclude pivcol) unz2x is now "ID"\n", unz2x)) ;
+ }
+
+ ASSERT (unz2x >= 0) ;
+
+#ifdef DROP
+ all_unz = 0 ;
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fu1 [i*nb] ;
+ if (IS_ZERO (x)) continue ;
+ all_unz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ unz++ ;
+ if (Upos [Pivcol [i]] == EMPTY) unz2i++ ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fu2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ all_unz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ unz++ ;
+ if (Upos [Fcols [i]] == EMPTY) unz2i++ ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ if (IS_ZERO (Fu1 [i*nb])) continue ;
+ unz++ ;
+ if (Upos [Pivcol [i]] == EMPTY) unz2i++ ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ if (IS_ZERO (Fu2 [i])) continue ;
+ unz++ ;
+ if (Upos [Fcols [i]] == EMPTY) unz2i++ ;
+ }
+
+#endif
+
+ unz2x += unz2i ;
+
+ ASSERT (IMPLIES (k == 0, ulen == 0)) ;
+
+ /* determine if we start a new Uchain or continue the old one */
+ if (ulen == 0 || zero_pivot)
+ {
+ /* ulen == 0 means there is no prior Uchain */
+ /* D [k] == 0 means the matrix is singular (pivot row might */
+ /* not be empty, however, but start a new Uchain to prune zero */
+ /* entries for the deg > 0 test in UMF_u*solve) */
+ newUchain = TRUE ;
+ }
+ else
+ {
+ newUchain =
+ /* approximate storage for starting a new Uchain */
+ UNITS (Entry, unz) + UNITS (Int, unz)
+ <=
+ /* approximate storage for continuing a prior Uchain */
+ UNITS (Entry, unz2x) + UNITS (Int, unz2i) ;
+
+ /* this would be exact, except for the Int to Unit rounding, */
+ /* because the Upattern is stored only at the end of the Uchain */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* allocate space for the row of U */
+ /* ------------------------------------------------------------------ */
+
+ size = 0 ;
+ if (newUchain)
+ {
+ /* store the pattern of the last row in the prior Uchain */
+ size += UNITS (Int, ulen) ;
+ unzx = unz ;
+ }
+ else
+ {
+ unzx = unz2x ;
+ }
+ size += UNITS (Entry, unzx) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0)
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage coll. (store LU)\n"));
+ }
+#endif
+
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ Int r2, c2 ;
+ /* Do garbage collection, realloc, and try again. */
+ /* Note that there are pivot rows/columns in current front. */
+ if (Work->do_grow)
+ {
+ /* full compaction of current frontal matrix, since
+ * UMF_grow_front will be called next anyway. */
+ r2 = fnrows ;
+ c2 = fncols ;
+ }
+ else
+ {
+ /* partial compaction. */
+ r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ c2 = MAX (fncols, Work->fncols_new + 1) ;
+ }
+ DEBUGm3 (("get_memory from umf_store_lu:\n")) ;
+ if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ {
+ /* :: get memory, column of L :: */
+ DEBUGm4 (("out of memory: store LU (1)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ /* :: out of memory, column of U :: */
+ DEBUGm4 (("out of memory: store LU (2)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ /* garbage collection may have moved the current front */
+ fnc_curr = Work->fnc_curr ;
+ fnr_curr = Work->fnr_curr ;
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fu1 = Flublock + kk ;
+ Fu2 = Fublock + kk * fnc_curr ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* store the row of U */
+ /* ------------------------------------------------------------------ */
+
+ uip = p ;
+
+ if (newUchain)
+ {
+ /* starting a new Uchain - flag this by negating Uip [k] */
+ uip = -uip ;
+ DEBUG2 (("Start new Uchain, k = "ID"\n", k)) ;
+
+ pivcol_position = EMPTY ;
+
+ /* end the prior Uchain */
+ /* save the current Upattern, and then */
+ /* clear it and start a new Upattern */
+ DEBUG2 (("Ending prior chain, k-1 = "ID"\n", k-1)) ;
+ uilen = ulen ;
+ Ui = (Int *) (Numeric->Memory + p) ;
+ Numeric->isize += ulen ;
+ p += UNITS (Int, ulen) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = Upattern [i] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ Upos [col] = EMPTY ;
+ Ui [i] = col ;
+ }
+
+ ulen = 0 ;
+
+ }
+ else
+ {
+ /* continue the prior Uchain */
+ DEBUG2 (("Continue Uchain, k = "ID"\n", k)) ;
+ ASSERT (k > 0) ;
+
+ /* remove pivot col index from current row of U */
+ /* if a new Uchain starts, then all entries are removed later */
+ DEBUG2 (("Removing pivcol from Upattern, k = "ID"\n", k)) ;
+
+ if (pivcol_position != EMPTY)
+ {
+ /* place the last entry in the row in the */
+ /* position of the pivot col index */
+ ASSERT (pivcol == Upattern [pivcol_position]) ;
+ col = Upattern [--ulen] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ Upattern [pivcol_position] = col ;
+ Upos [col] = pivcol_position ;
+ Upos [pivcol] = EMPTY ;
+ }
+
+ /* this row continues the Uchain. Keep track of how much */
+ /* to trim from the k-th length to get the length of the */
+ /* (k-1)st row of U */
+ uilen = unz2i ;
+
+ }
+
+ Uval = (Entry *) (Numeric->Memory + p) ;
+ /* p += UNITS (Entry, unzx), no need to increment p */
+
+ for (i = 0 ; i < unzx ; i++)
+ {
+ CLEAR (Uval [i]) ;
+ }
+
+ if (newUchain)
+ {
+ ASSERT (ulen == 0) ;
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Pivcol [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Fcols [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Pivcol [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Fcols [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+#endif
+
+ }
+ else
+ {
+
+ ASSERT (ulen > 0) ;
+
+ /* store the numerical entries and find new nonzeros */
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Pivcol [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Fcols [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Pivcol [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Fcols [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+#endif
+
+ }
+
+ ASSERT (ulen == unzx) ;
+ ASSERT (unz <= ulen) ;
+ DEBUG4 (("unz "ID" \n", unz)) ;
+
+#ifdef DROP
+
+ DEBUG4 (("all_unz "ID" \n", all_unz)) ;
+ ASSERT (unz <= all_unz) ;
+ Numeric->unz += unz ;
+ Numeric->all_unz += all_unz ;
+ /* count the "true" flops, based on LU pattern only */
+ Numeric->flops += DIV_FLOPS * Lnz [kk] /* scale pivot column */
+ + MULTSUB_FLOPS * (Lnz [kk] * all_unz) ; /* outer product */
+
+#else
+
+ Numeric->unz += unz ;
+ Numeric->all_unz += unz ;
+ /* count the "true" flops, based on LU pattern only */
+ Numeric->flops += DIV_FLOPS * Lnz [kk] /* scale pivot column */
+ + MULTSUB_FLOPS * (Lnz [kk] * unz) ; /* outer product */
+#endif
+
+ Numeric->nUentries += unzx ;
+ Work->ulen = ulen ;
+ DEBUG1 (("Work->ulen = "ID" at end of pivot step, k: "ID"\n", ulen, k));
+
+ /* ------------------------------------------------------------------ */
+ /* the pivot row is the k-th row of U */
+ /* ------------------------------------------------------------------ */
+
+ Upos [pivcol] = pivcol_position ; /* not aliased */
+ Uip [pivrow] = uip ; /* aliased with Row_tuples */
+ Uilen [pivrow] = uilen ; /* aliased with Row_tlen */
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* no more pivots in frontal working array */
+ /* ---------------------------------------------------------------------- */
+
+ Work->npiv += fnpiv ;
+ Work->fnpiv = 0 ;
+ Work->fnzeros = 0 ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.h b/src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.h
new file mode 100644
index 0000000..b78528f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_store_lu.h
@@ -0,0 +1,17 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_store_lu
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
+
+GLOBAL Int UMF_store_lu_drop
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c b/src/C/SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c
new file mode 100644
index 0000000..dff210e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c
@@ -0,0 +1,45 @@
+/* ========================================================================== */
+/* === UMF_symbolic_usage =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Returns the final size of the Symbolic object, in Units */
+
+#include "umf_internal.h"
+
+GLOBAL double UMF_symbolic_usage
+(
+ Int n_row,
+ Int n_col,
+ Int nchains,
+ Int nfr,
+ Int esize, /* zero if no dense rows. Otherwise, equal to the
+ * number of non-singleton, non-empty columns */
+ Int prefer_diagonal
+)
+{
+ double units ;
+
+ units =
+ DUNITS (SymbolicType, 1) /* Symbolic structure */
+ + 2 * DUNITS (Int, n_col+1) /* Cperm_init, Cdeg */
+ + 2 * DUNITS (Int, n_row+1) /* Rperm_init, Rdeg */
+ + 3 * DUNITS (Int, nchains+1) /* Chain_ */
+ + 4 * DUNITS (Int, nfr+1) ; /* Front_ */
+
+ /* if dense rows are present */
+ units += DUNITS (Int, esize) ; /* Esize */
+
+ /* for diagonal pivoting */
+ if (prefer_diagonal)
+ {
+ units += DUNITS (Int, n_col+1) ; /* Diagonal_map */
+ }
+
+ return (units) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_symbolic_usage.h b/src/C/SuiteSparse/UMFPACK/Source/umf_symbolic_usage.h
new file mode 100644
index 0000000..fbe979a
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_symbolic_usage.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_symbolic_usage
+(
+ Int n_row,
+ Int n_col,
+ Int nchains,
+ Int nfr,
+ Int esize,
+ Int prefer_diagonal
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_transpose.c b/src/C/SuiteSparse/UMFPACK/Source/umf_transpose.c
new file mode 100644
index 0000000..85cd34d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_transpose.c
@@ -0,0 +1,400 @@
+/* ========================================================================== */
+/* === UMF_transpose ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Not user-callable. Computes a permuted transpose, R = (A (P,Q(1:nq)))' in
+ MATLAB notation, where R is in column-form. A is n_row-by-n_col, the
+ row-form matrix R is n_row-by-nq, where nq <= n_col. A may be singular.
+ The complex version can do transpose (') or array transpose (.').
+
+ Uses Gustavson's method (Two Fast Algorithms for Sparse Matrices:
+ Multiplication and Permuted Transposition, ACM Trans. on Math. Softw.,
+ vol 4, no 3, pp. 250-269).
+*/
+
+#include "umf_internal.h"
+#include "umf_is_permutation.h"
+
+GLOBAL Int UMF_transpose
+(
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const double Ax [ ], /* size nz if present */
+
+ const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/
+ /* P is identity if not present */
+ /* size n_row, if present */
+
+ const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/
+ /* Q is identity if not present */
+ /* size nq, if present */
+ Int nq, /* size of Q, ignored if Q is (Int *) NULL */
+
+ /* output matrix: Rp, Ri, Rx, and Rz: */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ double Rx [ ], /* size nz, if present */
+
+ Int W [ ], /* size max (n_row,n_col) workspace */
+
+ Int check /* if true, then check inputs */
+#ifdef COMPLEX
+ , const double Az [ ] /* size nz */
+ , double Rz [ ] /* size nz */
+ , Int do_conjugate /* if true, then do conjugate transpose */
+ /* otherwise, do array transpose */
+#endif
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int i, j, k, p, bp, newj, do_values ;
+#ifdef COMPLEX
+ Int split ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ Int nz ;
+ ASSERT (n_col >= 0) ;
+ nz = (Ap != (Int *) NULL) ? Ap [n_col] : 0 ;
+ DEBUG2 (("UMF_transpose: "ID"-by-"ID" nz "ID"\n", n_row, n_col, nz)) ;
+#endif
+
+ if (check)
+ {
+ /* UMFPACK_symbolic skips this check */
+ /* UMFPACK_transpose always does this check */
+ if (!Ai || !Ap || !Ri || !Rp || !W)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ if (n_row <= 0 || n_col <= 0) /* n_row,n_col must be > 0 */
+ {
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+ if (!UMF_is_permutation (P, W, n_row, n_row) ||
+ !UMF_is_permutation (Q, W, nq, nq))
+ {
+ return (UMFPACK_ERROR_invalid_permutation) ;
+ }
+ if (AMD_valid (n_row, n_col, Ap, Ai) != AMD_OK)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG2 (("UMF_transpose, input matrix:\n")) ;
+ UMF_dump_col_matrix (Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Ai, Ap, n_row, n_col, nz) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* use W as workspace for RowCount */
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ W [i] = 0 ;
+ Rp [i] = 0 ;
+ }
+
+ if (Q != (Int *) NULL)
+ {
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ W [i]++ ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ W [i]++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers for R = A (P,Q) */
+ /* ---------------------------------------------------------------------- */
+
+ if (P != (Int *) NULL)
+ {
+ Rp [0] = 0 ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ i = P [k] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ Rp [k+1] = Rp [k] + W [i] ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ i = P [k] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ W [i] = Rp [k] ;
+ }
+ }
+ else
+ {
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ }
+ for (i = 0 ; i < n_row ; i++)
+ {
+ W [i] = Rp [i] ;
+ }
+ }
+ ASSERT (Rp [n_row] <= Ap [n_col]) ;
+
+ /* at this point, W holds the permuted row pointers */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row form of B */
+ /* ---------------------------------------------------------------------- */
+
+ do_values = Ax && Rx ;
+
+#ifdef COMPLEX
+ split = SPLIT (Az) && SPLIT (Rz) ;
+
+ if (do_conjugate && do_values)
+ {
+ if (Q != (Int *) NULL)
+ {
+ if (split)
+ {
+ /* R = A (P,Q)' */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [bp] = Ax [p] ;
+ Rz [bp] = -Az [p] ;
+ }
+ }
+ }
+ else
+ {
+ /* R = A (P,Q)' (merged complex values) */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = -Ax [2*p+1] ;
+ }
+ }
+ }
+ }
+ else
+ {
+ if (split)
+ {
+ /* R = A (P,:)' */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [bp] = Ax [p] ;
+ Rz [bp] = -Az [p] ;
+ }
+ }
+ }
+ else
+ {
+ /* R = A (P,:)' (merged complex values) */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = -Ax [2*p+1] ;
+ }
+ }
+ }
+ }
+ }
+ else
+#endif
+ {
+ if (Q != (Int *) NULL)
+ {
+ if (do_values)
+ {
+#ifdef COMPLEX
+ if (split)
+#endif
+ {
+ /* R = A (P,Q).' */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [bp] = Ax [p] ;
+#ifdef COMPLEX
+ Rz [bp] = Az [p] ;
+#endif
+ }
+ }
+ }
+#ifdef COMPLEX
+ else
+ {
+ /* R = A (P,Q).' (merged complex values) */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = Ax [2*p+1] ;
+ }
+ }
+ }
+#endif
+ }
+ else
+ {
+ /* R = pattern of A (P,Q).' */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ri [W [Ai [p]]++] = newj ;
+ }
+ }
+ }
+ }
+ else
+ {
+ if (do_values)
+ {
+#ifdef COMPLEX
+ if (split)
+#endif
+ {
+ /* R = A (P,:).' */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [bp] = Ax [p] ;
+#ifdef COMPLEX
+ Rz [bp] = Az [p] ;
+#endif
+ }
+ }
+ }
+#ifdef COMPLEX
+ else
+ {
+ /* R = A (P,:).' (merged complex values) */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = Ax [2*p+1] ;
+ }
+ }
+ }
+#endif
+ }
+ else
+ {
+ /* R = pattern of A (P,:).' */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ri [W [Ai [p]]++] = j ;
+ }
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n_row ; k++)
+ {
+ if (P != (Int *) NULL)
+ {
+ i = P [k] ;
+ }
+ else
+ {
+ i = k ;
+ }
+ DEBUG3 ((ID": W[i] "ID" Rp[k+1] "ID"\n", i, W [i], Rp [k+1])) ;
+ ASSERT (W [i] == Rp [k+1]) ;
+ }
+ DEBUG2 (("UMF_transpose, output matrix:\n")) ;
+ UMF_dump_col_matrix (Rx,
+#ifdef COMPLEX
+ Rz,
+#endif
+ Ri, Rp, n_col, n_row, Rp [n_row]) ;
+ ASSERT (AMD_valid (n_col, n_row, Rp, Ri) == AMD_OK) ;
+#endif
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_transpose.h b/src/C/SuiteSparse/UMFPACK/Source/umf_transpose.h
new file mode 100644
index 0000000..5d44106
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_transpose.h
@@ -0,0 +1,27 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_transpose
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+ const Int P [ ],
+ const Int Q [ ],
+ Int nq,
+ Int Rp [ ],
+ Int Ri [ ],
+ double Rx [ ],
+ Int W [ ],
+ Int check
+#ifdef COMPLEX
+ , const double Az [ ]
+ , double Rz [ ]
+ , Int do_conjugate
+#endif
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_triplet.c b/src/C/SuiteSparse/UMFPACK/Source/umf_triplet.c
new file mode 100644
index 0000000..363e7a4
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_triplet.c
@@ -0,0 +1,428 @@
+/* ========================================================================== */
+/* === UMF_triplet ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Not user callable. Converts triplet input to column-oriented form.
+ Duplicate entries may exist (they are summed in the output). The columns
+ of the column-oriented form are in sorted order. The input is not modified.
+ Returns 1 if OK, 0 if an error occurred.
+
+ Compiled into four different routines for each version (di, dl, zi, zl),
+ for a total of 16 different routines.
+*/
+
+#include "umf_internal.h"
+
+#ifdef DO_MAP
+#ifdef DO_VALUES
+GLOBAL Int UMF_triplet_map_x
+#else
+GLOBAL Int UMF_triplet_map_nox
+#endif
+#else
+#ifdef DO_VALUES
+GLOBAL Int UMF_triplet_nomap_x
+#else
+GLOBAL Int UMF_triplet_nomap_nox
+#endif
+#endif
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ], /* size nz */
+ const Int Tj [ ], /* size nz */
+ Int Ap [ ], /* size n_col + 1 */
+ Int Ai [ ], /* size nz */
+ Int Rp [ ], /* size n_row + 1 */
+ Int Rj [ ], /* size nz */
+ Int W [ ], /* size max (n_row, n_col) */
+ Int RowCount [ ] /* size n_row */
+#ifdef DO_VALUES
+ , const double Tx [ ] /* size nz */
+ , double Ax [ ] /* size nz */
+ , double Rx [ ] /* size nz */
+#ifdef COMPLEX
+ , const double Tz [ ] /* size nz */
+ , double Az [ ] /* size nz */
+ , double Rz [ ] /* size nz */
+#endif
+#endif
+#ifdef DO_MAP
+ , Int Map [ ] /* size nz */
+ , Int Map2 [ ] /* size nz */
+#endif
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int i, j, k, p, cp, p1, p2, pdest, pj ;
+#ifdef DO_MAP
+ Int duplicates ;
+#endif
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ Int split = SPLIT (Tz) && SPLIT (Az) && SPLIT (Rz) ;
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row (also counting duplicates) */
+ /* ---------------------------------------------------------------------- */
+
+ /* use W as workspace for row counts (including duplicates) */
+ for (i = 0 ; i < n_row ; i++)
+ {
+ W [i] = 0 ;
+ }
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= n_row || j < 0 || j >= n_col)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ W [i]++ ;
+#ifndef NDEBUG
+ DEBUG1 ((ID " triplet: "ID" "ID" ", k, i, j)) ;
+#ifdef DO_VALUES
+ {
+ Entry tt ;
+ ASSIGN (tt, Tx, Tz, k, split) ;
+ EDEBUG2 (tt) ;
+ DEBUG1 (("\n")) ;
+ }
+#endif
+#endif
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ W [i] = Rp [i] ;
+ }
+
+ /* W is now equal to the row pointers */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row form */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ p = W [Ti [k]]++ ;
+#ifdef DO_MAP
+ Map [k] = p ;
+#endif
+ Rj [p] = Tj [k] ;
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ if (split)
+ {
+ Rx [p] = Tx [k] ;
+ Rz [p] = Tz [k] ;
+ }
+ else
+ {
+ Rx [2*p ] = Tx [2*k ] ;
+ Rx [2*p+1] = Tx [2*k+1] ;
+ }
+#else
+ Rx [p] = Tx [k] ;
+#endif
+#endif
+ }
+
+ /* Rp stays the same, but W [i] is advanced to the start of row i+1 */
+
+#ifndef NDEBUG
+ for (i = 0 ; i < n_row ; i++)
+ {
+ ASSERT (W [i] == Rp [i+1]) ;
+ }
+#ifdef DO_MAP
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* make sure that kth triplet is mapped correctly */
+ p = Map [k] ;
+ DEBUG1 (("First row map: Map ["ID"] = "ID"\n", k, p)) ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ ASSERT (j == Rj [p]) ;
+ ASSERT (Rp [i] <= p && p < Rp [i+1]) ;
+ }
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* sum up duplicates */
+ /* ---------------------------------------------------------------------- */
+
+ /* use W [j] to hold position in Ri/Rx/Rz of a_ij, for row i [ */
+
+ for (j = 0 ; j < n_col ; j++)
+ {
+ W [j] = EMPTY ;
+ }
+
+#ifdef DO_MAP
+ duplicates = FALSE ;
+#endif
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ p1 = Rp [i] ;
+ p2 = Rp [i+1] ;
+ pdest = p1 ;
+ /* At this point, W [j] < p1 holds true for all columns j, */
+ /* because Ri/Rx/Rz is stored in row oriented order. */
+#ifndef NDEBUG
+ if (UMF_debug >= -2)
+ {
+ for (j = 0 ; j < n_col ; j++)
+ {
+ ASSERT (W [j] < p1) ;
+ }
+ }
+#endif
+ for (p = p1 ; p < p2 ; p++)
+ {
+ j = Rj [p] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ pj = W [j] ;
+ if (pj >= p1)
+ {
+ /* this column index, j, is already in row i, at position pj */
+ ASSERT (pj < p) ;
+ ASSERT (Rj [pj] == j) ;
+#ifdef DO_MAP
+ Map2 [p] = pj ;
+ duplicates = TRUE ;
+#endif
+#ifdef DO_VALUES
+ /* sum the entry */
+#ifdef COMPLEX
+ if (split)
+ {
+ Rx [pj] += Rx [p] ;
+ Rz [pj] += Rz [p] ;
+ }
+ else
+ {
+ Rx[2*pj ] += Rx[2*p ] ;
+ Rx[2*pj+1] += Rx[2*p+1] ;
+ }
+#else
+ Rx [pj] += Rx [p] ;
+#endif
+#endif
+ }
+ else
+ {
+ /* keep the entry */
+ /* also keep track in W[j] of position of a_ij for case above */
+ W [j] = pdest ;
+#ifdef DO_MAP
+ Map2 [p] = pdest ;
+#endif
+ /* no need to move the entry if pdest is equal to p */
+ if (pdest != p)
+ {
+ Rj [pdest] = j ;
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ if (split)
+ {
+ Rx [pdest] = Rx [p] ;
+ Rz [pdest] = Rz [p] ;
+ }
+ else
+ {
+ Rx [2*pdest ] = Rx [2*p ] ;
+ Rx [2*pdest+1] = Rx [2*p+1] ;
+ }
+#else
+ Rx [pdest] = Rx [p] ;
+#endif
+#endif
+ }
+ pdest++ ;
+ }
+ }
+ RowCount [i] = pdest - p1 ;
+ }
+
+ /* done using W for position of a_ij ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* merge Map and Map2 into a single Map */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef DO_MAP
+ if (duplicates)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Map [k] = Map2 [Map [k]] ;
+ }
+ }
+#ifndef NDEBUG
+ else
+ {
+ /* no duplicates, so no need to recompute Map */
+ for (k = 0 ; k < nz ; k++)
+ {
+ ASSERT (Map2 [k] == k) ;
+ }
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* make sure that kth triplet is mapped correctly */
+ p = Map [k] ;
+ DEBUG1 (("Second row map: Map ["ID"] = "ID"\n", k, p)) ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ ASSERT (j == Rj [p]) ;
+ ASSERT (Rp [i] <= p && p < Rp [i+1]) ;
+ }
+#endif
+#endif
+
+ /* now the kth triplet maps to p = Map [k], and thus to Rj/Rx [p] */
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each column */
+ /* ---------------------------------------------------------------------- */
+
+ /* [ use W as work space for column counts of A */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ W [j] = 0 ;
+ }
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++)
+ {
+ j = Rj [p] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ W [j]++ ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create the column pointers */
+ /* ---------------------------------------------------------------------- */
+
+ Ap [0] = 0 ;
+ for (j = 0 ; j < n_col ; j++)
+ {
+ Ap [j+1] = Ap [j] + W [j] ;
+ }
+ /* done using W as workspace for column counts of A ] */
+
+ for (j = 0 ; j < n_col ; j++)
+ {
+ W [j] = Ap [j] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the column form */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++)
+ {
+ cp = W [Rj [p]]++ ;
+#ifdef DO_MAP
+ Map2 [p] = cp ;
+#endif
+ Ai [cp] = i ;
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ if (split)
+ {
+ Ax [cp] = Rx [p] ;
+ Az [cp] = Rz [p] ;
+ }
+ else
+ {
+ Ax [2*cp ] = Rx [2*p ] ;
+ Ax [2*cp+1] = Rx [2*p+1] ;
+ }
+#else
+ Ax [cp] = Rx [p] ;
+#endif
+#endif
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* merge Map and Map2 into a single Map */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef DO_MAP
+ for (k = 0 ; k < nz ; k++)
+ {
+ Map [k] = Map2 [Map [k]] ;
+ }
+#endif
+
+ /* now the kth triplet maps to p = Map [k], and thus to Ai/Ax [p] */
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n_col ; j++)
+ {
+ ASSERT (W [j] == Ap [j+1]) ;
+ }
+
+ UMF_dump_col_matrix (
+#ifdef DO_VALUES
+ Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+#else
+ (double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+#endif
+ Ai, Ap, n_row, n_col, nz) ;
+
+#ifdef DO_MAP
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* make sure that kth triplet is mapped correctly */
+ p = Map [k] ;
+ DEBUG1 (("Col map: Map ["ID"] = "ID"\t", k, p)) ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ ASSERT (i == Ai [p]) ;
+ DEBUG1 ((" i "ID" j "ID" Ap[j] "ID" p "ID" Ap[j+1] "ID"\n",
+ i, j, Ap [j], p, Ap [j+1])) ;
+ ASSERT (Ap [j] <= p && p < Ap [j+1]) ;
+ }
+#endif
+#endif
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_triplet.h b/src/C/SuiteSparse/UMFPACK/Source/umf_triplet.h
new file mode 100644
index 0000000..5a3a9d9
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_triplet.h
@@ -0,0 +1,85 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_triplet_map_x
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+ , const double Tx [ ]
+ , double Ax [ ]
+ , double Rx [ ]
+#ifdef COMPLEX
+ , const double Tz [ ]
+ , double Az [ ]
+ , double Rz [ ]
+#endif
+ , Int Map [ ]
+ , Int Map2 [ ]
+) ;
+
+GLOBAL Int UMF_triplet_map_nox
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+ , Int Map [ ]
+ , Int Map2 [ ]
+) ;
+
+GLOBAL Int UMF_triplet_nomap_x
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+ , const double Tx [ ]
+ , double Ax [ ]
+ , double Rx [ ]
+#ifdef COMPLEX
+ , const double Tz [ ]
+ , double Az [ ]
+ , double Rz [ ]
+#endif
+) ;
+
+GLOBAL Int UMF_triplet_nomap_nox
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c b/src/C/SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c
new file mode 100644
index 0000000..cd8f9ea
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c
@@ -0,0 +1,135 @@
+/* ========================================================================== */
+/* === UMF_tuple_lengths ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Determine the tuple list lengths, and the amount of memory required for */
+/* them. Return the amount of memory needed to store all the tuples. */
+/* This routine assumes that the tuple lists themselves are either already */
+/* deallocated, or will be shortly (so Row[ ].tlen and Col[ ].tlen are */
+/* overwritten) */
+
+#include "umf_internal.h"
+
+GLOBAL Int UMF_tuple_lengths /* return memory usage */
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ double *p_dusage /* output argument */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double dusage ;
+ Int e, nrows, ncols, nel, i, *Rows, *Cols, row, col, n_row, n_col, *E,
+ *Row_degree, *Row_tlen, *Col_degree, *Col_tlen, usage, n1 ;
+ Element *ep ;
+ Unit *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ E = Work->E ;
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro only */
+ Row_tlen = Numeric->Uilen ;
+ Col_tlen = Numeric->Lilen ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ n1 = Work->n1 ;
+ nel = Work->nel ;
+
+ DEBUG3 (("TUPLE_LENGTHS: n_row "ID" n_col "ID" nel "ID"\n",
+ n_row, n_col, nel)) ;
+ ASSERT (nel < Work->elen) ;
+
+ /* tuple list lengths already initialized to zero */
+
+ /* ---------------------------------------------------------------------- */
+ /* scan each element: count tuple list lengths (include element 0) */
+ /* ---------------------------------------------------------------------- */
+
+ for (e = 1 ; e <= nel ; e++) /* for all elements, in any order */
+ {
+ if (E [e])
+ {
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ p = Numeric->Memory + E [e] ;
+ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncols) ;
+ nrows = ep->nrows ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ ASSERT (row == EMPTY || (row >= n1 && row < n_row)) ;
+ if (row >= n1)
+ {
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ Row_tlen [row] ++ ;
+ }
+ }
+ for (i = 0 ; i < ncols ; i++)
+ {
+ col = Cols [i] ;
+ ASSERT (col == EMPTY || (col >= n1 && col < n_col)) ;
+ if (col >= n1)
+ {
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ Col_tlen [col] ++ ;
+ }
+ }
+ }
+ }
+
+ /* note: tuple lengths are now modified, but the tuple lists are not */
+ /* updated to reflect that fact. */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the required memory to hold all the tuple lists */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG0 (("UMF_build_tuples_usage\n")) ;
+
+ usage = 0 ;
+ dusage = 0 ;
+
+ ASSERT (Col_tlen && Col_degree) ;
+
+ for (col = n1 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ usage += 1 + UNITS (Tuple, TUPLES (Col_tlen [col])) ;
+ dusage += 1 + DUNITS (Tuple, TUPLES (Col_tlen [col])) ;
+ DEBUG0 ((" col: "ID" tlen "ID" usage so far: "ID"\n",
+ col, Col_tlen [col], usage)) ;
+ }
+ }
+
+ ASSERT (Row_tlen && Row_degree) ;
+
+ for (row = n1 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ usage += 1 + UNITS (Tuple, TUPLES (Row_tlen [row])) ;
+ dusage += 1 + DUNITS (Tuple, TUPLES (Row_tlen [row])) ;
+ DEBUG0 ((" row: "ID" tlen "ID" usage so far: "ID"\n",
+ row, Row_tlen [row], usage)) ;
+ }
+ }
+
+ DEBUG0 (("UMF_build_tuples_usage "ID" %g\n", usage, dusage)) ;
+
+ *p_dusage = dusage ;
+ return (usage) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_tuple_lengths.h b/src/C/SuiteSparse/UMFPACK/Source/umf_tuple_lengths.h
new file mode 100644
index 0000000..e859092
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_tuple_lengths.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_tuple_lengths
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ double *dusage
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_usolve.c b/src/C/SuiteSparse/UMFPACK/Source/umf_usolve.c
new file mode 100644
index 0000000..043ebc4
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_usolve.c
@@ -0,0 +1,226 @@
+/* ========================================================================== */
+/* === UMF_usolve =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* solves Ux = b, where U is the upper triangular factor of a matrix. */
+/* B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+
+GLOBAL double UMF_usolve
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry xk ;
+ Entry *xp, *D, *Uval ;
+ Int k, deg, j, *ip, col, *Upos, *Uilen, pos,
+ *Uip, n, ulen, up, newUchain, npiv, n1, *Ui ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ n = Numeric->n_row ;
+ npiv = Numeric->npiv ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Usolve start: npiv = "ID" n = "ID"\n", npiv, n)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Usolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* singular case */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* handle the singular part of D, up to just before the last pivot */
+ for (k = n-1 ; k >= npiv ; k--)
+ {
+ /* This is an *** intentional *** divide-by-zero, to get Inf or Nan,
+ * as appropriate. It is not a bug. */
+ ASSERT (IS_ZERO (D [k])) ;
+ xk = X [k] ;
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+ }
+#else
+ /* Do not divide by zero */
+#endif
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* :: make last pivot row of U (singular matrices only) :: */
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG1 (("Last row of U: j="ID"\n", j)) ;
+ DEBUG1 (("Last row of U: Upattern[j]="ID"\n",
+ Numeric->Upattern [j]) );
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* nonsingletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* use row k of U */
+ /* ------------------------------------------------------------------ */
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+
+ xk = X [k] ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+ /* xk -= X [Pattern [j]] * (*xp) ; */
+ MULT_SUB (xk, X [Pattern [j]], *xp) ;
+ xp++ ;
+ }
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero */
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k == n1) break ;
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ deg = ulen ;
+ ASSERT (IMPLIES (k == 0, deg == 0)) ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+ else
+ {
+ deg -= ulen ;
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ;
+ ASSERT (deg >= 0) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at pos "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ deg = Uilen [k] ;
+ xk = X [k] ;
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ if (deg > 0)
+ {
+ up = Uip [k] ;
+ Ui = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ;
+ EDEBUG4 (Uval [j]) ;
+ DEBUG4 (("\n")) ;
+ /* xk -= X [Ui [j]] * Uval [j] ; */
+ ASSERT (Ui [j] >= 0 && Ui [j] < n) ;
+ MULT_SUB (xk, X [Ui [j]], Uval [j]) ;
+ }
+ }
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero */
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+ }
+#endif
+
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Usolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Usolve done.\n")) ;
+#endif
+
+ return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz));
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_usolve.h b/src/C/SuiteSparse/UMFPACK/Source/umf_usolve.h
new file mode 100644
index 0000000..5055278
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_usolve.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_usolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.c b/src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.c
new file mode 100644
index 0000000..fb3f4a8
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.c
@@ -0,0 +1,331 @@
+/* ========================================================================== */
+/* === UMF_utsolve ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* solves U'x = b or U.'x=b, where U is the upper triangular factor of a */
+/* matrix. B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+
+GLOBAL double
+#ifdef CONJUGATE_SOLVE
+UMF_uhsolve /* solve U'x=b (complex conjugate transpose) */
+#else
+UMF_utsolve /* solve U.'x=b (array transpose) */
+#endif
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry xk ;
+ Entry *xp, *D, *Uval ;
+ Int k, deg, j, *ip, col, *Upos, *Uilen, kstart, kend, up,
+ *Uip, n, uhead, ulen, pos, npiv, n1, *Ui ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ n = Numeric->n_row ;
+ npiv = Numeric->npiv ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+ kend = 0 ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Utsolve start: npiv "ID" n "ID"\n", npiv, n)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Utsolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero. */
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+ }
+#endif
+
+ X [k] = xk ;
+ deg = Uilen [k] ;
+ if (deg > 0 && IS_NONZERO (xk))
+ {
+ up = Uip [k] ;
+ Ui = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ;
+ EDEBUG4 (Uval [j]) ;
+ DEBUG4 (("\n")) ;
+#ifdef CONJUGATE_SOLVE
+ /* X [Ui [j]] -= xk * conjugate (Uval [j]) ; */
+ MULT_SUB_CONJ (X [Ui [j]], xk, Uval [j]) ;
+#else
+ /* X [Ui [j]] -= xk * Uval [j] ; */
+ MULT_SUB (X [Ui [j]], xk, Uval [j]) ;
+#endif
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* nonsingletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (kstart = n1 ; kstart < npiv ; kstart = kend + 1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* find the end of this Uchain */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG4 (("kstart "ID" kend "ID"\n", kstart, kend)) ;
+ /* for (kend = kstart ; kend < npiv && Uip [kend+1] > 0 ; kend++) ; */
+ kend = kstart ;
+ while (kend < npiv && Uip [kend+1] > 0)
+ {
+ kend++ ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* scan the whole Uchain to find the pattern of the first row of U */
+ /* ------------------------------------------------------------------ */
+
+ k = kend+1 ;
+ DEBUG4 (("\nKend "ID" K "ID"\n", kend, k)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* start with last row in Uchain of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k == npiv)
+ {
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* :: make last pivot row of U (singular matrices only) :: */
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+ }
+ else
+ {
+ ASSERT (k >= 0 && k < npiv) ;
+ up = -Uip [k] ;
+ ASSERT (up > 0) ;
+ deg = Uilen [k] ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+
+ /* empty the stack at the bottom of Pattern */
+ uhead = n ;
+
+ for (k = kend ; k > kstart ; k--)
+ {
+ /* Pattern [0..deg-1] is the pattern of row k of U */
+
+ /* -------------------------------------------------------------- */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (k >= 0 && k < npiv) ;
+ ulen = Uilen [k] ;
+ /* delete, and push on the stack */
+ for (j = 0 ; j < ulen ; j++)
+ {
+ ASSERT (uhead >= deg) ;
+ Pattern [--uhead] = Pattern [--deg] ;
+ }
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ;
+ ASSERT (deg >= 0) ;
+
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+
+ /* Pattern [0..deg-1] is now the pattern of the first row in Uchain */
+
+ /* ------------------------------------------------------------------ */
+ /* solve using this Uchain, in reverse order */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG4 (("Unwinding Uchain\n")) ;
+ for (k = kstart ; k <= kend ; k++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* construct row k */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (k >= 0 && k < npiv) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* remove the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (k > kstart) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ if (k > kstart)
+ {
+ /* concatenate the deleted pattern; pop from the stack */
+ for (j = 0 ; j < ulen ; j++)
+ {
+ ASSERT (deg <= uhead && uhead < n) ;
+ Pattern [deg++] = Pattern [uhead++] ;
+ }
+ DEBUG4 (("middle of chain, row of U "ID" deg "ID"\n", k, deg)) ;
+ ASSERT (deg >= 0) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* use row k of U */
+ /* -------------------------------------------------------------- */
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero. */
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+ }
+#endif
+
+ X [k] = xk ;
+ if (IS_NONZERO (xk))
+ {
+ if (k == kstart)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+#ifdef CONJUGATE_SOLVE
+ /* X [Pattern [j]] -= xk * conjugate (*xp) ; */
+ MULT_SUB_CONJ (X [Pattern [j]], xk, *xp) ;
+#else
+ /* X [Pattern [j]] -= xk * (*xp) ; */
+ MULT_SUB (X [Pattern [j]], xk, *xp) ;
+#endif
+ xp++ ;
+ }
+ }
+ }
+ ASSERT (uhead == n) ;
+ }
+
+#ifndef NO_DIVIDE_BY_ZERO
+ for (k = npiv ; k < n ; k++)
+ {
+ /* This is an *** intentional *** divide-by-zero, to get Inf or Nan,
+ * as appropriate. It is not a bug. */
+ ASSERT (IS_ZERO (D [k])) ;
+ /* For conjugate solve, D [k] == conjugate (D [k]), in this case */
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+ X [k] = xk ;
+ }
+#endif
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Utsolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Utsolve done.\n")) ;
+#endif
+
+ return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz));
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.h b/src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.h
new file mode 100644
index 0000000..59c0685
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_utsolve.h
@@ -0,0 +1,20 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_utsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
+
+
+GLOBAL double UMF_uhsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_valid_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_numeric.c
new file mode 100644
index 0000000..e43ebab
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_numeric.c
@@ -0,0 +1,46 @@
+/* ========================================================================== */
+/* === UMF_valid_numeric ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Returns TRUE if the Numeric object is valid, FALSE otherwise. */
+/* Does not check everything. UMFPACK_report_numeric checks more. */
+
+#include "umf_internal.h"
+
+GLOBAL Int UMF_valid_numeric
+(
+ NumericType *Numeric
+)
+{
+ /* This routine does not check the contents of the individual arrays, so */
+ /* it can miss some errors. All it checks for is the presence of the */
+ /* arrays, and the Numeric "valid" entry. */
+
+ if (!Numeric)
+ {
+ return (FALSE) ;
+ }
+
+ if (Numeric->valid != NUMERIC_VALID)
+ {
+ /* Numeric does not point to a NumericType object */
+ return (FALSE) ;
+ }
+
+ if (Numeric->n_row <= 0 || Numeric->n_col <= 0 || !Numeric->D ||
+ !Numeric->Rperm || !Numeric->Cperm ||
+ !Numeric->Lpos || !Numeric->Upos ||
+ !Numeric->Lilen || !Numeric->Uilen || !Numeric->Lip || !Numeric->Uip ||
+ !Numeric->Memory || (Numeric->ulen > 0 && !Numeric->Upattern))
+ {
+ return (FALSE) ;
+ }
+
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_valid_numeric.h b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_numeric.h
new file mode 100644
index 0000000..6d99218
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_numeric.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_valid_numeric
+(
+ NumericType *Numeric
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c
new file mode 100644
index 0000000..396d548
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c
@@ -0,0 +1,47 @@
+/* ========================================================================== */
+/* === UMF_valid_symbolic =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+
+/* Returns TRUE if the Symbolic object is valid, FALSE otherwise. */
+/* The UMFPACK_report_symbolic routine does a more thorough check. */
+
+GLOBAL Int UMF_valid_symbolic
+(
+ SymbolicType *Symbolic
+)
+{
+ /* This routine does not check the contents of the individual arrays, so */
+ /* it can miss some errors. All it checks for is the presence of the */
+ /* arrays, and the Symbolic "valid" entry. */
+
+ if (!Symbolic)
+ {
+ return (FALSE) ;
+ }
+
+ if (Symbolic->valid != SYMBOLIC_VALID)
+ {
+ /* Symbolic does not point to a SymbolicType object */
+ return (FALSE) ;
+ }
+
+ if (!Symbolic->Cperm_init || !Symbolic->Rperm_init ||
+ !Symbolic->Front_npivcol || !Symbolic->Front_1strow ||
+ !Symbolic->Front_leftmostdesc ||
+ !Symbolic->Front_parent || !Symbolic->Chain_start ||
+ !Symbolic->Chain_maxrows || !Symbolic->Chain_maxcols ||
+ Symbolic->n_row <= 0 || Symbolic->n_col <= 0)
+ {
+ return (FALSE) ;
+ }
+
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_valid_symbolic.h b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_symbolic.h
new file mode 100644
index 0000000..906f70c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_valid_symbolic.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_valid_symbolic
+(
+ SymbolicType *Symbolic
+) ;
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umf_version.h b/src/C/SuiteSparse/UMFPACK/Source/umf_version.h
new file mode 100644
index 0000000..d5fe456
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umf_version.h
@@ -0,0 +1,874 @@
+/* ========================================================================== */
+/* === umf_version.h ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Define routine names, depending on version being compiled.
+
+ DINT: double precision, int's as integers
+ DLONG: double precision, UF_long's as integers
+ ZLONG: complex double precision, UF_long's as integers
+ ZINT: complex double precision, int's as integers
+*/
+
+/* Set DINT as the default, if nothing is defined */
+#if !defined (DLONG) && !defined (DINT) && !defined (ZLONG) && !defined (ZINT)
+#define DINT
+#endif
+
+/* Determine if this is a real or complex version */
+#if defined (ZLONG) || defined (ZINT)
+#define COMPLEX
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* integer type (Int is int or UF_long) now defined in amd_internal.h */
+/* -------------------------------------------------------------------------- */
+
+#if defined (DLONG) || defined (ZLONG)
+#define LONG_INTEGER
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Numerical relop macros for correctly handling the NaN case */
+/* -------------------------------------------------------------------------- */
+
+/*
+SCALAR_IS_NAN(x):
+ True if x is NaN. False otherwise. The commonly-existing isnan(x)
+ function could be used, but it's not in Kernighan & Ritchie 2nd edition
+ (ANSI C). It may appear in <math.h>, but I'm not certain about
+ portability. The expression x != x is true if and only if x is NaN,
+ according to the IEEE 754 floating-point standard.
+
+SCALAR_IS_ZERO(x):
+ True if x is zero. False if x is nonzero, NaN, or +/- Inf.
+ This is (x == 0) if the compiler is IEEE 754 compliant.
+
+SCALAR_IS_NONZERO(x):
+ True if x is nonzero, NaN, or +/- Inf. False if x zero.
+ This is (x != 0) if the compiler is IEEE 754 compliant.
+
+SCALAR_IS_LTZERO(x):
+ True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf.
+ This is (x < 0) if the compiler is IEEE 754 compliant.
+*/
+
+#if defined (UMF_WINDOWS) && !defined (MATHWORKS)
+
+/* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */
+/* violates the IEEE 754 floating-point standard in a bizarre way. */
+/* If you're using an IEEE 754-compliant compiler, then x != x is true */
+/* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */
+/* So either way, this macro safely detects a NaN. */
+#define SCALAR_IS_NAN(x) (((x) != (x)) || (((x) < (x))))
+#define SCALAR_IS_ZERO(x) (((x) == 0.) && !SCALAR_IS_NAN(x))
+#define SCALAR_IS_NONZERO(x) (((x) != 0.) || SCALAR_IS_NAN(x))
+#define SCALAR_IS_LTZERO(x) (((x) < 0.) && !SCALAR_IS_NAN(x))
+
+#else
+
+/* These all work properly, according to the IEEE 754 standard ... except on */
+/* a PC with windows. Works fine in Linux on the same PC... */
+#define SCALAR_IS_NAN(x) ((x) != (x))
+#define SCALAR_IS_ZERO(x) ((x) == 0.)
+#define SCALAR_IS_NONZERO(x) ((x) != 0.)
+#define SCALAR_IS_LTZERO(x) ((x) < 0.)
+
+#endif
+
+/* scalar absolute value macro. If x is NaN, the result is NaN: */
+#define SCALAR_ABS(x) ((SCALAR_IS_LTZERO (x)) ? -(x) : (x))
+
+/* true if an integer (stored in double x) would overflow (or if x is NaN) */
+#define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \
+ || SCALAR_IS_NAN (x))
+
+/* print a scalar (avoid printing "-0" for negative zero). */
+#define PRINT_SCALAR(a) \
+{ \
+ if (SCALAR_IS_NONZERO (a)) \
+ { \
+ PRINTF ((" (%g)", (a))) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" (0)")) ; \
+ } \
+}
+
+/* -------------------------------------------------------------------------- */
+/* Real floating-point arithmetic */
+/* -------------------------------------------------------------------------- */
+
+#ifndef COMPLEX
+
+#define Entry double
+
+#define SPLIT(s) (1)
+#define REAL_COMPONENT(c) (c)
+#define IMAG_COMPONENT(c) (0.)
+#define ASSIGN(c,s1,s2,p,split) { (c) = (s1)[p] ; }
+#define CLEAR(c) { (c) = 0. ; }
+#define CLEAR_AND_INCREMENT(p) { *p++ = 0. ; }
+#define IS_NAN(a) SCALAR_IS_NAN (a)
+#define IS_ZERO(a) SCALAR_IS_ZERO (a)
+#define IS_NONZERO(a) SCALAR_IS_NONZERO (a)
+#define SCALE_DIV(c,s) { (c) /= (s) ; }
+#define SCALE(c,s) { (c) *= (s) ; }
+#define ASSEMBLE(c,a) { (c) += (a) ; }
+#define ASSEMBLE_AND_INCREMENT(c,p) { (c) += *p++ ; }
+#define DECREMENT(c,a) { (c) -= (a) ; }
+#define MULT(c,a,b) { (c) = (a) * (b) ; }
+#define MULT_CONJ(c,a,b) { (c) = (a) * (b) ; }
+#define MULT_SUB(c,a,b) { (c) -= (a) * (b) ; }
+#define MULT_SUB_CONJ(c,a,b) { (c) -= (a) * (b) ; }
+#define DIV(c,a,b) { (c) = (a) / (b) ; }
+#define DIV_CONJ(c,a,b) { (c) = (a) / (b) ; }
+#define APPROX_ABS(s,a) { (s) = SCALAR_ABS (a) ; }
+#define ABS(s,a) { (s) = SCALAR_ABS (a) ; }
+#define PRINT_ENTRY(a) PRINT_SCALAR (a)
+
+/* for flop counts */
+#define MULTSUB_FLOPS 2. /* c -= a*b */
+#define DIV_FLOPS 1. /* c = a/b */
+#define ABS_FLOPS 0. /* c = abs (a) */
+#define ASSEMBLE_FLOPS 1. /* c += a */
+#define DECREMENT_FLOPS 1. /* c -= a */
+#define MULT_FLOPS 1. /* c = a*b */
+#define SCALE_FLOPS 1. /* c = a/s */
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* Complex floating-point arithmetic */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Note: An alternative to this DoubleComplex type would be to use a
+ struct { double r ; double i ; }. The problem with that method
+ (used by the Sun Performance Library, for example) is that ANSI C provides
+ no guarantee about the layout of a struct. It is possible that the sizeof
+ the struct above would be greater than 2 * sizeof (double). This would
+ mean that the complex BLAS could not be used. The method used here avoids
+ that possibility. ANSI C *does* guarantee that an array of structs has
+ the same size as n times the size of one struct.
+
+ The ANSI C99 version of the C language includes a "double _Complex" type.
+ It should be possible in that case to do the following:
+
+ #define Entry double _Complex
+
+ and remove the DoubleComplex struct. The macros, below, could then be
+ replaced with instrinsic operators. Note that the #define Real and
+ #define Imag should also be removed (they only appear in this file).
+
+ For the MULT, MULT_SUB, MULT_SUB_CONJ, and MULT_CONJ macros,
+ the output argument c cannot be the same as any input argument.
+
+*/
+
+typedef struct
+{
+ double component [2] ; /* real and imaginary parts */
+
+} DoubleComplex ;
+
+#define Entry DoubleComplex
+#define Real component [0]
+#define Imag component [1]
+
+/* for flop counts */
+#define MULTSUB_FLOPS 8. /* c -= a*b */
+#define DIV_FLOPS 9. /* c = a/b */
+#define ABS_FLOPS 6. /* c = abs (a), count sqrt as one flop */
+#define ASSEMBLE_FLOPS 2. /* c += a */
+#define DECREMENT_FLOPS 2. /* c -= a */
+#define MULT_FLOPS 6. /* c = a*b */
+#define SCALE_FLOPS 2. /* c = a/s or c = a*s */
+
+/* -------------------------------------------------------------------------- */
+
+/* real part of c */
+#define REAL_COMPONENT(c) ((c).Real)
+
+/* -------------------------------------------------------------------------- */
+
+/* imag part of c */
+#define IMAG_COMPONENT(c) ((c).Imag)
+
+/* -------------------------------------------------------------------------- */
+
+/* Return TRUE if a complex number is in split form, FALSE if in packed form */
+#define SPLIT(sz) ((sz) != (double *) NULL)
+
+/* -------------------------------------------------------------------------- */
+
+/* c = (s1) + (s2)*i, if s2 is null, then X is in "packed" format (compatible
+ * with Entry and ANSI C99 double _Complex type). */
+#define ASSIGN(c,s1,s2,p,split) \
+{ \
+ if (split) \
+ { \
+ (c).Real = (s1)[p] ; \
+ (c).Imag = (s2)[p] ; \
+ } \
+ else \
+ { \
+ (c) = ((Entry *)(s1))[p] ; \
+ } \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = 0 */
+#define CLEAR(c) \
+{ \
+ (c).Real = 0. ; \
+ (c).Imag = 0. ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* *p++ = 0 */
+#define CLEAR_AND_INCREMENT(p) \
+{ \
+ p->Real = 0. ; \
+ p->Imag = 0. ; \
+ p++ ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a == 0 */
+#define IS_ZERO(a) \
+ (SCALAR_IS_ZERO ((a).Real) && SCALAR_IS_ZERO ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a is NaN */
+#define IS_NAN(a) \
+ (SCALAR_IS_NAN ((a).Real) || SCALAR_IS_NAN ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a != 0 */
+#define IS_NONZERO(a) \
+ (SCALAR_IS_NONZERO ((a).Real) || SCALAR_IS_NONZERO ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* c /= s */
+#define SCALE_DIV(c,s) \
+{ \
+ (c).Real /= (s) ; \
+ (c).Imag /= (s) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c *= s */
+#define SCALE(c,s) \
+{ \
+ (c).Real *= (s) ; \
+ (c).Imag *= (s) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c += a */
+#define ASSEMBLE(c,a) \
+{ \
+ (c).Real += (a).Real ; \
+ (c).Imag += (a).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c += *p++ */
+#define ASSEMBLE_AND_INCREMENT(c,p) \
+{ \
+ (c).Real += p->Real ; \
+ (c).Imag += p->Imag ; \
+ p++ ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a */
+#define DECREMENT(c,a) \
+{ \
+ (c).Real -= (a).Real ; \
+ (c).Imag -= (a).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a*b, assert because c cannot be the same as a or b */
+#define MULT(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real = (a).Real * (b).Real - (a).Imag * (b).Imag ; \
+ (c).Imag = (a).Imag * (b).Real + (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a*conjugate(b), assert because c cannot be the same as a or b */
+#define MULT_CONJ(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real = (a).Real * (b).Real + (a).Imag * (b).Imag ; \
+ (c).Imag = (a).Imag * (b).Real - (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a*b, assert because c cannot be the same as a or b */
+#define MULT_SUB(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real -= (a).Real * (b).Real - (a).Imag * (b).Imag ; \
+ (c).Imag -= (a).Imag * (b).Real + (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a*conjugate(b), assert because c cannot be the same as a or b */
+#define MULT_SUB_CONJ(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real -= (a).Real * (b).Real + (a).Imag * (b).Imag ; \
+ (c).Imag -= (a).Imag * (b).Real - (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a/b, using function pointer */
+#define DIV(c,a,b) \
+{ \
+ (void) umfpack_divcomplex ((a).Real, (a).Imag, (b).Real, (b).Imag, \
+ &((c).Real), &((c).Imag)) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a/conjugate(b), using function pointer */
+#define DIV_CONJ(c,a,b) \
+{ \
+ (void) umfpack_divcomplex ((a).Real, (a).Imag, (b).Real, (-(b).Imag), \
+ &((c).Real), &((c).Imag)) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* approximate absolute value, s = |r|+|i| */
+#define APPROX_ABS(s,a) \
+{ \
+ (s) = SCALAR_ABS ((a).Real) + SCALAR_ABS ((a).Imag) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* exact absolute value, s = sqrt (a.real^2 + a.imag^2) */
+#define ABS(s,a) \
+{ \
+ (s) = umfpack_hypot ((a).Real, (a).Imag) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* print an entry (avoid printing "-0" for negative zero). */
+#define PRINT_ENTRY(a) \
+{ \
+ if (SCALAR_IS_NONZERO ((a).Real)) \
+ { \
+ PRINTF ((" (%g", (a).Real)) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" (0")) ; \
+ } \
+ if (SCALAR_IS_LTZERO ((a).Imag)) \
+ { \
+ PRINTF ((" - %gi)", -(a).Imag)) ; \
+ } \
+ else if (SCALAR_IS_ZERO ((a).Imag)) \
+ { \
+ PRINTF ((" + 0i)")) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" + %gi)", (a).Imag)) ; \
+ } \
+}
+
+/* -------------------------------------------------------------------------- */
+
+#endif /* #ifndef COMPLEX */
+
+/* -------------------------------------------------------------------------- */
+/* Double precision, with int's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DINT
+
+#define UMF_analyze umf_i_analyze
+#define UMF_apply_order umf_i_apply_order
+#define UMF_assemble umfdi_assemble
+#define UMF_assemble_fixq umfdi_assemble_fixq
+#define UMF_blas3_update umfdi_blas3_update
+#define UMF_build_tuples umfdi_build_tuples
+#define UMF_build_tuples_usage umfdi_build_tuples_usage
+#define UMF_colamd umf_i_colamd
+#define UMF_colamd_set_defaults umf_i_colamd_set_defaults
+#define UMF_create_element umfdi_create_element
+#define UMF_extend_front umfdi_extend_front
+#define UMF_free umf_i_free
+#define UMF_fsize umf_i_fsize
+#define UMF_garbage_collection umfdi_garbage_collection
+#define UMF_get_memory umfdi_get_memory
+#define UMF_grow_front umfdi_grow_front
+#define UMF_init_front umfdi_init_front
+#define UMF_is_permutation umf_i_is_permutation
+#define UMF_kernel umfdi_kernel
+#define UMF_kernel_init umfdi_kernel_init
+#define UMF_kernel_init_usage umfdi_kernel_init_usage
+#define UMF_kernel_wrapup umfdi_kernel_wrapup
+#define UMF_local_search umfdi_local_search
+#define UMF_lsolve umfdi_lsolve
+#define UMF_ltsolve umfdi_ltsolve
+#define UMF_lhsolve umfdi_lhsolve
+#define UMF_malloc umf_i_malloc
+#define UMF_mem_alloc_element umfdi_mem_alloc_element
+#define UMF_mem_alloc_head_block umfdi_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfdi_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfdi_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfdi_mem_init_memoryspace
+#define UMF_realloc umf_i_realloc
+#define UMF_report_perm umf_i_report_perm
+#define UMF_report_vector umfdi_report_vector
+#define UMF_row_search umfdi_row_search
+#define UMF_scale umfdi_scale
+#define UMF_scale_column umfdi_scale_column
+#define UMF_set_stats umf_i_set_stats
+#define UMF_singletons umf_i_singletons
+#define UMF_solve umfdi_solve
+#define UMF_start_front umfdi_start_front
+#define UMF_store_lu umfdi_store_lu
+#define UMF_store_lu_drop umfdi_store_lu_drop
+#define UMF_symbolic_usage umfdi_symbolic_usage
+#define UMF_transpose umfdi_transpose
+#define UMF_tuple_lengths umfdi_tuple_lengths
+#define UMF_usolve umfdi_usolve
+#define UMF_utsolve umfdi_utsolve
+#define UMF_uhsolve umfdi_uhsolve
+#define UMF_valid_numeric umfdi_valid_numeric
+#define UMF_valid_symbolic umfdi_valid_symbolic
+#define UMF_triplet_map_x umfdi_triplet_map_x
+#define UMF_triplet_map_nox umfdi_triplet_map_nox
+#define UMF_triplet_nomap_x umfdi_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfdi_triplet_nomap_nox
+#define UMF_2by2 umfdi_2by2
+
+#define UMFPACK_col_to_triplet umfpack_di_col_to_triplet
+#define UMFPACK_defaults umfpack_di_defaults
+#define UMFPACK_free_numeric umfpack_di_free_numeric
+#define UMFPACK_free_symbolic umfpack_di_free_symbolic
+#define UMFPACK_get_lunz umfpack_di_get_lunz
+#define UMFPACK_get_numeric umfpack_di_get_numeric
+#define UMFPACK_get_symbolic umfpack_di_get_symbolic
+#define UMFPACK_get_determinant umfpack_di_get_determinant
+#define UMFPACK_numeric umfpack_di_numeric
+#define UMFPACK_qsymbolic umfpack_di_qsymbolic
+#define UMFPACK_report_control umfpack_di_report_control
+#define UMFPACK_report_info umfpack_di_report_info
+#define UMFPACK_report_matrix umfpack_di_report_matrix
+#define UMFPACK_report_numeric umfpack_di_report_numeric
+#define UMFPACK_report_perm umfpack_di_report_perm
+#define UMFPACK_report_status umfpack_di_report_status
+#define UMFPACK_report_symbolic umfpack_di_report_symbolic
+#define UMFPACK_report_triplet umfpack_di_report_triplet
+#define UMFPACK_report_vector umfpack_di_report_vector
+#define UMFPACK_save_numeric umfpack_di_save_numeric
+#define UMFPACK_save_symbolic umfpack_di_save_symbolic
+#define UMFPACK_load_numeric umfpack_di_load_numeric
+#define UMFPACK_load_symbolic umfpack_di_load_symbolic
+#define UMFPACK_scale umfpack_di_scale
+#define UMFPACK_solve umfpack_di_solve
+#define UMFPACK_symbolic umfpack_di_symbolic
+#define UMFPACK_transpose umfpack_di_transpose
+#define UMFPACK_triplet_to_col umfpack_di_triplet_to_col
+#define UMFPACK_wsolve umfpack_di_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_i_malloc_count
+#define UMF_debug umfdi_debug
+#define UMF_allocfail umfdi_allocfail
+#define UMF_gprob umfdi_gprob
+#define UMF_dump_dense umfdi_dump_dense
+#define UMF_dump_element umfdi_dump_element
+#define UMF_dump_rowcol umfdi_dump_rowcol
+#define UMF_dump_matrix umfdi_dump_matrix
+#define UMF_dump_current_front umfdi_dump_current_front
+#define UMF_dump_lu umfdi_dump_lu
+#define UMF_dump_memory umfdi_dump_memory
+#define UMF_dump_packed_memory umfdi_dump_packed_memory
+#define UMF_dump_col_matrix umfdi_dump_col_matrix
+#define UMF_dump_chain umfdi_dump_chain
+#define UMF_dump_start umfdi_dump_start
+#define UMF_dump_rowmerge umfdi_dump_rowmerge
+#define UMF_dump_diagonal_map umfdi_dump_diagonal_map
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Double precision, with UF_long's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DLONG
+
+#define UMF_analyze umf_l_analyze
+#define UMF_apply_order umf_l_apply_order
+#define UMF_assemble umfdl_assemble
+#define UMF_assemble_fixq umfdl_assemble_fixq
+#define UMF_blas3_update umfdl_blas3_update
+#define UMF_build_tuples umfdl_build_tuples
+#define UMF_build_tuples_usage umfdl_build_tuples_usage
+#define UMF_colamd umf_l_colamd
+#define UMF_colamd_set_defaults umf_l_colamd_set_defaults
+#define UMF_create_element umfdl_create_element
+#define UMF_extend_front umfdl_extend_front
+#define UMF_free umf_l_free
+#define UMF_fsize umf_l_fsize
+#define UMF_garbage_collection umfdl_garbage_collection
+#define UMF_get_memory umfdl_get_memory
+#define UMF_grow_front umfdl_grow_front
+#define UMF_init_front umfdl_init_front
+#define UMF_is_permutation umf_l_is_permutation
+#define UMF_kernel umfdl_kernel
+#define UMF_kernel_init umfdl_kernel_init
+#define UMF_kernel_init_usage umfdl_kernel_init_usage
+#define UMF_kernel_wrapup umfdl_kernel_wrapup
+#define UMF_local_search umfdl_local_search
+#define UMF_lsolve umfdl_lsolve
+#define UMF_ltsolve umfdl_ltsolve
+#define UMF_lhsolve umfdl_lhsolve
+#define UMF_malloc umf_l_malloc
+#define UMF_mem_alloc_element umfdl_mem_alloc_element
+#define UMF_mem_alloc_head_block umfdl_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfdl_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfdl_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfdl_mem_init_memoryspace
+#define UMF_realloc umf_l_realloc
+#define UMF_report_perm umf_l_report_perm
+#define UMF_report_vector umfdl_report_vector
+#define UMF_row_search umfdl_row_search
+#define UMF_scale umfdl_scale
+#define UMF_scale_column umfdl_scale_column
+#define UMF_set_stats umf_l_set_stats
+#define UMF_singletons umf_l_singletons
+#define UMF_solve umfdl_solve
+#define UMF_start_front umfdl_start_front
+#define UMF_store_lu umfdl_store_lu
+#define UMF_store_lu_drop umfdl_store_lu_drop
+#define UMF_symbolic_usage umfdl_symbolic_usage
+#define UMF_transpose umfdl_transpose
+#define UMF_tuple_lengths umfdl_tuple_lengths
+#define UMF_usolve umfdl_usolve
+#define UMF_utsolve umfdl_utsolve
+#define UMF_uhsolve umfdl_uhsolve
+#define UMF_valid_numeric umfdl_valid_numeric
+#define UMF_valid_symbolic umfdl_valid_symbolic
+#define UMF_triplet_map_x umfdl_triplet_map_x
+#define UMF_triplet_map_nox umfdl_triplet_map_nox
+#define UMF_triplet_nomap_x umfdl_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfdl_triplet_nomap_nox
+#define UMF_2by2 umfdl_2by2
+
+#define UMFPACK_col_to_triplet umfpack_dl_col_to_triplet
+#define UMFPACK_defaults umfpack_dl_defaults
+#define UMFPACK_free_numeric umfpack_dl_free_numeric
+#define UMFPACK_free_symbolic umfpack_dl_free_symbolic
+#define UMFPACK_get_lunz umfpack_dl_get_lunz
+#define UMFPACK_get_numeric umfpack_dl_get_numeric
+#define UMFPACK_get_symbolic umfpack_dl_get_symbolic
+#define UMFPACK_get_determinant umfpack_dl_get_determinant
+#define UMFPACK_numeric umfpack_dl_numeric
+#define UMFPACK_qsymbolic umfpack_dl_qsymbolic
+#define UMFPACK_report_control umfpack_dl_report_control
+#define UMFPACK_report_info umfpack_dl_report_info
+#define UMFPACK_report_matrix umfpack_dl_report_matrix
+#define UMFPACK_report_numeric umfpack_dl_report_numeric
+#define UMFPACK_report_perm umfpack_dl_report_perm
+#define UMFPACK_report_status umfpack_dl_report_status
+#define UMFPACK_report_symbolic umfpack_dl_report_symbolic
+#define UMFPACK_report_triplet umfpack_dl_report_triplet
+#define UMFPACK_report_vector umfpack_dl_report_vector
+#define UMFPACK_save_numeric umfpack_dl_save_numeric
+#define UMFPACK_save_symbolic umfpack_dl_save_symbolic
+#define UMFPACK_load_numeric umfpack_dl_load_numeric
+#define UMFPACK_load_symbolic umfpack_dl_load_symbolic
+#define UMFPACK_scale umfpack_dl_scale
+#define UMFPACK_solve umfpack_dl_solve
+#define UMFPACK_symbolic umfpack_dl_symbolic
+#define UMFPACK_transpose umfpack_dl_transpose
+#define UMFPACK_triplet_to_col umfpack_dl_triplet_to_col
+#define UMFPACK_wsolve umfpack_dl_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_l_malloc_count
+#define UMF_debug umfdl_debug
+#define UMF_allocfail umfdl_allocfail
+#define UMF_gprob umfdl_gprob
+#define UMF_dump_dense umfdl_dump_dense
+#define UMF_dump_element umfdl_dump_element
+#define UMF_dump_rowcol umfdl_dump_rowcol
+#define UMF_dump_matrix umfdl_dump_matrix
+#define UMF_dump_current_front umfdl_dump_current_front
+#define UMF_dump_lu umfdl_dump_lu
+#define UMF_dump_memory umfdl_dump_memory
+#define UMF_dump_packed_memory umfdl_dump_packed_memory
+#define UMF_dump_col_matrix umfdl_dump_col_matrix
+#define UMF_dump_chain umfdl_dump_chain
+#define UMF_dump_start umfdl_dump_start
+#define UMF_dump_rowmerge umfdl_dump_rowmerge
+#define UMF_dump_diagonal_map umfdl_dump_diagonal_map
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Complex double precision, with int's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef ZINT
+
+#define UMF_analyze umf_i_analyze
+#define UMF_apply_order umf_i_apply_order
+#define UMF_assemble umfzi_assemble
+#define UMF_assemble_fixq umfzi_assemble_fixq
+#define UMF_blas3_update umfzi_blas3_update
+#define UMF_build_tuples umfzi_build_tuples
+#define UMF_build_tuples_usage umfzi_build_tuples_usage
+#define UMF_colamd umf_i_colamd
+#define UMF_colamd_set_defaults umf_i_colamd_set_defaults
+#define UMF_create_element umfzi_create_element
+#define UMF_extend_front umfzi_extend_front
+#define UMF_free umf_i_free
+#define UMF_fsize umf_i_fsize
+#define UMF_garbage_collection umfzi_garbage_collection
+#define UMF_get_memory umfzi_get_memory
+#define UMF_grow_front umfzi_grow_front
+#define UMF_init_front umfzi_init_front
+#define UMF_is_permutation umf_i_is_permutation
+#define UMF_kernel umfzi_kernel
+#define UMF_kernel_init umfzi_kernel_init
+#define UMF_kernel_init_usage umfzi_kernel_init_usage
+#define UMF_kernel_wrapup umfzi_kernel_wrapup
+#define UMF_local_search umfzi_local_search
+#define UMF_lsolve umfzi_lsolve
+#define UMF_ltsolve umfzi_ltsolve
+#define UMF_lhsolve umfzi_lhsolve
+#define UMF_malloc umf_i_malloc
+#define UMF_mem_alloc_element umfzi_mem_alloc_element
+#define UMF_mem_alloc_head_block umfzi_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfzi_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfzi_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfzi_mem_init_memoryspace
+#define UMF_realloc umf_i_realloc
+#define UMF_report_perm umf_i_report_perm
+#define UMF_report_vector umfzi_report_vector
+#define UMF_row_search umfzi_row_search
+#define UMF_scale umfzi_scale
+#define UMF_scale_column umfzi_scale_column
+#define UMF_set_stats umfzi_set_stats
+#define UMF_singletons umf_i_singletons
+#define UMF_solve umfzi_solve
+#define UMF_start_front umfzi_start_front
+#define UMF_store_lu umfzi_store_lu
+#define UMF_store_lu_drop umfzi_store_lu_drop
+#define UMF_symbolic_usage umfzi_symbolic_usage
+#define UMF_transpose umfzi_transpose
+#define UMF_tuple_lengths umfzi_tuple_lengths
+#define UMF_usolve umfzi_usolve
+#define UMF_utsolve umfzi_utsolve
+#define UMF_uhsolve umfzi_uhsolve
+#define UMF_valid_numeric umfzi_valid_numeric
+#define UMF_valid_symbolic umfzi_valid_symbolic
+#define UMF_triplet_map_x umfzi_triplet_map_x
+#define UMF_triplet_map_nox umfzi_triplet_map_nox
+#define UMF_triplet_nomap_x umfzi_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfzi_triplet_nomap_nox
+#define UMF_2by2 umfzi_2by2
+
+#define UMFPACK_col_to_triplet umfpack_zi_col_to_triplet
+#define UMFPACK_defaults umfpack_zi_defaults
+#define UMFPACK_free_numeric umfpack_zi_free_numeric
+#define UMFPACK_free_symbolic umfpack_zi_free_symbolic
+#define UMFPACK_get_lunz umfpack_zi_get_lunz
+#define UMFPACK_get_numeric umfpack_zi_get_numeric
+#define UMFPACK_get_symbolic umfpack_zi_get_symbolic
+#define UMFPACK_get_determinant umfpack_zi_get_determinant
+#define UMFPACK_numeric umfpack_zi_numeric
+#define UMFPACK_qsymbolic umfpack_zi_qsymbolic
+#define UMFPACK_report_control umfpack_zi_report_control
+#define UMFPACK_report_info umfpack_zi_report_info
+#define UMFPACK_report_matrix umfpack_zi_report_matrix
+#define UMFPACK_report_numeric umfpack_zi_report_numeric
+#define UMFPACK_report_perm umfpack_zi_report_perm
+#define UMFPACK_report_status umfpack_zi_report_status
+#define UMFPACK_report_symbolic umfpack_zi_report_symbolic
+#define UMFPACK_report_triplet umfpack_zi_report_triplet
+#define UMFPACK_report_vector umfpack_zi_report_vector
+#define UMFPACK_save_numeric umfpack_zi_save_numeric
+#define UMFPACK_save_symbolic umfpack_zi_save_symbolic
+#define UMFPACK_load_numeric umfpack_zi_load_numeric
+#define UMFPACK_load_symbolic umfpack_zi_load_symbolic
+#define UMFPACK_scale umfpack_zi_scale
+#define UMFPACK_solve umfpack_zi_solve
+#define UMFPACK_symbolic umfpack_zi_symbolic
+#define UMFPACK_transpose umfpack_zi_transpose
+#define UMFPACK_triplet_to_col umfpack_zi_triplet_to_col
+#define UMFPACK_wsolve umfpack_zi_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_i_malloc_count
+#define UMF_debug umfzi_debug
+#define UMF_allocfail umfzi_allocfail
+#define UMF_gprob umfzi_gprob
+#define UMF_dump_dense umfzi_dump_dense
+#define UMF_dump_element umfzi_dump_element
+#define UMF_dump_rowcol umfzi_dump_rowcol
+#define UMF_dump_matrix umfzi_dump_matrix
+#define UMF_dump_current_front umfzi_dump_current_front
+#define UMF_dump_lu umfzi_dump_lu
+#define UMF_dump_memory umfzi_dump_memory
+#define UMF_dump_packed_memory umfzi_dump_packed_memory
+#define UMF_dump_col_matrix umfzi_dump_col_matrix
+#define UMF_dump_chain umfzi_dump_chain
+#define UMF_dump_start umfzi_dump_start
+#define UMF_dump_rowmerge umfzi_dump_rowmerge
+#define UMF_dump_diagonal_map umfzi_dump_diagonal_map
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Complex double precision, with UF_long's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef ZLONG
+
+#define UMF_analyze umf_l_analyze
+#define UMF_apply_order umf_l_apply_order
+#define UMF_assemble umfzl_assemble
+#define UMF_assemble_fixq umfzl_assemble_fixq
+#define UMF_blas3_update umfzl_blas3_update
+#define UMF_build_tuples umfzl_build_tuples
+#define UMF_build_tuples_usage umfzl_build_tuples_usage
+#define UMF_colamd umf_l_colamd
+#define UMF_colamd_set_defaults umf_l_colamd_set_defaults
+#define UMF_create_element umfzl_create_element
+#define UMF_extend_front umfzl_extend_front
+#define UMF_free umf_l_free
+#define UMF_fsize umf_l_fsize
+#define UMF_garbage_collection umfzl_garbage_collection
+#define UMF_get_memory umfzl_get_memory
+#define UMF_grow_front umfzl_grow_front
+#define UMF_init_front umfzl_init_front
+#define UMF_is_permutation umf_l_is_permutation
+#define UMF_kernel umfzl_kernel
+#define UMF_kernel_init umfzl_kernel_init
+#define UMF_kernel_init_usage umfzl_kernel_init_usage
+#define UMF_kernel_wrapup umfzl_kernel_wrapup
+#define UMF_local_search umfzl_local_search
+#define UMF_lsolve umfzl_lsolve
+#define UMF_ltsolve umfzl_ltsolve
+#define UMF_lhsolve umfzl_lhsolve
+#define UMF_malloc umf_l_malloc
+#define UMF_mem_alloc_element umfzl_mem_alloc_element
+#define UMF_mem_alloc_head_block umfzl_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfzl_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfzl_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfzl_mem_init_memoryspace
+#define UMF_realloc umf_l_realloc
+#define UMF_report_perm umf_l_report_perm
+#define UMF_report_vector umfzl_report_vector
+#define UMF_row_search umfzl_row_search
+#define UMF_scale umfzl_scale
+#define UMF_scale_column umfzl_scale_column
+#define UMF_set_stats umfzl_set_stats
+#define UMF_singletons umf_l_singletons
+#define UMF_solve umfzl_solve
+#define UMF_start_front umfzl_start_front
+#define UMF_store_lu umfzl_store_lu
+#define UMF_store_lu_drop umfzl_store_lu_drop
+#define UMF_symbolic_usage umfzl_symbolic_usage
+#define UMF_transpose umfzl_transpose
+#define UMF_tuple_lengths umfzl_tuple_lengths
+#define UMF_usolve umfzl_usolve
+#define UMF_utsolve umfzl_utsolve
+#define UMF_uhsolve umfzl_uhsolve
+#define UMF_valid_numeric umfzl_valid_numeric
+#define UMF_valid_symbolic umfzl_valid_symbolic
+#define UMF_triplet_map_x umfzl_triplet_map_x
+#define UMF_triplet_map_nox umfzl_triplet_map_nox
+#define UMF_triplet_nomap_x umfzl_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfzl_triplet_nomap_nox
+#define UMF_2by2 umfzl_2by2
+
+#define UMFPACK_col_to_triplet umfpack_zl_col_to_triplet
+#define UMFPACK_defaults umfpack_zl_defaults
+#define UMFPACK_free_numeric umfpack_zl_free_numeric
+#define UMFPACK_free_symbolic umfpack_zl_free_symbolic
+#define UMFPACK_get_lunz umfpack_zl_get_lunz
+#define UMFPACK_get_numeric umfpack_zl_get_numeric
+#define UMFPACK_get_symbolic umfpack_zl_get_symbolic
+#define UMFPACK_get_determinant umfpack_zl_get_determinant
+#define UMFPACK_numeric umfpack_zl_numeric
+#define UMFPACK_qsymbolic umfpack_zl_qsymbolic
+#define UMFPACK_report_control umfpack_zl_report_control
+#define UMFPACK_report_info umfpack_zl_report_info
+#define UMFPACK_report_matrix umfpack_zl_report_matrix
+#define UMFPACK_report_numeric umfpack_zl_report_numeric
+#define UMFPACK_report_perm umfpack_zl_report_perm
+#define UMFPACK_report_status umfpack_zl_report_status
+#define UMFPACK_report_symbolic umfpack_zl_report_symbolic
+#define UMFPACK_report_triplet umfpack_zl_report_triplet
+#define UMFPACK_report_vector umfpack_zl_report_vector
+#define UMFPACK_save_numeric umfpack_zl_save_numeric
+#define UMFPACK_save_symbolic umfpack_zl_save_symbolic
+#define UMFPACK_load_numeric umfpack_zl_load_numeric
+#define UMFPACK_load_symbolic umfpack_zl_load_symbolic
+#define UMFPACK_scale umfpack_zl_scale
+#define UMFPACK_solve umfpack_zl_solve
+#define UMFPACK_symbolic umfpack_zl_symbolic
+#define UMFPACK_transpose umfpack_zl_transpose
+#define UMFPACK_triplet_to_col umfpack_zl_triplet_to_col
+#define UMFPACK_wsolve umfpack_zl_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_l_malloc_count
+#define UMF_debug umfzl_debug
+#define UMF_allocfail umfzl_allocfail
+#define UMF_gprob umfzl_gprob
+#define UMF_dump_dense umfzl_dump_dense
+#define UMF_dump_element umfzl_dump_element
+#define UMF_dump_rowcol umfzl_dump_rowcol
+#define UMF_dump_matrix umfzl_dump_matrix
+#define UMF_dump_current_front umfzl_dump_current_front
+#define UMF_dump_lu umfzl_dump_lu
+#define UMF_dump_memory umfzl_dump_memory
+#define UMF_dump_packed_memory umfzl_dump_packed_memory
+#define UMF_dump_col_matrix umfzl_dump_col_matrix
+#define UMF_dump_chain umfzl_dump_chain
+#define UMF_dump_start umfzl_dump_start
+#define UMF_dump_rowmerge umfzl_dump_rowmerge
+#define UMF_dump_diagonal_map umfzl_dump_diagonal_map
+
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_col_to_triplet.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_col_to_triplet.c
new file mode 100644
index 0000000..3075e2a
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_col_to_triplet.c
@@ -0,0 +1,72 @@
+/* ========================================================================== */
+/* === UMFPACK_col_to_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User callable. Converts a column-oriented input matrix to triplet form by
+ constructing the column indices Tj from the column pointers Ap. The matrix
+ may be singular. See umfpack_col_to_triplet.h for details.
+
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_col_to_triplet
+(
+ Int n_col,
+ const Int Ap [ ],
+ Int Tj [ ]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int nz, j, p, p1, p2, length ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the column indices */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Ap || !Tj)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ if (n_col <= 0)
+ {
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+ if (Ap [0] != 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ nz = Ap [n_col] ;
+ if (nz < 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ for (j = 0 ; j < n_col ; j++)
+ {
+ p1 = Ap [j] ;
+ p2 = Ap [j+1] ;
+ length = p2 - p1 ;
+ if (length < 0 || p2 > nz)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ for (p = p1 ; p < p2 ; p++)
+ {
+ Tj [p] = j ;
+ }
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_defaults.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_defaults.c
new file mode 100644
index 0000000..b8205b7
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_defaults.c
@@ -0,0 +1,114 @@
+/* ========================================================================== */
+/* === UMFPACK_defaults ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Sets default control parameters. See umfpack_defaults.h
+ for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMFPACK_defaults
+(
+ double Control [UMFPACK_CONTROL]
+)
+{
+ Int i ;
+
+ if (!Control)
+ {
+ /* silently return if no Control array */
+ return ;
+ }
+
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++)
+ {
+ Control [i] = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* default control settings: can be modified at run-time */
+ /* ---------------------------------------------------------------------- */
+
+ /* used in UMFPACK_report_* routines: */
+ Control [UMFPACK_PRL] = UMFPACK_DEFAULT_PRL ;
+
+ /* used in UMFPACK_*symbolic: */
+ Control [UMFPACK_DENSE_ROW] = UMFPACK_DEFAULT_DENSE_ROW ;
+ Control [UMFPACK_DENSE_COL] = UMFPACK_DEFAULT_DENSE_COL ;
+ Control [UMFPACK_AMD_DENSE] = UMFPACK_DEFAULT_AMD_DENSE ;
+ Control [UMFPACK_STRATEGY] = UMFPACK_DEFAULT_STRATEGY ;
+ Control [UMFPACK_2BY2_TOLERANCE] = UMFPACK_DEFAULT_2BY2_TOLERANCE ;
+ Control [UMFPACK_AGGRESSIVE] = UMFPACK_DEFAULT_AGGRESSIVE ;
+
+ /* used in UMFPACK_numeric: */
+ Control [UMFPACK_PIVOT_TOLERANCE] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ;
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE] = UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE;
+ Control [UMFPACK_BLOCK_SIZE] = UMFPACK_DEFAULT_BLOCK_SIZE ;
+ Control [UMFPACK_ALLOC_INIT] = UMFPACK_DEFAULT_ALLOC_INIT ;
+ Control [UMFPACK_FRONT_ALLOC_INIT] = UMFPACK_DEFAULT_FRONT_ALLOC_INIT ;
+ Control [UMFPACK_SCALE] = UMFPACK_DEFAULT_SCALE ;
+
+ /* used in UMFPACK_*solve: */
+ Control [UMFPACK_IRSTEP] = UMFPACK_DEFAULT_IRSTEP ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compile-time settings: cannot be modified at run-time */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef NBLAS
+ /* do not use the BLAS - use in-line C code instead */
+ Control [UMFPACK_COMPILED_WITH_BLAS] = 0 ;
+#else
+ /* use externally-provided BLAS (dgemm, dger, dgemv, zgemm, zgeru, zgemv) */
+ Control [UMFPACK_COMPILED_WITH_BLAS] = 1 ;
+#endif
+
+#ifdef MATLAB_MEX_FILE
+ /* compiled as a MATLAB mexFunction */
+ Control [UMFPACK_COMPILED_FOR_MATLAB] = 1 ;
+#else
+#ifdef MATHWORKS
+ /* compiled for internal use in MATLAB */
+ Control [UMFPACK_COMPILED_FOR_MATLAB] = 2 ;
+#else
+ /* use ANSI C malloc, free, realloc, and printf */
+ Control [UMFPACK_COMPILED_FOR_MATLAB] = 0 ;
+#endif
+#endif
+
+#ifdef NO_TIMER
+ /* no timer used */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 3 ;
+#ifndef NPOSIX
+ /* uses the POSIX sysconf ( ) and times ( ) routines in UMFPACK_tic, toc */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 2 ;
+#else
+#ifdef GETRUSAGE
+ /* uses the non-standard getrusage to get CPU time (Solaris) */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 1 ;
+#else
+ /* uses the ANSI standard clock routine to get CPU time */
+ /* this may wrap around */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 0 ;
+#endif
+#endif
+#endif
+
+#ifndef NDEBUG
+ /* UMFPACK is compiled in debug mode. */
+ /* This is exceedingly slow. */
+ DEBUG0 (("UMFPACK is running in debug mode. This is very slow!\n")) ;
+ Control [UMFPACK_COMPILED_IN_DEBUG_MODE] = 1 ;
+#else
+ /* UMFPACK is compiled in normal (non-debug) mode */
+ Control [UMFPACK_COMPILED_IN_DEBUG_MODE] = 0 ;
+#endif
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c
new file mode 100644
index 0000000..36a6af1
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c
@@ -0,0 +1,57 @@
+/* ========================================================================== */
+/* === UMFPACK_free_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* User-callable. Free the entire Numeric object (consists of 11 to 13
+ * malloc'd objects. See UMFPACK_free_numeric.h for details.
+ */
+
+#include "umf_internal.h"
+#include "umf_free.h"
+
+GLOBAL void UMFPACK_free_numeric
+(
+ void **NumericHandle
+)
+{
+
+ NumericType *Numeric ;
+ if (!NumericHandle)
+ {
+ return ;
+ }
+ Numeric = *((NumericType **) NumericHandle) ;
+ if (!Numeric)
+ {
+ return ;
+ }
+
+ /* these 9 objects always exist */
+ (void) UMF_free ((void *) Numeric->D) ;
+ (void) UMF_free ((void *) Numeric->Rperm) ;
+ (void) UMF_free ((void *) Numeric->Cperm) ;
+ (void) UMF_free ((void *) Numeric->Lpos) ;
+ (void) UMF_free ((void *) Numeric->Lilen) ;
+ (void) UMF_free ((void *) Numeric->Lip) ;
+ (void) UMF_free ((void *) Numeric->Upos) ;
+ (void) UMF_free ((void *) Numeric->Uilen) ;
+ (void) UMF_free ((void *) Numeric->Uip) ;
+
+ /* Rs does not exist if scaling was not performed */
+ (void) UMF_free ((void *) Numeric->Rs) ;
+
+ /* Upattern can only exist for singular or rectangular matrices */
+ (void) UMF_free ((void *) Numeric->Upattern) ;
+
+ /* these 2 objects always exist */
+ (void) UMF_free ((void *) Numeric->Memory) ;
+ (void) UMF_free ((void *) Numeric) ;
+
+ *NumericHandle = (void *) NULL ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c
new file mode 100644
index 0000000..ccd4834
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c
@@ -0,0 +1,56 @@
+/* ========================================================================== */
+/* === UMFPACK_free_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. See umfpack_free_symbolic.h for details.
+ All 10 objects comprising the Symbolic object are free'd via UMF_free.
+*/
+
+#include "umf_internal.h"
+#include "umf_free.h"
+
+GLOBAL void UMFPACK_free_symbolic
+(
+ void **SymbolicHandle
+)
+{
+
+ SymbolicType *Symbolic ;
+ if (!SymbolicHandle)
+ {
+ return ;
+ }
+ Symbolic = *((SymbolicType **) SymbolicHandle) ;
+ if (!Symbolic)
+ {
+ return ;
+ }
+
+ (void) UMF_free ((void *) Symbolic->Cperm_init) ;
+ (void) UMF_free ((void *) Symbolic->Rperm_init) ;
+ (void) UMF_free ((void *) Symbolic->Front_npivcol) ;
+ (void) UMF_free ((void *) Symbolic->Front_parent) ;
+ (void) UMF_free ((void *) Symbolic->Front_1strow) ;
+ (void) UMF_free ((void *) Symbolic->Front_leftmostdesc) ;
+ (void) UMF_free ((void *) Symbolic->Chain_start) ;
+ (void) UMF_free ((void *) Symbolic->Chain_maxrows) ;
+ (void) UMF_free ((void *) Symbolic->Chain_maxcols) ;
+ (void) UMF_free ((void *) Symbolic->Cdeg) ;
+ (void) UMF_free ((void *) Symbolic->Rdeg) ;
+
+ /* only when dense rows are present */
+ (void) UMF_free ((void *) Symbolic->Esize) ;
+
+ /* only when diagonal pivoting is prefered */
+ (void) UMF_free ((void *) Symbolic->Diagonal_map) ;
+
+ (void) UMF_free ((void *) Symbolic) ;
+ *SymbolicHandle = (void *) NULL ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_determinant.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_determinant.c
new file mode 100644
index 0000000..0f47e79
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_determinant.c
@@ -0,0 +1,308 @@
+/* ========================================================================== */
+/* === UMFPACK_get_determinant ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. From the LU factors, scale factor, and permutation vectors
+ held in the Numeric object, calculates the determinant of the matrix A.
+ See umfpack_get_determinant.h for a more detailed description.
+
+ Dynamic memory usage: calls UMF_malloc once, for a total space of
+ n integers, and then frees all of it via UMF_free when done.
+
+ Contributed by David Bateman, Motorola, Nov. 2004.
+ Modified for V4.4, Jan. 2005.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+/* ========================================================================== */
+/* === rescale_determinant ================================================== */
+/* ========================================================================== */
+
+/* If the mantissa is too big or too small, rescale it and change exponent */
+
+PRIVATE Int rescale_determinant
+(
+ Entry *d_mantissa,
+ double *d_exponent
+)
+{
+ double d_abs ;
+
+ ABS (d_abs, *d_mantissa) ;
+
+ if (SCALAR_IS_ZERO (d_abs))
+ {
+ /* the determinant is zero */
+ *d_exponent = 0 ;
+ return (FALSE) ;
+ }
+
+ if (SCALAR_IS_NAN (d_abs))
+ {
+ /* the determinant is NaN */
+ return (FALSE) ;
+ }
+
+ while (d_abs < 1.)
+ {
+ SCALE (*d_mantissa, 10.0) ;
+ *d_exponent = *d_exponent - 1.0 ;
+ ABS (d_abs, *d_mantissa) ;
+ }
+
+ while (d_abs >= 10.)
+ {
+ SCALE (*d_mantissa, 0.1) ;
+ *d_exponent = *d_exponent + 1.0 ;
+ ABS (d_abs, *d_mantissa) ;
+ }
+
+ return (TRUE) ;
+}
+
+/* ========================================================================== */
+/* === UMFPACK_get_determinant ============================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_get_determinant
+(
+ double *Mx,
+#ifdef COMPLEX
+ double *Mz,
+#endif
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry d_mantissa, d_tmp ;
+ double d_exponent, Info2 [UMFPACK_INFO], one [2] = {1.0, 0.0}, d_sign ;
+ Entry *D ;
+ double *Info, *Rs ;
+ NumericType *Numeric ;
+ Int i, n, itmp, npiv, *Wi, *Rperm, *Cperm, do_scale ;
+
+#ifndef NRECIPROCAL
+ Int do_recip ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check input parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ if (Numeric->n_row != Numeric->n_col)
+ {
+ /* only square systems can be handled */
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
+ return (UMFPACK_ERROR_invalid_system) ;
+ }
+
+ if (Mx == (double *) NULL)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ n = Numeric->n_row ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Wi = (Int *) UMF_malloc (n, sizeof (Int)) ;
+
+ if (!Wi)
+ {
+ DEBUGm4 (("out of memory: get determinant\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ Rs = Numeric->Rs ; /* row scale factors */
+ do_scale = (Rs != (double *) NULL) ;
+
+#ifndef NRECIPROCAL
+ do_recip = Numeric->do_recip ;
+#endif
+
+ d_mantissa = ((Entry *) one) [0] ;
+ d_exponent = 0.0 ;
+ D = Numeric->D ;
+
+ /* compute product of diagonal entries of U */
+ for (i = 0 ; i < n ; i++)
+ {
+ MULT (d_tmp, d_mantissa, D [i]) ;
+ d_mantissa = d_tmp ;
+
+ if (!rescale_determinant (&d_mantissa, &d_exponent))
+ {
+ /* the determinant is zero or NaN */
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ;
+ /* no need to compute the determinant of R */
+ do_scale = FALSE ;
+ break ;
+ }
+ }
+
+ /* compute product of diagonal entries of R (or its inverse) */
+ if (do_scale)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* compute determinant of R inverse */
+ SCALE_DIV (d_mantissa, Rs [i]) ;
+ }
+ else
+#endif
+ {
+ /* compute determinant of R */
+ SCALE (d_mantissa, Rs [i]) ;
+ }
+ if (!rescale_determinant (&d_mantissa, &d_exponent))
+ {
+ /* the determinant is zero or NaN. This is very unlikey to
+ * occur here, since the scale factors for a tiny or zero row
+ * are set to 1. */
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ;
+ break ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if P and Q are odd or even permutations */
+ /* ---------------------------------------------------------------------- */
+
+ npiv = 0 ;
+ Rperm = Numeric->Rperm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = Rperm [i] ;
+ }
+
+ for (i = 0 ; i < n ; i++)
+ {
+ while (Wi [i] != i)
+ {
+ itmp = Wi [Wi [i]] ;
+ Wi [Wi [i]] = Wi [i] ;
+ Wi [i] = itmp ;
+ npiv++ ;
+ }
+ }
+
+ Cperm = Numeric->Cperm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = Cperm [i] ;
+ }
+
+ for (i = 0 ; i < n ; i++)
+ {
+ while (Wi [i] != i)
+ {
+ itmp = Wi [Wi [i]] ;
+ Wi [Wi [i]] = Wi [i] ;
+ Wi [i] = itmp ;
+ npiv++ ;
+ }
+ }
+
+ /* if npiv is odd, the sign is -1. if it is even, the sign is +1 */
+ d_sign = (npiv % 2) ? -1. : 1. ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) Wi) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the magnitude and exponent of the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ if (Ex == (double *) NULL)
+ {
+ /* Ex is not provided, so return the entire determinant in d_mantissa */
+ SCALE (d_mantissa, pow (10.0, d_exponent)) ;
+ }
+ else
+ {
+ Ex [0] = d_exponent ;
+ }
+
+ Mx [0] = d_sign * REAL_COMPONENT (d_mantissa) ;
+
+#ifdef COMPLEX
+ if (SPLIT (Mz))
+ {
+ Mz [0] = d_sign * IMAG_COMPONENT (d_mantissa) ;
+ }
+ else
+ {
+ Mx [1] = d_sign * IMAG_COMPONENT (d_mantissa) ;
+ }
+#endif
+
+ /* determine if the determinant has (or will) overflow or underflow */
+ if (d_exponent + 1.0 > log10 (DBL_MAX))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_determinant_overflow ;
+ }
+ else if (d_exponent - 1.0 < log10 (DBL_MIN))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_determinant_underflow ;
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_lunz.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_lunz.c
new file mode 100644
index 0000000..2bfc714
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_lunz.c
@@ -0,0 +1,55 @@
+/* ========================================================================== */
+/* === UMFPACK_get_lunz ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Determines the number of nonzeros in L and U, and the size
+ of L and U.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+GLOBAL Int UMFPACK_get_lunz
+(
+ Int *lnz,
+ Int *unz,
+ Int *n_row,
+ Int *n_col,
+ Int *nz_udiag,
+ void *NumericHandle
+)
+{
+ NumericType *Numeric ;
+
+ Numeric = (NumericType *) NumericHandle ;
+
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+ if (!lnz || !unz || !n_row || !n_col || !nz_udiag)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ *n_row = Numeric->n_row ;
+ *n_col = Numeric->n_col ;
+
+ /* number of nz's in L below diagonal, plus the unit diagonal of L */
+ *lnz = Numeric->lnz + MIN (Numeric->n_row, Numeric->n_col) ;
+
+ /* number of nz's in U above diagonal, plus nz's on diagaonal of U */
+ *unz = Numeric->unz + Numeric->nnzpiv ;
+
+ /* number of nz's on the diagonal */
+ *nz_udiag = Numeric->nnzpiv ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_numeric.c
new file mode 100644
index 0000000..8028a86
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_numeric.c
@@ -0,0 +1,1057 @@
+/* ========================================================================== */
+/* === UMFPACK_get_numeric ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Gets the LU factors and the permutation vectors held in the
+ Numeric object. L is returned in sparse row form with sorted rows, U is
+ returned in sparse column form with sorted columns, and P and Q are
+ returned as permutation vectors. See umfpack_get_numeric.h for a more
+ detailed description.
+
+ Returns TRUE if successful, FALSE if the Numeric object is invalid or
+ if out of memory.
+
+ Dynamic memory usage: calls UMF_malloc twice, for a total space of
+ 2*n integers, and then frees all of it via UMF_free when done.
+
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+PRIVATE void get_L
+(
+ Int Lp [ ],
+ Int Lj [ ],
+ double Lx [ ],
+#ifdef COMPLEX
+ double Lz [ ],
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int Wi [ ]
+) ;
+
+PRIVATE void get_U
+(
+ Int Up [ ],
+ Int Ui [ ],
+ double Ux [ ],
+#ifdef COMPLEX
+ double Uz [ ],
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int Wi [ ]
+) ;
+
+/* ========================================================================== */
+/* === UMFPACK_get_numeric ================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_get_numeric
+(
+ Int Lp [ ],
+ Int Lj [ ],
+ double Lx [ ],
+#ifdef COMPLEX
+ double Lz [ ],
+#endif
+ Int Up [ ],
+ Int Ui [ ],
+ double Ux [ ],
+#ifdef COMPLEX
+ double Uz [ ],
+#endif
+ Int P [ ],
+ Int Q [ ],
+ double Dx [ ],
+#ifdef COMPLEX
+ double Dz [ ],
+#endif
+ Int *p_do_recip,
+ double Rs [ ],
+ void *NumericHandle
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ NumericType *Numeric ;
+ Int getL, getU, *Rperm, *Cperm, k, nn, n_row, n_col, *Wi, *Pattern,
+ n_inner ;
+ double *Rs1 ;
+ Entry *D ;
+
+#ifndef NDEBUG
+ init_count = UMF_malloc_count ;
+#endif
+
+ Wi = (Int *) NULL ;
+ Pattern = (Int *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check input parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ getL = Lp && Lj && Lx ;
+ getU = Up && Ui && Ux ;
+
+ if (getL || getU)
+ {
+ Wi = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ Pattern = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!Wi || !Pattern)
+ {
+ (void) UMF_free ((void *) Wi) ;
+ (void) UMF_free ((void *) Pattern) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ DEBUGm4 (("out of memory: get numeric\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ ASSERT (UMF_malloc_count == init_count + 2) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get contents of Numeric */
+ /* ---------------------------------------------------------------------- */
+
+ if (P != (Int *) NULL)
+ {
+ Rperm = Numeric->Rperm ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ P [k] = Rperm [k] ;
+ }
+ }
+
+ if (Q != (Int *) NULL)
+ {
+ Cperm = Numeric->Cperm ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Q [k] = Cperm [k] ;
+ }
+ }
+
+ if (getL)
+ {
+ get_L (Lp, Lj, Lx,
+#ifdef COMPLEX
+ Lz,
+#endif
+ Numeric, Pattern, Wi) ;
+ }
+
+ if (getU)
+ {
+ get_U (Up, Ui, Ux,
+#ifdef COMPLEX
+ Uz,
+#endif
+ Numeric, Pattern, Wi) ;
+ }
+
+ if (Dx != (double *) NULL)
+ {
+ D = Numeric->D ;
+#ifdef COMPLEX
+ if (SPLIT (Dz))
+ {
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ Dx [k] = REAL_COMPONENT (D [k]) ;
+ Dz [k] = IMAG_COMPONENT (D [k]) ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ Dx [2*k ] = REAL_COMPONENT (D [k]) ;
+ Dx [2*k+1] = IMAG_COMPONENT (D [k]) ;
+ }
+ }
+#else
+ {
+ D = Numeric->D ;
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ Dx [k] = D [k] ;
+ }
+ }
+#endif
+ }
+
+ /* return the flag stating whether the scale factors are to be multiplied,
+ * or divided. If do_recip is TRUE, multiply. Otherwise, divided.
+ * If NRECIPROCAL is defined at compile time, the scale factors are always
+ * to be used by dividing.
+ */
+ if (p_do_recip != (Int *) NULL)
+ {
+#ifndef NRECIPROCAL
+ *p_do_recip = Numeric->do_recip ;
+#else
+ *p_do_recip = FALSE ;
+#endif
+ }
+
+ if (Rs != (double *) NULL)
+ {
+ Rs1 = Numeric->Rs ;
+ if (Rs1 == (double *) NULL)
+ {
+ /* R is the identity matrix. */
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rs [k] = 1.0 ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rs [k] = Rs1 [k] ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) Wi) ;
+ (void) UMF_free ((void *) Pattern) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+
+ return (UMFPACK_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === get_L ================================================================ */
+/* ========================================================================== */
+
+/*
+ The matrix L is stored in the following arrays in the Numeric object:
+
+ Int Lpos [0..npiv]
+ Int Lip [0..npiv], index into Numeric->Memory
+ Int Lilen [0..npiv]
+ Unit *(Numeric->Memory), pointer to memory space holding row indices
+ and numerical values
+
+ where npiv is the number of pivot entries found. If A is n_row-by-n_col,
+ then npiv <= MIN (n_row,n_col).
+
+ Let L_k denote the pattern of entries in column k of L (excluding the
+ diagonal).
+
+ An Lchain is a sequence of columns of L whose nonzero patterns are related.
+ The start of an Lchain is denoted by a negative value of Lip [k].
+
+ To obtain L_k:
+
+ (1) If column k starts an Lchain, then L_k is stored in its entirety.
+ |Lip [k]| is an index into Numeric->Memory for the integer row indices
+ in L_k. The number of entries in the column is |L_k| = Lilen [k].
+ This defines the pattern of the "leading" column of this chain.
+ Lpos [k] is not used for the first column in the chain. Column zero
+ is always a leading column.
+
+ (2) If column k does not start an Lchain, then L_k is represented as a
+ superset of L_k-1. Define Lnew_k such that (L_k-1 - {k} union Lnew_k)
+ = L_k, where Lnew_k and (L_k-1)-{k} are disjoint. Lnew_k are the
+ entries in L_k that are not in L_k-1. Lpos [k] holds the position of
+ pivot row index k in the prior pattern L_k-1 (if it is present), so
+ that the set subtraction (L_k-1)-{k} can be computed quickly, when
+ computing the pattern of L_k from L_k-1. The number of new entries in
+ L_k is stored in Lilen [k] = |Lnew_k|.
+
+ Note that this means we must have the pattern L_k-1 to compute L_k.
+
+ In both cases (1) and (2), we obtain the pattern L_k.
+
+ The numerical values are stored in Numeric->Memory, starting at the index
+ |Lip [k]| + Lilen [k]. It is stored in the same order as the entries
+ in L_k, after L_k is obtained from cases (1) or (2), above.
+
+ The advantage of using this "packed" data structure is that it can
+ dramatically reduce the amount of storage needed for the pattern of L.
+ The disadvantage is that it can be difficult for the user to access,
+ and it does not match the sparse matrix data structure used in MATLAB.
+ Thus, this routine is provided to create a conventional sparse matrix
+ data structure for L, in sparse-row form. A row-form of L appears to
+ MATLAB to be a column-oriented from of the transpose of L. If you would
+ like a column-form of L, then use UMFPACK_transpose (an example of this
+ is in umfpackmex.c).
+
+*/
+/* ========================================================================== */
+
+PRIVATE void get_L
+(
+ Int Lp [ ], /* of size n_row+1 */
+ Int Lj [ ], /* of size lnz, where lnz = Lp [n_row] */
+ double Lx [ ], /* of size lnz */
+#ifdef COMPLEX
+ double Lz [ ], /* of size lnz */
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ], /* workspace of size n_row */
+ Int Wi [ ] /* workspace of size n_row */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry value ;
+ Entry *xp, *Lval ;
+ Int deg, *ip, j, row, n_row, n_col, n_inner, *Lpos, *Lilen, *Lip, p, llen,
+ lnz2, lp, newLchain, k, pos, npiv, *Li, n1 ;
+#ifdef COMPLEX
+ Int split = SPLIT (Lz) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG4 (("get_L start:\n")) ;
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+ npiv = Numeric->npiv ;
+ n1 = Numeric->n1 ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ deg = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the nonzeros in each row of L */
+ /* ---------------------------------------------------------------------- */
+
+#pragma ivdep
+ for (row = 0 ; row < n_inner ; row++)
+ {
+ /* include the diagonal entry in the row counts */
+ Wi [row] = 1 ;
+ }
+#pragma ivdep
+ for (row = n_inner ; row < n_row ; row++)
+ {
+ Wi [row] = 0 ;
+ }
+
+ /* singletons */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ deg = Lilen [k] ;
+ if (deg > 0)
+ {
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Li [j] ;
+ value = Lval [j] ;
+ DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [row]++ ;
+ }
+ }
+ }
+ }
+
+ /* non-singletons */
+ for (k = n1 ; k < npiv ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ }
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (!newLchain) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k && row < n_row) ;
+ Pattern [deg++] = row ;
+ }
+
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ row = Pattern [j] ;
+ value = *xp++ ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [row]++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the final row form of L */
+ /* ---------------------------------------------------------------------- */
+
+ /* create the row pointers */
+ lnz2 = 0 ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Lp [row] = lnz2 ;
+ lnz2 += Wi [row] ;
+ Wi [row] = Lp [row] ;
+ }
+ Lp [n_row] = lnz2 ;
+ ASSERT (Numeric->lnz + n_inner == lnz2) ;
+
+ /* add entries from the rows of L (singletons) */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ deg = Lilen [k] ;
+ if (deg > 0)
+ {
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Li [j] ;
+ value = Lval [j] ;
+ DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = Wi [row]++ ;
+ Lj [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+
+ Lx [p] = REAL_COMPONENT (value) ;
+ Lz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Lx [2*p ] = REAL_COMPONENT (value) ;
+ Lx [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Lx [p] = value ;
+#endif
+ }
+ }
+ }
+ }
+
+ /* add entries from the rows of L (non-singletons) */
+ for (k = n1 ; k < npiv ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ }
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (!newLchain) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k) ;
+ Pattern [deg++] = row ;
+ }
+
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ row = Pattern [j] ;
+ value = *xp++ ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = Wi [row]++ ;
+ Lj [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+ Lx [p] = REAL_COMPONENT (value) ;
+ Lz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Lx [2*p ] = REAL_COMPONENT (value) ;
+ Lx [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Lx [p] = value ;
+#endif
+ }
+ }
+ }
+
+ /* add all of the diagonal entries (L is unit diagonal) */
+ for (row = 0 ; row < n_inner ; row++)
+ {
+ p = Wi [row]++ ;
+ Lj [p] = row ;
+
+#ifdef COMPLEX
+ if (split)
+ {
+ Lx [p] = 1. ;
+ Lz [p] = 0. ;
+ }
+ else
+ {
+ Lx [2*p ] = 1. ;
+ Lx [2*p+1] = 0. ;
+ }
+#else
+ Lx [p] = 1. ;
+#endif
+
+ ASSERT (Wi [row] == Lp [row+1]) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG6 (("L matrix (stored by rows):")) ;
+ UMF_dump_col_matrix (Lx,
+#ifdef COMPLEX
+ Lz,
+#endif
+ Lj, Lp, n_inner, n_row, Numeric->lnz+n_inner) ;
+#endif
+
+ DEBUG4 (("get_L done:\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === get_U ================================================================ */
+/* ========================================================================== */
+
+/*
+ The matrix U is stored in the following arrays in the Numeric object:
+
+ Int Upos [0..npiv]
+ Int Uip [0..npiv], index into Numeric->Memory
+ Int Uilen [0..npiv]
+ Unit *(Numeric->Memory), pointer to memory space holding column indices
+ and numerical values
+
+ where npiv is the number of pivot entries found. If A is n_row-by-n_col,
+ then npiv <= MIN (n_row,n_col).
+
+ Let U_k denote the pattern of entries in row k of U (excluding the
+ diagonal).
+
+ A Uchain is a sequence of columns of U whose nonzero patterns are related.
+ The start of a Uchain is denoted by a negative value of Uip [k].
+
+ To obtain U_k-1:
+
+ (1) If row k is the start of a Uchain then Uip [k] is negative and |Uip [k]|
+ is an index into Numeric->Memory for the integer column indices in
+ U_k-1. The number of entries in the row is |U_k-1| = Uilen [k]. This
+ defines the pattern of the "trailing" row of this chain that ends at
+ row k-1.
+
+
+ (2) If row k is not the start of a Uchain, then U_k-1 is a subset of U_k.
+ The indices in U_k are arranged so that last Uilen [k] entries of
+ U_k are those indices not in U_k-1. Next, the pivot column index k is
+ added if it appears in row U_k-1 (it never appears in U_k). Upos [k]
+ holds the position of pivot column index k in the pattern U_k-1 (if it
+ is present), so that the set union (U_k-1)+{k} can be computed quickly,
+ when computing the pattern of U_k-1 from U_k.
+
+ Note that this means we must have the pattern U_k to compute L_k-1.
+
+ In both cases (1) and (2), we obtain the pattern U_k.
+
+ The numerical values are stored in Numeric->Memory. If k is the start of a
+ Uchain, then the offset is |Uip [k]| plus the size of the space needed to
+ store the pattern U_k-1. Otherwise, Uip [k] is the offset itself of the
+ numerical values, since in this case no pattern is stored.
+ The numerical values are stored in the same order as the entries in U_k,
+ after U_k is obtained from cases (1) or (2), above.
+
+ The advantage of using this "packed" data structure is that it can
+ dramatically reduce the amount of storage needed for the pattern of U.
+ The disadvantage is that it can be difficult for the user to access,
+ and it does not match the sparse matrix data structure used in MATLAB.
+ Thus, this routine is provided to create a conventional sparse matrix
+ data structure for U, in sparse-column form.
+
+*/
+/* ========================================================================== */
+
+PRIVATE void get_U
+(
+ Int Up [ ], /* of size n_col+1 */
+ Int Ui [ ], /* of size unz, where unz = Up [n_col] */
+ double Ux [ ], /* of size unz */
+#ifdef COMPLEX
+ double Uz [ ], /* of size unz */
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ], /* workspace of size n_col */
+ Int Wi [ ] /* workspace of size n_col */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry value ;
+ Entry *xp, *D, *Uval ;
+ Int deg, j, *ip, col, *Upos, *Uilen, *Uip, n_col, ulen, *Usi,
+ unz2, p, k, up, newUchain, pos, npiv, n1 ;
+#ifdef COMPLEX
+ Int split = SPLIT (Uz) ;
+#endif
+#ifndef NDEBUG
+ Int nnzpiv = 0 ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG4 (("get_U start:\n")) ;
+ n_col = Numeric->n_col ;
+ n1 = Numeric->n1 ;
+ npiv = Numeric->npiv ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the nonzeros in each column of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < npiv ; col++)
+ {
+ /* include the diagonal entry in the column counts */
+ DEBUG4 (("D ["ID"] = ", col)) ;
+ EDEBUG4 (D [col]) ;
+ Wi [col] = IS_NONZERO (D [col]) ;
+ DEBUG4 ((" is nonzero: "ID"\n", Wi [col])) ;
+#ifndef NDEBUG
+ nnzpiv += IS_NONZERO (D [col]) ;
+#endif
+ }
+ DEBUG4 (("nnzpiv "ID" "ID"\n", nnzpiv, Numeric->nnzpiv)) ;
+ ASSERT (nnzpiv == Numeric->nnzpiv) ;
+ for (col = npiv ; col < n_col ; col++)
+ {
+ /* diagonal entries are zero for structurally singular part */
+ Wi [col] = 0 ;
+ }
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* make last pivot row of U (singular matrices only) */
+ DEBUG0 (("Last pivot row of U: ulen "ID"\n", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ DEBUG0 ((" column "ID"\n", Pattern [j])) ;
+ }
+ }
+
+ /* non-singletons */
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* use row k of U */
+ /* ------------------------------------------------------------------ */
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value\n", k, Pattern [j])) ;
+ col = Pattern [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ value = *xp++ ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [col]++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k == n1) break ;
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ deg = ulen ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+ else
+ {
+ deg -= ulen ;
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg));
+ ASSERT (deg >= 0) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* singletons */
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ deg = Uilen [k] ;
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ if (deg > 0)
+ {
+ up = Uip [k] ;
+ Usi = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Usi [j] ;
+ value = Uval [j] ;
+ DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [col]++ ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the final column form of U */
+ /* ---------------------------------------------------------------------- */
+
+ /* create the column pointers */
+ unz2 = 0 ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Up [col] = unz2 ;
+ unz2 += Wi [col] ;
+ }
+ Up [n_col] = unz2 ;
+ DEBUG1 (("Numeric->unz "ID" npiv "ID" nnzpiv "ID" unz2 "ID"\n",
+ Numeric->unz, npiv, Numeric->nnzpiv, unz2)) ;
+ ASSERT (Numeric->unz + Numeric->nnzpiv == unz2) ;
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Wi [col] = Up [col+1] ;
+ }
+
+ /* add all of the diagonal entries */
+ for (col = 0 ; col < npiv ; col++)
+ {
+ if (IS_NONZERO (D [col]))
+ {
+ p = --(Wi [col]) ;
+ Ui [p] = col ;
+#ifdef COMPLEX
+ if (split)
+ {
+
+ Ux [p] = REAL_COMPONENT (D [col]) ;
+ Uz [p] = IMAG_COMPONENT (D [col]) ;
+ }
+ else
+ {
+ Ux [2*p ] = REAL_COMPONENT (D [col]) ;
+ Ux [2*p+1] = IMAG_COMPONENT (D [col]) ;
+ }
+#else
+ Ux [p] = D [col] ;
+#endif
+ }
+ }
+
+ /* add all the entries from the rows of U */
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* make last pivot row of U (singular matrices only) */
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+
+ /* non-singletons */
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* use row k of U */
+ /* ------------------------------------------------------------------ */
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+
+ xp += deg ;
+ for (j = deg-1 ; j >= 0 ; j--)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
+ col = Pattern [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ value = *(--xp) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = --(Wi [col]) ;
+ Ui [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+ Ux [p] = REAL_COMPONENT (value) ;
+ Uz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Ux [2*p ] = REAL_COMPONENT (value) ;
+ Ux [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Ux [p] = value ;
+#endif
+
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ deg = ulen ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+ else
+ {
+ deg -= ulen ;
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg));
+ ASSERT (deg >= 0) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* singletons */
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ deg = Uilen [k] ;
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ if (deg > 0)
+ {
+ up = Uip [k] ;
+ Usi = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Usi [j] ;
+ value = Uval [j] ;
+ DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = --(Wi [col]) ;
+ Ui [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+ Ux [p] = REAL_COMPONENT (value) ;
+ Uz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Ux [2*p ] = REAL_COMPONENT (value) ;
+ Ux [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Ux [p] = value ;
+#endif
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG6 (("U matrix:")) ;
+ UMF_dump_col_matrix (Ux,
+#ifdef COMPLEX
+ Uz,
+#endif
+ Ui, Up, Numeric->n_row, n_col, Numeric->unz + Numeric->nnzpiv) ;
+#endif
+
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_symbolic.c
new file mode 100644
index 0000000..9363534
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_get_symbolic.c
@@ -0,0 +1,191 @@
+/* ========================================================================== */
+/* === UMFPACK_get_symbolic ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Gets the symbolic information held in the Symbolic object.
+ See umfpack_get_symbolic.h for a more detailed description.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+
+GLOBAL Int UMFPACK_get_symbolic
+(
+ Int *p_n_row,
+ Int *p_n_col,
+ Int *p_n1, /* number of singletons */
+ Int *p_nz,
+ Int *p_nfr,
+ Int *p_nchains,
+ Int P [ ],
+ Int Q [ ],
+ Int Front_npivcol [ ],
+ Int Front_parent [ ],
+ Int Front_1strow [ ],
+ Int Front_leftmostdesc [ ],
+ Int Chain_start [ ],
+ Int Chain_maxrows [ ],
+ Int Chain_maxcols [ ],
+ void *SymbolicHandle
+)
+{
+ SymbolicType *Symbolic ;
+ Int k, n_row, n_col, n1, nfr, nchains, *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get contents of Symbolic */
+ /* ---------------------------------------------------------------------- */
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n1 = Symbolic->n1 ;
+ nfr = Symbolic->nfr ;
+ nchains = Symbolic->nchains ;
+
+ if (p_n_row)
+ {
+ *p_n_row = n_row ;
+ }
+
+ if (p_n_col)
+ {
+ *p_n_col = n_col ;
+ }
+
+ if (p_n1)
+ {
+ *p_n1 = n1 ;
+ }
+
+ if (p_nz)
+ {
+ *p_nz = Symbolic->nz ;
+ }
+
+ if (p_nfr)
+ {
+ *p_nfr = nfr ;
+ }
+
+ if (p_nchains)
+ {
+ *p_nchains = nchains ;
+ }
+
+ if (P != (Int *) NULL)
+ {
+ Int *Rperm_init, *Diagonal_map ;
+ Rperm_init = Symbolic->Rperm_init ;
+ Diagonal_map = Symbolic->Diagonal_map ;
+ if (Diagonal_map != (Int *) NULL)
+ {
+ ASSERT (n_row == n_col) ;
+ /* next pivot rows are found in the diagonal map */
+ for (k = 0 ; k < n_row ; k++)
+ {
+ P [k] = Rperm_init [Diagonal_map [k]] ;
+ }
+ }
+ else
+ {
+ /* there is no diagonal map. */
+ for (k = 0 ; k < n_row ; k++)
+ {
+ P [k] = Rperm_init [k] ;
+ }
+ }
+ }
+
+ if (Q != (Int *) NULL)
+ {
+ p = Symbolic->Cperm_init ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Q [k] = p [k] ;
+ }
+ }
+
+ if (Front_npivcol != (Int *) NULL)
+ {
+ p = Symbolic->Front_npivcol ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_npivcol [k] = p [k] ;
+ }
+ }
+
+ if (Front_parent != (Int *) NULL)
+ {
+ p = Symbolic->Front_parent ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_parent [k] = p [k] ;
+ }
+ }
+
+ if (Front_1strow != (Int *) NULL)
+ {
+ p = Symbolic->Front_1strow ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_1strow [k] = p [k] ;
+ }
+ }
+
+ if (Front_leftmostdesc != (Int *) NULL)
+ {
+ p = Symbolic->Front_leftmostdesc ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_leftmostdesc [k] = p [k] ;
+ }
+ }
+
+ if (Chain_start != (Int *) NULL)
+ {
+ p = Symbolic->Chain_start ;
+ for (k = 0 ; k <= nchains ; k++)
+ {
+ Chain_start [k] = p [k] ;
+ }
+ }
+
+ if (Chain_maxrows != (Int *) NULL)
+ {
+ p = Symbolic->Chain_maxrows ;
+ for (k = 0 ; k < nchains ; k++)
+ {
+ Chain_maxrows [k] = p [k] ;
+ }
+ Chain_maxrows [nchains] = 0 ;
+ }
+
+ if (Chain_maxcols != (Int *) NULL)
+ {
+ p = Symbolic->Chain_maxcols ;
+ for (k = 0 ; k < nchains ; k++)
+ {
+ Chain_maxcols [k] = p [k] ;
+ }
+ Chain_maxcols [nchains] = 0 ;
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_global.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_global.c
new file mode 100644
index 0000000..b612c1e
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_global.c
@@ -0,0 +1,130 @@
+/* ========================================================================== */
+/* === UMFPACK_global ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Global variables. UMFPACK uses these function pointers for several
+ user-redefinable functions. The amd_* functions are defined in
+ AMD/Source/amd_global.c.
+
+ Function pointer default for mexFunction
+ (see MATLAB/umfpackmex.c)
+ ---------------- ------- ---------------
+ amd_malloc malloc mxMalloc
+ amd_free free mxFree
+ amd_realloc realloc mxRealloc
+ amd_calloc calloc mxCalloc
+ amd_printf printf mexPrintf
+
+ umfpack_hypot umf_hypot umf_hypot
+ umfpack_divcomplex umf_divcomplex umf_divcomplex
+
+ This routine is compiled just once for all four versions of UMFPACK
+ (int/UF_long, double/complex).
+*/
+
+#include "umf_internal.h"
+
+double (*umfpack_hypot) (double, double) = umf_hypot ;
+int (*umfpack_divcomplex) (double, double, double, double, double *, double *)
+ = umf_divcomplex ;
+
+
+/* ========================================================================== */
+/* === umf_hypot ============================================================ */
+/* ========================================================================== */
+
+/* There is an equivalent routine called hypot in <math.h>, which conforms
+ * to ANSI C99. However, UMFPACK does not assume that ANSI C99 is available.
+ * You can use the ANSI C99 hypot routine with:
+ *
+ * #include <math.h>
+ * umfpack_hypot = hypot ;
+ *
+ * prior to calling any UMFPACK routine.
+ *
+ * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately.
+ *
+ * The NaN case for the double relops x >= y and x+y == x is safely ignored.
+ */
+
+double umf_hypot (double x, double y)
+{
+ double s, r ;
+ x = SCALAR_ABS (x) ;
+ y = SCALAR_ABS (y) ;
+ if (x >= y)
+ {
+ if (x + y == x)
+ {
+ s = x ;
+ }
+ else
+ {
+ r = y / x ;
+ s = x * sqrt (1.0 + r*r) ;
+ }
+ }
+ else
+ {
+ if (y + x == y)
+ {
+ s = y ;
+ }
+ else
+ {
+ r = x / y ;
+ s = y * sqrt (1.0 + r*r) ;
+ }
+ }
+ return (s) ;
+}
+
+
+/* ========================================================================== */
+/* === umf_divcomplex ======================================================= */
+/* ========================================================================== */
+
+/* c = a/b where c, a, and b are complex. The real and imaginary parts are
+ * passed as separate arguments to this routine. The NaN case is ignored
+ * for the double relop br >= bi. Returns TRUE (1) if the denominator is
+ * zero, FALSE (0) otherwise.
+ *
+ * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid
+ * underflow and overflow.
+ *
+ * c can be the same variable as a or b.
+ */
+
+int umf_divcomplex
+(
+ double ar, double ai, /* real and imaginary parts of a */
+ double br, double bi, /* real and imaginary parts of b */
+ double *cr, double *ci /* real and imaginary parts of c */
+)
+{
+ double tr, ti, r, den ;
+ if (SCALAR_ABS (br) >= SCALAR_ABS (bi))
+ {
+ r = bi / br ;
+ den = br + r * bi ;
+ tr = (ar + ai * r) / den ;
+ ti = (ai - ar * r) / den ;
+ }
+ else
+ {
+ r = br / bi ;
+ den = r * br + bi ;
+ tr = (ar * r + ai) / den ;
+ ti = (ai * r - ar) / den ;
+ }
+ *cr = tr ;
+ *ci = ti ;
+ return (SCALAR_IS_ZERO (den)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_load_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_load_numeric.c
new file mode 100644
index 0000000..18dfcfe
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_load_numeric.c
@@ -0,0 +1,161 @@
+/* ========================================================================== */
+/* === UMFPACK_load_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Loads a Numeric object from a file created by
+ umfpack_*_save_numeric.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#define READ(object,type,n) \
+{ \
+ object = (type *) UMF_malloc (n, sizeof (type)) ; \
+ if (object == (type *) NULL) \
+ { \
+ UMFPACK_free_numeric ((void **) &Numeric) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_out_of_memory) ; \
+ } \
+ if (fread (object, sizeof (type), n, f) != n) \
+ { \
+ UMFPACK_free_numeric ((void **) &Numeric) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+ if (ferror (f)) \
+ { \
+ UMFPACK_free_numeric ((void **) &Numeric) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_load_numeric ================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_load_numeric
+(
+ void **NumericHandle,
+ char *user_filename
+)
+{
+ NumericType *Numeric ;
+ char *filename ;
+ FILE *f ;
+
+ *NumericHandle = (void *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the filename, or use the default name if filename is NULL */
+ /* ---------------------------------------------------------------------- */
+
+ if (user_filename == (char *) NULL)
+ {
+ filename = "numeric.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "rb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the Numeric header from the file, in binary */
+ /* ---------------------------------------------------------------------- */
+
+ Numeric = (NumericType *) UMF_malloc (1, sizeof (NumericType)) ;
+ if (Numeric == (NumericType *) NULL)
+ {
+ fclose (f) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ if (fread (Numeric, sizeof (NumericType), 1, f) != 1)
+ {
+ (void) UMF_free ((void *) Numeric) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+ if (ferror (f))
+ {
+ (void) UMF_free ((void *) Numeric) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ if (Numeric->valid != NUMERIC_VALID || Numeric->n_row <= 0 ||
+ Numeric->n_col <= 0 || Numeric->npiv < 0 || Numeric->ulen < 0 ||
+ Numeric->size <= 0)
+ {
+ /* Numeric does not point to a NumericType object */
+ (void) UMF_free ((void *) Numeric) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ Numeric->D = (Entry *) NULL ;
+ Numeric->Rperm = (Int *) NULL ;
+ Numeric->Cperm = (Int *) NULL ;
+ Numeric->Lpos = (Int *) NULL ;
+ Numeric->Lilen = (Int *) NULL ;
+ Numeric->Lip = (Int *) NULL ;
+ Numeric->Upos = (Int *) NULL ;
+ Numeric->Uilen = (Int *) NULL ;
+ Numeric->Uip = (Int *) NULL ;
+ Numeric->Rs = (double *) NULL ;
+ Numeric->Memory = (Unit *) NULL ;
+ Numeric->Upattern = (Int *) NULL ;
+
+ /* umfpack_free_numeric can now be safely called if an error occurs */
+
+ /* ---------------------------------------------------------------------- */
+ /* read the rest of the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ READ (Numeric->D, Entry, MIN (Numeric->n_row, Numeric->n_col)+1) ;
+ READ (Numeric->Rperm, Int, Numeric->n_row+1) ;
+ READ (Numeric->Cperm, Int, Numeric->n_col+1) ;
+ READ (Numeric->Lpos, Int, Numeric->npiv+1) ;
+ READ (Numeric->Lilen, Int, Numeric->npiv+1) ;
+ READ (Numeric->Lip, Int, Numeric->npiv+1) ;
+ READ (Numeric->Upos, Int, Numeric->npiv+1) ;
+ READ (Numeric->Uilen, Int, Numeric->npiv+1) ;
+ READ (Numeric->Uip, Int, Numeric->npiv+1) ;
+ if (Numeric->scale != UMFPACK_SCALE_NONE)
+ {
+ READ (Numeric->Rs, double, Numeric->n_row) ;
+ }
+ if (Numeric->ulen > 0)
+ {
+ READ (Numeric->Upattern, Int, Numeric->ulen+1) ;
+ }
+ READ (Numeric->Memory, Unit, Numeric->size) ;
+
+ /* close the file */
+ fclose (f) ;
+
+ /* make sure the Numeric object is valid */
+ if (!UMF_valid_numeric (Numeric))
+ {
+ UMFPACK_free_numeric ((void **) &Numeric) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ *NumericHandle = (void *) Numeric ;
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_load_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_load_symbolic.c
new file mode 100644
index 0000000..6401645
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_load_symbolic.c
@@ -0,0 +1,165 @@
+/* ========================================================================== */
+/* === UMFPACK_load_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Loads a Symbolic object from a file created by
+ umfpack_*_save_symbolic.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#define READ(object,type,n) \
+{ \
+ object = (type *) UMF_malloc (n, sizeof (type)) ; \
+ if (object == (type *) NULL) \
+ { \
+ UMFPACK_free_symbolic ((void **) &Symbolic) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_out_of_memory) ; \
+ } \
+ if (fread (object, sizeof (type), n, f) != n) \
+ { \
+ UMFPACK_free_symbolic ((void **) &Symbolic) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+ if (ferror (f)) \
+ { \
+ UMFPACK_free_symbolic ((void **) &Symbolic) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_load_symbolic ================================================ */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_load_symbolic
+(
+ void **SymbolicHandle,
+ char *user_filename
+)
+{
+ SymbolicType *Symbolic ;
+ char *filename ;
+ FILE *f ;
+
+ *SymbolicHandle = (void *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the filename, or use the default name if filename is NULL */
+ /* ---------------------------------------------------------------------- */
+
+ if (user_filename == (char *) NULL)
+ {
+ filename = "symbolic.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "rb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the Symbolic header from the file, in binary */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ;
+ if (Symbolic == (SymbolicType *) NULL)
+ {
+ fclose (f) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ if (fread (Symbolic, sizeof (SymbolicType), 1, f) != 1)
+ {
+ (void) UMF_free ((void *) Symbolic) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+ if (ferror (f))
+ {
+ (void) UMF_free ((void *) Symbolic) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ if (Symbolic->valid != SYMBOLIC_VALID || Symbolic->n_row <= 0 ||
+ Symbolic->n_col <= 0 || Symbolic->nfr < 0 || Symbolic->nchains < 0 ||
+ Symbolic->esize < 0)
+ {
+ /* Symbolic does not point to a Symbolic object */
+ (void) UMF_free ((void *) Symbolic) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ Symbolic->Cperm_init = (Int *) NULL ;
+ Symbolic->Rperm_init = (Int *) NULL ;
+ Symbolic->Front_npivcol = (Int *) NULL ;
+ Symbolic->Front_parent = (Int *) NULL ;
+ Symbolic->Front_1strow = (Int *) NULL ;
+ Symbolic->Front_leftmostdesc = (Int *) NULL ;
+ Symbolic->Chain_start = (Int *) NULL ;
+ Symbolic->Chain_maxrows = (Int *) NULL ;
+ Symbolic->Chain_maxcols = (Int *) NULL ;
+ Symbolic->Cdeg = (Int *) NULL ;
+ Symbolic->Rdeg = (Int *) NULL ;
+ Symbolic->Esize = (Int *) NULL ;
+ Symbolic->Diagonal_map = (Int *) NULL ;
+
+ /* umfpack_free_symbolic can now be safely called if an error occurs */
+
+ /* ---------------------------------------------------------------------- */
+ /* read the rest of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ READ (Symbolic->Cperm_init, Int, Symbolic->n_col+1) ;
+ READ (Symbolic->Rperm_init, Int, Symbolic->n_row+1) ;
+ READ (Symbolic->Front_npivcol, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Front_parent, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Front_1strow, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Front_leftmostdesc, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Chain_start, Int, Symbolic->nchains+1) ;
+ READ (Symbolic->Chain_maxrows, Int, Symbolic->nchains+1) ;
+ READ (Symbolic->Chain_maxcols, Int, Symbolic->nchains+1) ;
+ READ (Symbolic->Cdeg, Int, Symbolic->n_col+1) ;
+ READ (Symbolic->Rdeg, Int, Symbolic->n_row+1) ;
+ if (Symbolic->esize > 0)
+ {
+ /* only when dense rows are present */
+ READ (Symbolic->Esize, Int, Symbolic->esize) ;
+ }
+ if (Symbolic->prefer_diagonal)
+ {
+ /* only when diagonal pivoting is prefered */
+ READ (Symbolic->Diagonal_map, Int, Symbolic->n_col+1) ;
+ }
+
+ /* close the file */
+ fclose (f) ;
+
+ /* make sure the Symbolic object is valid */
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ UMFPACK_free_symbolic ((void **) &Symbolic) ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ *SymbolicHandle = (void *) Symbolic ;
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_numeric.c
new file mode 100644
index 0000000..0a8d67f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_numeric.c
@@ -0,0 +1,792 @@
+/* ========================================================================== */
+/* === UMFPACK_numeric ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Factorizes A into its LU factors, given a symbolic
+ pre-analysis computed by UMFPACK_symbolic. See umfpack_numeric.h for a
+ description.
+
+ Dynamic memory allocation: substantial. See comments (1) through (7),
+ below. If an error occurs, all allocated space is free'd by UMF_free.
+ If successful, the Numeric object contains 11 to 13 objects allocated by
+ UMF_malloc that hold the LU factors of the input matrix.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+#include "umf_set_stats.h"
+#include "umf_kernel.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+#include "umf_realloc.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+PRIVATE Int work_alloc
+(
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
+
+PRIVATE void free_work
+(
+ WorkType *Work
+) ;
+
+PRIVATE Int numeric_alloc
+(
+ NumericType **NumericHandle,
+ SymbolicType *Symbolic,
+ double alloc_init,
+ Int scale
+) ;
+
+PRIVATE void error
+(
+ NumericType **Numeric,
+ WorkType *Work
+) ;
+
+
+/* ========================================================================== */
+/* === UMFPACK_numeric ====================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_numeric
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ void *SymbolicHandle,
+ void **NumericHandle,
+ const double Control [UMFPACK_CONTROL],
+ double User_Info [UMFPACK_INFO]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double Info2 [UMFPACK_INFO], alloc_init, relpt, relpt2, droptol,
+ front_alloc_init, stats [2] ;
+ double *Info ;
+ WorkType WorkSpace, *Work ;
+ NumericType *Numeric ;
+ SymbolicType *Symbolic ;
+ Int n_row, n_col, n_inner, newsize, i, status, *inew, npiv, ulen, scale ;
+ Unit *mnew ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the amount of time used by the process so far */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (stats) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize and check inputs */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ init_count = UMF_malloc_count ;
+ DEBUGm4 (("\nUMFPACK numeric: U transpose version\n")) ;
+#endif
+
+ /* If front_alloc_init negative then allocate that size of front in
+ * UMF_start_front. If alloc_init negative, then allocate that initial
+ * size of Numeric->Memory. */
+
+ relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_PIVOT_TOLERANCE) ;
+ relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ;
+ alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ;
+ front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT,
+ UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ;
+ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
+ droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ;
+
+ relpt = MAX (0.0, MIN (relpt, 1.0)) ;
+ relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ;
+ droptol = MAX (0.0, droptol) ;
+ front_alloc_init = MIN (1.0, front_alloc_init) ;
+
+ if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX)
+ {
+ scale = UMFPACK_DEFAULT_SCALE ;
+ }
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ /* clear the parts of Info that are set by UMFPACK_numeric */
+ for (i = UMFPACK_NUMERIC_SIZE ; i <= UMFPACK_MAX_FRONT_NCOLS ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ for (i = UMFPACK_NUMERIC_DEFRAG ; i < UMFPACK_IR_TAKEN ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+ Numeric = (NumericType *) NULL ;
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Symbolic_object ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ /* compute alloc_init automatically for AMD ordering */
+ if (Symbolic->ordering == UMFPACK_ORDERING_AMD && alloc_init >= 0)
+ {
+ alloc_init = (Symbolic->nz + Symbolic->amd_lunz) / Symbolic->lunz_bound;
+ alloc_init = MIN (1.0, alloc_init) ;
+ alloc_init *= UMF_REALLOC_INCREASE ;
+ }
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+
+ /* check for integer overflow in Numeric->Memory minimum size */
+ if (INT_OVERFLOW (Symbolic->dnum_mem_init_usage * sizeof (Unit)))
+ {
+ /* :: int overflow, initial Numeric->Memory size :: */
+ /* There's no hope to allocate a Numeric object big enough simply to
+ * hold the initial matrix, so return an out-of-memory condition */
+ DEBUGm4 (("out of memory: numeric int overflow\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+ Info [UMFPACK_NROW] = n_row ;
+ Info [UMFPACK_NCOL] = n_col ;
+ Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ;
+
+ if (!Ap || !Ai || !Ax || !NumericHandle)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ Info [UMFPACK_NZ] = Ap [n_col] ;
+ *NumericHandle = (void *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the Work object */
+ /* ---------------------------------------------------------------------- */
+
+ /* (1) calls UMF_malloc 15 or 17 times, to obtain temporary workspace of
+ * size c+1 Entry's and 2*(n_row+1) + 3*(n_col+1) + (n_col+n_inner+1) +
+ * (nn+1) + * 3*(c+1) + 2*(r+1) + max(r,c) + (nfr+1) integers plus 2*nn
+ * more integers if diagonal pivoting is to be done. r is the maximum
+ * number of rows in any frontal matrix, c is the maximum number of columns
+ * in any frontal matrix, n_inner is min (n_row,n_col), nn is
+ * max (n_row,n_col), and nfr is the number of frontal matrices. For a
+ * square matrix, this is c+1 Entry's and about 8n + 3c + 2r + max(r,c) +
+ * nfr integers, plus 2n more for diagonal pivoting.
+ */
+
+ Work = &WorkSpace ;
+ Work->n_row = n_row ;
+ Work->n_col = n_col ;
+ Work->nfr = Symbolic->nfr ;
+ Work->nb = Symbolic->nb ;
+ Work->n1 = Symbolic->n1 ;
+
+ if (!work_alloc (Work, Symbolic))
+ {
+ DEBUGm4 (("out of memory: numeric work\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Numeric, Work) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ ASSERT (UMF_malloc_count == init_count + 16 + 2*Symbolic->prefer_diagonal) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ /* (2) calls UMF_malloc 10 or 11 times, for a total space of
+ * sizeof (NumericType) bytes, 4*(n_row+1) + 4*(n_row+1) integers, and
+ * (n_inner+1) Entry's, plus n_row Entry's if row scaling is to be done.
+ * sizeof (NumericType) is a small constant. Next, it calls UMF_malloc
+ * once, for the variable-sized part of the Numeric object
+ * (Numeric->Memory). The size of this object is the larger of
+ * (Control [UMFPACK_ALLOC_INIT]) * (the approximate upper bound computed
+ * by UMFPACK_symbolic), and the minimum required to start the numerical
+ * factorization. * This request is reduced if it fails.
+ */
+
+ if (!numeric_alloc (&Numeric, Symbolic, alloc_init, scale))
+ {
+ DEBUGm4 (("out of memory: initial numeric\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Numeric, Work) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+ ASSERT (UMF_malloc_count == init_count
+ + (16 + 2*Symbolic->prefer_diagonal)
+ + (11 + (scale != UMFPACK_SCALE_NONE))) ;
+
+ /* set control parameters */
+ Numeric->relpt = relpt ;
+ Numeric->relpt2 = relpt2 ;
+ Numeric->droptol = droptol ;
+ Numeric->alloc_init = alloc_init ;
+ Numeric->front_alloc_init = front_alloc_init ;
+ Numeric->scale = scale ;
+
+ DEBUG0 (("umf relpt %g %g init %g %g inc %g red %g\n",
+ relpt, relpt2, alloc_init, front_alloc_init,
+ UMF_REALLOC_INCREASE, UMF_REALLOC_REDUCTION)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scale and factorize */
+ /* ---------------------------------------------------------------------- */
+
+ /* (3) During numerical factorization (inside UMF_kernel), the variable-size
+ * block of memory is increased in size via a call to UMF_realloc if it is
+ * found to be too small. During factorization, this block holds the
+ * pattern and values of L and U at the top end, and the elements
+ * (contibution blocks) and the current frontal matrix (Work->F*) at the
+ * bottom end. The peak size of the variable-sized object is estimated in
+ * UMFPACK_*symbolic (Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]), although this
+ * upper bound can be very loose. The size of the Symbolic object
+ * (which is currently allocated) is in Info [UMFPACK_SYMBOLIC_SIZE], and
+ * is between 2*n and 13*n integers.
+ */
+
+ DEBUG0 (("Calling umf_kernel\n")) ;
+ status = UMF_kernel (Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Numeric, Work, Symbolic) ;
+
+ Info [UMFPACK_STATUS] = status ;
+ if (status < UMFPACK_OK)
+ {
+ /* out of memory, or pattern has changed */
+ error (&Numeric, Work) ;
+ return (status) ;
+ }
+
+ Info [UMFPACK_FORCED_UPDATES] = Work->nforced ;
+ Info [UMFPACK_VARIABLE_INIT] = Numeric->init_usage ;
+ if (Symbolic->prefer_diagonal)
+ {
+ Info [UMFPACK_NOFF_DIAG] = Work->noff_diagonal ;
+ }
+
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+
+ npiv = Numeric->npiv ; /* = n_inner for nonsingular matrices */
+ ulen = Numeric->ulen ; /* = 0 for square nonsingular matrices */
+
+ /* ---------------------------------------------------------------------- */
+ /* free Work object */
+ /* ---------------------------------------------------------------------- */
+
+ /* (4) After numerical factorization all of the objects allocated in step
+ * (1) are freed via UMF_free, except that one object of size n_col+1 is
+ * kept if there are off-diagonal nonzeros in the last pivot row (can only
+ * occur for singular or rectangular matrices). This is Work->Upattern,
+ * which is transfered to Numeric->Upattern if ulen > 0.
+ */
+
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+
+ free_work (Work) ;
+
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+ DEBUG0 (("Numeric->ulen: "ID" scale: "ID"\n", ulen, scale)) ;
+ ASSERT (UMF_malloc_count == init_count + (ulen > 0) +
+ (11 + (scale != UMFPACK_SCALE_NONE))) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce Lpos, Lilen, Lip, Upos, Uilen and Uip to size npiv+1 */
+ /* ---------------------------------------------------------------------- */
+
+ /* (5) Six components of the Numeric object are reduced in size if the
+ * matrix is singular or rectangular. The original size is 3*(n_row+1) +
+ * 3*(n_col+1) integers. The new size is 6*(npiv+1) integers. For
+ * square non-singular matrices, these two sizes are the same.
+ */
+
+ if (npiv < n_row)
+ {
+ /* reduce Lpos, Uilen, and Uip from size n_row+1 to size npiv */
+ inew = (Int *) UMF_realloc (Numeric->Lpos, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Lpos = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Uilen, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Uilen = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Uip, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Uip = inew ;
+ }
+ }
+
+ if (npiv < n_col)
+ {
+ /* reduce Upos, Lilen, and Lip from size n_col+1 to size npiv */
+ inew = (Int *) UMF_realloc (Numeric->Upos, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Upos = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Lilen, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Lilen = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Lip, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Lip = inew ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce Numeric->Upattern from size n_col+1 to size ulen+1 */
+ /* ---------------------------------------------------------------------- */
+
+ /* (6) The size of Numeric->Upattern (formerly Work->Upattern) is reduced
+ * from size n_col+1 to size ulen + 1. If ulen is zero, the object does
+ * not exist. */
+
+ DEBUG4 (("ulen: "ID" Upattern "ID"\n", ulen, (Int) Numeric->Upattern)) ;
+ ASSERT (IMPLIES (ulen == 0, Numeric->Upattern == (Int *) NULL)) ;
+ if (ulen > 0 && ulen < n_col)
+ {
+ inew = (Int *) UMF_realloc (Numeric->Upattern, ulen+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Upattern = inew ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce Numeric->Memory to hold just the LU factors at the head */
+ /* ---------------------------------------------------------------------- */
+
+ /* (7) The variable-sized block (Numeric->Memory) is reduced to hold just L
+ * and U, via a call to UMF_realloc, since the frontal matrices are no
+ * longer needed.
+ */
+
+ newsize = Numeric->ihead ;
+ if (newsize < Numeric->size)
+ {
+ mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ;
+ if (mnew)
+ {
+ /* realloc succeeded (how can it fail since the size is reduced?) */
+ Numeric->Memory = mnew ;
+ Numeric->size = newsize ;
+ }
+ }
+ Numeric->ihead = Numeric->size ;
+ Numeric->itail = Numeric->ihead ;
+ Numeric->tail_usage = 0 ;
+ Numeric->ibig = EMPTY ;
+ /* UMF_mem_alloc_tail_block can no longer be called (no tail marker) */
+
+ /* ---------------------------------------------------------------------- */
+ /* report the results and return the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_set_stats (
+ Info,
+ Symbolic,
+ (double) Numeric->max_usage, /* actual peak Numeric->Memory */
+ (double) Numeric->size, /* actual final Numeric->Memory */
+ Numeric->flops, /* actual "true flops" */
+ (double) Numeric->lnz + n_inner, /* actual nz in L */
+ (double) Numeric->unz + Numeric->nnzpiv, /* actual nz in U */
+ (double) Numeric->maxfrsize, /* actual largest front size */
+ (double) ulen, /* actual Numeric->Upattern size */
+ (double) npiv, /* actual # pivots found */
+ (double) Numeric->maxnrows, /* actual largest #rows in front */
+ (double) Numeric->maxncols, /* actual largest #cols in front */
+ scale != UMFPACK_SCALE_NONE,
+ Symbolic->prefer_diagonal,
+ ACTUAL) ;
+
+ Info [UMFPACK_ALLOC_INIT_USED] = Numeric->alloc_init ;
+ Info [UMFPACK_NUMERIC_DEFRAG] = Numeric->ngarbage ;
+ Info [UMFPACK_NUMERIC_REALLOC] = Numeric->nrealloc ;
+ Info [UMFPACK_NUMERIC_COSTLY_REALLOC] = Numeric->ncostly ;
+ Info [UMFPACK_COMPRESSED_PATTERN] = Numeric->isize ;
+ Info [UMFPACK_LU_ENTRIES] = Numeric->nLentries + Numeric->nUentries +
+ Numeric->npiv ;
+ Info [UMFPACK_UDIAG_NZ] = Numeric->nnzpiv ;
+ Info [UMFPACK_RSMIN] = Numeric->rsmin ;
+ Info [UMFPACK_RSMAX] = Numeric->rsmax ;
+ Info [UMFPACK_WAS_SCALED] = Numeric->scale ;
+
+ /* nz in L and U with no dropping of small entries */
+ Info [UMFPACK_ALL_LNZ] = Numeric->all_lnz + n_inner ;
+ Info [UMFPACK_ALL_UNZ] = Numeric->all_unz + Numeric->nnzpiv ;
+ Info [UMFPACK_NZDROPPED] =
+ (Numeric->all_lnz - Numeric->lnz)
+ + (Numeric->all_unz - Numeric->unz) ;
+
+ /* estimate of the reciprocal of the condition number. */
+ if (SCALAR_IS_ZERO (Numeric->min_udiag)
+ || SCALAR_IS_ZERO (Numeric->max_udiag)
+ || SCALAR_IS_NAN (Numeric->min_udiag)
+ || SCALAR_IS_NAN (Numeric->max_udiag))
+ {
+ /* rcond is zero if there is any zero or NaN on the diagonal */
+ Numeric->rcond = 0.0 ;
+ }
+ else
+ {
+ /* estimate of the recipricol of the condition number. */
+ /* This is NaN if diagonal is zero-free, but has one or more NaN's. */
+ Numeric->rcond = Numeric->min_udiag / Numeric->max_udiag ;
+ }
+ Info [UMFPACK_UMIN] = Numeric->min_udiag ;
+ Info [UMFPACK_UMAX] = Numeric->max_udiag ;
+ Info [UMFPACK_RCOND] = Numeric->rcond ;
+
+ if (Numeric->nnzpiv < n_inner
+ || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
+ {
+ /* there are zeros and/or NaN's on the diagonal of U */
+ DEBUG0 (("Warning, matrix is singular in umfpack_numeric\n")) ;
+ DEBUG0 (("nnzpiv "ID" n_inner "ID" rcond %g\n", Numeric->nnzpiv,
+ n_inner, Numeric->rcond)) ;
+ status = UMFPACK_WARNING_singular_matrix ;
+ Info [UMFPACK_STATUS] = status ;
+ }
+
+ Numeric->valid = NUMERIC_VALID ;
+ *NumericHandle = (void *) Numeric ;
+
+ /* Numeric has 11 to 13 objects */
+ ASSERT (UMF_malloc_count == init_count + 11 +
+ + (ulen > 0) /* Numeric->Upattern */
+ + (scale != UMFPACK_SCALE_NONE)) ; /* Numeric->Rs */
+
+ /* ---------------------------------------------------------------------- */
+ /* get the time used by UMFPACK_numeric */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (stats) ;
+ Info [UMFPACK_NUMERIC_WALLTIME] = stats [0] ;
+ Info [UMFPACK_NUMERIC_TIME] = stats [1] ;
+
+ /* return UMFPACK_OK or UMFPACK_WARNING_singular_matrix */
+ return (status) ;
+
+}
+
+
+/* ========================================================================== */
+/* === numeric_alloc ======================================================== */
+/* ========================================================================== */
+
+/* Allocate the Numeric object */
+
+PRIVATE Int numeric_alloc
+(
+ NumericType **NumericHandle,
+ SymbolicType *Symbolic,
+ double alloc_init,
+ Int scale
+)
+{
+ double nsize, bsize ;
+ Int n_row, n_col, n_inner, min_usage, trying ;
+ NumericType *Numeric ;
+
+ DEBUG0 (("numeric alloc:\n")) ;
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+ *NumericHandle = (NumericType *) NULL ;
+
+ /* 1 allocation: accounted for in UMF_set_stats (num_On_size1),
+ * free'd in umfpack_free_numeric */
+ Numeric = (NumericType *) UMF_malloc (1, sizeof (NumericType)) ;
+
+ if (!Numeric)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ Numeric->valid = 0 ;
+ *NumericHandle = Numeric ;
+
+ /* 9 allocations: accounted for in UMF_set_stats (num_On_size1),
+ * free'd in umfpack_free_numeric */
+ Numeric->D = (Entry *) UMF_malloc (n_inner+1, sizeof (Entry)) ;
+ Numeric->Rperm = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Numeric->Cperm = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Lpos = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Numeric->Lilen = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Lip = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Upos = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Uilen = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Numeric->Uip = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+
+ /* 1 allocation if scaling: in UMF_set_stats (num_On_size1),
+ * free'd in umfpack_free_numeric */
+ if (scale != UMFPACK_SCALE_NONE)
+ {
+ DEBUG0 (("Allocating scale factors\n")) ;
+ Numeric->Rs = (double *) UMF_malloc (n_row, sizeof (double)) ;
+ }
+ else
+ {
+ DEBUG0 (("No scale factors allocated (R = I)\n")) ;
+ Numeric->Rs = (double *) NULL ;
+ }
+
+ Numeric->Memory = (Unit *) NULL ;
+
+ /* Upattern has already been allocated as part of the Work object. If
+ * the matrix is singular or rectangular, and there are off-diagonal
+ * nonzeros in the last pivot row, then Work->Upattern is not free'd.
+ * Instead it is transfered to Numeric->Upattern. If it exists,
+ * Numeric->Upattern is free'd in umfpack_free_numeric. */
+ Numeric->Upattern = (Int *) NULL ; /* used for singular matrices only */
+
+ if (!Numeric->D || !Numeric->Rperm || !Numeric->Cperm || !Numeric->Upos ||
+ !Numeric->Lpos || !Numeric->Lilen || !Numeric->Uilen || !Numeric->Lip ||
+ !Numeric->Uip || (scale != UMFPACK_SCALE_NONE && !Numeric->Rs))
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate initial Numeric->Memory for LU factors and elements */
+ /* ---------------------------------------------------------------------- */
+
+ if (alloc_init < 0)
+ {
+ /* -alloc_init is the exact size to initially allocate */
+ nsize = -alloc_init ;
+ }
+ else
+ {
+ /* alloc_init is a ratio of the upper bound memory usage */
+ nsize = (alloc_init * Symbolic->num_mem_usage_est) + 1 ;
+ }
+ min_usage = Symbolic->num_mem_init_usage ;
+
+ /* Numeric->Memory must be large enough for UMF_kernel_init */
+ nsize = MAX (min_usage, nsize) ;
+
+ /* Numeric->Memory cannot be larger in size than Int_MAX / sizeof(Unit) */
+ /* For ILP32 mode: 2GB (nsize cannot be bigger than 256 Mwords) */
+ bsize = ((double) Int_MAX) / sizeof (Unit) - 1 ;
+ DEBUG0 (("bsize %g\n", bsize)) ;
+ nsize = MIN (nsize, bsize) ;
+
+ Numeric->size = (Int) nsize ;
+
+ DEBUG0 (("Num init %g usage_est %g numsize "ID" minusage "ID"\n",
+ alloc_init, Symbolic->num_mem_usage_est, Numeric->size, min_usage)) ;
+
+ /* allocates 1 object: */
+ /* keep trying until successful, or memory request is too small */
+ trying = TRUE ;
+ while (trying)
+ {
+ Numeric->Memory = (Unit *) UMF_malloc (Numeric->size, sizeof (Unit)) ;
+ if (Numeric->Memory)
+ {
+ DEBUG0 (("Successful Numeric->size: "ID"\n", Numeric->size)) ;
+ return (TRUE) ;
+ }
+ /* too much, reduce the request (but not below the minimum) */
+ /* and try again */
+ trying = Numeric->size > min_usage ;
+ Numeric->size = (Int)
+ (UMF_REALLOC_REDUCTION * ((double) Numeric->size)) ;
+ Numeric->size = MAX (min_usage, Numeric->size) ;
+ }
+
+ return (FALSE) ; /* we failed to allocate Numeric->Memory */
+}
+
+
+/* ========================================================================== */
+/* === work_alloc =========================================================== */
+/* ========================================================================== */
+
+/* Allocate the Work object. Return TRUE if successful. */
+
+PRIVATE Int work_alloc
+(
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ Int n_row, n_col, nn, maxnrows, maxncols, nfr, ok, maxnrc, n1 ;
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nn = MAX (n_row, n_col) ;
+ nfr = Work->nfr ;
+ n1 = Symbolic->n1 ;
+ ASSERT (n1 <= n_row && n1 <= n_col) ;
+
+ maxnrows = Symbolic->maxnrows + Symbolic->nb ;
+ maxnrows = MIN (n_row, maxnrows) ;
+ maxncols = Symbolic->maxncols + Symbolic->nb ;
+ maxncols = MIN (n_col, maxncols) ;
+ maxnrc = MAX (maxnrows, maxncols) ;
+
+ DEBUG0 (("work alloc: maxnrows+nb "ID" maxncols+nb "ID"\n",
+ maxnrows, maxncols)) ;
+
+ /* 15 allocations, freed in free_work: */
+ /* accounted for in UMF_set_stats (work_usage) */
+ Work->Wx = (Entry *) UMF_malloc (maxnrows + 1, sizeof (Entry)) ;
+ Work->Wy = (Entry *) UMF_malloc (maxnrows + 1, sizeof (Entry)) ;
+ Work->Frpos = (Int *) UMF_malloc (n_row + 1, sizeof (Int)) ;
+ Work->Lpattern = (Int *) UMF_malloc (n_row + 1, sizeof (Int)) ;
+ Work->Fcpos = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ Work->Wp = (Int *) UMF_malloc (nn + 1, sizeof (Int)) ;
+ Work->Wrp = (Int *) UMF_malloc (MAX (n_col,maxnrows) + 1, sizeof (Int)) ;
+ Work->Frows = (Int *) UMF_malloc (maxnrows + 1, sizeof (Int)) ;
+ Work->Wm = (Int *) UMF_malloc (maxnrows + 1, sizeof (Int)) ;
+ Work->Fcols = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ;
+ Work->Wio = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ;
+ Work->Woi = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ;
+ Work->Woo = (Int *) UMF_malloc (maxnrc + 1, sizeof (Int));
+ Work->elen = (n_col - n1) + (n_row - n1) + MIN (n_col-n1, n_row-n1) + 1 ;
+ Work->E = (Int *) UMF_malloc (Work->elen, sizeof (Int)) ;
+ Work->Front_new1strow = (Int *) UMF_malloc (nfr + 1, sizeof (Int)) ;
+
+ ok = (Work->Frpos && Work->Fcpos && Work->Lpattern
+ && Work->Wp && Work->Wrp && Work->Frows && Work->Fcols
+ && Work->Wio && Work->Woi && Work->Woo && Work->Wm
+ && Work->E && Work->Front_new1strow && Work->Wx && Work->Wy) ;
+
+ /* 2 allocations: accounted for in UMF_set_stats (work_usage) */
+ if (Symbolic->prefer_diagonal)
+ {
+ Work->Diagonal_map = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ Work->Diagonal_imap = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ ok = ok && Work->Diagonal_map && Work->Diagonal_imap ;
+ }
+ else
+ {
+ /* no diagonal map needed for rectangular matrices */
+ Work->Diagonal_map = (Int *) NULL ;
+ Work->Diagonal_imap = (Int *) NULL ;
+ }
+
+ /* 1 allocation, may become part of Numeric (if singular or rectangular): */
+ Work->Upattern = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ ok = ok && Work->Upattern ;
+
+ /* current frontal matrix does not yet exist */
+ Work->Flublock = (Entry *) NULL ;
+ Work->Flblock = (Entry *) NULL ;
+ Work->Fublock = (Entry *) NULL ;
+ Work->Fcblock = (Entry *) NULL ;
+
+ DEBUG0 (("work alloc done.\n")) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === free_work ============================================================ */
+/* ========================================================================== */
+
+PRIVATE void free_work
+(
+ WorkType *Work
+)
+{
+ DEBUG0 (("work free:\n")) ;
+ if (Work)
+ {
+ /* these 16 objects do exist */
+ Work->Wx = (Entry *) UMF_free ((void *) Work->Wx) ;
+ Work->Wy = (Entry *) UMF_free ((void *) Work->Wy) ;
+ Work->Frpos = (Int *) UMF_free ((void *) Work->Frpos) ;
+ Work->Fcpos = (Int *) UMF_free ((void *) Work->Fcpos) ;
+ Work->Lpattern = (Int *) UMF_free ((void *) Work->Lpattern) ;
+ Work->Upattern = (Int *) UMF_free ((void *) Work->Upattern) ;
+ Work->Wp = (Int *) UMF_free ((void *) Work->Wp) ;
+ Work->Wrp = (Int *) UMF_free ((void *) Work->Wrp) ;
+ Work->Frows = (Int *) UMF_free ((void *) Work->Frows) ;
+ Work->Fcols = (Int *) UMF_free ((void *) Work->Fcols) ;
+ Work->Wio = (Int *) UMF_free ((void *) Work->Wio) ;
+ Work->Woi = (Int *) UMF_free ((void *) Work->Woi) ;
+ Work->Woo = (Int *) UMF_free ((void *) Work->Woo) ;
+ Work->Wm = (Int *) UMF_free ((void *) Work->Wm) ;
+ Work->E = (Int *) UMF_free ((void *) Work->E) ;
+ Work->Front_new1strow =
+ (Int *) UMF_free ((void *) Work->Front_new1strow) ;
+
+ /* these objects might not exist */
+ Work->Diagonal_map = (Int *) UMF_free ((void *) Work->Diagonal_map) ;
+ Work->Diagonal_imap = (Int *) UMF_free ((void *) Work->Diagonal_imap) ;
+ }
+ DEBUG0 (("work free done.\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === error ================================================================ */
+/* ========================================================================== */
+
+/* Error return from UMFPACK_numeric. Free all allocated memory. */
+
+PRIVATE void error
+(
+ NumericType **Numeric,
+ WorkType *Work
+)
+{
+ free_work (Work) ;
+ UMFPACK_free_numeric ((void **) Numeric) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c
new file mode 100644
index 0000000..fc7f267
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c
@@ -0,0 +1,2411 @@
+/* ========================================================================== */
+/* === UMFPACK_qsymbolic ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Performs a symbolic factorization.
+ See umfpack_qsymbolic.h and umfpack_symbolic.h for details.
+
+ Dynamic memory usage: about (3.4nz + 8n + n) integers and n double's as
+ workspace (via UMF_malloc, for a square matrix). All of it is free'd via
+ UMF_free if an error occurs. If successful, the Symbolic object contains
+ 12 to 14 objects allocated by UMF_malloc, with a total size of no more
+ than about 13*n integers.
+*/
+
+#include "umf_internal.h"
+#include "umf_symbolic_usage.h"
+#include "umf_colamd.h"
+#include "umf_set_stats.h"
+#include "umf_analyze.h"
+#include "umf_transpose.h"
+#include "umf_is_permutation.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+#include "umf_2by2.h"
+#include "umf_singletons.h"
+
+typedef struct /* SWType */
+{
+ Int *Front_npivcol ; /* size n_col + 1 */
+ Int *Front_nrows ; /* size n_col */
+ Int *Front_ncols ; /* size n_col */
+ Int *Front_parent ; /* size n_col */
+ Int *Front_cols ; /* size n_col */
+ Int *InFront ; /* size n_row */
+ Int *Ci ; /* size Clen */
+ Int *Cperm1 ; /* size n_col */
+ Int *Rperm1 ; /* size n_row */
+ Int *InvRperm1 ; /* size n_row */
+ Int *Si ; /* size nz */
+ Int *Sp ; /* size n_col + 1 */
+ double *Rs ; /* size n_row */
+ Int *Rperm_2by2 ; /* size n_row */
+
+} SWType ;
+
+PRIVATE void free_work
+(
+ SWType *SW
+) ;
+
+PRIVATE void error
+(
+ SymbolicType **Symbolic,
+ SWType *SW
+) ;
+
+/* worst-case usage for SW object */
+#define SYM_WORK_USAGE(n_col,n_row,Clen) \
+ (DUNITS (Int, Clen) + \
+ DUNITS (Int, nz) + \
+ 4 * DUNITS (Int, n_row) + \
+ 4 * DUNITS (Int, n_col) + \
+ 2 * DUNITS (Int, n_col + 1) + \
+ DUNITS (double, n_row))
+
+/* required size of Ci for code that calls UMF_transpose and UMF_analyze below*/
+#define UMF_ANALYZE_CLEN(nz,n_row,n_col,nn) \
+ ((n_col) + MAX ((nz),(n_col)) + 3*(nn)+1 + (n_col))
+
+/* size of an element (in Units), including tuples */
+#define ELEMENT_SIZE(r,c) \
+ (DGET_ELEMENT_SIZE (r, c) + 1 + (r + c) * UNITS (Tuple, 1))
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+/* ========================================================================== */
+/* === do_amd =============================================================== */
+/* ========================================================================== */
+
+PRIVATE void do_amd
+(
+ Int n,
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+ Int Q [ ], /* output permutation, j = Q [k] */
+ Int Qinv [ ], /* output inverse permutation, Qinv [j] = k */
+ Int Sdeg [ ], /* degree of A+A', from AMD_aat */
+ Int Clen, /* size of Ci */
+ Int Ci [ ], /* size Ci workspace */
+ double amd_Control [ ], /* AMD control parameters */
+ double amd_Info [ ], /* AMD info */
+ SymbolicType *Symbolic, /* Symbolic object */
+ double Info [ ] /* UMFPACK info */
+)
+{
+
+ if (n == 0)
+ {
+ Symbolic->amd_dmax = 0 ;
+ Symbolic->amd_lunz = 0 ;
+ Info [UMFPACK_SYMMETRIC_LUNZ] = 0 ;
+ Info [UMFPACK_SYMMETRIC_FLOPS] = 0 ;
+ Info [UMFPACK_SYMMETRIC_DMAX] = 0 ;
+ Info [UMFPACK_SYMMETRIC_NDENSE] = 0 ;
+ }
+ else
+ {
+ AMD_1 (n, Ap, Ai, Q, Qinv, Sdeg, Clen, Ci, amd_Control, amd_Info) ;
+
+ /* return estimates computed from AMD on PA+PA' */
+ Symbolic->amd_dmax = amd_Info [AMD_DMAX] ;
+ Symbolic->amd_lunz = 2 * amd_Info [AMD_LNZ] + n ;
+ Info [UMFPACK_SYMMETRIC_LUNZ] = Symbolic->amd_lunz ;
+ Info [UMFPACK_SYMMETRIC_FLOPS] = DIV_FLOPS * amd_Info [AMD_NDIV] +
+ MULTSUB_FLOPS * amd_Info [AMD_NMULTSUBS_LU] ;
+ Info [UMFPACK_SYMMETRIC_DMAX] = Symbolic->amd_dmax ;
+ Info [UMFPACK_SYMMETRIC_NDENSE] = amd_Info [AMD_NDENSE] ;
+ Info [UMFPACK_SYMBOLIC_DEFRAG] += amd_Info [AMD_NCMPA] ;
+ }
+}
+
+/* ========================================================================== */
+/* === prune_singletons ===================================================== */
+/* ========================================================================== */
+
+/* Create the submatrix after removing the n1 singletons. The matrix has
+ * row and column indices in the range 0 to n_row-n1 and 0 to n_col-n1,
+ * respectively. */
+
+PRIVATE Int prune_singletons
+(
+ Int n1,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ Int Cperm1 [ ],
+ Int InvRperm1 [ ],
+ Int Si [ ],
+ Int Sp [ ]
+#ifndef NDEBUG
+ , Int Rperm1 [ ]
+ , Int n_row
+#endif
+)
+{
+ Int row, k, pp, p, oldcol, newcol, newrow, nzdiag, do_nzdiag ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+
+ nzdiag = 0 ;
+ do_nzdiag = (Ax != (double *) NULL) ;
+
+#ifndef NDEBUG
+ DEBUGm4 (("Prune : S = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end))\n")) ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n_row) ;
+ ASSERT (InvRperm1 [Rperm1 [k]] == k) ;
+ }
+#endif
+
+ /* create the submatrix after removing singletons */
+
+ pp = 0 ;
+ for (k = n1 ; k < n_col ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ newcol = k - n1 ;
+ DEBUG5 (("Prune singletons k "ID" oldcol "ID" newcol "ID": "ID"\n",
+ k, oldcol, newcol, pp)) ;
+ Sp [newcol] = pp ; /* load column pointers */
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG5 ((" "ID": row "ID, pp, row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ newrow = InvRperm1 [row] - n1 ;
+ ASSERT (newrow < n_row - n1) ;
+ if (newrow >= 0)
+ {
+ DEBUG5 ((" newrow "ID, newrow)) ;
+ Si [pp++] = newrow ;
+ if (do_nzdiag)
+ {
+ /* count the number of truly nonzero entries on the
+ * diagonal of S, excluding entries that are present,
+ * but numerically zero */
+ if (newrow == newcol)
+ {
+ /* this is the diagonal entry */
+#ifdef COMPLEX
+ if (split)
+ {
+ if (SCALAR_IS_NONZERO (Ax [p]) ||
+ SCALAR_IS_NONZERO (Az [p]))
+ {
+ nzdiag++ ;
+ }
+ }
+ else
+ {
+ if (SCALAR_IS_NONZERO (Ax [2*p ]) ||
+ SCALAR_IS_NONZERO (Ax [2*p+1]))
+ {
+ nzdiag++ ;
+ }
+ }
+#else
+ if (SCALAR_IS_NONZERO (Ax [p]))
+ {
+ nzdiag++ ;
+ }
+#endif
+ }
+ }
+ }
+ DEBUG5 (("\n")) ;
+ }
+ }
+ Sp [n_col - n1] = pp ;
+
+ return (nzdiag) ;
+}
+
+/* ========================================================================== */
+/* === combine_ordering ===================================================== */
+/* ========================================================================== */
+
+PRIVATE void combine_ordering
+(
+ Int n1,
+ Int nempty_col,
+ Int n_col,
+ Int Cperm_init [ ], /* output permutation */
+ Int Cperm1 [ ], /* singleton and empty column ordering */
+ Int Qinv [ ] /* Qinv from AMD or COLAMD */
+)
+{
+ Int k, oldcol, newcol, knew ;
+
+ /* combine the singleton ordering with Qinv */
+#ifndef NDEBUG
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm_init [k] = EMPTY ;
+ }
+#endif
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG1 ((ID" Initial singleton: "ID"\n", k, Cperm1 [k])) ;
+ Cperm_init [k] = Cperm1 [k] ;
+ }
+ for (k = n1 ; k < n_col - nempty_col ; k++)
+ {
+ /* this is a non-singleton column */
+ oldcol = Cperm1 [k] ; /* user's name for this column */
+ newcol = k - n1 ; /* Qinv's name for this column */
+ knew = Qinv [newcol] ; /* Qinv's ordering for this column */
+ knew += n1 ; /* shift order, after singletons */
+ DEBUG1 ((" k "ID" oldcol "ID" newcol "ID" knew "ID"\n",
+ k, oldcol, newcol, knew)) ;
+ ASSERT (knew >= 0 && knew < n_col - nempty_col) ;
+ ASSERT (Cperm_init [knew] == EMPTY) ;
+ Cperm_init [knew] = oldcol ;
+ }
+ for (k = n_col - nempty_col ; k < n_col ; k++)
+ {
+ Cperm_init [k] = Cperm1 [k] ;
+ }
+#ifndef NDEBUG
+ {
+ Int *W = (Int *) malloc ((n_col + 1) * sizeof (Int)) ;
+ ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ;
+ free (W) ;
+ }
+#endif
+
+}
+
+/* ========================================================================== */
+/* === UMFPACK_qsymbolic ==================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_qsymbolic
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ const Int Quser [ ],
+ void **SymbolicHandle,
+ const double Control [UMFPACK_CONTROL],
+ double User_Info [UMFPACK_INFO]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double knobs [COLAMD_KNOBS], flops, f, r, c, force_fixQ,
+ Info2 [UMFPACK_INFO], drow, dcol, dtail_usage, dlf, duf, dmax_usage,
+ dhead_usage, dlnz, dunz, dmaxfrsize, dClen, dClen_analyze, sym,
+ amd_Info [AMD_INFO], dClen_amd, dr, dc, cr, cc, cp,
+ amd_Control [AMD_CONTROL], stats [2], tol ;
+ double *Info ;
+ Int i, nz, j, newj, status, f1, f2, maxnrows, maxncols, nfr, col,
+ nchains, maxrows, maxcols, p, nb, nn, *Chain_start, *Chain_maxrows,
+ *Chain_maxcols, *Front_npivcol, *Ci, Clen, colamd_stats [COLAMD_STATS],
+ fpiv, n_inner, child, parent, *Link, row, *Front_parent,
+ analyze_compactions, k, chain, is_sym, *Si, *Sp, n2, do_UMF_analyze,
+ fpivcol, fallrows, fallcols, *InFront, *F1, snz, *Front_1strow, f1rows,
+ kk, *Cperm_init, *Rperm_init, newrow, *InvRperm1, *Front_leftmostdesc,
+ Clen_analyze, strategy, Clen_amd, fixQ, prefer_diagonal, nzdiag, nzaat,
+ *Wq, *Sdeg, *Fr_npivcol, nempty, *Fr_nrows, *Fr_ncols, *Fr_parent,
+ *Fr_cols, nempty_row, nempty_col, user_auto_strategy, fail, max_rdeg,
+ head_usage, tail_usage, lnz, unz, esize, *Esize, rdeg, *Cdeg, *Rdeg,
+ *Cperm1, *Rperm1, n1, oldcol, newcol, n1c, n1r, *Rperm_2by2, oldrow,
+ dense_row_threshold, tlen, aggressive, scale, *Rp, *Ri ;
+
+ SymbolicType *Symbolic ;
+ SWType SWspace, *SW ;
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ init_count = UMF_malloc_count ;
+ PRINTF ((
+"**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n"
+ )) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get the amount of time used by the process so far */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (stats) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control settings and check input parameters */
+ /* ---------------------------------------------------------------------- */
+
+ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ;
+ dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ;
+ nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ;
+ strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ;
+ tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ;
+ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
+ force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ;
+ AMD_defaults (amd_Control) ;
+ amd_Control [AMD_DENSE] =
+ GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ;
+ aggressive =
+ (GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) != 0) ;
+ amd_Control [AMD_AGGRESSIVE] = aggressive ;
+
+ nb = MAX (2, nb) ;
+ nb = MIN (nb, MAXNB) ;
+ ASSERT (nb >= 0) ;
+ if (nb % 2 == 1) nb++ ; /* make sure nb is even */
+ DEBUG0 (("UMFPACK_qsymbolic: nb = "ID" aggressive = "ID"\n", nb,
+ aggressive)) ;
+
+ tol = MAX (0.0, MIN (tol, 1.0)) ;
+ if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX)
+ {
+ scale = UMFPACK_DEFAULT_SCALE ;
+ }
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ }
+ /* clear all of Info */
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+ Info [UMFPACK_NROW] = n_row ;
+ Info [UMFPACK_NCOL] = n_col ;
+ Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ;
+ Info [UMFPACK_SIZE_OF_INT] = (double) (sizeof (int)) ;
+ Info [UMFPACK_SIZE_OF_LONG] = (double) (sizeof (UF_long)) ;
+ Info [UMFPACK_SIZE_OF_POINTER] = (double) (sizeof (void *)) ;
+ Info [UMFPACK_SIZE_OF_ENTRY] = (double) (sizeof (Entry)) ;
+ Info [UMFPACK_SYMBOLIC_DEFRAG] = 0 ;
+
+ if (!Ai || !Ap || !SymbolicHandle)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ *SymbolicHandle = (void *) NULL ;
+
+ if (n_row <= 0 || n_col <= 0) /* n_row, n_col must be > 0 */
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_n_nonpositive ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ nz = Ap [n_col] ;
+ DEBUG0 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, nz)) ;
+ Info [UMFPACK_NZ] = nz ;
+ if (nz < 0)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_matrix ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the requested strategy */
+ /* ---------------------------------------------------------------------- */
+
+ if (n_row != n_col)
+ {
+ /* if the matrix is rectangular, the only available strategy is
+ * unsymmetric */
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ DEBUGm3 (("Rectangular: forcing unsymmetric strategy\n")) ;
+ }
+
+ if (strategy < UMFPACK_STRATEGY_AUTO
+ || strategy > UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ /* unrecognized strategy */
+ strategy = UMFPACK_STRATEGY_AUTO ;
+ }
+
+ if (Quser != (Int *) NULL)
+ {
+ /* when the user provides Q, only symmetric and unsymmetric strategies
+ * are available */
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ strategy = UMFPACK_STRATEGY_SYMMETRIC ;
+ }
+ if (strategy != UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ }
+
+ user_auto_strategy = (strategy == UMFPACK_STRATEGY_AUTO) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine amount of memory required for UMFPACK_symbolic */
+ /* ---------------------------------------------------------------------- */
+
+ /* The size of Clen required for UMF_colamd is always larger than */
+ /* UMF_analyze, but the max is included here in case that changes in */
+ /* future versions. */
+
+ /* This is about 2.2*nz + 9*n_col + 6*n_row, or nz/5 + 13*n_col + 6*n_row,
+ * whichever is bigger. For square matrices, it works out to
+ * 2.2nz + 15n, or nz/5 + 19n, whichever is bigger (typically 2.2nz+15n). */
+ dClen = UMF_COLAMD_RECOMMENDED ((double) nz, (double) n_row,
+ (double) n_col) ;
+
+ /* This is defined above, as max (nz,n_col) + 3*nn+1 + 2*n_col, where
+ * nn = max (n_row,n_col). It is always smaller than the space required
+ * for colamd or amd. */
+ dClen_analyze = UMF_ANALYZE_CLEN ((double) nz, (double) n_row,
+ (double) n_col, (double) nn) ;
+ dClen = MAX (dClen, dClen_analyze) ;
+
+ /* The space for AMD can be larger than what's required for colamd: */
+ dClen_amd = 2.4 * (double) nz + 8 * (double) n_inner ;
+ /* additional space for the 2-by-2 strategy */
+ dClen_amd += (double) MAX (nn, nz) ;
+ dClen = MAX (dClen, dClen_amd) ;
+
+ /* worst case total memory usage for UMFPACK_symbolic (revised below) */
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] =
+ SYM_WORK_USAGE (n_col, n_row, dClen) +
+ UMF_symbolic_usage (n_row, n_col, n_col, n_col, n_col, TRUE) ;
+
+ if (INT_OVERFLOW (dClen * sizeof (Int)))
+ {
+ /* :: int overflow, Clen too large :: */
+ /* Problem is too large for array indexing (Ci [i]) with an Int i. */
+ /* Cannot even analyze the problem to determine upper bounds on */
+ /* memory usage. Need to use the UF_long version, umfpack_*l_*. */
+ DEBUGm4 (("out of memory: symbolic int overflow\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* repeat the size calculations, in integers */
+ Clen = UMF_COLAMD_RECOMMENDED (nz, n_row, n_col) ;
+ Clen_analyze = UMF_ANALYZE_CLEN (nz, n_row, n_col, nn) ;
+ Clen = MAX (Clen, Clen_analyze) ;
+ Clen_amd = 2.4 * nz + 8 * n_inner ;
+ Clen_amd += MAX (nn, nz) ; /* for Ri, in UMF_2by2 */
+ Clen = MAX (Clen, Clen_amd) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the first part of the Symbolic object (header and Cperm_init) */
+ /* ---------------------------------------------------------------------- */
+
+ /* (1) Five calls to UMF_malloc are made, for a total space of
+ * 2 * (n_row + n_col) + 4 integers + sizeof (SymbolicType).
+ * sizeof (SymbolicType) is a small constant. This space is part of the
+ * Symbolic object and is not freed unless an error occurs. If A is square
+ * then this is about 4*n integers.
+ */
+
+ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ;
+
+ if (!Symbolic)
+ {
+ /* If we fail here, Symbolic is NULL and thus it won't be */
+ /* dereferenced by UMFPACK_free_symbolic, as called by error ( ). */
+ DEBUGm4 (("out of memory: symbolic object\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, (SWType *) NULL) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* We now know that Symbolic has been allocated */
+ Symbolic->valid = 0 ;
+ Symbolic->Chain_start = (Int *) NULL ;
+ Symbolic->Chain_maxrows = (Int *) NULL ;
+ Symbolic->Chain_maxcols = (Int *) NULL ;
+ Symbolic->Front_npivcol = (Int *) NULL ;
+ Symbolic->Front_parent = (Int *) NULL ;
+ Symbolic->Front_1strow = (Int *) NULL ;
+ Symbolic->Front_leftmostdesc = (Int *) NULL ;
+ Symbolic->Esize = (Int *) NULL ;
+ Symbolic->esize = 0 ;
+
+ Symbolic->Cperm_init = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Symbolic->Rperm_init = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Symbolic->Cdeg = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Symbolic->Rdeg = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Symbolic->Diagonal_map = (Int *) NULL ;
+
+ Cperm_init = Symbolic->Cperm_init ;
+ Rperm_init = Symbolic->Rperm_init ;
+ Cdeg = Symbolic->Cdeg ;
+ Rdeg = Symbolic->Rdeg ;
+
+ if (!Cperm_init || !Rperm_init || !Cdeg || !Rdeg)
+ {
+ DEBUGm4 (("out of memory: symbolic perm\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, (SWType *) NULL) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ Symbolic->n_row = n_row ;
+ Symbolic->n_col = n_col ;
+ Symbolic->nz = nz ;
+ Symbolic->nb = nb ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check user's input permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL)
+ {
+ /* use Cperm_init as workspace to check input permutation */
+ if (!UMF_is_permutation (Quser, Cperm_init, n_col, n_col))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_permutation ;
+ error (&Symbolic, (SWType *) NULL) ;
+ return (UMFPACK_ERROR_invalid_permutation) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* (2) Eleven calls to UMF_malloc are made, for workspace of size
+ * Clen + nz + 7*n_col + 2*n_row + 2 integers. Clen is the larger of
+ * MAX (2*nz, 4*n_col) + 8*n_col + 6*n_row + n_col + nz/5 and
+ * 2.4*nz + 8 * MIN (n_row, n_col) + MAX (n_row, n_col, nz)
+ * If A is square and non-singular, then Clen is
+ * MAX (MAX (2*nz, 4*n) + 7*n + nz/5, 3.4*nz) + 8*n
+ * If A has at least 4*n nonzeros then Clen is
+ * MAX (2.2*nz + 7*n, 3.4*nz) + 8*n
+ * If A has at least (7/1.2)*n nonzeros, (about 5.8*n), then Clen is
+ * 3.4*nz + 8*n
+ * This space will be free'd when this routine finishes.
+ *
+ * Total space thus far is about 3.4nz + 12n integers.
+ * For the double precision, 32-bit integer version, the user's matrix
+ * requires an equivalent space of 3*nz + n integers. So this space is just
+ * slightly larger than the user's input matrix (including the numerical
+ * values themselves).
+ */
+
+ SW = &SWspace ; /* used for UMFPACK_symbolic only */
+
+ /* Note that SW->Front_* does not include the dummy placeholder front. */
+ /* This space is accounted for by the SYM_WORK_USAGE macro. */
+
+ /* this is free'd early */
+ SW->Si = (Int *) UMF_malloc (nz, sizeof (Int)) ;
+ SW->Sp = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ SW->InvRperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+ SW->Cperm1 = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+
+ /* this is free'd late */
+ SW->Ci = (Int *) UMF_malloc (Clen, sizeof (Int)) ;
+ SW->Front_npivcol = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ SW->Front_nrows = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Front_ncols = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Front_parent = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Front_cols = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Rperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+ SW->InFront = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+
+ /* this is allocated later, and free'd after Cperm1 but before Ci */
+ SW->Rperm_2by2 = (Int *) NULL ; /* will be nn Int's */
+
+ /* this is allocated last, and free'd first */
+ SW->Rs = (double *) NULL ; /* will be n_row double's */
+
+ Ci = SW->Ci ;
+ Fr_npivcol = SW->Front_npivcol ;
+ Fr_nrows = SW->Front_nrows ;
+ Fr_ncols = SW->Front_ncols ;
+ Fr_parent = SW->Front_parent ;
+ Fr_cols = SW->Front_cols ;
+ Cperm1 = SW->Cperm1 ;
+ Rperm1 = SW->Rperm1 ;
+ Si = SW->Si ;
+ Sp = SW->Sp ;
+ InvRperm1 = SW->InvRperm1 ;
+ Rperm_2by2 = (Int *) NULL ;
+ InFront = SW->InFront ;
+
+ if (!Ci || !Fr_npivcol || !Fr_nrows || !Fr_ncols || !Fr_parent || !Fr_cols
+ || !Cperm1 || !Rperm1 || !Si || !Sp || !InvRperm1 || !InFront)
+ {
+ DEBUGm4 (("out of memory: symbolic work\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n",
+ UMF_malloc_count - init_count)) ;
+ ASSERT (UMF_malloc_count == init_count + 17) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the row and column singletons */
+ /* ---------------------------------------------------------------------- */
+
+ /* [ use first nz + n_row + MAX (n_row, n_col) entries in Ci as workspace,
+ * and use Rperm_init as workspace */
+ ASSERT (Clen >= nz + n_row + MAX (n_row, n_col)) ;
+
+ status = UMF_singletons (n_row, n_col, Ap, Ai, Quser, strategy,
+ Cdeg, Cperm1, Rdeg,
+ Rperm1, InvRperm1, &n1, &n1c, &n1r, &nempty_col, &nempty_row, &is_sym,
+ &max_rdeg, /* workspace: */ Rperm_init, Ci, Ci + nz, Ci + nz + n_row) ;
+
+ /* ] done using Rperm_init and Ci as workspace */
+
+ /* InvRperm1 is now the inverse of Rperm1 */
+
+ if (status != UMFPACK_OK)
+ {
+ DEBUGm4 (("matrix invalid: UMF_singletons\n")) ;
+ Info [UMFPACK_STATUS] = status ;
+ error (&Symbolic, SW) ;
+ return (status) ;
+ }
+ Info [UMFPACK_NEMPTY_COL] = nempty_col ;
+ Info [UMFPACK_NEMPTY_ROW] = nempty_row ;
+ Info [UMFPACK_NDENSE_COL] = 0 ; /* # dense rows/cols recomputed below */
+ Info [UMFPACK_NDENSE_ROW] = 0 ;
+ Info [UMFPACK_COL_SINGLETONS] = n1c ;
+ Info [UMFPACK_ROW_SINGLETONS] = n1r ;
+ Info [UMFPACK_S_SYMMETRIC] = is_sym ;
+
+ nempty = MIN (nempty_col, nempty_row) ;
+ Symbolic->nempty_row = nempty_row ;
+ Symbolic->nempty_col = nempty_col ;
+
+ /* UMF_singletons has verified that the user's input matrix is valid */
+ ASSERT (AMD_valid (n_row, n_col, Ap, Ai) == AMD_OK) ;
+
+ Symbolic->n1 = n1 ;
+ Symbolic->nempty = nempty ;
+ ASSERT (n1 <= n_inner) ;
+ n2 = nn - n1 - nempty ;
+
+ dense_row_threshold =
+ UMFPACK_DENSE_DEGREE_THRESHOLD (drow, n_col - n1 - nempty_col) ;
+ Symbolic->dense_row_threshold = dense_row_threshold ;
+
+ if (!is_sym)
+ {
+ /* either the pruned submatrix rectangular, or it is square and
+ * Rperm [n1 .. n-nempty-1] is not the same as Cperm [n1 .. n-nempty-1].
+ * Switch to the unsymmetric strategy, ignoring user-requested
+ * strategy. */
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ DEBUGm4 (("Strategy: Unsymmetric singletons\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine symmetry, nzdiag, and degrees of S+S' */
+ /* ---------------------------------------------------------------------- */
+
+ /* S is the matrix obtained after removing singletons
+ * = A (Cperm1 [n1..n_col-nempty_col-1], Rperm1 [n1..n_row-nempty_row-1])
+ */
+
+ Wq = Rperm_init ; /* use Rperm_init as workspace for Wq [ */
+ Sdeg = Cperm_init ; /* use Cperm_init as workspace for Sdeg [ */
+ sym = EMPTY ;
+ nzaat = EMPTY ;
+ nzdiag = EMPTY ;
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ amd_Info [i] = EMPTY ;
+ }
+
+ if (strategy != UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ /* This also determines the degree of each node in S+S' (Sdeg), which
+ * is needed by the 2-by-2 strategy, the symmetry of S, and the number
+ * of nonzeros on the diagonal of S. */
+ ASSERT (n_row == n_col) ;
+ ASSERT (nempty_row == nempty_col) ;
+
+ /* get the count of nonzeros on the diagonal of S, excluding explicitly
+ * zero entries. nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries
+ * in S. */
+
+ nzdiag = prune_singletons (n1, nn, Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Cperm1, InvRperm1, Si, Sp
+#ifndef NDEBUG
+ , Rperm1, nn
+#endif
+ ) ;
+
+ /* use Ci as workspace to sort S into R, if needed [ */
+ if (Quser != (Int *) NULL)
+ {
+ /* need to sort the columns of S first */
+ Rp = Ci ;
+ Ri = Ci + (n_row) + 1 ;
+ (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL,
+ (Int *) NULL, (Int *) NULL, 0,
+ Rp, Ri, (double *) NULL, Wq, FALSE
+#ifdef COMPLEX
+ , (double *) NULL, (double *) NULL, FALSE
+#endif
+ ) ;
+ }
+ else
+ {
+ /* S already has sorted columns */
+ Rp = Sp ;
+ Ri = Si ;
+ }
+ ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
+
+ nzaat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ;
+ sym = amd_Info [AMD_SYMMETRY] ;
+ Info [UMFPACK_N2] = n2 ;
+ /* nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries of S too */
+
+ /* done using Ci as workspace to sort S into R ] */
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n2 ; k++)
+ {
+ ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ;
+ }
+ ASSERT (Sp [n2] - n2 <= nzaat && nzaat <= 2 * Sp [n2]) ;
+ DEBUG0 (("Explicit zeros: "ID" %g\n", nzdiag, amd_Info [AMD_NZDIAG])) ;
+#endif
+
+ }
+
+ /* get statistics from amd_aat, if computed */
+ Symbolic->sym = sym ;
+ Symbolic->nzaat = nzaat ;
+ Symbolic->nzdiag = nzdiag ;
+ Symbolic->amd_dmax = EMPTY ;
+
+ Info [UMFPACK_PATTERN_SYMMETRY] = sym ;
+ Info [UMFPACK_NZ_A_PLUS_AT] = nzaat ;
+ Info [UMFPACK_NZDIAG] = nzdiag ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the initial strategy based on symmetry and nnz (diag (S)) */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_AUTO)
+ {
+ if (sym < 0.10)
+ {
+ /* highly unsymmetric: use the unsymmetric strategy */
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ DEBUGm4 (("Strategy: select unsymmetric\n")) ;
+ }
+ else if (sym >= 0.7 && nzdiag == n2)
+ {
+ /* mostly symmetric, zero-free diagonal: use symmetric strategy */
+ strategy = UMFPACK_STRATEGY_SYMMETRIC ;
+ DEBUGm4 (("Strategy: select symmetric\n")) ;
+ }
+ else
+ {
+ /* Evaluate the symmetric 2-by-2 strategy, and select it, or
+ * the unsymmetric strategy if the 2-by-2 strategy doesn't look
+ * promising. */
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ DEBUGm4 (("Strategy: try 2-by-2\n")) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* try the 2-by-2 strategy */
+ /* ---------------------------------------------------------------------- */
+
+ /* (3) If the 2-by-2 strategy is attempted, additional workspace of size
+ * nn integers and nn double's is allocated, where nn = n_row = n_col.
+ * The real workspace is immediately free'd. The integer workspace of
+ * size nn remains until the end of umfpack_qsymbolic. */
+
+ /* If the resulting matrix S (Rperm_2by2, :) is too unsymmetric, then the
+ * unsymmetric strategy will be used instead. */
+
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ double sym2 ;
+ Int *Blen, *W, nz_papat, nzd2, nweak, unmatched, Clen3 ;
+
+ /* ------------------------------------------------------------------ */
+ /* get workspace for UMF_2by2 */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT (n_row == n_col && nn == n_row) ;
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n2 ; k++)
+ {
+ ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ;
+ }
+#endif
+
+ /* allocate Rperm_2by2 */
+ SW->Rperm_2by2 = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ Rperm_2by2 = SW->Rperm_2by2 ;
+ if (Rperm_2by2 == (Int *) NULL)
+ {
+ DEBUGm4 (("out of memory: Rperm_2by2\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* allocate Ri from the tail end of Ci [ */
+ Clen3 = Clen - (MAX (nn, nz) + 1) ;
+ Ri = Ci + Clen3 ;
+ ASSERT (Clen3 >= nz) ; /* space required for UMF_2by2 */
+
+ /* use Fr_* as workspace for Rp, Blen, and W [ */
+ Rp = Fr_npivcol ;
+ Blen = Fr_ncols ;
+ W = Fr_cols ;
+
+ if (scale != UMFPACK_SCALE_NONE)
+ {
+ SW->Rs = (double *) UMF_malloc (nn, sizeof (double)) ;
+ if (SW->Rs == (double *) NULL)
+ {
+ DEBUGm4 (("out of memory: scale factors for 2-by-2\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* find the 2-by-2 row permutation */
+ /* ------------------------------------------------------------------ */
+
+ /* find a row permutation Rperm_2by2 such that S (Rperm_2by2, :)
+ * has a healthy diagonal */
+
+ UMF_2by2 (nn, Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ tol, scale, Cperm1,
+#ifndef NDEBUG
+ Rperm1,
+#endif
+ InvRperm1, n1, nempty, Sdeg, Rperm_2by2, &nweak, &unmatched,
+ Ri, Rp, SW->Rs, Blen, W, Ci, Wq) ;
+ DEBUGm3 (("2by2: nweak "ID" unmatched "ID"\n", nweak, unmatched)) ;
+ Info [UMFPACK_2BY2_NWEAK] = nweak ;
+ Info [UMFPACK_2BY2_UNMATCHED] = unmatched ;
+
+ SW->Rs = (double *) UMF_free ((void *) SW->Rs) ;
+
+ /* R = S (Rperm_2by2,:)' */
+ (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL, Rperm_2by2,
+ (Int *) NULL, 0, Rp, Ri, (double *) NULL, W, FALSE
+#ifdef COMPLEX
+ , (double *) NULL, (double *) NULL, FALSE
+#endif
+ ) ;
+ ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
+
+ /* contents of Si and Sp no longer needed, but the space is
+ * still needed */
+
+ /* ------------------------------------------------------------------ */
+ /* find symmetry of S (Rperm_2by2, :)', and prepare to order with AMD */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ amd_Info [i] = EMPTY ;
+ }
+ nz_papat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ;
+ sym2 = amd_Info [AMD_SYMMETRY] ;
+ nzd2 = amd_Info [AMD_NZDIAG] ;
+
+ Info [UMFPACK_2BY2_PATTERN_SYMMETRY] = sym2 ;
+ Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT] = nz_papat ;
+ Info [UMFPACK_2BY2_NZDIAG] = nzd2 ;
+
+ DEBUG0 (("2by2: sym2 %g nzd2 "ID" n2 "ID"\n", sym2, nzd2, n2)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate the 2-by-2 results */
+ /* ------------------------------------------------------------------ */
+
+ if (user_auto_strategy)
+ {
+ if ((sym2 > 1.1 * sym) && (nzd2 > 0.9 * n2))
+ {
+ /* 2-by-2 made it much more symmetric */
+ DEBUGm4 (("eval Strategy 2by2: much more symmetric: 2by2\n")) ;
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else if (sym2 < 0.7 * sym)
+ {
+ /* 2-by-2 made it much more unsymmetric */
+ DEBUGm4 (("eval Strategy 2by2: much more UNsymmetric:unsym\n"));
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ else if (sym2 < 0.25)
+ {
+ DEBUGm4 (("eval Strategy 2by2: is UNsymmetric: unsym\n"));
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ else if (sym2 >= 0.51)
+ {
+ DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.51: 2by2\n")) ;
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else if (sym2 >= 0.999 * sym)
+ {
+ /* 2-by-2 improved symmetry, or made it only slightly worse */
+ DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.999 sym: 2by2\n")) ;
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else
+ {
+ /* can't decide what to do, so pick the unsymmetric strategy */
+ DEBUGm4 (("eval Strategy 2by2: punt: unsym\n"));
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* if the 2-by-2 strategy is selected: */
+ /* ------------------------------------------------------------------ */
+
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ if (Quser == (Int *) NULL)
+ {
+ /* 2-by-2 strategy is successful */
+ /* compute amd (S) */
+ Int *Qinv = Fr_npivcol ;
+ ASSERT (Clen3 >= (nz_papat + nz_papat/5 + nn) + 7*nn) ;
+ do_amd (n2, Rp, Ri, Wq, Qinv, Sdeg, Clen3, Ci,
+ amd_Control, amd_Info, Symbolic, Info) ;
+ /* combine the singleton ordering and the AMD ordering */
+ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ;
+ }
+ /* fix Rperm_2by2 to reflect A, not S */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ i = k ;
+ oldrow = Rperm1 [k] ;
+ W [oldcol] = oldrow ;
+ }
+ for (k = n1 ; k < nn - nempty ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ i = Rperm_2by2 [k - n1] + n1 ;
+ oldrow = Rperm1 [i] ;
+ W [oldcol] = oldrow ;
+ }
+ for (k = nn - nempty ; k < nn ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ i = k ;
+ oldrow = Rperm1 [k] ;
+ W [oldcol] = oldrow ;
+ }
+ for (k = 0 ; k < nn ; k++)
+ {
+ Rperm_2by2 [k] = W [k] ;
+ }
+
+ /* Now, the "diagonal" entry in oldcol (where oldcol is the user's
+ * name for a column, is the entry in row oldrow (where oldrow is
+ * the user's name for a row, and oldrow = Rperm_2by2 [oldcol] */
+ }
+
+ /* Fr_* no longer needed for Rp, Blen, W ] */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize the strategy, including fixQ and prefer_diagonal */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ /* use given Quser or AMD (A+A'), fix Q during factorization,
+ * prefer diagonal */
+ DEBUG0 (("\nStrategy: symmetric\n")) ;
+ ASSERT (n_row == n_col) ;
+ Symbolic->ordering = UMFPACK_ORDERING_AMD ;
+ fixQ = TRUE ;
+ prefer_diagonal = TRUE ;
+ }
+ else if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ /* use Q = given Quser or Q = AMD (PA+PA'), fix Q during factorization,
+ * prefer diagonal, and factorize PAQ, where P is found by UMF_2by2. */
+ DEBUG0 (("\nStrategy: symmetric 2-by-2\n")) ;
+ ASSERT (n_row == n_col) ;
+ Symbolic->ordering = UMFPACK_ORDERING_AMD ;
+ fixQ = TRUE ;
+ prefer_diagonal = TRUE ;
+ }
+ else
+ {
+ /* use given Quser or COLAMD (A), refine Q during factorization,
+ * no diagonal preference */
+ ASSERT (strategy == UMFPACK_STRATEGY_UNSYMMETRIC) ;
+ DEBUG0 (("\nStrategy: unsymmetric\n")) ;
+ Symbolic->ordering = UMFPACK_ORDERING_COLAMD ;
+ fixQ = FALSE ;
+ prefer_diagonal = FALSE ;
+ }
+
+ if (Quser != (Int *) NULL)
+ {
+ Symbolic->ordering = UMFPACK_ORDERING_GIVEN ;
+ }
+
+ if (force_fixQ > 0)
+ {
+ fixQ = TRUE ;
+ DEBUG0 (("Force fixQ true\n")) ;
+ }
+ else if (force_fixQ < 0)
+ {
+ fixQ = FALSE ;
+ DEBUG0 (("Force fixQ false\n")) ;
+ }
+
+ DEBUG0 (("Strategy: ordering: "ID"\n", Symbolic->ordering)) ;
+ DEBUG0 (("Strategy: fixQ: "ID"\n", fixQ)) ;
+ DEBUG0 (("Strategy: prefer diag "ID"\n", prefer_diagonal)) ;
+
+ /* get statistics from amd_aat, if computed */
+ Symbolic->strategy = strategy ;
+ Symbolic->fixQ = fixQ ;
+ Symbolic->prefer_diagonal = prefer_diagonal ;
+
+ Info [UMFPACK_STRATEGY_USED] = strategy ;
+ Info [UMFPACK_ORDERING_USED] = Symbolic->ordering ;
+ Info [UMFPACK_QFIXED] = fixQ ;
+ Info [UMFPACK_DIAG_PREFERRED] = prefer_diagonal ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the AMD ordering for the symmetric strategy */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC && Quser == (Int *) NULL)
+ {
+ /* symmetric strategy for a matrix with mostly symmetric pattern */
+ Int *Qinv = Fr_npivcol ;
+ ASSERT (n_row == n_col && nn == n_row) ;
+ ASSERT (Clen >= (nzaat + nzaat/5 + nn) + 7*nn) ;
+ do_amd (n2, Sp, Si, Wq, Qinv, Sdeg, Clen, Ci,
+ amd_Control, amd_Info, Symbolic, Info) ;
+ /* combine the singleton ordering and the AMD ordering */
+ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ;
+ }
+ /* Sdeg no longer needed ] */
+ /* done using Rperm_init as workspace for Wq ] */
+
+ /* Contents of Si and Sp no longer needed, but the space is still needed */
+
+ /* ---------------------------------------------------------------------- */
+ /* use the user's input column ordering (already in Cperm1) */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL)
+ {
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm_init [k] = Cperm1 [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* use COLAMD to order the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC && Quser == (Int *) NULL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy the matrix into colamd workspace (colamd destroys its input) */
+ /* ------------------------------------------------------------------ */
+
+ /* C = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end)), where Ci is used as
+ * the row indices and Cperm_init (on input) is used as the column
+ * pointers. */
+
+ (void) prune_singletons (n1, n_col, Ap, Ai,
+ (double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+ Cperm1, InvRperm1, Ci, Cperm_init
+#ifndef NDEBUG
+ , Rperm1, n_row
+#endif
+ ) ;
+
+ /* ------------------------------------------------------------------ */
+ /* set UMF_colamd defaults */
+ /* ------------------------------------------------------------------ */
+
+ UMF_colamd_set_defaults (knobs) ;
+ knobs [COLAMD_DENSE_ROW] = drow ;
+ knobs [COLAMD_DENSE_COL] = dcol ;
+ knobs [COLAMD_AGGRESSIVE] = aggressive ;
+
+ /* ------------------------------------------------------------------ */
+ /* check input matrix and find the initial column pre-ordering */
+ /* ------------------------------------------------------------------ */
+
+ /* NOTE: umf_colamd is not given any original empty rows or columns.
+ * Those have already been removed via prune_singletons, above. The
+ * umf_colamd routine has been modified to assume that all rows and
+ * columns have at least one entry in them. It will break if it is
+ * given empty rows or columns (an assertion is triggered when running
+ * in debug mode. */
+
+ (void) UMF_colamd (
+ n_row - n1 - nempty_row,
+ n_col - n1 - nempty_col,
+ Clen, Ci, Cperm_init, knobs, colamd_stats,
+ Fr_npivcol, Fr_nrows, Fr_ncols, Fr_parent, Fr_cols, &nfr,
+ InFront) ;
+ ASSERT (colamd_stats [COLAMD_EMPTY_ROW] == 0) ;
+ ASSERT (colamd_stats [COLAMD_EMPTY_COL] == 0) ;
+
+ /* # of dense rows will be recomputed below */
+ Info [UMFPACK_NDENSE_ROW] = colamd_stats [COLAMD_DENSE_ROW] ;
+ Info [UMFPACK_NDENSE_COL] = colamd_stats [COLAMD_DENSE_COL] ;
+ Info [UMFPACK_SYMBOLIC_DEFRAG] = colamd_stats [COLAMD_DEFRAG_COUNT] ;
+
+ /* re-analyze if any "dense" rows or cols ignored by UMF_colamd */
+ do_UMF_analyze =
+ colamd_stats [COLAMD_DENSE_ROW] > 0 ||
+ colamd_stats [COLAMD_DENSE_COL] > 0 ;
+
+ /* Combine the singleton and colamd ordering into Cperm_init */
+ /* Note that colamd returns its inverse permutation in Ci */
+ combine_ordering (n1, nempty_col, n_col, Cperm_init, Cperm1, Ci) ;
+
+ /* contents of Ci no longer needed */
+
+#ifndef NDEBUG
+ for (col = 0 ; col < n_col ; col++)
+ {
+ DEBUG1 (("Cperm_init ["ID"] = "ID"\n", col, Cperm_init[col]));
+ }
+ /* make sure colamd returned a valid permutation */
+ ASSERT (Cperm_init != (Int *) NULL) ;
+ ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ;
+#endif
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* do not call colamd - use input Quser or AMD instead */
+ /* ------------------------------------------------------------------ */
+
+ /* The ordering (Quser or Qamd) is already in Cperm_init */
+ do_UMF_analyze = TRUE ;
+
+ }
+
+ Cperm_init [n_col] = EMPTY ; /* unused in Cperm_init */
+
+ /* ---------------------------------------------------------------------- */
+ /* AMD ordering, if it exists, has been copied into Cperm_init */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG3 (("Cperm_init column permutation:\n")) ;
+ ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ DEBUG3 ((ID"\n", Cperm_init [k])) ;
+ }
+ /* ensure that empty columns have been placed last in A (:,Cperm_init) */
+ for (newj = 0 ; newj < n_col ; newj++)
+ {
+ /* empty columns will be last in A (:, Cperm_init (1:n_col)) */
+ j = Cperm_init [newj] ;
+ ASSERT (IMPLIES (newj >= n_col-nempty_col, Cdeg [j] == 0)) ;
+ ASSERT (IMPLIES (newj < n_col-nempty_col, Cdeg [j] > 0)) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization (unless colamd has already done it) */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_UMF_analyze)
+ {
+
+ Int *W, *Bp, *Bi, *Cperm2, ok, *P, Clen2, bsize, Clen0 ;
+
+ /* ------------------------------------------------------------------ */
+ /* construct column pre-ordered, pruned submatrix */
+ /* ------------------------------------------------------------------ */
+
+ /* S = column form submatrix after removing singletons and applying
+ * initial column ordering (includes singleton ordering) */
+ (void) prune_singletons (n1, n_col, Ap, Ai,
+ (double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+ Cperm_init, InvRperm1, Si, Sp
+#ifndef NDEBUG
+ , Rperm1, n_row
+#endif
+ ) ;
+
+ /* ------------------------------------------------------------------ */
+ /* Ci [0 .. Clen-1] holds the following work arrays:
+
+ first Clen0 entries empty space, where Clen0 =
+ Clen - (nn+1 + 2*nn + n_col)
+ and Clen0 >= nz + n_col
+ next nn+1 entries Bp [0..nn]
+ next nn entries Link [0..nn-1]
+ next nn entries W [0..nn-1]
+ last n_col entries Cperm2 [0..n_col-1]
+
+ We have Clen >= n_col + MAX (nz,n_col) + 3*nn+1 + n_col,
+ So Clen0 >= 2*n_col as required for AMD_postorder
+ and Clen0 >= n_col + nz as required
+ */
+
+ Clen0 = Clen - (nn+1 + 2*nn + n_col) ;
+ Bp = Ci + Clen0 ;
+ Link = Bp + (nn+1) ;
+ W = Link + nn ;
+ Cperm2 = W + nn ;
+ ASSERT (Cperm2 + n_col == Ci + Clen) ;
+ ASSERT (Clen0 >= nz + n_col) ;
+ ASSERT (Clen0 >= 2*n_col) ;
+
+ /* ------------------------------------------------------------------ */
+ /* P = order that rows will be used in UMF_analyze */
+ /* ------------------------------------------------------------------ */
+
+ /* use W to mark rows, and use Link for row permutation P [ [ */
+ for (row = 0 ; row < n_row - n1 ; row++)
+ {
+ W [row] = FALSE ;
+ }
+ P = Link ;
+
+ k = 0 ;
+
+ for (col = 0 ; col < n_col - n1 ; col++)
+ {
+ /* empty columns are last in S */
+ for (p = Sp [col] ; p < Sp [col+1] ; p++)
+ {
+ row = Si [p] ;
+ if (!W [row])
+ {
+ /* this row has just been seen for the first time */
+ W [row] = TRUE ;
+ P [k++] = row ;
+ }
+ }
+ }
+
+ /* If the matrix has truly empty rows, then P will not be */
+ /* complete, and visa versa. The matrix is structurally singular. */
+ nempty_row = n_row - n1 - k ;
+ if (k < n_row - n1)
+ {
+ /* complete P by putting empty rows last in their natural order, */
+ /* rather than declaring an error (the matrix is singular) */
+ for (row = 0 ; row < n_row - n1 ; row++)
+ {
+ if (!W [row])
+ {
+ /* W [row] = TRUE ; (not required) */
+ P [k++] = row ;
+ }
+ }
+ }
+
+ /* contents of W no longer needed ] */
+
+#ifndef NDEBUG
+ DEBUG3 (("Induced row permutation:\n")) ;
+ ASSERT (k == n_row - n1) ;
+ ASSERT (UMF_is_permutation (P, W, n_row - n1, n_row - n1)) ;
+ for (k = 0 ; k < n_row - n1 ; k++)
+ {
+ DEBUG3 ((ID"\n", P [k])) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* B = row-form of the pattern of S (excluding empty columns) */
+ /* ------------------------------------------------------------------ */
+
+ /* Ci [0 .. Clen-1] holds the following work arrays:
+
+ first Clen2 entries empty space, must be at least >= n_col
+ next max (nz,1) Bi [0..max (nz,1)-1]
+ next nn+1 entries Bp [0..nn]
+ next nn entries Link [0..nn-1]
+ next nn entries W [0..nn-1]
+ last n_col entries Cperm2 [0..n_col-1]
+
+ This memory usage is accounted for by the UMF_ANALYZE_CLEN
+ macro.
+ */
+
+ Clen2 = Clen0 ;
+ snz = Sp [n_col - n1] ;
+ bsize = MAX (snz, 1) ;
+ Clen2 -= bsize ;
+ Bi = Ci + Clen2 ;
+ ASSERT (Clen2 >= n_col) ;
+
+ (void) UMF_transpose (n_row - n1, n_col - n1 - nempty_col,
+ Sp, Si, (double *) NULL,
+ P, (Int *) NULL, 0, Bp, Bi, (double *) NULL, W, FALSE
+#ifdef COMPLEX
+ , (double *) NULL, (double *) NULL, FALSE
+#endif
+ ) ;
+
+ /* contents of Si and Sp no longer needed */
+
+ /* contents of P (same as Link) and W not needed */
+ /* still need Link and W as work arrays, though ] */
+
+ ASSERT (Bp [0] == 0) ;
+ ASSERT (Bp [n_row - n1] == snz) ;
+
+ /* increment Bp to point into Ci, not Bi */
+ for (i = 0 ; i <= n_row - n1 ; i++)
+ {
+ Bp [i] += Clen2 ;
+ }
+ ASSERT (Bp [0] == Clen0 - bsize) ;
+ ASSERT (Bp [n_row - n1] <= Clen0) ;
+
+ /* Ci [0 .. Clen-1] holds the following work arrays:
+
+ first Clen0 entries Ci [0 .. Clen0-1], where the col indices
+ of B are at the tail end of this part,
+ and Bp [0] = Clen2 >= n_col. Note
+ that Clen0 = Clen2 + max (snz,1).
+ next nn+1 entries Bp [0..nn]
+ next nn entries Link [0..nn-1]
+ next nn entries W [0..nn-1]
+ last n_col entries Cperm2 [0..n_col-1]
+ */
+
+ /* ------------------------------------------------------------------ */
+ /* analyze */
+ /* ------------------------------------------------------------------ */
+
+ /* only analyze the non-empty, non-singleton part of the matrix */
+ ok = UMF_analyze (
+ n_row - n1 - nempty_row,
+ n_col - n1 - nempty_col,
+ Ci, Bp, Cperm2, fixQ, W, Link,
+ Fr_ncols, Fr_nrows, Fr_npivcol,
+ Fr_parent, &nfr, &analyze_compactions) ;
+ if (!ok)
+ {
+ /* :: internal error in umf_analyze :: */
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_internal_error) ;
+ }
+ Info [UMFPACK_SYMBOLIC_DEFRAG] += analyze_compactions ;
+
+ /* ------------------------------------------------------------------ */
+ /* combine the input permutation and UMF_analyze's permutation */
+ /* ------------------------------------------------------------------ */
+
+ if (!fixQ)
+ {
+ /* Cperm2 is the column etree post-ordering */
+ ASSERT (UMF_is_permutation (Cperm2, W,
+ n_col-n1-nempty_col, n_col-n1-nempty_col)) ;
+
+ /* Note that the empty columns remain at the end of Cperm_init */
+ for (k = 0 ; k < n_col - n1 - nempty_col ; k++)
+ {
+ W [k] = Cperm_init [n1 + Cperm2 [k]] ;
+ }
+
+ for (k = 0 ; k < n_col - n1 - nempty_col ; k++)
+ {
+ Cperm_init [n1 + k] = W [k] ;
+ }
+ }
+
+ ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free some of the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* (4) The real workspace, Rs, of size n_row doubles has already been
+ * free'd. An additional workspace of size nz + n_col+1 + n_col integers
+ * is now free'd as well. */
+
+ SW->Si = (Int *) UMF_free ((void *) SW->Si) ;
+ SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ;
+ SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ;
+ ASSERT (SW->Rs == (double *) NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the size of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the size of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ nchains = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ if (Fr_parent [i] != i+1)
+ {
+ nchains++ ;
+ }
+ }
+
+ Symbolic->nchains = nchains ;
+ Symbolic->nfr = nfr ;
+ Symbolic->esize
+ = (max_rdeg > dense_row_threshold) ? (n_col - n1 - nempty_col) : 0 ;
+
+ /* true size of Symbolic object */
+ Info [UMFPACK_SYMBOLIC_SIZE] = UMF_symbolic_usage (n_row, n_col, nchains,
+ nfr, Symbolic->esize, prefer_diagonal) ;
+
+ /* actual peak memory usage for UMFPACK_symbolic (actual nfr, nchains) */
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] =
+ SYM_WORK_USAGE (n_col, n_row, Clen) + Info [UMFPACK_SYMBOLIC_SIZE] ;
+ Symbolic->peak_sym_usage = Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] ;
+
+ DEBUG0 (("Number of fronts: "ID"\n", nfr)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the second part of the Symbolic object (Front_*, Chain_*) */
+ /* ---------------------------------------------------------------------- */
+
+ /* (5) UMF_malloc is called 7 or 8 times, for a total space of
+ * (4*(nfr+1) + 3*(nchains+1) + esize) integers, where nfr is the total
+ * number of frontal matrices and nchains is the total number of frontal
+ * matrix chains, and where nchains <= nfr <= n_col. esize is zero if there
+ * are no dense rows, or n_col-n1-nempty_col otherwise (n1 is the number of
+ * singletons and nempty_col is the number of empty columns). This space is
+ * part of the Symbolic object and is not free'd unless an error occurs.
+ * This is between 7 and about 8n integers when A is square.
+ */
+
+ /* Note that Symbolic->Front_* does include the dummy placeholder front */
+ Symbolic->Front_npivcol = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Front_parent = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Front_1strow = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Front_leftmostdesc = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Chain_start = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ;
+ Symbolic->Chain_maxrows = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ;
+ Symbolic->Chain_maxcols = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ;
+
+ fail = (!Symbolic->Front_npivcol || !Symbolic->Front_parent ||
+ !Symbolic->Front_1strow || !Symbolic->Front_leftmostdesc ||
+ !Symbolic->Chain_start || !Symbolic->Chain_maxrows ||
+ !Symbolic->Chain_maxcols) ;
+
+ if (Symbolic->esize > 0)
+ {
+ Symbolic->Esize = (Int *) UMF_malloc (Symbolic->esize, sizeof (Int)) ;
+ fail = fail || !Symbolic->Esize ;
+ }
+
+ if (fail)
+ {
+ DEBUGm4 (("out of memory: rest of symbolic object\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n",
+ UMF_malloc_count - init_count)) ;
+ ASSERT (UMF_malloc_count == init_count + 21
+ + (SW->Rperm_2by2 != (Int *) NULL)
+ + (Symbolic->Esize != (Int *) NULL)) ;
+
+ Front_npivcol = Symbolic->Front_npivcol ;
+ Front_parent = Symbolic->Front_parent ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+
+ Chain_start = Symbolic->Chain_start ;
+ Chain_maxrows = Symbolic->Chain_maxrows ;
+ Chain_maxcols = Symbolic->Chain_maxcols ;
+
+ Esize = Symbolic->Esize ;
+
+ /* ---------------------------------------------------------------------- */
+ /* assign rows to fronts */
+ /* ---------------------------------------------------------------------- */
+
+ /* find InFront, unless colamd has already computed it */
+ if (do_UMF_analyze)
+ {
+
+ DEBUGm4 ((">>>>>>>>>Computing Front_1strow from scratch\n")) ;
+ /* empty rows go to dummy front nfr */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = nfr ;
+ }
+ /* assign the singleton pivot rows to the "empty" front */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ row = Rperm1 [k] ;
+ InFront [row] = EMPTY ;
+ }
+ DEBUG1 (("Front (EMPTY), singleton nrows "ID" ncols "ID"\n", k, k)) ;
+ newj = n1 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fpivcol = Fr_npivcol [i] ;
+ f1rows = 0 ;
+ /* for all pivot columns in front i */
+ for (kk = 0 ; kk < fpivcol ; kk++, newj++)
+ {
+ j = Cperm_init [newj] ;
+ ASSERT (IMPLIES (newj >= n_col-nempty_col,
+ Ap [j+1] - Ap [j] == 0));
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ row = Ai [p] ;
+ if (InFront [row] == nfr)
+ {
+ /* this row belongs to front i */
+ DEBUG1 ((" Row "ID" in Front "ID"\n", row, i)) ;
+ InFront [row] = i ;
+ f1rows++ ;
+ }
+ }
+ }
+ Front_1strow [i] = f1rows ;
+ DEBUG1 ((" Front "ID" has 1strows: "ID" pivcols "ID"\n",
+ i, f1rows, fpivcol)) ;
+ }
+
+ }
+ else
+ {
+
+ /* COLAMD has already computed InFront, but it is not yet
+ * InFront [row] = front i, where row is an original row. It is
+ * InFront [k-n1] = i for k in the range n1 to n_row-nempty_row,
+ * and where row = Rperm1 [k]. Need to permute InFront. Also compute
+ * # of original rows assembled into each front.
+ * [ use Ci as workspace */
+ DEBUGm4 ((">>>>>>>>>Computing Front_1strow from colamd's InFront\n")) ;
+ for (i = 0 ; i <= nfr ; i++)
+ {
+ Front_1strow [i] = 0 ;
+ }
+ /* assign the singleton pivot rows to "empty" front */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ row = Rperm1 [k] ;
+ Ci [row] = EMPTY ;
+ }
+ /* assign the non-empty rows to the front that assembled them */
+ for ( ; k < n_row - nempty_row ; k++)
+ {
+ row = Rperm1 [k] ;
+ i = InFront [k - n1] ;
+ ASSERT (i >= EMPTY && i < nfr) ;
+ if (i != EMPTY)
+ {
+ Front_1strow [i]++ ;
+ }
+ /* use Ci as permuted version of InFront */
+ Ci [row] = i ;
+ }
+ /* empty rows go to the "dummy" front */
+ for ( ; k < n_row ; k++)
+ {
+ row = Rperm1 [k] ;
+ Ci [row] = nfr ;
+ }
+ /* permute InFront so that InFront [row] = i if the original row is
+ * in front i */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = Ci [row] ;
+ }
+ /* ] no longer need Ci as workspace */
+ }
+
+#ifndef NDEBUG
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (InFront [row] == nfr)
+ {
+ DEBUG1 ((" Row "ID" in Dummy Front "ID"\n", row, nfr)) ;
+ }
+ else if (InFront [row] == EMPTY)
+ {
+ DEBUG1 ((" singleton Row "ID"\n", row)) ;
+ }
+ else
+ {
+ DEBUG1 ((" Row "ID" in Front "ID"\n", row, nfr)) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* copy front information into Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ k = n1 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fpivcol = Fr_npivcol [i] ;
+ DEBUG1 (("Front "ID" k "ID" npivcol "ID" nrows "ID" ncols "ID"\n",
+ i, k, fpivcol, Fr_nrows [i], Fr_ncols [i])) ;
+ k += fpivcol ;
+ /* copy Front info into Symbolic object from SW */
+ Front_npivcol [i] = fpivcol ;
+ Front_parent [i] = Fr_parent [i] ;
+ }
+
+ /* assign empty columns to dummy placehold front nfr */
+ DEBUG1 (("Dummy Cols in Front "ID" : "ID"\n", nfr, n_col-k)) ;
+ Front_npivcol [nfr] = n_col - k ;
+ Front_parent [nfr] = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find initial row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* order the singleton pivot rows */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ Rperm_init [k] = Rperm1 [k] ;
+ }
+
+ /* determine the first row in each front (in the new row ordering) */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ f1rows = Front_1strow [i] ;
+ DEBUG1 (("Front "ID" : npivcol "ID" parent "ID,
+ i, Front_npivcol [i], Front_parent [i])) ;
+ DEBUG1 ((" 1st rows in Front "ID" : "ID"\n", i, f1rows)) ;
+ Front_1strow [i] = k ;
+ k += f1rows ;
+ }
+
+ /* assign empty rows to dummy placehold front nfr */
+ DEBUG1 (("Rows in Front "ID" (dummy): "ID"\n", nfr, n_row-k)) ;
+ Front_1strow [nfr] = k ;
+ DEBUG1 (("nfr "ID" 1strow[nfr] "ID" nrow "ID"\n", nfr, k, n_row)) ;
+
+ /* Use Ci as temporary workspace for F1 */
+ F1 = Ci ; /* [ of size nfr+1 */
+ ASSERT (Clen >= 2*n_row + nfr+1) ;
+
+ for (i = 0 ; i <= nfr ; i++)
+ {
+ F1 [i] = Front_1strow [i] ;
+ }
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ i = InFront [row] ;
+ if (i != EMPTY)
+ {
+ newrow = F1 [i]++ ;
+ ASSERT (newrow >= n1) ;
+ Rperm_init [newrow] = row ;
+ }
+ }
+ Rperm_init [n_row] = EMPTY ; /* unused */
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n_row ; k++)
+ {
+ DEBUG2 (("Rperm_init ["ID"] = "ID"\n", k, Rperm_init [k])) ;
+ }
+#endif
+
+ /* ] done using F1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the diagonal map */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rperm_init [newrow] = row gives the row permutation that is implied
+ * by the column permutation, where "row" is a row index of the original
+ * matrix A. It is not dependent on the Rperm_2by2 permutation, which
+ * only redefines the "diagonal". Both are used to construct the
+ * Diagonal_map. Diagonal_map only needs to be defined for
+ * k = n1 to nn - nempty, but go ahead and define it for all of
+ * k = 0 to nn */
+
+ if (prefer_diagonal)
+ {
+ Int *Diagonal_map ;
+ ASSERT (n_row == n_col && nn == n_row) ;
+ ASSERT (nempty_row == nempty_col && nempty == nempty_row) ;
+
+ /* allocate the Diagonal_map */
+ Symbolic->Diagonal_map = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Diagonal_map = Symbolic->Diagonal_map ;
+ if (Diagonal_map == (Int *) NULL)
+ {
+ /* :: out of memory (diagonal map) :: */
+ DEBUGm4 (("out of memory: Diagonal map\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* use Ci as workspace to compute the inverse of Rperm_init [ */
+ for (newrow = 0 ; newrow < nn ; newrow++)
+ {
+ oldrow = Rperm_init [newrow] ;
+ ASSERT (oldrow >= 0 && oldrow < nn) ;
+ Ci [oldrow] = newrow ;
+ }
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ ASSERT (Rperm_2by2 != (Int *) NULL) ;
+ for (newcol = 0 ; newcol < nn ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ /* 2-by-2 pivoting done in S */
+ oldrow = Rperm_2by2 [oldcol] ;
+ newrow = Ci [oldrow] ;
+ Diagonal_map [newcol] = newrow ;
+ }
+ }
+ else
+ {
+ for (newcol = 0 ; newcol < nn ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ /* no 2-by-2 pivoting in S */
+ oldrow = oldcol ;
+ newrow = Ci [oldrow] ;
+ Diagonal_map [newcol] = newrow ;
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("\nDiagonal map:\n")) ;
+ for (newcol = 0 ; newcol < nn ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ DEBUG3 (("oldcol "ID" newcol "ID":\n", oldcol, newcol)) ;
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ Entry aij ;
+ CLEAR (aij) ;
+ oldrow = Ai [p] ;
+ newrow = Ci [oldrow] ;
+ if (Ax != (double *) NULL)
+ {
+ ASSIGN (aij, Ax, Az, p, SPLIT (Az)) ;
+ }
+ if (oldrow == oldcol)
+ {
+ DEBUG2 ((" old diagonal : oldcol "ID" oldrow "ID" ",
+ oldcol, oldrow)) ;
+ EDEBUG2 (aij) ;
+ DEBUG2 (("\n")) ;
+ }
+ if (newrow == Diagonal_map [newcol])
+ {
+ DEBUG2 ((" MAP diagonal : newcol "ID" MAProw "ID" ",
+ newcol, Diagonal_map [newrow])) ;
+ EDEBUG2 (aij) ;
+ DEBUG2 (("\n")) ;
+ }
+ }
+ }
+#endif
+ /* done using Ci as workspace ] */
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the leftmost descendant of each front */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i <= nfr ; i++)
+ {
+ Front_leftmostdesc [i] = EMPTY ;
+ }
+
+ for (i = 0 ; i < nfr ; i++)
+ {
+ /* start at i and walk up the tree */
+ DEBUG2 (("Walk up front tree from "ID"\n", i)) ;
+ j = i ;
+ while (j != EMPTY && Front_leftmostdesc [j] == EMPTY)
+ {
+ DEBUG3 ((" Leftmost desc of "ID" is "ID"\n", j, i)) ;
+ Front_leftmostdesc [j] = i ;
+ j = Front_parent [j] ;
+ DEBUG3 ((" go to j = "ID"\n", j)) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the frontal matrix chains and max frontal matrix sizes */
+ /* ---------------------------------------------------------------------- */
+
+ maxnrows = 1 ; /* max # rows in any front */
+ maxncols = 1 ; /* max # cols in any front */
+ dmaxfrsize = 1 ; /* max frontal matrix size */
+
+ /* start the first chain */
+ nchains = 0 ; /* number of chains */
+ Chain_start [0] = 0 ; /* front 0 starts a new chain */
+ maxrows = 1 ; /* max # rows for any front in current chain */
+ maxcols = 1 ; /* max # cols for any front in current chain */
+ DEBUG1 (("Constructing chains:\n")) ;
+
+ for (i = 0 ; i < nfr ; i++)
+ {
+ /* get frontal matrix info */
+ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */
+ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp) */
+ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp) */
+ parent = Front_parent [i] ; /* parent in column etree */
+ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */
+ maxrows = MAX (maxrows, fallrows) ;
+ maxcols = MAX (maxcols, fallcols) ;
+
+ DEBUG1 (("Front: "ID", pivcol "ID", "ID"-by-"ID" parent "ID
+ ", npiv "ID" Chain: maxrows "ID" maxcols "ID"\n", i, fpivcol,
+ fallrows, fallcols, parent, fpiv, maxrows, maxcols)) ;
+
+ if (parent != i+1)
+ {
+ /* this is the end of a chain */
+ double s ;
+ DEBUG1 (("\nEnd of chain "ID"\n", nchains)) ;
+
+ /* make sure maxrows is an odd number */
+ ASSERT (maxrows >= 0) ;
+ if (maxrows % 2 == 0) maxrows++ ;
+
+ DEBUG1 (("Chain maxrows "ID" maxcols "ID"\n", maxrows, maxcols)) ;
+
+ Chain_maxrows [nchains] = maxrows ;
+ Chain_maxcols [nchains] = maxcols ;
+
+ /* keep track of the maximum front size for all chains */
+
+ /* for Info only: */
+ s = (double) maxrows * (double) maxcols ;
+ dmaxfrsize = MAX (dmaxfrsize, s) ;
+
+ /* for the subsequent numerical factorization */
+ maxnrows = MAX (maxnrows, maxrows) ;
+ maxncols = MAX (maxncols, maxcols) ;
+
+ DEBUG1 (("Chain dmaxfrsize %g\n\n", dmaxfrsize)) ;
+
+ /* start the next chain */
+ nchains++ ;
+ Chain_start [nchains] = i+1 ;
+ maxrows = 1 ;
+ maxcols = 1 ;
+ }
+ }
+
+ /* for Info only: */
+ dmaxfrsize = ceil (dmaxfrsize) ;
+ DEBUGm1 (("dmaxfrsize %30.20g Int_MAX "ID"\n", dmaxfrsize, Int_MAX)) ;
+ ASSERT (Symbolic->nchains == nchains) ;
+
+ /* For allocating objects in umfpack_numeric (does not include all possible
+ * pivots, particularly pivots from prior fronts in the chain. Need to add
+ * nb to these to get the # of columns in the L block, for example. This
+ * is the largest row dimension and largest column dimension of any frontal
+ * matrix. maxnrows is always odd. */
+ Symbolic->maxnrows = maxnrows ;
+ Symbolic->maxncols = maxncols ;
+ DEBUGm3 (("maxnrows "ID" maxncols "ID"\n", maxnrows, maxncols)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the initial element sizes */
+ /* ---------------------------------------------------------------------- */
+
+ if (max_rdeg > dense_row_threshold)
+ {
+ /* there are one or more dense rows in the input matrix */
+ /* count the number of dense rows in each column */
+ /* use Ci as workspace for inverse of Rperm_init [ */
+ ASSERT (Esize != (Int *) NULL) ;
+ for (newrow = 0 ; newrow < n_row ; newrow++)
+ {
+ oldrow = Rperm_init [newrow] ;
+ ASSERT (oldrow >= 0 && oldrow < nn) ;
+ Ci [oldrow] = newrow ;
+ }
+ for (col = n1 ; col < n_col - nempty_col ; col++)
+ {
+ oldcol = Cperm_init [col] ;
+ esize = Cdeg [oldcol] ;
+ ASSERT (esize > 0) ;
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Ci [oldrow] ;
+ if (newrow >= n1 && Rdeg [oldrow] > dense_row_threshold)
+ {
+ esize-- ;
+ }
+ }
+ ASSERT (esize >= 0) ;
+ Esize [col - n1] = esize ;
+ }
+ /* done using Ci as workspace ] */
+ }
+
+ /* If there are no dense rows, then Esize [col-n1] is identical to
+ * Cdeg [col], once Cdeg is permuted below */
+
+ /* ---------------------------------------------------------------------- */
+ /* permute Cdeg and Rdeg according to initial column and row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Ci as workspace [ */
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Ci [k] = Cdeg [Cperm_init [k]] ;
+ }
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cdeg [k] = Ci [k] ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Ci [k] = Rdeg [Rperm_init [k]] ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rdeg [k] = Ci [k] ;
+ }
+ /* done using Ci as workspace ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* simulate UMF_kernel_init */
+ /* ---------------------------------------------------------------------- */
+
+ /* count elements and tuples at tail, LU factors of singletons, and
+ * head and tail markers */
+
+ dlnz = n_inner ; /* upper limit of nz in L (incl diag) */
+ dunz = dlnz ; /* upper limit of nz in U (incl diag) */
+
+ /* head marker */
+ head_usage = 1 ;
+ dhead_usage = 1 ;
+
+ /* tail markers: */
+ tail_usage = 2 ;
+ dtail_usage = 2 ;
+
+ /* allocate the Rpi and Rpx workspace for UMF_kernel_init (incl. headers) */
+ tail_usage += UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) + 2 ;
+ dtail_usage += DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) + 2 ;
+ DEBUG1 (("Symbolic usage after Rpi/Rpx allocation: head "ID" tail "ID"\n",
+ head_usage, tail_usage)) ;
+
+ /* LU factors for singletons, at the head of memory */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ lnz = Cdeg [k] - 1 ;
+ unz = Rdeg [k] - 1 ;
+ dlnz += lnz ;
+ dunz += unz ;
+ DEBUG1 (("singleton k "ID" pivrow "ID" pivcol "ID" lnz "ID" unz "ID"\n",
+ k, Rperm_init [k], Cperm_init [k], lnz, unz)) ;
+ head_usage += UNITS (Int, lnz) + UNITS (Entry, lnz)
+ + UNITS (Int, unz) + UNITS (Entry, unz) ;
+ dhead_usage += DUNITS (Int, lnz) + DUNITS (Entry, lnz)
+ + DUNITS (Int, unz) + DUNITS (Entry, unz) ;
+ }
+ DEBUG1 (("Symbolic init head usage: "ID" for LU singletons\n",head_usage)) ;
+
+ /* column elements: */
+ for (k = n1 ; k < n_col - nempty_col; k++)
+ {
+ esize = Esize ? Esize [k-n1] : Cdeg [k] ;
+ DEBUG2 ((" esize: "ID"\n", esize)) ;
+ ASSERT (esize >= 0) ;
+ if (esize > 0)
+ {
+ tail_usage += GET_ELEMENT_SIZE (esize, 1) + 1 ;
+ dtail_usage += DGET_ELEMENT_SIZE (esize, 1) + 1 ;
+ }
+ }
+
+ /* dense row elements */
+ if (Esize)
+ {
+ Int nrow_elements = 0 ;
+ for (k = n1 ; k < n_row - nempty_row ; k++)
+ {
+ rdeg = Rdeg [k] ;
+ if (rdeg > dense_row_threshold)
+ {
+ tail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ;
+ dtail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ;
+ nrow_elements++ ;
+ }
+ }
+ Info [UMFPACK_NDENSE_ROW] = nrow_elements ;
+ }
+
+ DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" after els\n",
+ head_usage + tail_usage, head_usage, tail_usage)) ;
+
+ /* compute the tuple lengths */
+ if (Esize)
+ {
+ /* row tuples */
+ for (row = n1 ; row < n_row ; row++)
+ {
+ rdeg = Rdeg [row] ;
+ tlen = (rdeg > dense_row_threshold) ? 1 : rdeg ;
+ tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ;
+ }
+ /* column tuples */
+ for (col = n1 ; col < n_col - nempty_col ; col++)
+ {
+ /* tlen is 1 plus the number of dense rows in this column */
+ esize = Esize [col - n1] ;
+ tlen = (esize > 0) + (Cdeg [col] - esize) ;
+ tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ;
+ }
+ for ( ; col < n_col ; col++)
+ {
+ tail_usage += 1 + UNITS (Tuple, TUPLES (0)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (0)) ;
+ }
+ }
+ else
+ {
+ /* row tuples */
+ for (row = n1 ; row < n_row ; row++)
+ {
+ tlen = Rdeg [row] ;
+ tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ;
+ }
+ /* column tuples */
+ for (col = n1 ; col < n_col ; col++)
+ {
+ tail_usage += 1 + UNITS (Tuple, TUPLES (1)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (1)) ;
+ }
+ }
+
+ Symbolic->num_mem_init_usage = head_usage + tail_usage ;
+ DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" final\n",
+ Symbolic->num_mem_init_usage, head_usage, tail_usage)) ;
+
+ ASSERT (UMF_is_permutation (Rperm_init, Ci, n_row, n_row)) ;
+
+ /* initial head and tail usage in Numeric->Memory */
+ dmax_usage = dhead_usage + dtail_usage ;
+ dmax_usage = MAX (Symbolic->num_mem_init_usage, ceil (dmax_usage)) ;
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE] = dmax_usage ;
+
+ /* In case Symbolic->num_mem_init_usage overflows, keep as a double, too */
+ Symbolic->dnum_mem_init_usage = dmax_usage ;
+
+ /* free the Rpi and Rpx workspace */
+ tail_usage -= UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) ;
+ dtail_usage -= DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* simulate UMF_kernel, assuming unsymmetric pivoting */
+ /* ---------------------------------------------------------------------- */
+
+ /* Use Ci as temporary workspace for link lists [ */
+ Link = Ci ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ Link [i] = EMPTY ;
+ }
+
+ flops = 0 ; /* flop count upper bound */
+
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ double fsize ;
+ f1 = Chain_start [chain] ;
+ f2 = Chain_start [chain+1] - 1 ;
+
+ /* allocate frontal matrix working array (C, L, and U) */
+ dr = Chain_maxrows [chain] ;
+ dc = Chain_maxcols [chain] ;
+ fsize =
+ nb*nb /* LU is nb-by-nb */
+ + dr*nb /* L is dr-by-nb */
+ + nb*dc /* U is nb-by-dc, stored by rows */
+ + dr*dc ; /* C is dr by dc */
+ dtail_usage += DUNITS (Entry, fsize) ;
+ dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ;
+
+ for (i = f1 ; i <= f2 ; i++)
+ {
+
+ /* get frontal matrix info */
+ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */
+ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp*/
+ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp*/
+ parent = Front_parent [i] ; /* parent in column etree */
+ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */
+ f = (double) fpiv ;
+ r = fallrows - fpiv ; /* # rows in Schur comp. */
+ c = fallcols - fpiv ; /* # cols in Schur comp. */
+
+ /* assemble all children of front i in column etree */
+ for (child = Link [i] ; child != EMPTY ; child = Link [child])
+ {
+ ASSERT (child >= 0 && child < i) ;
+ ASSERT (Front_parent [child] == i) ;
+ /* free the child element and remove it from tuple lists */
+ cp = MIN (Front_npivcol [child], Fr_nrows [child]) ;
+ cr = Fr_nrows [child] - cp ;
+ cc = Fr_ncols [child] - cp ;
+ ASSERT (cp >= 0 && cr >= 0 && cc >= 0) ;
+ dtail_usage -= ELEMENT_SIZE (cr, cc) ;
+
+ }
+
+ /* The flop count computed here is "canonical". */
+
+ /* factorize the frontal matrix */
+ flops += DIV_FLOPS * (f*r + (f-1)*f/2) /* scale pivot columns */
+ /* f outer products: */
+ + MULTSUB_FLOPS * (f*r*c + (r+c)*(f-1)*f/2 + (f-1)*f*(2*f-1)/6);
+
+ /* count nonzeros and memory usage in double precision */
+ dlf = (f*f-f)/2 + f*r ; /* nz in L below diagonal */
+ duf = (f*f-f)/2 + f*c ; /* nz in U above diagonal */
+ dlnz += dlf ;
+ dunz += duf ;
+
+ /* store f columns of L and f rows of U */
+ dhead_usage +=
+ DUNITS (Entry, dlf + duf) /* numerical values (excl diag) */
+ + DUNITS (Int, r + c + f) ; /* indices (compressed) */
+
+ if (parent != EMPTY)
+ {
+ /* create new element and place in tuple lists */
+ dtail_usage += ELEMENT_SIZE (r, c) ;
+
+ /* place in link list of parent */
+ Link [i] = Link [parent] ;
+ Link [parent] = i ;
+ }
+
+ /* keep track of peak Numeric->Memory usage */
+ dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ;
+
+ }
+
+ /* free the current frontal matrix */
+ dtail_usage -= DUNITS (Entry, fsize) ;
+ }
+
+ dhead_usage = ceil (dhead_usage) ;
+ dmax_usage = ceil (dmax_usage) ;
+ Symbolic->num_mem_size_est = dhead_usage ;
+ Symbolic->num_mem_usage_est = dmax_usage ;
+ Symbolic->lunz_bound = dlnz + dunz - n_inner ;
+
+ /* ] done using Ci as workspace for Link array */
+
+ /* ---------------------------------------------------------------------- */
+ /* estimate total memory usage in UMFPACK_numeric */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_set_stats (
+ Info,
+ Symbolic,
+ dmax_usage, /* estimated peak size of Numeric->Memory */
+ dhead_usage, /* estimated final size of Numeric->Memory */
+ flops, /* estimated "true flops" */
+ dlnz, /* estimated nz in L */
+ dunz, /* estimated nz in U */
+ dmaxfrsize, /* estimated largest front size */
+ (double) n_col, /* worst case Numeric->Upattern size */
+ (double) n_inner, /* max possible pivots to be found */
+ (double) maxnrows, /* estimated largest #rows in front */
+ (double) maxncols, /* estimated largest #cols in front */
+ TRUE, /* assume scaling is to be performed */
+ prefer_diagonal,
+ ESTIMATE) ;
+
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ for (i = 0 ; i < nchains ; i++)
+ {
+ DEBUG2 (("Chain "ID" start "ID" end "ID" maxrows "ID" maxcols "ID"\n",
+ i, Chain_start [i], Chain_start [i+1] - 1,
+ Chain_maxrows [i], Chain_maxcols [i])) ;
+ UMF_dump_chain (Chain_start [i], Fr_parent, Fr_npivcol, Fr_nrows,
+ Fr_ncols, nfr) ;
+ }
+ fpivcol = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fpivcol = MAX (fpivcol, Front_npivcol [i]) ;
+ }
+ DEBUG0 (("Max pivot cols in any front: "ID"\n", fpivcol)) ;
+ DEBUG1 (("Largest front: maxnrows "ID" maxncols "ID" dmaxfrsize %g\n",
+ maxnrows, maxncols, dmaxfrsize)) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* UMFPACK_symbolic was successful, return the object handle */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic->valid = SYMBOLIC_VALID ;
+ *SymbolicHandle = (void *) Symbolic ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* (6) The last of the workspace is free'd. The final Symbolic object
+ * consists of 12 to 14 allocated objects. Its final total size is lies
+ * roughly between 4*n and 13*n for a square matrix, which is all that is
+ * left of the memory allocated by this routine. If an error occurs, the
+ * entire Symbolic object is free'd when this routine returns (the error
+ * return routine, below).
+ */
+
+ free_work (SW) ;
+
+ DEBUG0 (("(3)Symbolic UMF_malloc_count - init_count = "ID"\n",
+ UMF_malloc_count - init_count)) ;
+ ASSERT (UMF_malloc_count == init_count + 12
+ + (Symbolic->Esize != (Int *) NULL)
+ + (Symbolic->Diagonal_map != (Int *) NULL)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the time used by UMFPACK_*symbolic */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (stats) ;
+ Info [UMFPACK_SYMBOLIC_WALLTIME] = stats [0] ;
+ Info [UMFPACK_SYMBOLIC_TIME] = stats [1] ;
+
+ return (UMFPACK_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === free_work ============================================================ */
+/* ========================================================================== */
+
+PRIVATE void free_work
+(
+ SWType *SW
+)
+{
+ if (SW)
+ {
+ SW->Rperm_2by2 = (Int *) UMF_free ((void *) SW->Rperm_2by2) ;
+ SW->InvRperm1 = (Int *) UMF_free ((void *) SW->InvRperm1) ;
+ SW->Rs = (double *) UMF_free ((void *) SW->Rs) ;
+ SW->Si = (Int *) UMF_free ((void *) SW->Si) ;
+ SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ;
+ SW->Ci = (Int *) UMF_free ((void *) SW->Ci) ;
+ SW->Front_npivcol = (Int *) UMF_free ((void *) SW->Front_npivcol);
+ SW->Front_nrows = (Int *) UMF_free ((void *) SW->Front_nrows) ;
+ SW->Front_ncols = (Int *) UMF_free ((void *) SW->Front_ncols) ;
+ SW->Front_parent = (Int *) UMF_free ((void *) SW->Front_parent) ;
+ SW->Front_cols = (Int *) UMF_free ((void *) SW->Front_cols) ;
+ SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ;
+ SW->Rperm1 = (Int *) UMF_free ((void *) SW->Rperm1) ;
+ SW->InFront = (Int *) UMF_free ((void *) SW->InFront) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === error ================================================================ */
+/* ========================================================================== */
+
+/* Error return from UMFPACK_symbolic. Free all allocated memory. */
+
+PRIVATE void error
+(
+ SymbolicType **Symbolic,
+ SWType *SW
+)
+{
+
+ free_work (SW) ;
+ UMFPACK_free_symbolic ((void **) Symbolic) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_control.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_control.c
new file mode 100644
index 0000000..74a2ed7
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_control.c
@@ -0,0 +1,361 @@
+/* ========================================================================== */
+/* === UMFPACK_report_control =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the control settings. See umfpack_report_control.h
+ for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMFPACK_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ double drow, dcol, relpt, relpt2, alloc_init, front_alloc_init, amd_alpha,
+ tol, force_fixQ, droptol, aggr ;
+ Int prl, nb, irstep, strategy, scale, s ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl < 2)
+ {
+ /* default is to print nothing */
+ return ;
+ }
+
+ PRINTF (("UMFPACK V%d.%d.%d (%s), Control:\n", UMFPACK_MAIN_VERSION,
+ UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* run-time options */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is a "run-time" option because all four umfpack_* versions */
+ /* compiled into the UMFPACK library. */
+
+#ifdef DINT
+ PRINTF ((" Matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef DLONG
+ PRINTF ((" Matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+#ifdef ZINT
+ PRINTF ((" Matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef ZLONG
+ PRINTF ((" Matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* printing level */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("\n "ID": print level: "ID"\n",
+ (Int) INDEX (UMFPACK_PRL), prl)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* dense row/col parameters */
+ /* ---------------------------------------------------------------------- */
+
+ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ;
+ dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ;
+
+ PRINTF ((" "ID": dense row parameter: %g\n",
+ (Int) INDEX (UMFPACK_DENSE_ROW), drow)) ;
+ PRINTF ((" \"dense\" rows have > max (16, (%g)*16*sqrt(n_col)"
+ " entries)\n", drow)) ;
+ PRINTF ((" "ID": dense column parameter: %g\n",
+ (Int) INDEX (UMFPACK_DENSE_COL), dcol)) ;
+ PRINTF ((" \"dense\" columns have > max (16, (%g)*16*sqrt(n_row)"
+ " entries)\n", dcol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* pivot tolerance */
+ /* ---------------------------------------------------------------------- */
+
+ relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_PIVOT_TOLERANCE) ;
+ relpt = MAX (0.0, MIN (relpt, 1.0)) ;
+ PRINTF ((" "ID": pivot tolerance: %g\n",
+ (Int) INDEX (UMFPACK_PIVOT_TOLERANCE), relpt)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* block size */
+ /* ---------------------------------------------------------------------- */
+
+ nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ;
+ nb = MAX (1, nb) ;
+ PRINTF ((" "ID": block size for dense matrix kernels: "ID"\n",
+ (Int) INDEX (UMFPACK_BLOCK_SIZE), nb)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* strategy */
+ /* ---------------------------------------------------------------------- */
+
+ strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ;
+ if (strategy < UMFPACK_STRATEGY_AUTO
+ || strategy > UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ strategy = UMFPACK_STRATEGY_AUTO ;
+ }
+
+ PRINTF ((" "ID": strategy: "ID,
+ (Int) INDEX (UMFPACK_STRATEGY), strategy)) ;
+
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ PRINTF ((" (symmetric)\n"
+ " Q = AMD (A+A'), Q not refined during numerical\n"
+ " factorization, and diagonal pivoting (P=Q') attempted.\n")) ;
+ }
+ else if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ PRINTF ((" (unsymmetric)\n"
+ " Q = COLAMD (A), Q refined during numerical\n"
+ " factorization, and no attempt at diagonal pivoting.\n")) ;
+ }
+ else if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ PRINTF ((" (symmetric, with 2-by-2 block pivoting)\n"
+ " P2 = row permutation that tries to place large entries on\n"
+ " the diagonal. Q = AMD (P2*A+(P2*A)'), Q not refined during\n"
+ " numerical factorization, attempt to select pivots from the\n"
+ " diagonal of P2*A.\n")) ;
+ }
+ else /* auto strategy */
+ {
+ strategy = UMFPACK_STRATEGY_AUTO ;
+ PRINTF ((" (auto)\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* initial allocation parameter */
+ /* ---------------------------------------------------------------------- */
+
+ alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ;
+ if (alloc_init >= 0)
+ {
+ PRINTF ((" "ID": initial allocation ratio: %g\n",
+ (Int) INDEX (UMFPACK_ALLOC_INIT), alloc_init)) ;
+ }
+ else
+ {
+ s = -alloc_init ;
+ s = MAX (1, s) ;
+ PRINTF ((" "ID": initial allocation (in Units): "ID"\n",
+ (Int) INDEX (UMFPACK_ALLOC_INIT), s)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* maximum iterative refinement steps */
+ /* ---------------------------------------------------------------------- */
+
+ irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ;
+ irstep = MAX (0, irstep) ;
+ PRINTF ((" "ID": max iterative refinement steps: "ID"\n",
+ (Int) INDEX (UMFPACK_IRSTEP), irstep)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* 2-by-2 pivot tolerance */
+ /* ---------------------------------------------------------------------- */
+
+ tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ;
+ tol = MAX (0.0, MIN (tol, 1.0)) ;
+ PRINTF ((" "ID": 2-by-2 pivot tolerance: %g\n",
+ (Int) INDEX (UMFPACK_2BY2_TOLERANCE), tol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* force fixQ */
+ /* ---------------------------------------------------------------------- */
+
+ force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ;
+ PRINTF ((" "ID": Q fixed during numerical factorization: %g ",
+ (Int) INDEX (UMFPACK_FIXQ), force_fixQ)) ;
+ if (force_fixQ > 0)
+ {
+ PRINTF (("(yes)\n")) ;
+ }
+ else if (force_fixQ < 0)
+ {
+ PRINTF (("(no)\n")) ;
+ }
+ else
+ {
+ PRINTF (("(auto)\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* AMD parameters */
+ /* ---------------------------------------------------------------------- */
+
+ amd_alpha = GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ;
+ PRINTF ((" "ID": AMD dense row/col parameter: %g\n",
+ (Int) INDEX (UMFPACK_AMD_DENSE), amd_alpha)) ;
+ if (amd_alpha < 0)
+ {
+ PRINTF ((" no \"dense\" rows/columns\n")) ;
+ }
+ else
+ {
+ PRINTF ((" \"dense\" rows/columns have > max (16, (%g)*sqrt(n))"
+ " entries\n", amd_alpha)) ;
+ }
+ PRINTF ((" Only used if the AMD ordering is used.\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* pivot tolerance for symmetric pivoting */
+ /* ---------------------------------------------------------------------- */
+
+ relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ;
+ relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ;
+ PRINTF ((" "ID": diagonal pivot tolerance: %g\n"
+ " Only used if diagonal pivoting is attempted.\n",
+ (Int) INDEX (UMFPACK_SYM_PIVOT_TOLERANCE), relpt2)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scaling */
+ /* ---------------------------------------------------------------------- */
+
+ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
+ if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX)
+ {
+ scale = UMFPACK_DEFAULT_SCALE ;
+ }
+ PRINTF ((" "ID": scaling: "ID, (Int) INDEX (UMFPACK_SCALE), scale)) ;
+ if (scale == UMFPACK_SCALE_NONE)
+ {
+ PRINTF ((" (no)")) ;
+ }
+ else if (scale == UMFPACK_SCALE_SUM)
+ {
+ PRINTF ((" (divide each row by sum of abs. values in each row)")) ;
+ }
+ else if (scale == UMFPACK_SCALE_MAX)
+ {
+ PRINTF ((" (divide each row by max. abs. value in each row)")) ;
+ }
+ PRINTF (("\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* frontal matrix allocation parameter */
+ /* ---------------------------------------------------------------------- */
+
+ front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT,
+ UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ;
+ front_alloc_init = MIN (1.0, front_alloc_init) ;
+ if (front_alloc_init >= 0)
+ {
+ PRINTF ((" "ID": frontal matrix allocation ratio: %g\n",
+ (Int) INDEX (UMFPACK_FRONT_ALLOC_INIT), front_alloc_init)) ;
+ }
+ else
+ {
+ s = -front_alloc_init ;
+ s = MAX (1, s) ;
+ PRINTF ((" "ID": initial frontal matrix size (# of Entry's): "ID"\n",
+ (Int) INDEX (UMFPACK_FRONT_ALLOC_INIT), s)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* drop tolerance */
+ /* ---------------------------------------------------------------------- */
+
+ droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ;
+ PRINTF ((" "ID": drop tolerance: %g\n",
+ (Int) INDEX (UMFPACK_DROPTOL), droptol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* aggressive absorption */
+ /* ---------------------------------------------------------------------- */
+
+ aggr = GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) ;
+ PRINTF ((" "ID": AMD and COLAMD aggressive absorption: %g",
+ (Int) INDEX (UMFPACK_AGGRESSIVE), aggr)) ;
+ if (aggr != 0.0)
+ {
+ PRINTF ((" (yes)\n")) ;
+ }
+ else
+ {
+ PRINTF ((" (no)\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compile-time options */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF ((
+ "\n The following options can only be changed at compile-time:\n")) ;
+
+ PRINTF ((" "ID": BLAS library used: ",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_BLAS))) ;
+
+#ifdef NBLAS
+ PRINTF (("none. UMFPACK will be slow.\n")) ;
+#else
+ PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n",
+ (Int) (sizeof (BLAS_INT)))) ;
+#endif
+
+#ifdef MATLAB_MEX_FILE
+ PRINTF ((" "ID": compiled for MATLAB\n",
+ (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ;
+#else
+#ifdef MATHWORKS
+ PRINTF ((" "ID": compiled for MATLAB\n",
+ (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ;
+#else
+ PRINTF ((" "ID": compiled for ANSI C\n",
+ (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ;
+#endif
+#endif
+
+#ifdef NO_TIMER
+ PRINTF ((" "ID": no CPU timer \n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#else
+#ifndef NPOSIX
+ PRINTF ((" "ID": CPU timer is POSIX times ( ) routine.\n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#else
+#ifdef GETRUSAGE
+ PRINTF ((" "ID": CPU timer is getrusage.\n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#else
+ PRINTF ((" "ID": CPU timer is ANSI C clock (may wrap around).\n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#endif
+#endif
+#endif
+
+#ifndef NDEBUG
+ PRINTF ((
+"**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n"
+" "ID": compiled with debugging enabled. ",
+ (Int) INDEX (UMFPACK_COMPILED_IN_DEBUG_MODE))) ;
+#else
+ PRINTF ((" "ID": compiled for normal operation (debugging disabled)\n",
+ (Int) INDEX (UMFPACK_COMPILED_IN_DEBUG_MODE))) ;
+#endif
+
+ PRINTF ((" computer/operating system: %s\n", UMFPACK_ARCHITECTURE)) ;
+ PRINTF ((" size of int: %g UF_long: %g Int: %g pointer: %g"
+ " double: %g Entry: %g (in bytes)\n\n", (double) sizeof (int),
+ (double) sizeof (UF_long), (double) sizeof (Int),
+ (double) sizeof (void *), (double) sizeof (double),
+ (double) sizeof (Entry))) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_info.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_info.c
new file mode 100644
index 0000000..ff7818b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_info.c
@@ -0,0 +1,611 @@
+/* ========================================================================== */
+/* === UMFPACK_report_info ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the Info array. See umfpack_report_info.h for
+ details.
+*/
+
+#include "umf_internal.h"
+
+#define PRINT_INFO(format,x) \
+{ \
+ if (SCALAR_IS_NAN (x) || (!SCALAR_IS_LTZERO (x))) \
+ { \
+ PRINTF ((format, x)) ; \
+ } \
+}
+
+/* RATIO macro uses a double relop, but ignore NaN case: */
+#define RATIO(a,b,c) (((b) == 0) ? (c) : (((double) a)/((double) b)))
+
+/* ========================================================================== */
+/* === print_ratio ========================================================== */
+/* ========================================================================== */
+
+PRIVATE void print_ratio
+(
+ char *what,
+ char *format,
+ double estimate,
+ double actual
+)
+{
+ if (estimate < 0 && actual < 0) /* double relop, but ignore Nan case */
+ {
+ return ;
+ }
+ PRINTF ((" %-27s", what)) ;
+ if (estimate >= 0) /* double relop, but ignore Nan case */
+ {
+ PRINTF ((format, estimate)) ;
+ }
+ else
+ {
+ PRINTF ((" -")) ;
+ }
+ if (actual >= 0) /* double relop, but ignore Nan case */
+ {
+ PRINTF ((format, actual)) ;
+ }
+ else
+ {
+ PRINTF ((" -")) ;
+ }
+ if (estimate >= 0 && actual >= 0) /* double relop, but ignore Nan case */
+ {
+ PRINTF ((" %5.0f%%\n", 100 * RATIO (actual, estimate, 1))) ;
+ }
+ else
+ {
+ PRINTF ((" -\n")) ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMFPACK_report_info ================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMFPACK_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+)
+{
+
+ double lnz_est, unz_est, lunz_est, lnz, unz, lunz, tsym, tnum, fnum, tsolve,
+ fsolve, ttot, ftot, twsym, twnum, twsolve, twtot, n2 ;
+ Int n_row, n_col, n_inner, prl, is_sym ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control settings and status to determine what to print */
+ /* ---------------------------------------------------------------------- */
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (!Info || prl < 2)
+ {
+ /* no output generated if Info is (double *) NULL */
+ /* or if prl is less than 2 */
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print umfpack version */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("UMFPACK V%d.%d.%d (%s), Info:\n", UMFPACK_MAIN_VERSION,
+ UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ;
+
+#ifndef NDEBUG
+ PRINTF ((
+"**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n"
+ )) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print run-time options */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef DINT
+ PRINTF ((" matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef DLONG
+ PRINTF ((" matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+#ifdef ZINT
+ PRINTF ((" matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef ZLONG
+ PRINTF ((" matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print compile-time options */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF ((" BLAS library used: ")) ;
+
+#ifdef NBLAS
+ PRINTF (("none. UMFPACK will be slow.\n")) ;
+#else
+ PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n",
+ (Int) (sizeof (BLAS_INT)))) ;
+#endif
+
+ PRINTF ((" MATLAB: ")) ;
+#ifdef MATLAB_MEX_FILE
+ PRINTF (("yes.\n")) ;
+#else
+#ifdef MATHWORKS
+ PRINTF (("yes.\n")) ;
+#else
+ PRINTF (("no.\n")) ;
+#endif
+#endif
+
+ PRINTF ((" CPU timer: ")) ;
+#ifdef NO_TIMER
+ PRINTF (("none.\n")) ;
+#else
+#ifndef NPOSIX
+ PRINTF (("POSIX times ( ) routine.\n")) ;
+#else
+#ifdef GETRUSAGE
+ PRINTF (("getrusage ( ) routine.\n")) ;
+#else
+ PRINTF (("ANSI clock ( ) routine.\n")) ;
+#endif
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print n and nz */
+ /* ---------------------------------------------------------------------- */
+
+ n_row = (Int) Info [UMFPACK_NROW] ;
+ n_col = (Int) Info [UMFPACK_NCOL] ;
+ n_inner = MIN (n_row, n_col) ;
+
+ PRINT_INFO (" number of rows in matrix A: "ID"\n", n_row) ;
+ PRINT_INFO (" number of columns in matrix A: "ID"\n", n_col) ;
+ PRINT_INFO (" entries in matrix A: "ID"\n",
+ (Int) Info [UMFPACK_NZ]) ;
+ PRINT_INFO (" memory usage reported in: "ID"-byte Units\n",
+ (Int) Info [UMFPACK_SIZE_OF_UNIT]) ;
+
+ PRINT_INFO (" size of int: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_INT]) ;
+ PRINT_INFO (" size of UF_long: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_LONG]) ;
+ PRINT_INFO (" size of pointer: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_POINTER]) ;
+ PRINT_INFO (" size of numerical entry: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_ENTRY]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ PRINTF (("\n strategy used: symmetric\n")) ;
+ }
+ else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ PRINTF (("\n strategy used: unsymmetric\n")) ;
+ }
+ else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_2BY2)
+ {
+ PRINTF (("\n strategy used: symmetric 2-by-2\n"));
+ }
+
+ if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD)
+ {
+ PRINTF ((" ordering used: amd on A+A'\n")) ;
+ }
+ else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_COLAMD)
+ {
+ PRINTF ((" ordering used: colamd on A\n")) ;
+ }
+ else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_GIVEN)
+ {
+ PRINTF ((" ordering used: provided by user\n")) ;
+ }
+
+ if (Info [UMFPACK_QFIXED] == 1)
+ {
+ PRINTF ((" modify Q during factorization: no\n")) ;
+ }
+ else if (Info [UMFPACK_QFIXED] == 0)
+ {
+ PRINTF ((" modify Q during factorization: yes\n")) ;
+ }
+
+ if (Info [UMFPACK_DIAG_PREFERRED] == 0)
+ {
+ PRINTF ((" prefer diagonal pivoting: no\n")) ;
+ }
+ else if (Info [UMFPACK_DIAG_PREFERRED] == 1)
+ {
+ PRINTF ((" prefer diagonal pivoting: yes\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* singleton statistics */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT_INFO (" pivots with zero Markowitz cost: %0.f\n",
+ Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS]) ;
+ PRINT_INFO (" submatrix S after removing zero-cost pivots:\n"
+ " number of \"dense\" rows: %.0f\n",
+ Info [UMFPACK_NDENSE_ROW]) ;
+ PRINT_INFO (" number of \"dense\" columns: %.0f\n",
+ Info [UMFPACK_NDENSE_COL]) ;
+ PRINT_INFO (" number of empty rows: %.0f\n",
+ Info [UMFPACK_NEMPTY_ROW]) ;
+ PRINT_INFO (" number of empty columns %.0f\n",
+ Info [UMFPACK_NEMPTY_COL]) ;
+ is_sym = Info [UMFPACK_S_SYMMETRIC] ;
+ if (is_sym > 0)
+ {
+ PRINTF ((" submatrix S square and diagonal preserved\n")) ;
+ }
+ else if (is_sym == 0)
+ {
+ PRINTF ((" submatrix S not square or diagonal not preserved\n"));
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics from amd_aat */
+ /* ---------------------------------------------------------------------- */
+
+ n2 = Info [UMFPACK_N2] ;
+ if (n2 >= 0)
+ {
+ PRINTF ((" pattern of square submatrix S:\n")) ;
+ }
+ PRINT_INFO (" number rows and columns %.0f\n",
+ n2) ;
+ PRINT_INFO (" symmetry of nonzero pattern: %.6f\n",
+ Info [UMFPACK_PATTERN_SYMMETRY]) ;
+ PRINT_INFO (" nz in S+S' (excl. diagonal): %.0f\n",
+ Info [UMFPACK_NZ_A_PLUS_AT]) ;
+ PRINT_INFO (" nz on diagonal of matrix S: %.0f\n",
+ Info [UMFPACK_NZDIAG]) ;
+ if (Info [UMFPACK_NZDIAG] >= 0 && n2 > 0)
+ {
+ PRINTF ((" fraction of nz on diagonal: %.6f\n",
+ Info [UMFPACK_NZDIAG] / n2)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics from 2-by-2 permutation */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT_INFO (" 2-by-2 pivoting to place large entries on diagonal:\n"
+ " # of small diagonal entries of S: %.0f\n",
+ Info [UMFPACK_2BY2_NWEAK]) ;
+ PRINT_INFO (" # unmatched: %.0f\n",
+ Info [UMFPACK_2BY2_UNMATCHED]) ;
+ PRINT_INFO (" symmetry of P2*S: %.6f\n",
+ Info [UMFPACK_2BY2_PATTERN_SYMMETRY]) ;
+ PRINT_INFO (" nz in P2*S+(P2*S)' (excl. diag.): %.0f\n",
+ Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT]) ;
+ PRINT_INFO (" nz on diagonal of P2*S: %.0f\n",
+ Info [UMFPACK_2BY2_NZDIAG]) ;
+ if (Info [UMFPACK_2BY2_NZDIAG] >= 0 && n2 > 0)
+ {
+ PRINTF ((" fraction of nz on diag of P2*S: %.6f\n",
+ Info [UMFPACK_2BY2_NZDIAG] / n2)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics from AMD */
+ /* ---------------------------------------------------------------------- */
+
+ if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD)
+ {
+ double dmax = Info [UMFPACK_SYMMETRIC_DMAX] ;
+ PRINTF ((" AMD statistics, for strict diagonal pivoting:\n")) ;
+ PRINT_INFO (" est. flops for LU factorization: %.5e\n",
+ Info [UMFPACK_SYMMETRIC_FLOPS]) ;
+ PRINT_INFO (" est. nz in L+U (incl. diagonal): %.0f\n",
+ Info [UMFPACK_SYMMETRIC_LUNZ]) ;
+ PRINT_INFO (" est. largest front (# entries): %.0f\n",
+ dmax*dmax) ;
+ PRINT_INFO (" est. max nz in any column of L: %.0f\n",
+ dmax) ;
+ PRINT_INFO (
+ " number of \"dense\" rows/columns in S+S': %.0f\n",
+ Info [UMFPACK_SYMMETRIC_NDENSE]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ tsym = Info [UMFPACK_SYMBOLIC_TIME] ;
+ twsym = Info [UMFPACK_SYMBOLIC_WALLTIME] ;
+
+ PRINT_INFO (" symbolic factorization defragmentations: %.0f\n",
+ Info [UMFPACK_SYMBOLIC_DEFRAG]) ;
+ PRINT_INFO (" symbolic memory usage (Units): %.0f\n",
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]) ;
+ PRINT_INFO (" symbolic memory usage (MBytes): %.1f\n",
+ MBYTES (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY])) ;
+ PRINT_INFO (" Symbolic size (Units): %.0f\n",
+ Info [UMFPACK_SYMBOLIC_SIZE]) ;
+ PRINT_INFO (" Symbolic size (MBytes): %.0f\n",
+ MBYTES (Info [UMFPACK_SYMBOLIC_SIZE])) ;
+ PRINT_INFO (" symbolic factorization CPU time (sec): %.2f\n",
+ tsym) ;
+ PRINT_INFO (" symbolic factorization wallclock time(sec): %.2f\n",
+ twsym) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scaling, from numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_NONE)
+ {
+ PRINTF (("\n matrix scaled: no\n")) ;
+ }
+ else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_SUM)
+ {
+ PRINTF (("\n matrix scaled: yes ")) ;
+ PRINTF (("(divided each row by sum of abs values in each row)\n")) ;
+ PRINTF ((" minimum sum (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMIN])) ;
+ PRINTF ((" maximum sum (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMAX])) ;
+ }
+ else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_MAX)
+ {
+ PRINTF (("\n matrix scaled: yes ")) ;
+ PRINTF (("(divided each row by max abs value in each row)\n")) ;
+ PRINTF ((" minimum max (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMIN])) ;
+ PRINTF ((" maximum max (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMAX])) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* estimate/actual in symbolic/numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* double relop, but ignore NaN case: */
+ if (Info [UMFPACK_SYMBOLIC_DEFRAG] >= 0 /* UMFPACK_*symbolic called */
+ || Info [UMFPACK_NUMERIC_DEFRAG] >= 0) /* UMFPACK_numeric called */
+ {
+ PRINTF (("\n symbolic/numeric factorization: upper bound")) ;
+ PRINTF ((" actual %%\n")) ;
+ PRINTF ((" variable-sized part of Numeric object:\n")) ;
+ }
+ print_ratio (" initial size (Units)", " %20.0f",
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE], Info [UMFPACK_VARIABLE_INIT]) ;
+ print_ratio (" peak size (Units)", " %20.0f",
+ Info [UMFPACK_VARIABLE_PEAK_ESTIMATE], Info [UMFPACK_VARIABLE_PEAK]) ;
+ print_ratio (" final size (Units)", " %20.0f",
+ Info [UMFPACK_VARIABLE_FINAL_ESTIMATE], Info [UMFPACK_VARIABLE_FINAL]) ;
+ print_ratio ("Numeric final size (Units)", " %20.0f",
+ Info [UMFPACK_NUMERIC_SIZE_ESTIMATE], Info [UMFPACK_NUMERIC_SIZE]) ;
+ print_ratio ("Numeric final size (MBytes)", " %20.1f",
+ MBYTES (Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]),
+ MBYTES (Info [UMFPACK_NUMERIC_SIZE])) ;
+ print_ratio ("peak memory usage (Units)", " %20.0f",
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE], Info [UMFPACK_PEAK_MEMORY]) ;
+ print_ratio ("peak memory usage (MBytes)", " %20.1f",
+ MBYTES (Info [UMFPACK_PEAK_MEMORY_ESTIMATE]),
+ MBYTES (Info [UMFPACK_PEAK_MEMORY])) ;
+ print_ratio ("numeric factorization flops", " %20.5e",
+ Info [UMFPACK_FLOPS_ESTIMATE], Info [UMFPACK_FLOPS]) ;
+
+ lnz_est = Info [UMFPACK_LNZ_ESTIMATE] ;
+ unz_est = Info [UMFPACK_UNZ_ESTIMATE] ;
+ if (lnz_est >= 0 && unz_est >= 0) /* double relop, but ignore NaN case */
+ {
+ lunz_est = lnz_est + unz_est - n_inner ;
+ }
+ else
+ {
+ lunz_est = EMPTY ;
+ }
+ lnz = Info [UMFPACK_LNZ] ;
+ unz = Info [UMFPACK_UNZ] ;
+ if (lnz >= 0 && unz >= 0) /* double relop, but ignore NaN case */
+ {
+ lunz = lnz + unz - n_inner ;
+ }
+ else
+ {
+ lunz = EMPTY ;
+ }
+ print_ratio ("nz in L (incl diagonal)", " %20.0f", lnz_est, lnz) ;
+ print_ratio ("nz in U (incl diagonal)", " %20.0f", unz_est, unz) ;
+ print_ratio ("nz in L+U (incl diagonal)", " %20.0f", lunz_est, lunz) ;
+
+ print_ratio ("largest front (# entries)", " %20.0f",
+ Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE], Info [UMFPACK_MAX_FRONT_SIZE]) ;
+ print_ratio ("largest # rows in front", " %20.0f",
+ Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE],
+ Info [UMFPACK_MAX_FRONT_NROWS]) ;
+ print_ratio ("largest # columns in front", " %20.0f",
+ Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE],
+ Info [UMFPACK_MAX_FRONT_NCOLS]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ tnum = Info [UMFPACK_NUMERIC_TIME] ;
+ twnum = Info [UMFPACK_NUMERIC_WALLTIME] ;
+ fnum = Info [UMFPACK_FLOPS] ;
+
+ PRINT_INFO ("\n initial allocation ratio used: %0.3g\n",
+ Info [UMFPACK_ALLOC_INIT_USED]) ;
+ PRINT_INFO (" # of forced updates due to frontal growth: %.0f\n",
+ Info [UMFPACK_FORCED_UPDATES]) ;
+ PRINT_INFO (" number of off-diagonal pivots: %.0f\n",
+ Info [UMFPACK_NOFF_DIAG]) ;
+ PRINT_INFO (" nz in L (incl diagonal), if none dropped %.0f\n",
+ Info [UMFPACK_ALL_LNZ]) ;
+ PRINT_INFO (" nz in U (incl diagonal), if none dropped %.0f\n",
+ Info [UMFPACK_ALL_UNZ]) ;
+ PRINT_INFO (" number of small entries dropped %.0f\n",
+ Info [UMFPACK_NZDROPPED]) ;
+ PRINT_INFO (" nonzeros on diagonal of U: %.0f\n",
+ Info [UMFPACK_UDIAG_NZ]) ;
+ PRINT_INFO (" min abs. value on diagonal of U: %.2e\n",
+ Info [UMFPACK_UMIN]) ;
+ PRINT_INFO (" max abs. value on diagonal of U: %.2e\n",
+ Info [UMFPACK_UMAX]) ;
+ PRINT_INFO (" estimate of reciprocal of condition number: %.2e\n",
+ Info [UMFPACK_RCOND]) ;
+ PRINT_INFO (" indices in compressed pattern: %.0f\n",
+ Info [UMFPACK_COMPRESSED_PATTERN]) ;
+ PRINT_INFO (" numerical values stored in Numeric object: %.0f\n",
+ Info [UMFPACK_LU_ENTRIES]) ;
+ PRINT_INFO (" numeric factorization defragmentations: %.0f\n",
+ Info [UMFPACK_NUMERIC_DEFRAG]) ;
+ PRINT_INFO (" numeric factorization reallocations: %.0f\n",
+ Info [UMFPACK_NUMERIC_REALLOC]) ;
+ PRINT_INFO (" costly numeric factorization reallocations: %.0f\n",
+ Info [UMFPACK_NUMERIC_COSTLY_REALLOC]) ;
+ PRINT_INFO (" numeric factorization CPU time (sec): %.2f\n",
+ tnum) ;
+ PRINT_INFO (" numeric factorization wallclock time (sec): %.2f\n",
+ twnum) ;
+
+#define TMIN 0.001
+
+ if (tnum > TMIN && fnum > 0)
+ {
+ PRINT_INFO (
+ " numeric factorization mflops (CPU time): %.2f\n",
+ 1e-6 * fnum / tnum) ;
+ }
+ if (twnum > TMIN && fnum > 0)
+ {
+ PRINT_INFO (
+ " numeric factorization mflops (wallclock): %.2f\n",
+ 1e-6 * fnum / twnum) ;
+ }
+
+ ttot = EMPTY ;
+ ftot = fnum ;
+ if (tsym >= TMIN && tnum >= 0)
+ {
+ ttot = tsym + tnum ;
+ PRINT_INFO (" symbolic + numeric CPU time (sec): %.2f\n",
+ ttot) ;
+ if (ftot > 0 && ttot > TMIN)
+ {
+ PRINT_INFO (
+ " symbolic + numeric mflops (CPU time): %.2f\n",
+ 1e-6 * ftot / ttot) ;
+ }
+ }
+
+ twtot = EMPTY ;
+ if (twsym >= TMIN && twnum >= TMIN)
+ {
+ twtot = twsym + twnum ;
+ PRINT_INFO (" symbolic + numeric wall clock time (sec): %.2f\n",
+ twtot) ;
+ if (ftot > 0 && twtot > TMIN)
+ {
+ PRINT_INFO (
+ " symbolic + numeric mflops (wall clock): %.2f\n",
+ 1e-6 * ftot / twtot) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve */
+ /* ---------------------------------------------------------------------- */
+
+ tsolve = Info [UMFPACK_SOLVE_TIME] ;
+ twsolve = Info [UMFPACK_SOLVE_WALLTIME] ;
+ fsolve = Info [UMFPACK_SOLVE_FLOPS] ;
+
+ PRINT_INFO ("\n solve flops: %.5e\n",
+ fsolve) ;
+ PRINT_INFO (" iterative refinement steps taken: %.0f\n",
+ Info [UMFPACK_IR_TAKEN]) ;
+ PRINT_INFO (" iterative refinement steps attempted: %.0f\n",
+ Info [UMFPACK_IR_ATTEMPTED]) ;
+ PRINT_INFO (" sparse backward error omega1: %.2e\n",
+ Info [UMFPACK_OMEGA1]) ;
+ PRINT_INFO (" sparse backward error omega2: %.2e\n",
+ Info [UMFPACK_OMEGA2]) ;
+ PRINT_INFO (" solve CPU time (sec): %.2f\n",
+ tsolve) ;
+ PRINT_INFO (" solve wall clock time (sec): %.2f\n",
+ twsolve) ;
+ if (fsolve > 0 && tsolve > TMIN)
+ {
+ PRINT_INFO (
+ " solve mflops (CPU time): %.2f\n",
+ 1e-6 * fsolve / tsolve) ;
+ }
+ if (fsolve > 0 && twsolve > TMIN)
+ {
+ PRINT_INFO (
+ " solve mflops (wall clock time): %.2f\n",
+ 1e-6 * fsolve / twsolve) ;
+ }
+
+ if (ftot >= 0 && fsolve >= 0)
+ {
+ ftot += fsolve ;
+ PRINT_INFO (
+ "\n total symbolic + numeric + solve flops: %.5e\n", ftot) ;
+ }
+
+ if (tsolve >= TMIN)
+ {
+ if (ttot >= TMIN && ftot >= 0)
+ {
+ ttot += tsolve ;
+ PRINT_INFO (
+ " total symbolic + numeric + solve CPU time: %.2f\n",
+ ttot) ;
+ if (ftot > 0 && ttot > TMIN)
+ {
+ PRINT_INFO (
+ " total symbolic + numeric + solve mflops (CPU): %.2f\n",
+ 1e-6 * ftot / ttot) ;
+ }
+ }
+ }
+
+ if (twsolve >= TMIN)
+ {
+ if (twtot >= TMIN && ftot >= 0)
+ {
+ twtot += tsolve ;
+ PRINT_INFO (
+ " total symbolic+numeric+solve wall clock time: %.2f\n",
+ twtot) ;
+ if (ftot > 0 && twtot > TMIN)
+ {
+ PRINT_INFO (
+ " total symbolic+numeric+solve mflops(wallclock) %.2f\n",
+ 1e-6 * ftot / twtot) ;
+ }
+ }
+ }
+ PRINTF (("\n")) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_matrix.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_matrix.c
new file mode 100644
index 0000000..6add888
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_matrix.c
@@ -0,0 +1,201 @@
+/* ========================================================================== */
+/* === UMFPACK_report_matrix ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a column or row-oriented matrix. See
+ umfpack_report_matrix.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_report_matrix
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ Int col_form, /* 1: column form, 0: row form */
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Entry a ;
+ Int prl, i, k, length, ilast, p, nz, prl1, p1, p2, n, n_i, do_values ;
+ char *vector, *index ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the form, and check if inputs exist */
+ /* ---------------------------------------------------------------------- */
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ if (col_form)
+ {
+ vector = "column" ; /* column vectors */
+ index = "row" ; /* with row indices */
+ n = n_col ;
+ n_i = n_row ;
+ }
+ else
+ {
+ vector = "row" ; /* row vectors */
+ index = "column" ; /* with column indices */
+ n = n_row ;
+ n_i = n_col ;
+ }
+
+ PRINTF (("%s-form matrix, n_row "ID" n_col "ID", ", vector, n_row, n_col)) ;
+
+ if (n_row <= 0 || n_col <= 0)
+ {
+ PRINTF (("ERROR: n_row <= 0 or n_col <= 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (!Ap)
+ {
+ PRINTF (("ERROR: Ap missing\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ nz = Ap [n] ;
+ PRINTF (("nz = "ID". ", nz)) ;
+ if (nz < 0)
+ {
+ PRINTF (("ERROR: number of entries < 0\n\n")) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ if (Ap [0] != 0)
+ {
+ PRINTF (("ERROR: Ap ["ID"] = "ID" must be "ID"\n\n",
+ (Int) INDEX (0), INDEX (Ap [0]), (Int) INDEX (0))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ if (!Ai)
+ {
+ PRINTF (("ERROR: Ai missing\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ do_values = Ax != (double *) NULL ;
+
+ PRINTF4 (("\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check the row/column pointers, Ap */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ if (Ap [k] < 0)
+ {
+ PRINTF (("ERROR: Ap ["ID"] < 0\n\n", INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ if (Ap [k] > nz)
+ {
+ PRINTF (("ERROR: Ap ["ID"] > size of Ai\n\n", INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ length = Ap [k+1] - Ap [k] ;
+ if (length < 0)
+ {
+ PRINTF (("ERROR: # entries in %s "ID" is < 0\n\n",
+ vector, INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print each vector */
+ /* ---------------------------------------------------------------------- */
+
+ prl1 = prl ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ /* if prl is 4, print the first 10 entries of the first 10 vectors */
+ if (k < 10)
+ {
+ prl = prl1 ;
+ }
+ /* get the vector pointers */
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+ length = p2 - p1 ;
+ PRINTF4 (("\n %s "ID": start: "ID" end: "ID" entries: "ID"\n",
+ vector, INDEX (k), p1, p2-1, length)) ;
+ ilast = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ PRINTF4 (("\t%s "ID" ", index, INDEX (i))) ;
+ if (do_values && prl >= 4)
+ {
+ PRINTF ((":")) ;
+ ASSIGN (a, Ax, Az, p, split) ;
+ PRINT_ENTRY (a) ;
+ }
+ if (i < 0 || i >= n_i)
+ {
+ PRINTF ((" ERROR: %s index "ID" out of range in %s "ID"\n\n",
+ index, INDEX (i), vector, INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ if (i <= ilast)
+ {
+ PRINTF ((" ERROR: %s index "ID" out of order (or duplicate) in "
+ "%s "ID"\n\n", index, INDEX (i), vector, INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ PRINTF4 (("\n")) ;
+ /* truncate printout, but continue to check matrix */
+ if (prl == 4 && (p - p1) == 9 && length > 10)
+ {
+ PRINTF4 (("\t...\n")) ;
+ prl-- ;
+ }
+ ilast = i ;
+ }
+ /* truncate printout, but continue to check matrix */
+ if (prl == 4 && k == 9 && n > 10)
+ {
+ PRINTF4 (("\n ...\n")) ;
+ prl-- ;
+ }
+ }
+ prl = prl1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return the status of the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF4 ((" %s-form matrix ", vector)) ;
+ PRINTF (("OK\n\n")) ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_numeric.c
new file mode 100644
index 0000000..73a5d24
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_numeric.c
@@ -0,0 +1,663 @@
+/* ========================================================================== */
+/* === UMFPACK_report_numeric =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the Numeric object.
+ See umfpack_report_numeric.h for details.
+
+ Dynamic memory usage: Allocates a size n*sizeof(Int) workspace via a single
+ call to UMF_malloc and then frees all of it via UMF_free on return. The
+ workspace is not allocated if an early error return occurs before the
+ workspace is needed.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_report_perm.h"
+#include "umf_report_vector.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+
+PRIVATE Int report_L
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+) ;
+
+
+PRIVATE Int report_U
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+) ;
+
+/* ========================================================================== */
+/* === UMFPACK_report_numeric =============================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_report_numeric
+(
+ void *NumericHandle,
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int prl, *W, nn, n_row, n_col, n_inner, num_fixed_size, numeric_size,
+ npiv ;
+ NumericType *Numeric ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ PRINTF (("Numeric object: ")) ;
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ PRINTF (("ERROR: LU factors invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ npiv = Numeric->npiv ;
+
+ DEBUG1 (("n_row "ID" n_col "ID" nn "ID" n_inner "ID" npiv "ID"\n",
+ n_row, n_col, nn, n_inner, npiv)) ;
+
+ /* size of Numeric object, except Numeric->Memory and Numeric->Upattern */
+ /* see also UMF_set_stats */
+ num_fixed_size =
+ UNITS (NumericType, 1) /* Numeric structure */
+ + UNITS (Entry, n_inner+1) /* D */
+ + UNITS (Int, n_row+1) /* Rperm */
+ + UNITS (Int, n_col+1) /* Cperm */
+ + 6 * UNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */
+ + ((Numeric->scale != UMFPACK_SCALE_NONE) ?
+ UNITS (Entry, n_row) : 0) ; /* Rs */
+
+ DEBUG1 (("num fixed size: "ID"\n", num_fixed_size)) ;
+ DEBUG1 (("Numeric->size "ID"\n", Numeric->size)) ;
+ DEBUG1 (("ulen units "ID"\n", UNITS (Int, Numeric->ulen))) ;
+
+ /* size of Numeric->Memory is Numeric->size */
+ /* size of Numeric->Upattern is Numeric->ulen */
+ numeric_size = num_fixed_size + Numeric->size
+ + UNITS (Int, Numeric->ulen) ;
+
+ DEBUG1 (("numeric total size "ID"\n", numeric_size)) ;
+
+ if (prl >= 4)
+ {
+ PRINTF (("\n n_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
+
+ PRINTF ((" relative pivot tolerance used: %g\n",
+ Numeric->relpt)) ;
+ PRINTF ((" relative symmetric pivot tolerance used: %g\n",
+ Numeric->relpt2)) ;
+
+ PRINTF ((" matrix scaled: ")) ;
+ if (Numeric->scale == UMFPACK_SCALE_NONE)
+ {
+ PRINTF (("no")) ;
+ }
+ else if (Numeric->scale == UMFPACK_SCALE_SUM)
+ {
+ PRINTF (("yes (divided each row by sum abs value in each row)\n")) ;
+ PRINTF ((" minimum sum (abs (rows of A)): %.5e\n",
+ Numeric->rsmin)) ;
+ PRINTF ((" maximum sum (abs (rows of A)): %.5e",
+ Numeric->rsmax)) ;
+ }
+ else if (Numeric->scale == UMFPACK_SCALE_MAX)
+ {
+ PRINTF (("yes (divided each row by max abs value in each row)\n")) ;
+ PRINTF ((" minimum max (abs (rows of A)): %.5e\n",
+ Numeric->rsmin)) ;
+ PRINTF ((" maximum max (abs (rows of A)): %.5e",
+ Numeric->rsmax)) ;
+ }
+ PRINTF (("\n")) ;
+
+ PRINTF ((" initial allocation parameter used: %g\n",
+ Numeric->alloc_init)) ;
+ PRINTF ((" frontal matrix allocation parameter used: %g\n",
+ Numeric->front_alloc_init)) ;
+ PRINTF ((" final total size of Numeric object (Units): "ID"\n",
+ numeric_size)) ;
+ PRINTF ((" final total size of Numeric object (MBytes): %.1f\n",
+ MBYTES (numeric_size))) ;
+ PRINTF ((" peak size of variable-size part (Units): "ID"\n",
+ Numeric->max_usage)) ;
+ PRINTF ((" peak size of variable-size part (MBytes): %.1f\n",
+ MBYTES (Numeric->max_usage))) ;
+ PRINTF ((" largest actual frontal matrix size: "ID"\n",
+ Numeric->maxfrsize)) ;
+ PRINTF ((" memory defragmentations: "ID"\n",
+ Numeric->ngarbage)) ;
+ PRINTF ((" memory reallocations: "ID"\n",
+ Numeric->nrealloc)) ;
+ PRINTF ((" costly memory reallocations: "ID"\n",
+ Numeric->ncostly)) ;
+ PRINTF ((" entries in compressed pattern (L and U): "ID"\n",
+ Numeric->isize)) ;
+ PRINTF ((" number of nonzeros in L (excl diag): "ID"\n",
+ Numeric->lnz)) ;
+ PRINTF ((" number of entries stored in L (excl diag): "ID"\n",
+ Numeric->nLentries)) ;
+ PRINTF ((" number of nonzeros in U (excl diag): "ID"\n",
+ Numeric->unz)) ;
+ PRINTF ((" number of entries stored in U (excl diag): "ID"\n",
+ Numeric->nUentries)) ;
+ PRINTF ((" factorization floating-point operations: %g\n",
+ Numeric->flops)) ;
+ PRINTF ((" number of nonzeros on diagonal of U: "ID"\n",
+ Numeric->nnzpiv)) ;
+ PRINTF ((" min abs. value on diagonal of U: %.5e\n",
+ Numeric->min_udiag)) ;
+ PRINTF ((" max abs. value on diagonal of U: %.5e\n",
+ Numeric->max_udiag)) ;
+ PRINTF ((" reciprocal condition number estimate: %.2e\n",
+ Numeric->rcond)) ;
+ }
+
+ W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!W)
+ {
+ PRINTF ((" ERROR: out of memory to check Numeric object\n\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ if (Numeric->Rs)
+ {
+#ifndef NRECIPROCAL
+ if (Numeric->do_recip)
+ {
+ PRINTF4 (("\nScale factors applied via multiplication\n")) ;
+ }
+ else
+#endif
+ {
+ PRINTF4 (("\nScale factors applied via division\n")) ;
+ }
+ PRINTF4 (("Scale factors, Rs: ")) ;
+ (void) UMF_report_vector (n_row, Numeric->Rs, (double *) NULL,
+ prl, FALSE, TRUE) ;
+ }
+ else
+ {
+ PRINTF4 (("Scale factors, Rs: (not present)\n")) ;
+ }
+
+ PRINTF4 (("\nP: row ")) ;
+ if (UMF_report_perm (n_row, Numeric->Rperm, W, prl, 0) != UMFPACK_OK)
+ {
+ (void) UMF_free ((void *) W) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ PRINTF4 (("\nQ: column ")) ;
+ if (UMF_report_perm (n_col, Numeric->Cperm, W, prl, 0) != UMFPACK_OK)
+ {
+ (void) UMF_free ((void *) W) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ if (!report_L (Numeric, W, prl))
+ {
+ (void) UMF_free ((void *) W) ;
+ PRINTF ((" ERROR: L factor invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ if (!report_U (Numeric, W, prl))
+ {
+ (void) UMF_free ((void *) W) ;
+ PRINTF ((" ERROR: U factor invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ /* The diagonal of U is in "merged" (Entry) form, not "split" form. */
+ PRINTF4 (("\ndiagonal of U: ")) ;
+ (void) UMF_report_vector (n_inner, (double *) Numeric->D, (double *) NULL,
+ prl, FALSE, FALSE) ;
+
+ (void) UMF_free ((void *) W) ;
+
+ PRINTF4 ((" Numeric object: ")) ;
+ PRINTF (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === report_L ============================================================= */
+/* ========================================================================== */
+
+PRIVATE Int report_L
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+)
+{
+ Int k, deg, *ip, j, row, n_row, *Lpos, *Lilen, valid, k1,
+ *Lip, newLchain, llen, prl1, pos, lp, p, npiv, n1, *Li ;
+ Entry *xp, *Lval ;
+
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (prl >= 3) ;
+
+ n_row = Numeric->n_row ;
+ npiv = Numeric->npiv ;
+ n1 = Numeric->n1 ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ prl1 = prl ;
+ deg = 0 ;
+
+ PRINTF4 ((
+ "\nL in Numeric object, in column-oriented compressed-pattern form:\n"
+ " Diagonal entries are all equal to 1.0 (not stored)\n")) ;
+
+ ASSERT (Pattern != (Int *) NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print L */
+ /* ---------------------------------------------------------------------- */
+
+ k1 = 12 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the singleton columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+ lp = Lip [k] ;
+ deg = Lilen [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ PRINTF4 (("\n column "ID":", INDEX (k))) ;
+ PRINTF4 ((" length "ID".\n", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Li [j] ;
+ PRINTF4 (("\trow "ID" : ", INDEX (row))) ;
+ if (prl >= 4) PRINT_ENTRY (Lval [j]) ;
+ if (row <= k || row >= n_row)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ /* truncate printout, but continue to check L */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print the regular columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+ /* if prl is 4, print the first 10 entries of the first 10 columns */
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ }
+
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+
+ PRINTF4 (("\n column "ID":", INDEX (k))) ;
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ PRINTF4 ((" remove row "ID" at position "ID".",
+ INDEX (Pattern [pos]), INDEX (pos))) ;
+ valid = (!newLchain) && (deg > 0) && (pos < deg) && (pos >= 0)
+ && (Pattern [pos] == k) ;
+ if (!valid)
+ {
+ return (FALSE) ;
+ }
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ llen = Lilen [k] ;
+ if (llen < 0)
+ {
+ return (FALSE) ;
+ }
+ p = lp + UNITS (Int, llen) ;
+ xp = (Entry *) (Numeric->Memory + p) ;
+ if ((llen > 0 || deg > 0)
+ && (p + (Int) UNITS (Entry, deg) > Numeric->size))
+ {
+ return (FALSE) ;
+ }
+ if (llen > 0)
+ {
+ PRINTF4 ((" add "ID" entries.", llen)) ;
+ ip = (Int *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ Pattern [deg++] = *ip++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* print column k of L */
+ /* ------------------------------------------------------------------ */
+
+ PRINTF4 ((" length "ID".", deg)) ;
+ if (newLchain)
+ {
+ PRINTF4 ((" Start of Lchain.")) ;
+ }
+ PRINTF4 (("\n")) ;
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Pattern [j] ;
+ PRINTF4 (("\trow "ID" : ", INDEX (row))) ;
+ if (prl >= 4) PRINT_ENTRY (*xp) ;
+ if (row <= k || row >= n_row)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ xp++ ;
+ /* truncate printout, but continue to check L */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+ }
+
+ PRINTF4 (("\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === report_U ============================================================= */
+/* ========================================================================== */
+
+PRIVATE Int report_U
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+)
+{
+ /* ---------------------------------------------------------------------- */
+
+ Int k, deg, j, *ip, col, *Upos, *Uilen, k1, prl1, pos,
+ *Uip, n_col, ulen, p, newUchain, up, npiv, n1, *Ui ;
+ Entry *xp, *Uval ;
+
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (prl >= 3) ;
+
+ n_col = Numeric->n_col ;
+ npiv = Numeric->npiv ;
+ n1 = Numeric->n1 ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ prl1 = prl ;
+
+ PRINTF4 ((
+ "\nU in Numeric object, in row-oriented compressed-pattern form:\n"
+ " Diagonal is stored separately.\n")) ;
+
+ ASSERT (Pattern != (Int *) NULL) ;
+
+ k1 = 12 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the sparse part of U */
+ /* ---------------------------------------------------------------------- */
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* make last pivot row of U (singular matrices only) */
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+
+ PRINTF4 (("\n row "ID": length "ID". End of Uchain.\n", INDEX (npiv-1),
+ deg)) ;
+
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* print row k of U */
+ /* ------------------------------------------------------------------ */
+
+ /* if prl is 3, print the first 10 entries of the first 10 columns */
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ if (ulen < 0)
+ {
+ return (FALSE) ;
+ }
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ p = up + UNITS (Int, ulen) ;
+ }
+ else
+ {
+ p = up ;
+ }
+ xp = (Entry *) (Numeric->Memory + p) ;
+ if (deg > 0 && (p + (Int) UNITS (Entry, deg) > Numeric->size))
+ {
+ return (FALSE) ;
+ }
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Pattern [j] ;
+ PRINTF4 (("\tcol "ID" :", INDEX (col))) ;
+ if (prl >= 4) PRINT_ENTRY (*xp) ;
+ if (col <= k || col >= n_col)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ xp++ ;
+ /* truncate printout, but continue to check U */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+
+ if (k > 0)
+ {
+ PRINTF4 (("\n row "ID": ", INDEX (k-1))) ;
+ }
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ if (k > 0)
+ {
+ deg = ulen ;
+ PRINTF4 (("length "ID". End of Uchain.\n", deg)) ;
+ if (up + (Int) UNITS (Int, ulen) > Numeric->size)
+ {
+ return (FALSE) ;
+ }
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = *ip++ ;
+ }
+ }
+ }
+ else
+ {
+ if (ulen > 0)
+ {
+ PRINTF4 (("remove "ID" entries. ", ulen)) ;
+ }
+ deg -= ulen ;
+ if (deg < 0)
+ {
+ return (FALSE) ;
+ }
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ PRINTF4 (("add column "ID" at position "ID". ",
+ INDEX (k), INDEX (pos))) ;
+ if (pos < 0 || pos > deg)
+ {
+ return (FALSE) ;
+ }
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ PRINTF4 (("length "ID".\n", deg)) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print the singleton rows of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+ up = Uip [k] ;
+ deg = Uilen [k] ;
+ Ui = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ PRINTF4 (("\n row "ID":", INDEX (k))) ;
+ PRINTF4 ((" length "ID".\n", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Ui [j] ;
+ PRINTF4 (("\tcol "ID" : ", INDEX (col))) ;
+ if (prl >= 4) PRINT_ENTRY (Uval [j]) ;
+ if (col <= k || col >= n_col)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ /* truncate printout, but continue to check U */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+ }
+
+ prl = prl1 ;
+ PRINTF4 (("\n")) ;
+ return (TRUE) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_perm.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_perm.c
new file mode 100644
index 0000000..591122b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_perm.c
@@ -0,0 +1,44 @@
+/* ========================================================================== */
+/* === UMFPACK_report_perm ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a permutation vector. See umfpack_report_perm.h
+ for details.
+
+ Dynamic memory usage: Allocates a size max(np,1)*sizeof(Int) workspace via
+ a single call to UMF_malloc and then frees all of it via UMF_free on return.
+*/
+
+#include "umf_internal.h"
+#include "umf_report_perm.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+GLOBAL Int UMFPACK_report_perm
+(
+ Int np,
+ const Int Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int prl, *W, status ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ W = (Int *) UMF_malloc (MAX (np,1), sizeof (Int)) ;
+ status = UMF_report_perm (np, Perm, W, prl, 1) ;
+ (void) UMF_free ((void *) W) ;
+ return (status) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_status.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_status.c
new file mode 100644
index 0000000..068bb7c
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_status.c
@@ -0,0 +1,119 @@
+/* ========================================================================== */
+/* === UMFPACK_report_status ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the return value from other UMFPACK_* routines.
+ See umfpack_report_status.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMFPACK_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ Int status
+)
+{
+ Int prl ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control settings and status to determine what to print */
+ /* ---------------------------------------------------------------------- */
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl < 1)
+ {
+ /* no output generated if prl is less than 1 */
+ return ;
+ }
+
+ if (status == UMFPACK_OK && prl <= 1)
+ {
+ /* no output generated if prl is 1 or less and no error occurred. */
+ /* note that the default printing level is 1. */
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print umfpack license, copyright, version, and status condition */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("\n")) ;
+ PRINTF4 (("%s\n", UMFPACK_COPYRIGHT)) ;
+ PRINTF6 (("%s", UMFPACK_LICENSE_PART1)) ;
+ PRINTF6 (("%s", UMFPACK_LICENSE_PART2)) ;
+ PRINTF6 (("%s", UMFPACK_LICENSE_PART3)) ;
+ PRINTF (("UMFPACK V%d.%d.%d (%s): ", UMFPACK_MAIN_VERSION,
+ UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ;
+
+ switch (status)
+ {
+ case UMFPACK_OK:
+ PRINTF (("OK\n")) ;
+ break ;
+
+ case UMFPACK_WARNING_singular_matrix:
+ PRINTF (("WARNING: matrix is singular\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_out_of_memory:
+ PRINTF (("ERROR: out of memory\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_Numeric_object:
+ PRINTF (("ERROR: Numeric object is invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_Symbolic_object:
+ PRINTF (("ERROR: Symbolic object is invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_argument_missing:
+ PRINTF (("ERROR: required argument(s) missing\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_n_nonpositive:
+ PRINTF (("ERROR: dimension (n_row or n_col) must be > 0\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_matrix:
+ PRINTF (("ERROR: input matrix is invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_system:
+ PRINTF (("ERROR: system argument invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_permutation:
+ PRINTF (("ERROR: invalid permutation\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_different_pattern:
+ PRINTF (("ERROR: pattern of matrix (Ap and/or Ai) has changed\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_internal_error:
+ PRINTF (("INTERNAL ERROR!\n"
+ "Input arguments might be corrupted or aliased, or an internal\n"
+ "error has occurred. Check your input arguments with the\n"
+ "umfpack_*_report_* routines before calling the umfpack_*\n"
+ "computational routines. Recompile UMFPACK with debugging\n"
+ "enabled, and look for failed assertions. If all else fails\n"
+ "please report this error to Tim Davis (davis at cise.ufl.edu).\n"
+ )) ;
+ break ;
+
+ default:
+ PRINTF (("ERROR: Unrecognized error code: "ID"\n", status)) ;
+
+ }
+ PRINTF (("\n")) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_symbolic.c
new file mode 100644
index 0000000..4142834
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_symbolic.c
@@ -0,0 +1,228 @@
+/* ========================================================================== */
+/* === UMFPACK_report_symbolic ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the Symbolic object. See umfpack_report_symbolic.h
+ for details. Does not print new Cdeg, Rdeg, Esize, and the Diagonal_map.
+
+ Dynamic memory usage: Allocates a size MAX (n_row,n_col)*sizeof(Int)
+ workspace via a single call to UMF_malloc and then frees all of it via
+ UMF_free on return. The workspace is not allocated if an early error
+ return occurs before the workspace is needed.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+#include "umf_report_perm.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+GLOBAL Int UMFPACK_report_symbolic
+(
+ void *SymbolicHandle,
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int n_row, n_col, nz, nchains, nfr, maxnrows, maxncols, prl,
+ k, chain, frontid, frontid1, frontid2, kk, *Chain_start, *W,
+ *Chain_maxrows, *Chain_maxcols, *Front_npivcol, *Front_1strow,
+ *Front_leftmostdesc, *Front_parent, done, status1, status2 ;
+ SymbolicType *Symbolic ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ PRINTF (("Symbolic object: ")) ;
+
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ PRINTF (("ERROR: invalid\n")) ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+
+ nz = Symbolic->nz ;
+
+ nchains = Symbolic->nchains ;
+ nfr = Symbolic->nfr ;
+ maxnrows = Symbolic->maxnrows ;
+ maxncols = Symbolic->maxncols ;
+
+ Chain_start = Symbolic->Chain_start ;
+ Chain_maxrows = Symbolic->Chain_maxrows ;
+ Chain_maxcols = Symbolic->Chain_maxcols ;
+ Front_npivcol = Symbolic->Front_npivcol ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+ Front_parent = Symbolic->Front_parent ;
+
+ if (prl >= 4)
+ {
+
+ PRINTF (("\n matrix to be factorized:\n")) ;
+ PRINTF (("\tn_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
+ PRINTF (("\tnumber of entries: "ID"\n", nz)) ;
+ PRINTF ((" block size used for dense matrix kernels: "ID"\n",
+ Symbolic->nb)) ;
+
+ PRINTF ((" strategy used: ")) ;
+ /* strategy cannot be auto */
+ if (Symbolic->strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ PRINTF (("symmetric")) ;
+ }
+ else if (Symbolic->strategy == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ PRINTF (("unsymmetric")) ;
+ }
+ else if (Symbolic->strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ PRINTF (("symmetric 2-by-2")) ;
+ }
+ PRINTF (("\n")) ;
+
+ PRINTF ((" ordering used: ")) ;
+ if (Symbolic->ordering == UMFPACK_ORDERING_COLAMD)
+ {
+ PRINTF (("colamd on A\n")) ;
+ }
+ else if (Symbolic->ordering == UMFPACK_ORDERING_AMD)
+ {
+ PRINTF (("amd on A+A'\n")) ;
+ }
+ else if (Symbolic->ordering == UMFPACK_ORDERING_GIVEN)
+ {
+ PRINTF (("provided by user")) ;
+ }
+ PRINTF (("\n")) ;
+
+ PRINTF ((" performn column etree postorder: ")) ;
+ if (Symbolic->fixQ)
+ {
+ PRINTF (("no\n")) ;
+ }
+ else
+ {
+ PRINTF (("yes\n")) ;
+ }
+
+ PRINTF ((" prefer diagonal pivoting (attempt P=Q): ")) ;
+ if (Symbolic->prefer_diagonal)
+ {
+ PRINTF (("yes\n")) ;
+ }
+ else
+ {
+ PRINTF (("no\n")) ;
+ }
+
+ PRINTF ((" variable-size part of Numeric object:\n")) ;
+ PRINTF (("\tminimum initial size (Units): %.20g (MBytes): %.1f\n",
+ Symbolic->dnum_mem_init_usage,
+ MBYTES (Symbolic->dnum_mem_init_usage))) ;
+ PRINTF (("\testimated peak size (Units): %.20g (MBytes): %.1f\n",
+ Symbolic->num_mem_usage_est,
+ MBYTES (Symbolic->num_mem_usage_est))) ;
+ PRINTF (("\testimated final size (Units): %.20g (MBytes): %.1f\n",
+ Symbolic->num_mem_size_est,
+ MBYTES (Symbolic->num_mem_size_est))) ;
+ PRINTF ((" symbolic factorization memory usage (Units):"
+ " %.20g (MBytes): %.1f\n",
+ Symbolic->peak_sym_usage,
+ MBYTES (Symbolic->peak_sym_usage))) ;
+ PRINTF ((" frontal matrices / supercolumns:\n")) ;
+ PRINTF (("\tnumber of frontal chains: "ID"\n", nchains)) ;
+ PRINTF (("\tnumber of frontal matrices: "ID"\n", nfr)) ;
+ PRINTF (("\tlargest frontal matrix row dimension: "ID"\n", maxnrows)) ;
+ PRINTF (("\tlargest frontal matrix column dimension: "ID"\n",maxncols));
+ }
+
+ k = 0 ;
+ done = FALSE ;
+
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ frontid1 = Chain_start [chain] ;
+ frontid2 = Chain_start [chain+1] - 1 ;
+ PRINTF4 (("\n Frontal chain: "ID". Frontal matrices "ID" to "ID"\n",
+ INDEX (chain), INDEX (frontid1), INDEX (frontid2))) ;
+ PRINTF4 (("\tLargest frontal matrix in Frontal chain: "ID"-by-"ID"\n",
+ Chain_maxrows [chain], Chain_maxcols [chain])) ;
+ for (frontid = frontid1 ; frontid <= frontid2 ; frontid++)
+ {
+ kk = Front_npivcol [frontid] ;
+ PRINTF4 (("\tFront: "ID" pivot cols: "ID" (pivot columns "ID" to "
+ ID")\n", INDEX (frontid), kk, INDEX (k), INDEX (k+kk-1))) ;
+ PRINTF4 (("\t pivot row candidates: "ID" to "ID"\n",
+ INDEX (Front_1strow [Front_leftmostdesc [frontid]]),
+ INDEX (Front_1strow [frontid+1]-1))) ;
+ PRINTF4 (("\t leftmost descendant: "ID"\n",
+ INDEX (Front_leftmostdesc [frontid]))) ;
+ PRINTF4 (("\t 1st new candidate row : "ID"\n",
+ INDEX (Front_1strow [frontid]))) ;
+ PRINTF4 (("\t parent:")) ;
+ if (Front_parent [frontid] == EMPTY)
+ {
+ PRINTF4 ((" (none)\n")) ;
+ }
+ else
+ {
+ PRINTF4 ((" "ID"\n", INDEX (Front_parent [frontid]))) ;
+ }
+ done = (frontid == 20 && frontid < nfr-1 && prl == 4) ;
+ if (done)
+ {
+ PRINTF4 (("\t...\n")) ;
+ break ;
+ }
+ k += kk ;
+ }
+ if (Front_npivcol [nfr] != 0)
+ {
+ PRINTF4 (("\tFront: "ID" placeholder for "ID" empty columns\n",
+ INDEX (nfr), Front_npivcol [nfr])) ;
+ }
+ if (done)
+ {
+ break ;
+ }
+ }
+
+ W = (Int *) UMF_malloc (MAX (n_row, n_col), sizeof (Int)) ;
+ if (!W)
+ {
+ PRINTF (("ERROR: out of memory to check Symbolic object\n\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ PRINTF4 (("\nInitial column permutation, Q1: ")) ;
+ status1 = UMF_report_perm (n_col, Symbolic->Cperm_init, W, prl, 0) ;
+
+ PRINTF4 (("\nInitial row permutation, P1: ")) ;
+ status2 = UMF_report_perm (n_row, Symbolic->Rperm_init, W, prl, 0) ;
+
+ (void) UMF_free ((void *) W) ;
+
+ if (status1 != UMFPACK_OK || status2 != UMFPACK_OK)
+ {
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ PRINTF4 ((" Symbolic object: ")) ;
+ PRINTF (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_triplet.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_triplet.c
new file mode 100644
index 0000000..6bb6fb8
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_triplet.c
@@ -0,0 +1,99 @@
+/* ========================================================================== */
+/* === UMFPACK_report_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a matrix in triplet form. See
+ umfpack_report_triplet.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_report_triplet
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ const double Tx [ ],
+#ifdef COMPLEX
+ const double Tz [ ],
+#endif
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Entry t ;
+ Int prl, prl1, k, i, j, do_values ;
+#ifdef COMPLEX
+ Int split = SPLIT (Tz) ;
+#endif
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ PRINTF (("triplet-form matrix, n_row = "ID", n_col = "ID" nz = "ID". ",
+ n_row, n_col, nz)) ;
+
+ if (!Ti || !Tj)
+ {
+ PRINTF (("ERROR: indices not present\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ if (n_row <= 0 || n_col <= 0)
+ {
+ PRINTF (("ERROR: n_row or n_col is <= 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (nz < 0)
+ {
+ PRINTF (("ERROR: nz is < 0\n\n")) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ PRINTF4 (("\n")) ;
+
+ do_values = Tx != (double *) NULL ;
+
+ prl1 = prl ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ PRINTF4 ((" "ID" : "ID" "ID" ", INDEX (k), INDEX (i), INDEX (j))) ;
+ if (do_values && prl >= 4)
+ {
+ ASSIGN (t, Tx, Tz, k, split) ;
+ PRINT_ENTRY (t) ;
+ }
+ PRINTF4 (("\n")) ;
+ if (i < 0 || i >= n_row || j < 0 || j >= n_col)
+ {
+ /* invalid triplet */
+ PRINTF (("ERROR: invalid triplet\n\n")) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ if (prl == 4 && k == 9 && nz > 10)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ }
+ prl = prl1 ;
+
+ PRINTF4 ((" triplet-form matrix ")) ;
+ PRINTF (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_vector.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_vector.c
new file mode 100644
index 0000000..3b27d3f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_report_vector.c
@@ -0,0 +1,43 @@
+/* ========================================================================== */
+/* === UMFPACK_report_vector ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a real or complex vector.
+ See umfpack_report_vector.h for details.
+*/
+
+#include "umf_internal.h"
+#include "umf_report_vector.h"
+
+GLOBAL Int UMFPACK_report_vector
+(
+ Int n,
+ const double Xx [ ],
+#ifdef COMPLEX
+ const double Xz [ ],
+#endif
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int prl ;
+
+#ifndef COMPLEX
+ double *Xz = (double *) NULL ;
+#endif
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ return (UMF_report_vector (n, Xx, Xz, prl, TRUE, FALSE)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_save_numeric.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_save_numeric.c
new file mode 100644
index 0000000..2d8a73f
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_save_numeric.c
@@ -0,0 +1,92 @@
+/* ========================================================================== */
+/* === UMFPACK_save_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Saves a Numeric object to a file. It can later be read back
+ in via a call to umfpack_*_load_numeric.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+#define WRITE(object,type,n) \
+{ \
+ ASSERT (object != (type *) NULL) ; \
+ if (fwrite (object, sizeof (type), n, f) != n) \
+ { \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_save_numeric ================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_save_numeric
+(
+ void *NumericHandle,
+ char *user_filename
+)
+{
+ NumericType *Numeric ;
+ char *filename ;
+ FILE *f ;
+
+ /* get the Numeric object */
+ Numeric = (NumericType *) NumericHandle ;
+
+ /* make sure the Numeric object is valid */
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ /* get the filename, or use the default name if filename is NULL */
+ if (user_filename == (char *) NULL)
+ {
+ filename = "numeric.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "wb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* write the Numeric object to the file, in binary */
+ WRITE (Numeric, NumericType, 1) ;
+ WRITE (Numeric->D, Entry, MIN (Numeric->n_row, Numeric->n_col)+1) ;
+ WRITE (Numeric->Rperm, Int, Numeric->n_row+1) ;
+ WRITE (Numeric->Cperm, Int, Numeric->n_col+1) ;
+ WRITE (Numeric->Lpos, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Lilen, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Lip, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Upos, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Uilen, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Uip, Int, Numeric->npiv+1) ;
+ if (Numeric->scale != UMFPACK_SCALE_NONE)
+ {
+ WRITE (Numeric->Rs, double, Numeric->n_row) ;
+ }
+ if (Numeric->ulen > 0)
+ {
+ WRITE (Numeric->Upattern, Int, Numeric->ulen+1) ;
+ }
+ WRITE (Numeric->Memory, Unit, Numeric->size) ;
+
+ /* close the file */
+ fclose (f) ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_save_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_save_symbolic.c
new file mode 100644
index 0000000..c326b28
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_save_symbolic.c
@@ -0,0 +1,95 @@
+/* ========================================================================== */
+/* === UMFPACK_save_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Saves a Symbolic object to a file. It can later be read
+ back in via a call to umfpack_*_load_symbolic.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+
+#define WRITE(object,type,n) \
+{ \
+ ASSERT (object != (type *) NULL) ; \
+ if (fwrite (object, sizeof (type), n, f) != n) \
+ { \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_save_symbolic ================================================ */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_save_symbolic
+(
+ void *SymbolicHandle,
+ char *user_filename
+)
+{
+ SymbolicType *Symbolic ;
+ char *filename ;
+ FILE *f ;
+
+ /* get the Symbolic object */
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+
+ /* make sure the Symbolic object is valid */
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ /* get the filename, or use the default name if filename is NULL */
+ if (user_filename == (char *) NULL)
+ {
+ filename = "symbolic.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "wb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* write the Symbolic object to the file, in binary */
+ WRITE (Symbolic, SymbolicType, 1) ;
+ WRITE (Symbolic->Cperm_init, Int, Symbolic->n_col+1) ;
+ WRITE (Symbolic->Rperm_init, Int, Symbolic->n_row+1) ;
+ WRITE (Symbolic->Front_npivcol, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Front_parent, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Front_1strow, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Front_leftmostdesc, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Chain_start, Int, Symbolic->nchains+1) ;
+ WRITE (Symbolic->Chain_maxrows, Int, Symbolic->nchains+1) ;
+ WRITE (Symbolic->Chain_maxcols, Int, Symbolic->nchains+1) ;
+ WRITE (Symbolic->Cdeg, Int, Symbolic->n_col+1) ;
+ WRITE (Symbolic->Rdeg, Int, Symbolic->n_row+1) ;
+ if (Symbolic->esize > 0)
+ {
+ /* only when dense rows are present */
+ WRITE (Symbolic->Esize, Int, Symbolic->esize) ;
+ }
+ if (Symbolic->prefer_diagonal)
+ {
+ /* only when diagonal pivoting is prefered */
+ WRITE (Symbolic->Diagonal_map, Int, Symbolic->n_col+1) ;
+ }
+
+ /* close the file */
+ fclose (f) ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_scale.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_scale.c
new file mode 100644
index 0000000..5a08616
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_scale.c
@@ -0,0 +1,158 @@
+/* ========================================================================== */
+/* === UMFPACK_scale ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Applies the scale factors computed during numerical
+ factorization to a vector. See umfpack_scale.h for more details.
+
+ The LU factorization is L*U = P*R*A*Q, where P and Q are permutation
+ matrices, and R is diagonal. This routine computes X = R * B using the
+ matrix R stored in the Numeric object.
+
+ Returns FALSE if any argument is invalid, TRUE otherwise.
+
+ If R not present in the Numeric object, then R = I and no floating-point
+ work is done. B is simply copied into X.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+GLOBAL Int UMFPACK_scale
+(
+ double Xx [ ],
+#ifdef COMPLEX
+ double Xz [ ],
+#endif
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Bz [ ],
+#endif
+ void *NumericHandle
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ NumericType *Numeric ;
+ Int n, i ;
+ double *Rs ;
+#ifdef COMPLEX
+ Int split = SPLIT (Xz) && SPLIT (Bz) ;
+#endif
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ n = Numeric->n_row ;
+ Rs = Numeric->Rs ;
+
+ if (!Xx || !Bx)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* X = R*B or R\B */
+ /* ---------------------------------------------------------------------- */
+
+ if (Rs != (double *) NULL)
+ {
+#ifndef NRECIPROCAL
+ if (Numeric->do_recip)
+ {
+ /* multiply by the scale factors */
+#ifdef COMPLEX
+ if (split)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] * Rs [i] ;
+ Xz [i] = Bz [i] * Rs [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2*i ] = Bx [2*i ] * Rs [i] ;
+ Xx [2*i+1] = Bx [2*i+1] * Rs [i] ;
+ }
+ }
+#else
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] * Rs [i] ;
+ }
+#endif
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+#ifdef COMPLEX
+ if (split)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] / Rs [i] ;
+ Xz [i] = Bz [i] / Rs [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2*i ] = Bx [2*i ] / Rs [i] ;
+ Xx [2*i+1] = Bx [2*i+1] / Rs [i] ;
+ }
+ }
+#else
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] / Rs [i] ;
+ }
+#endif
+ }
+ }
+ else
+ {
+ /* no scale factors, just copy B into X */
+#ifdef COMPLEX
+ if (split)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] ;
+ Xz [i] = Bz [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2*i ] = Bx [2*i ] ;
+ Xx [2*i+1] = Bx [2*i+1] ;
+ }
+ }
+#else
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] ;
+ }
+#endif
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_solve.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_solve.c
new file mode 100644
index 0000000..fcdebe2
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_solve.c
@@ -0,0 +1,245 @@
+/* ========================================================================== */
+/* === UMFPACK_solve ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Solves a linear system using the numerical factorization
+ computed by UMFPACK_numeric. See umfpack_solve.h for more details.
+
+ For umfpack_*_solve:
+ Dynamic memory usage: UMFPACK_solve calls UMF_malloc twice, for
+ workspace of size c*n*sizeof(double) + n*sizeof(Int), where c is
+ defined below. On return, all of this workspace is free'd via UMF_free.
+
+ For umfpack_*_wsolve:
+ No dynamic memory usage. Input arrays are used for workspace instead.
+ Pattern is a workspace of size n Integers. The double array W must be
+ at least of size c*n, where c is defined below.
+
+ If iterative refinement is requested, and Ax=b, A'x=b or A.'x=b is being
+ solved, and the matrix A is not singular, then c is 5 for the real version
+ and 10 for the complex version. Otherwise, c is 1 for the real version and
+ 4 for the complex version.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_solve.h"
+
+#ifndef WSOLVE
+#include "umf_malloc.h"
+#include "umf_free.h"
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+#endif
+
+GLOBAL Int
+#ifdef WSOLVE
+UMFPACK_wsolve
+#else
+UMFPACK_solve
+#endif
+(
+ Int sys,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ double Xx [ ],
+#ifdef COMPLEX
+ double Xz [ ],
+#endif
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Bz [ ],
+#endif
+ void *NumericHandle,
+ const double Control [UMFPACK_CONTROL],
+ double User_Info [UMFPACK_INFO]
+#ifdef WSOLVE
+ , Int Pattern [ ],
+ double W [ ]
+#endif
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double Info2 [UMFPACK_INFO], stats [2] ;
+ double *Info ;
+ NumericType *Numeric ;
+ Int n, i, irstep, status ;
+#ifndef WSOLVE
+ Int *Pattern, wsize ;
+ double *W ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get the amount of time used by the process so far */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (stats) ;
+
+#ifndef WSOLVE
+#ifndef NDEBUG
+ init_count = UMF_malloc_count ;
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ;
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ /* clear the parts of Info that are set by UMFPACK_solve */
+ for (i = UMFPACK_IR_TAKEN ; i <= UMFPACK_SOLVE_TIME ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+ Info [UMFPACK_SOLVE_FLOPS] = 0 ;
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ Info [UMFPACK_NROW] = Numeric->n_row ;
+ Info [UMFPACK_NCOL] = Numeric->n_col ;
+
+ if (Numeric->n_row != Numeric->n_col)
+ {
+ /* only square systems can be handled */
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
+ return (UMFPACK_ERROR_invalid_system) ;
+ }
+ n = Numeric->n_row ;
+ if (Numeric->nnzpiv < n
+ || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
+ {
+ /* turn off iterative refinement if A is singular */
+ /* or if U has NaN's on the diagonal. */
+ irstep = 0 ;
+ }
+
+ if (!Xx || !Bx)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ if (sys >= UMFPACK_Pt_L)
+ {
+ /* no iterative refinement except for nonsingular Ax=b, A'x=b, A.'x=b */
+ irstep = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate or check the workspace */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef WSOLVE
+
+ if (!W || !Pattern)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+#else
+
+#ifdef COMPLEX
+ if (irstep > 0)
+ {
+ wsize = 10*n ; /* W, X, Z, S, Y, B2 */
+ }
+ else
+ {
+ wsize = 4*n ; /* W, X */
+ }
+#else
+ if (irstep > 0)
+ {
+ wsize = 5*n ; /* W, Z, S, Y, B2 */
+ }
+ else
+ {
+ wsize = n ; /* W */
+ }
+#endif
+
+ Pattern = (Int *) UMF_malloc (n, sizeof (Int)) ;
+ W = (double *) UMF_malloc (wsize, sizeof (double)) ;
+ if (!W || !Pattern)
+ {
+ DEBUGm4 (("out of memory: solve work\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ (void) UMF_free ((void *) W) ;
+ (void) UMF_free ((void *) Pattern) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+#endif /* WSOLVE */
+
+ /* ---------------------------------------------------------------------- */
+ /* solve the system */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMF_solve (sys, Ap, Ai, Ax, Xx, Bx,
+#ifdef COMPLEX
+ Az, Xz, Bz,
+#endif
+ Numeric, irstep, Info, Pattern, W) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace (if allocated) */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef WSOLVE
+ (void) UMF_free ((void *) W) ;
+ (void) UMF_free ((void *) Pattern) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get the time used by UMFPACK_*solve */
+ /* ---------------------------------------------------------------------- */
+
+ Info [UMFPACK_STATUS] = status ;
+ if (status >= 0)
+ {
+ umfpack_toc (stats) ;
+ Info [UMFPACK_SOLVE_WALLTIME] = stats [0] ;
+ Info [UMFPACK_SOLVE_TIME] = stats [1] ;
+ }
+
+ return (status) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_symbolic.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_symbolic.c
new file mode 100644
index 0000000..39ee106
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_symbolic.c
@@ -0,0 +1,39 @@
+/* ========================================================================== */
+/* === UMFPACK_symbolic ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Performs a symbolic factorization.
+ See umfpack_symbolic.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_symbolic
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ void **SymbolicHandle,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+)
+{
+ Int *Qinit = (Int *) NULL ;
+ return (UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Qinit, SymbolicHandle, Control, Info)) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_tictoc.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_tictoc.c
new file mode 100644
index 0000000..605f789
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_tictoc.c
@@ -0,0 +1,106 @@
+/* ========================================================================== */
+/* === umfpack_tictoc ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Returns the time in seconds used by the process, and
+ the current wall clock time. BE CAREFUL: if you compare the run time of
+ UMFPACK with other sparse matrix packages, be sure to use the same timer.
+ See umfpack_tictoc.h for details.
+
+ These routines conform to the POSIX standard. See umf_config.h for
+ more details.
+*/
+
+#include "umf_internal.h"
+
+#ifdef NO_TIMER
+
+/* -------------------------------------------------------------------------- */
+/* no timer used if -DNO_TIMER is defined at compile time */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_tic (double stats [2])
+{
+ stats [0] = 0 ;
+ stats [1] = 0 ;
+}
+
+void umfpack_toc (double stats [2])
+{
+ stats [0] = 0 ;
+ stats [1] = 0 ;
+}
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* timer routines, using either times() or clock() */
+/* -------------------------------------------------------------------------- */
+
+#define TINY_TIME 1e-4
+
+#ifndef NPOSIX
+
+#include <unistd.h>
+#include <sys/times.h>
+
+void umfpack_tic (double stats [2])
+{
+ /* Return the current time */
+ /* stats [0]: current wallclock time, in seconds */
+ /* stats [1]: user + system time for the process, in seconds */
+
+ double ticks ;
+ struct tms t ;
+
+ ticks = (double) sysconf (_SC_CLK_TCK) ;
+ stats [0] = (double) times (&t) / ticks ;
+ stats [1] = (double) (t.tms_utime + t.tms_stime) / ticks ;
+
+ /* if time is tiny, just return zero */
+ if (stats [0] < TINY_TIME) stats [0] = 0 ;
+ if (stats [1] < TINY_TIME) stats [1] = 0 ;
+}
+
+#else
+
+/* Generic ANSI C: use the ANSI clock function. No wallclock time. */
+
+#include <time.h>
+
+void umfpack_tic (double stats [2])
+{
+ stats [0] = 0 ;
+ stats [1] = ((double) (clock ( ))) / ((double) (CLOCKS_PER_SEC)) ;
+ if (stats [1] < TINY_TIME) stats [1] = 0 ;
+}
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+void umfpack_toc (double stats [2])
+{
+ /* Return the current time since the last call to umfpack_tic. */
+ /* On input, stats holds the values returned by umfpack_tic. */
+ /* On ouput, stats holds the time since the last umfpack_tic. */
+
+ double done [2] ;
+ umfpack_tic (done) ;
+
+ stats [0] = done [0] - stats [0] ;
+ stats [1] = done [1] - stats [1] ;
+
+ if (stats [0] < 0) stats [0] = 0 ;
+ if (stats [1] < 0) stats [1] = 0 ;
+
+}
+
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_timer.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_timer.c
new file mode 100644
index 0000000..7e8d20b
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_timer.c
@@ -0,0 +1,83 @@
+/* ========================================================================== */
+/* === umfpack_timer ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Returns the time in seconds used by the process. BE
+ CAREFUL: if you compare the run time of UMFPACK with other sparse matrix
+ packages, be sure to use the same timer. See umfpack_timer.h for details.
+ See umfpack_tictoc.h, which is the timer used internally by UMFPACK.
+*/
+
+#ifdef NO_TIMER
+
+/* -------------------------------------------------------------------------- */
+/* no timer used if -DNO_TIMER is defined at compile time */
+/* -------------------------------------------------------------------------- */
+
+double umfpack_timer ( void )
+{
+ return (0) ;
+}
+
+#else
+
+#ifdef GETRUSAGE
+
+/* -------------------------------------------------------------------------- */
+/* use getrusage for accurate process times (and no overflow) */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This works under Solaris, SGI Irix, Linux, IBM RS 6000 (AIX), and Compaq
+ Alpha. It might work on other Unix systems, too. Includes both the "user
+ time" and the "system time". The system time is the time spent by the
+ operating system on behalf of the process, and thus should be charged to
+ the process.
+*/
+
+#include <sys/time.h>
+#include <sys/resource.h>
+
+double umfpack_timer ( void )
+{
+ struct rusage ru ;
+ double user_time, sys_time ;
+
+ (void) getrusage (RUSAGE_SELF, &ru) ;
+
+ user_time =
+ ru.ru_utime.tv_sec /* user time (seconds) */
+ + 1e-6 * ru.ru_utime.tv_usec ; /* user time (microseconds) */
+
+ sys_time =
+ ru.ru_stime.tv_sec /* system time (seconds) */
+ + 1e-6 * ru.ru_stime.tv_usec ; /* system time (microseconds) */
+
+ return (user_time + sys_time) ;
+}
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* Generic ANSI C: use the ANSI clock function */
+/* -------------------------------------------------------------------------- */
+
+/* This is portable, but may overflow. On Sun Solaris, when compiling in */
+/* 32-bit mode, the overflow occurs in only 2147 seconds (about 36 minutes). */
+
+#include <time.h>
+
+double umfpack_timer ( void )
+{
+ return (((double) (clock ( ))) / ((double) (CLOCKS_PER_SEC))) ;
+}
+
+#endif
+#endif
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_transpose.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_transpose.c
new file mode 100644
index 0000000..4a6b9ba
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_transpose.c
@@ -0,0 +1,108 @@
+/* ========================================================================== */
+/* === UMFPACK_transpose ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User callable. Computes a permuted transpose, R = (A (P,Q))' in MATLAB
+ notation. See umfpack_transpose.h for details. A and R can be rectangular.
+ The matrix A may be singular.
+ The complex version can do transpose (') or array transpose (.').
+
+ Dynamic memory usage: A single call to UMF_malloc is made, for a workspace
+ of size max (n_row,n_col,1) * sizeof(Int). This is then free'd on return,
+ via UMF_free.
+*/
+
+#include "umf_internal.h"
+#include "umf_transpose.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_transpose
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const double Ax [ ], /* size nz, if present */
+#ifdef COMPLEX
+ const double Az [ ], /* size nz, if present */
+#endif
+
+ const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/
+ /* P is identity if not present */
+ /* size n_row, if present */
+
+ const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/
+ /* Q is identity if not present */
+ /* size n_col, if present */
+
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ double Rx [ ] /* size nz, if present */
+#ifdef COMPLEX
+ , double Rz [ ] /* size nz, if present */
+ , Int do_conjugate /* if true, then to conjugate transpose */
+ /* otherwise, do array transpose */
+#endif
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int status, *W, nn ;
+
+#ifndef NDEBUG
+ init_count = UMF_malloc_count ;
+ UMF_dump_start ( ) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nn = MAX (n_row, n_col) ;
+ nn = MAX (nn, 1) ;
+ W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!W)
+ {
+ DEBUGm4 (("out of memory: transpose work\n")) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ ASSERT (UMF_malloc_count == init_count + 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = (A (P,Q))' or (A (P,Q)).' */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMF_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, n_col, Rp, Ri, Rx,
+ W, TRUE
+#ifdef COMPLEX
+ , Az, Rz, do_conjugate
+#endif
+ ) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) W) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+
+ return (status) ;
+}
diff --git a/src/C/SuiteSparse/UMFPACK/Source/umfpack_triplet_to_col.c b/src/C/SuiteSparse/UMFPACK/Source/umfpack_triplet_to_col.c
new file mode 100644
index 0000000..92f5a8d
--- /dev/null
+++ b/src/C/SuiteSparse/UMFPACK/Source/umfpack_triplet_to_col.c
@@ -0,0 +1,225 @@
+/* ========================================================================== */
+/* === UMFPACK_triplet_to_col =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User callable. Converts triplet input to column-oriented form. Duplicate
+ entries may exist (they are summed in the output). The columns of the
+ column-oriented form are in sorted order. The input is not modified.
+ Returns 1 if OK, 0 if an error occurred. See umfpack_triplet_to_col.h for
+ details.
+
+ If Map is present (a non-NULL pointer to an Int array of size nz), then on
+ output it holds the position of the triplets in the column-form matrix.
+ That is, suppose p = Map [k], and the k-th triplet is i=Ti[k], j=Tj[k], and
+ aij=Tx[k]. Then i=Ai[p], and aij will have been summed into Ax[p]. Also,
+ Ap[j] <= p < Ap[j+1]. The Map array is not computed if it is (Int *) NULL.
+
+ Dynamic memory usage:
+
+ If numerical values are present, then one (two for complex version)
+ workspace of size (nz+1)*sizeof(double) is allocated via UMF_malloc.
+ Next, 4 calls to UMF_malloc are made to obtain workspace of size
+ ((nz+1) + (n_row+1) + n_row + MAX (n_row,n_col)) * sizeof(Int). All of
+ this workspace (4 to 6 objects) are free'd via UMF_free on return.
+
+ For the complex version, additional space is allocated.
+
+ An extra array of size nz*sizeof(Int) is allocated if Map is present.
+*/
+
+#include "umf_internal.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+#include "umf_triplet.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_triplet_to_col
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ], /* size nz */
+ const Int Tj [ ], /* size nz */
+ const double Tx [ ], /* size nz */
+#ifdef COMPLEX
+ const double Tz [ ], /* size nz */
+#endif
+ Int Ap [ ], /* size n_col + 1 */
+ Int Ai [ ], /* size nz */
+ double Ax [ ] /* size nz */
+#ifdef COMPLEX
+ , double Az [ ] /* size nz */
+#endif
+ , Int Map [ ] /* size nz */
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int *RowCount, *Rp, *Rj, *W, nn, do_values, do_map, *Map2, status ;
+ double *Rx ;
+#ifdef COMPLEX
+ double *Rz ;
+ Int split ;
+#endif
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ init_count = UMF_malloc_count ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Ai || !Ap || !Ti || !Tj)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ if (n_row <= 0 || n_col <= 0) /* must be > 0 */
+ {
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (nz < 0) /* nz must be >= 0 (singular matrices are OK) */
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ nn = MAX (n_row, n_col) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Rx = (double *) NULL ;
+
+ do_values = Ax && Tx ;
+
+ if (do_values)
+ {
+#ifdef COMPLEX
+ Rx = (double *) UMF_malloc (2*nz+2, sizeof (double)) ;
+ split = SPLIT (Tz) && SPLIT (Az) ;
+ if (split)
+ {
+ Rz = Rx + nz ;
+ }
+ else
+ {
+ Rz = (double *) NULL ;
+ }
+#else
+ Rx = (double *) UMF_malloc (nz+1, sizeof (double)) ;
+#endif
+ if (!Rx)
+ {
+ DEBUGm4 (("out of memory: triplet work \n")) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ }
+
+ do_map = (Map != (Int *) NULL) ;
+ Map2 = (Int *) NULL ;
+ if (do_map)
+ {
+ DEBUG0 (("Do map:\n")) ;
+ Map2 = (Int *) UMF_malloc (nz+1, sizeof (Int)) ;
+ if (!Map2)
+ {
+ DEBUGm4 (("out of memory: triplet map\n")) ;
+ (void) UMF_free ((void *) Rx) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ }
+
+ Rj = (Int *) UMF_malloc (nz+1, sizeof (Int)) ;
+ Rp = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ RowCount = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+ W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!Rj || !Rp || !RowCount || !W)
+ {
+ DEBUGm4 (("out of memory: triplet work (int)\n")) ;
+ (void) UMF_free ((void *) Rx) ;
+ (void) UMF_free ((void *) Map2) ;
+ (void) UMF_free ((void *) Rp) ;
+ (void) UMF_free ((void *) Rj) ;
+ (void) UMF_free ((void *) RowCount) ;
+ (void) UMF_free ((void *) W) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ ASSERT (UMF_malloc_count == init_count + 4 +
+ (Rx != (double *) NULL) + do_map) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert from triplet to column form */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_map)
+ {
+ if (do_values)
+ {
+ status = UMF_triplet_map_x (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp,
+ Rj, W, RowCount, Tx, Ax, Rx
+#ifdef COMPLEX
+ , Tz, Az, Rz
+#endif
+ , Map, Map2) ;
+ }
+ else
+ {
+ status = UMF_triplet_map_nox (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp,
+ Rj, W, RowCount, Map, Map2) ;
+ }
+ }
+ else
+ {
+ if (do_values)
+ {
+ status = UMF_triplet_nomap_x (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp,
+ Rj, W, RowCount , Tx, Ax, Rx
+#ifdef COMPLEX
+ , Tz, Az, Rz
+#endif
+ ) ;
+ }
+ else
+ {
+ status = UMF_triplet_nomap_nox (n_row, n_col, nz, Ti, Tj, Ap, Ai,
+ Rp, Rj, W, RowCount) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) Rx) ;
+ (void) UMF_free ((void *) Map2) ;
+ (void) UMF_free ((void *) Rp) ;
+ (void) UMF_free ((void *) Rj) ;
+ (void) UMF_free ((void *) RowCount) ;
+ (void) UMF_free ((void *) W) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+
+ return (status) ;
+}
diff --git a/src/C/SuiteSparse_cvxopt_extra/README b/src/C/SuiteSparse_cvxopt_extra/README
new file mode 100644
index 0000000..952cf9e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/README
@@ -0,0 +1,7 @@
+This directory contains CVXOPT specific modifications to the libraries
+in SuiteSparse necessary to build them with CVXOPT using distutils.
+
+The additions are very minor; the directory contains a number of
+files for different numerical types (int, long, single and double
+precision floating point etc.) that would normally be automatically
+generated by the C preprocessor.
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_global.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_global.c
new file mode 100644
index 0000000..e8c9e8e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_global.c
@@ -0,0 +1 @@
+#include "../../SuiteSparse/AMD/Source/amd_global.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_1.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_1.c
new file mode 100644
index 0000000..4353630
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_1.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_1.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_2.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_2.c
new file mode 100644
index 0000000..75d8670
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_2.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_2.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_aat.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_aat.c
new file mode 100644
index 0000000..16042e2
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_aat.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_aat.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_defaults.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_defaults.c
new file mode 100644
index 0000000..9ec8227
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_defaults.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_defaults.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_dump.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_dump.c
new file mode 100644
index 0000000..ba46149
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_dump.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_dump.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_order.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_order.c
new file mode 100644
index 0000000..9a396e5
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_order.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_order.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_post_tree.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_post_tree.c
new file mode 100644
index 0000000..bfbf2ce
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_post_tree.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_post_tree.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_postorder.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_postorder.c
new file mode 100644
index 0000000..6f51bad
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_postorder.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_postorder.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_preprocess.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_preprocess.c
new file mode 100644
index 0000000..b5fb2c3
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_preprocess.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_preprocess.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_valid.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_valid.c
new file mode 100644
index 0000000..18f02d9
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_i_valid.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/AMD/Source/amd_valid.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_1.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_1.c
new file mode 100644
index 0000000..d5ecba0
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_1.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_1.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_2.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_2.c
new file mode 100644
index 0000000..5a18aca
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_2.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_2.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_aat.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_aat.c
new file mode 100644
index 0000000..77f7ac8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_aat.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_aat.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_defaults.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_defaults.c
new file mode 100644
index 0000000..5c8c865
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_defaults.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_defaults.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_dump.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_dump.c
new file mode 100644
index 0000000..c598601
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_dump.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_dump.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_order.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_order.c
new file mode 100644
index 0000000..4003f6d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_order.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_order.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_post_tree.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_post_tree.c
new file mode 100644
index 0000000..cb4851c
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_post_tree.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_post_tree.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_postorder.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_postorder.c
new file mode 100644
index 0000000..db6e9d7
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_postorder.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_postorder.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_preprocess.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_preprocess.c
new file mode 100644
index 0000000..a7c9c30
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_preprocess.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_preprocess.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_valid.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_valid.c
new file mode 100644
index 0000000..3804def
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/amd_l_valid.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/AMD/Source/amd_valid.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_2by2.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_2by2.c
new file mode 100644
index 0000000..c27a474
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_2by2.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_2by2.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_assemble.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_assemble.c
new file mode 100644
index 0000000..84212ac
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_assemble.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_assemble_fixq.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_assemble_fixq.c
new file mode 100644
index 0000000..d5eeb60
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_assemble_fixq.c
@@ -0,0 +1,3 @@
+#define DINT
+#define FIXQ
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_blas3_update.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_blas3_update.c
new file mode 100644
index 0000000..f8dc40d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_blas3_update.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_blas3_update.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_build_tuples.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_build_tuples.c
new file mode 100644
index 0000000..1b7fcda
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_build_tuples.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_build_tuples.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_create_element.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_create_element.c
new file mode 100644
index 0000000..026507f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_create_element.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_create_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_extend_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_extend_front.c
new file mode 100644
index 0000000..97583a0
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_extend_front.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_extend_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_garbage_collection.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_garbage_collection.c
new file mode 100644
index 0000000..5a8f268
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_garbage_collection.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_garbage_collection.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_get_memory.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_get_memory.c
new file mode 100644
index 0000000..fedad1e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_get_memory.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_get_memory.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_grow_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_grow_front.c
new file mode 100644
index 0000000..c11fb7a
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_grow_front.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_grow_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_init_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_init_front.c
new file mode 100644
index 0000000..1952f39
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_init_front.c
@@ -0,0 +1,3 @@
+#define DINT
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_init_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel.c
new file mode 100644
index 0000000..f1837ba
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel_init.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel_init.c
new file mode 100644
index 0000000..46bf880
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel_init.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_init.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel_wrapup.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel_wrapup.c
new file mode 100644
index 0000000..a09a080
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_kernel_wrapup.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_lhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_lhsolve.c
new file mode 100644
index 0000000..49c9547
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_lhsolve.c
@@ -0,0 +1,3 @@
+#define DINT
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_local_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_local_search.c
new file mode 100644
index 0000000..fcbbdb8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_local_search.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_local_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_lsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_lsolve.c
new file mode 100644
index 0000000..b6c592f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_lsolve.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_lsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_ltsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_ltsolve.c
new file mode 100644
index 0000000..a4b7882
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_ltsolve.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_element.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_element.c
new file mode 100644
index 0000000..044733d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_element.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_head_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_head_block.c
new file mode 100644
index 0000000..7ff901e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_head_block.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_tail_block.c
new file mode 100644
index 0000000..32afac8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_alloc_tail_block.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_free_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_free_tail_block.c
new file mode 100644
index 0000000..e0ac11b
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_free_tail_block.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_init_memoryspace.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_init_memoryspace.c
new file mode 100644
index 0000000..2faaf74
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_mem_init_memoryspace.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_row_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_row_search.c
new file mode 100644
index 0000000..50e4cab
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_row_search.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_row_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_scale.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_scale.c
new file mode 100644
index 0000000..a89fe95
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_scale.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_scale_column.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_scale_column.c
new file mode 100644
index 0000000..f86b9f8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_scale_column.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale_column.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_set_stats.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_set_stats.c
new file mode 100644
index 0000000..339c537
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_set_stats.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_set_stats.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_solve.c
new file mode 100644
index 0000000..2a1f680
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_solve.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_start_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_start_front.c
new file mode 100644
index 0000000..3f6ead3
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_start_front.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_start_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_store_lu.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_store_lu.c
new file mode 100644
index 0000000..b38ea09
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_store_lu.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_store_lu_drop.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_store_lu_drop.c
new file mode 100644
index 0000000..7cb0fce
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_store_lu_drop.c
@@ -0,0 +1,3 @@
+#define DINT
+#define DROP
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_symbolic_usage.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_symbolic_usage.c
new file mode 100644
index 0000000..3e72467
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_symbolic_usage.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_transpose.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_transpose.c
new file mode 100644
index 0000000..2401dfe
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_transpose.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_transpose.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_tuple_lengths.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_tuple_lengths.c
new file mode 100644
index 0000000..1f80970
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_tuple_lengths.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_uhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_uhsolve.c
new file mode 100644
index 0000000..441f34f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_uhsolve.c
@@ -0,0 +1,3 @@
+#define DINT
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_usolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_usolve.c
new file mode 100644
index 0000000..c0cd333
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_usolve.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_usolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_utsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_utsolve.c
new file mode 100644
index 0000000..70de72b
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_utsolve.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_valid_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_valid_numeric.c
new file mode 100644
index 0000000..81ade90
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_valid_numeric.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_valid_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_valid_symbolic.c
new file mode 100644
index 0000000..4b5f446
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_di_valid_symbolic.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_2by2.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_2by2.c
new file mode 100644
index 0000000..12b54c4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_2by2.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_2by2.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_assemble.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_assemble.c
new file mode 100644
index 0000000..f49c736
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_assemble.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_assemble_fixq.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_assemble_fixq.c
new file mode 100644
index 0000000..1796089
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_assemble_fixq.c
@@ -0,0 +1,3 @@
+#define DLONG
+#define FIXQ
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_blas3_update.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_blas3_update.c
new file mode 100644
index 0000000..b73b37d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_blas3_update.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_blas3_update.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_build_tuples.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_build_tuples.c
new file mode 100644
index 0000000..dc8b4fc
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_build_tuples.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_build_tuples.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_create_elememt.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_create_elememt.c
new file mode 100644
index 0000000..dcf93a3
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_create_elememt.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_create_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_extend_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_extend_front.c
new file mode 100644
index 0000000..25e91aa
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_extend_front.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_extend_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_garbage_collection.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_garbage_collection.c
new file mode 100644
index 0000000..3cf1c70
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_garbage_collection.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_garbage_collection.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_get_memory.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_get_memory.c
new file mode 100644
index 0000000..760a8e4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_get_memory.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_get_memory.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_grow_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_grow_front.c
new file mode 100644
index 0000000..e15ed69
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_grow_front.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_grow_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_init_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_init_front.c
new file mode 100644
index 0000000..5a13725
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_init_front.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_init_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel.c
new file mode 100644
index 0000000..83b565f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel_init.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel_init.c
new file mode 100644
index 0000000..a20b9c0
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel_init.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_init.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel_wrapup.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel_wrapup.c
new file mode 100644
index 0000000..ab63c41
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_kernel_wrapup.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_lhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_lhsolve.c
new file mode 100644
index 0000000..135efdd
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_lhsolve.c
@@ -0,0 +1,4 @@
+#define DLONG
+
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_local_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_local_search.c
new file mode 100644
index 0000000..cd14206
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_local_search.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_local_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_lsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_lsolve.c
new file mode 100644
index 0000000..a3a912c
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_lsolve.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_lsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_ltsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_ltsolve.c
new file mode 100644
index 0000000..3a40f06
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_ltsolve.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_element.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_element.c
new file mode 100644
index 0000000..4557361
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_element.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_head_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_head_block.c
new file mode 100644
index 0000000..7553478
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_head_block.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_tail_block.c
new file mode 100644
index 0000000..00e7617
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_alloc_tail_block.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_free_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_free_tail_block.c
new file mode 100644
index 0000000..cce27ae
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_free_tail_block.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_init_memoryspace.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_init_memoryspace.c
new file mode 100644
index 0000000..db0ce68
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_mem_init_memoryspace.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_row_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_row_search.c
new file mode 100644
index 0000000..ca116ac
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_row_search.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_row_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_scale.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_scale.c
new file mode 100644
index 0000000..3843545
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_scale.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_scale_column.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_scale_column.c
new file mode 100644
index 0000000..3fc1fa7
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_scale_column.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale_column.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_set_stats.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_set_stats.c
new file mode 100644
index 0000000..b79cd00
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_set_stats.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_set_stats.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_solve.c
new file mode 100644
index 0000000..58ec5e6
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_solve.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_start_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_start_front.c
new file mode 100644
index 0000000..9724290
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_start_front.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_start_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_store_lu.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_store_lu.c
new file mode 100644
index 0000000..cf7d91e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_store_lu.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_store_lu_drop.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_store_lu_drop.c
new file mode 100644
index 0000000..de8fcfc
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_store_lu_drop.c
@@ -0,0 +1,3 @@
+#define DLONG
+#define DROP
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_symbolic_usage.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_symbolic_usage.c
new file mode 100644
index 0000000..e86dba6
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_symbolic_usage.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_transpose.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_transpose.c
new file mode 100644
index 0000000..4283da4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_transpose.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_transpose.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_tuple_lengths.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_tuple_lengths.c
new file mode 100644
index 0000000..0c15b26
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_tuple_lengths.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_uhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_uhsolve.c
new file mode 100644
index 0000000..c966c08
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_uhsolve.c
@@ -0,0 +1,4 @@
+#define DLONG
+
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_usolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_usolve.c
new file mode 100644
index 0000000..e17eb16
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_usolve.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_usolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_utsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_utsolve.c
new file mode 100644
index 0000000..a9c3e99
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_utsolve.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_valid_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_valid_numeric.c
new file mode 100644
index 0000000..55cc2f7
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_valid_numeric.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_valid_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_valid_symbolic.c
new file mode 100644
index 0000000..0979643
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_dl_valid_symbolic.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_analyze.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_analyze.c
new file mode 100644
index 0000000..76e3f5d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_analyze.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_analyze.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_apply_order.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_apply_order.c
new file mode 100644
index 0000000..3d2ad76
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_apply_order.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_apply_order.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_colamd.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_colamd.c
new file mode 100644
index 0000000..aa018f1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_colamd.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_colamd.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_free.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_free.c
new file mode 100644
index 0000000..0600fb5
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_free.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_free.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_fsize.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_fsize.c
new file mode 100644
index 0000000..27191c0
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_fsize.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_fsize.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_is_permutation.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_is_permutation.c
new file mode 100644
index 0000000..c874291
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_is_permutation.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_is_permutation.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_malloc.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_malloc.c
new file mode 100644
index 0000000..b9026e3
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_malloc.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_malloc.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_realloc.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_realloc.c
new file mode 100644
index 0000000..1f32b99
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_realloc.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_realloc.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_singletons.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_singletons.c
new file mode 100644
index 0000000..57c713d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_i_singletons.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_singletons.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_analyze.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_analyze.c
new file mode 100644
index 0000000..df42f24
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_analyze.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_analyze.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_apply_order.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_apply_order.c
new file mode 100644
index 0000000..91a3027
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_apply_order.c
@@ -0,0 +1,2 @@
+#define DLONG
+#include "../../SuiteSparse/UMFPACK/Source/umf_apply_order.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_colamd.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_colamd.c
new file mode 100644
index 0000000..a974488
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_colamd.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_colamd.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_free.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_free.c
new file mode 100644
index 0000000..7ce0a3a
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_free.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_free.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_fsize.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_fsize.c
new file mode 100644
index 0000000..359c9b3
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_fsize.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_fsize.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_is_permutation.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_is_permutation.c
new file mode 100644
index 0000000..bc2846c
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_is_permutation.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_is_permutation.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_malloc.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_malloc.c
new file mode 100644
index 0000000..bfc2e26
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_malloc.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_malloc.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_realloc.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_realloc.c
new file mode 100644
index 0000000..410060f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_realloc.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_realloc.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_singletons.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_singletons.c
new file mode 100644
index 0000000..c991f08
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_l_singletons.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_singletons.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_2by2.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_2by2.c
new file mode 100644
index 0000000..7ab8cfa
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_2by2.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_2by2.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_assemble.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_assemble.c
new file mode 100644
index 0000000..d1717bd
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_assemble.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_assemble_fixq.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_assemble_fixq.c
new file mode 100644
index 0000000..9eeccc1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_assemble_fixq.c
@@ -0,0 +1,3 @@
+#define ZINT
+#define FIXQ
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_blas3_update.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_blas3_update.c
new file mode 100644
index 0000000..297ed18
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_blas3_update.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_blas3_update.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_build_tuples.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_build_tuples.c
new file mode 100644
index 0000000..c22f9c6
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_build_tuples.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_build_tuples.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_create_element.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_create_element.c
new file mode 100644
index 0000000..12be344
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_create_element.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_create_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_extend_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_extend_front.c
new file mode 100644
index 0000000..92eb622
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_extend_front.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_extend_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_garbage_collection.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_garbage_collection.c
new file mode 100644
index 0000000..98f9cf7
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_garbage_collection.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_garbage_collection.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_get_memory.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_get_memory.c
new file mode 100644
index 0000000..d3a35d9
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_get_memory.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_get_memory.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_grow_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_grow_front.c
new file mode 100644
index 0000000..e5c10f2
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_grow_front.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_grow_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_init_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_init_front.c
new file mode 100644
index 0000000..b90e7fe
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_init_front.c
@@ -0,0 +1,3 @@
+#define ZINT
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_init_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel.c
new file mode 100644
index 0000000..dbdfde4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel_init.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel_init.c
new file mode 100644
index 0000000..3c55c35
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel_init.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_init.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel_wrapup.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel_wrapup.c
new file mode 100644
index 0000000..0dae817
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_kernel_wrapup.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_lhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_lhsolve.c
new file mode 100644
index 0000000..1cdbad9
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_lhsolve.c
@@ -0,0 +1,3 @@
+#define ZINT
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_local_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_local_search.c
new file mode 100644
index 0000000..751cf5c
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_local_search.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_local_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_lsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_lsolve.c
new file mode 100644
index 0000000..9260f15
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_lsolve.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_lsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_ltsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_ltsolve.c
new file mode 100644
index 0000000..6a19361
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_ltsolve.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_element.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_element.c
new file mode 100644
index 0000000..b4e411f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_element.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_head_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_head_block.c
new file mode 100644
index 0000000..180a21a
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_head_block.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_tail_block.c
new file mode 100644
index 0000000..b00850a
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_alloc_tail_block.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_free_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_free_tail_block.c
new file mode 100644
index 0000000..1579e4e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_free_tail_block.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_init_memoryspace.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_init_memoryspace.c
new file mode 100644
index 0000000..5b8cbbb
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_mem_init_memoryspace.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_row_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_row_search.c
new file mode 100644
index 0000000..82218a9
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_row_search.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_row_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_scale.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_scale.c
new file mode 100644
index 0000000..0f24eaa
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_scale.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_scale_column.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_scale_column.c
new file mode 100644
index 0000000..dd71747
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_scale_column.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale_column.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_set_stats.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_set_stats.c
new file mode 100644
index 0000000..b2fccdd
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_set_stats.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_set_stats.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_solve.c
new file mode 100644
index 0000000..05774ed
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_solve.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_start_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_start_front.c
new file mode 100644
index 0000000..578992d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_start_front.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_start_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_store_lu.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_store_lu.c
new file mode 100644
index 0000000..2d5f40d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_store_lu.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_store_lu_drop.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_store_lu_drop.c
new file mode 100644
index 0000000..123ec11
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_store_lu_drop.c
@@ -0,0 +1,3 @@
+#define ZINT
+#define DROP
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_symbolic_usage.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_symbolic_usage.c
new file mode 100644
index 0000000..3b7bc05
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_symbolic_usage.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_transpose.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_transpose.c
new file mode 100644
index 0000000..152e783
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_transpose.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_transpose.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_tuple_lengths.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_tuple_lengths.c
new file mode 100644
index 0000000..3a23016
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_tuple_lengths.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_uhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_uhsolve.c
new file mode 100644
index 0000000..e6d78d8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_uhsolve.c
@@ -0,0 +1,3 @@
+#define ZINT
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_usolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_usolve.c
new file mode 100644
index 0000000..3aa1c43
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_usolve.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_usolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_utsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_utsolve.c
new file mode 100644
index 0000000..56c47b5
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_utsolve.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_valid_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_valid_numeric.c
new file mode 100644
index 0000000..206be5b
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_valid_numeric.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_valid_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_valid_symbolic.c
new file mode 100644
index 0000000..d3aa54d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zi_valid_symbolic.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_2by2.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_2by2.c
new file mode 100644
index 0000000..2d3d097
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_2by2.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_2by2.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_assemble.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_assemble.c
new file mode 100644
index 0000000..c5f9f0f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_assemble.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_assemble_fixq.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_assemble_fixq.c
new file mode 100644
index 0000000..b94d2da
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_assemble_fixq.c
@@ -0,0 +1,3 @@
+#define ZLONG
+#define FIXQ
+#include "../../SuiteSparse/UMFPACK/Source/umf_assemble.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_blas3_update.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_blas3_update.c
new file mode 100644
index 0000000..d7827ab
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_blas3_update.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_blas3_update.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_build_tuples.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_build_tuples.c
new file mode 100644
index 0000000..00845e4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_build_tuples.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_build_tuples.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_create_elememt.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_create_elememt.c
new file mode 100644
index 0000000..ffd7567
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_create_elememt.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_create_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_extend_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_extend_front.c
new file mode 100644
index 0000000..b149b7d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_extend_front.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_extend_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_garbage_collection.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_garbage_collection.c
new file mode 100644
index 0000000..b7edc57
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_garbage_collection.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_garbage_collection.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_get_memory.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_get_memory.c
new file mode 100644
index 0000000..eff5a54
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_get_memory.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_get_memory.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_grow_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_grow_front.c
new file mode 100644
index 0000000..52a23f8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_grow_front.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_grow_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_init_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_init_front.c
new file mode 100644
index 0000000..902f850
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_init_front.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_init_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel.c
new file mode 100644
index 0000000..3387f55
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel_init.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel_init.c
new file mode 100644
index 0000000..eeee308
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel_init.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_init.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel_wrapup.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel_wrapup.c
new file mode 100644
index 0000000..5a2cdd4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_kernel_wrapup.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_kernel_wrapup.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_lhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_lhsolve.c
new file mode 100644
index 0000000..fa34f01
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_lhsolve.c
@@ -0,0 +1,4 @@
+#define ZLONG
+
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_local_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_local_search.c
new file mode 100644
index 0000000..8f89985
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_local_search.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_local_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_lsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_lsolve.c
new file mode 100644
index 0000000..59ea2a8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_lsolve.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_lsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_ltsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_ltsolve.c
new file mode 100644
index 0000000..39a4a88
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_ltsolve.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_ltsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_element.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_element.c
new file mode 100644
index 0000000..96c27a2
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_element.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_element.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_head_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_head_block.c
new file mode 100644
index 0000000..1683bb6
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_head_block.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_head_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_tail_block.c
new file mode 100644
index 0000000..d85c8a5
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_alloc_tail_block.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_alloc_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_free_tail_block.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_free_tail_block.c
new file mode 100644
index 0000000..65fd652
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_free_tail_block.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_free_tail_block.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_init_memoryspace.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_init_memoryspace.c
new file mode 100644
index 0000000..e535032
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_mem_init_memoryspace.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_mem_init_memoryspace.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_row_search.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_row_search.c
new file mode 100644
index 0000000..ed44055
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_row_search.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_row_search.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_scale.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_scale.c
new file mode 100644
index 0000000..af82c54
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_scale.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_scale_column.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_scale_column.c
new file mode 100644
index 0000000..a6097d1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_scale_column.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_scale_column.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_set_stats.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_set_stats.c
new file mode 100644
index 0000000..80af787
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_set_stats.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_set_stats.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_solve.c
new file mode 100644
index 0000000..76a3c0f
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_solve.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_start_front.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_start_front.c
new file mode 100644
index 0000000..f0e4a41
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_start_front.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_start_front.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_store_lu.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_store_lu.c
new file mode 100644
index 0000000..b5b9c27
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_store_lu.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_store_lu_drop.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_store_lu_drop.c
new file mode 100644
index 0000000..b817454
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_store_lu_drop.c
@@ -0,0 +1,3 @@
+#define ZLONG
+#define DROP
+#include "../../SuiteSparse/UMFPACK/Source/umf_store_lu.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_symbolic_usage.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_symbolic_usage.c
new file mode 100644
index 0000000..fe745bb
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_symbolic_usage.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_symbolic_usage.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_transpose.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_transpose.c
new file mode 100644
index 0000000..a8cf3ed
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_transpose.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_transpose.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_tuple_lengths.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_tuple_lengths.c
new file mode 100644
index 0000000..3c21f97
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_tuple_lengths.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_tuple_lengths.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_uhsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_uhsolve.c
new file mode 100644
index 0000000..e5eb0ad
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_uhsolve.c
@@ -0,0 +1,4 @@
+#define ZLONG
+
+#define CONJUGATE_SOLVE
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_usolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_usolve.c
new file mode 100644
index 0000000..2cca779
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_usolve.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_usolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_utsolve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_utsolve.c
new file mode 100644
index 0000000..4794601
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_utsolve.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_utsolve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_valid_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_valid_numeric.c
new file mode 100644
index 0000000..5c220b0
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_valid_numeric.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_valid_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_valid_symbolic.c
new file mode 100644
index 0000000..d286f11
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umf_zl_valid_symbolic.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umf_valid_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_free_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_free_numeric.c
new file mode 100644
index 0000000..7a28cf4
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_free_numeric.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_free_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_free_symbolic.c
new file mode 100644
index 0000000..207c715
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_free_symbolic.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_numeric.c
new file mode 100644
index 0000000..63dcda5
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_numeric.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_qsymbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_qsymbolic.c
new file mode 100644
index 0000000..7039606
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_qsymbolic.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_solve.c
new file mode 100644
index 0000000..bb764dc
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_solve.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_symbolic.c
new file mode 100644
index 0000000..3d947c0
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_di_symbolic.c
@@ -0,0 +1,2 @@
+#define DINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_free_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_free_numeric.c
new file mode 100644
index 0000000..20ed153
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_free_numeric.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_free_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_free_symbolic.c
new file mode 100644
index 0000000..0b108a1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_free_symbolic.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_numeric.c
new file mode 100644
index 0000000..0d1e3aa
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_numeric.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_qsymbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_qsymbolic.c
new file mode 100644
index 0000000..946c59e
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_qsymbolic.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_solve.c
new file mode 100644
index 0000000..137d9f1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_solve.c
@@ -0,0 +1,3 @@
+#define DLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_symbolic.c
new file mode 100644
index 0000000..464d39d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_dl_symbolic.c
@@ -0,0 +1,2 @@
+#define DLONG
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_free_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_free_numeric.c
new file mode 100644
index 0000000..bd507da
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_free_numeric.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_free_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_free_symbolic.c
new file mode 100644
index 0000000..9c4cdb5
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_free_symbolic.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_numeric.c
new file mode 100644
index 0000000..364afe7
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_numeric.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_qsymbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_qsymbolic.c
new file mode 100644
index 0000000..d748f9d
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_qsymbolic.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_solve.c
new file mode 100644
index 0000000..de050f7
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_solve.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_symbolic.c
new file mode 100644
index 0000000..559c7d1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zi_symbolic.c
@@ -0,0 +1,2 @@
+#define ZINT
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_free_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_free_numeric.c
new file mode 100644
index 0000000..2c9bb10
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_free_numeric.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_free_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_free_symbolic.c
new file mode 100644
index 0000000..8f30367
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_free_symbolic.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_free_symbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_numeric.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_numeric.c
new file mode 100644
index 0000000..da89bc8
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_numeric.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_numeric.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_qsymbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_qsymbolic.c
new file mode 100644
index 0000000..a630f6c
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_qsymbolic.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_qsymbolic.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_solve.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_solve.c
new file mode 100644
index 0000000..1c23ab1
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_solve.c
@@ -0,0 +1,3 @@
+#define ZLONG
+
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_solve.c"
diff --git a/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_symbolic.c b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_symbolic.c
new file mode 100644
index 0000000..0f23a02
--- /dev/null
+++ b/src/C/SuiteSparse_cvxopt_extra/umfpack/umfpack_zl_symbolic.c
@@ -0,0 +1,2 @@
+#define ZLONG
+#include "../../SuiteSparse/UMFPACK/Source/umfpack_symbolic.c"
diff --git a/src/C/amd.c b/src/C/amd.c
new file mode 100644
index 0000000..3d1f41d
--- /dev/null
+++ b/src/C/amd.c
@@ -0,0 +1,198 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "cvxopt.h"
+#include "amd.h"
+#include "misc.h"
+
+/* defined in pyconfig.h */
+#if (SIZEOF_INT < SIZEOF_LONG)
+#define amd_order amd_l_order
+#define amd_defaults amd_l_defaults
+#endif
+
+
+PyDoc_STRVAR(amd__doc__,"Interface to the AMD library.\n\n"
+"Approximate minimum degree ordering of sparse matrices.\n\n"
+"The default values of the control parameterse in the AMD 'Control' "
+"array\n"
+"described in the AMD User Guide are used. The values can be modified "
+"by\n"
+"making an entry in the dictionary amd.options, with possible key "
+"values\n"
+"'AMD_DENSE' and 'AMD_AGGRESSIVE'.\n\n"
+"AMD is available from http://www.cise.ufl.edu/research/sparse/amd.");
+
+
+static PyObject *amd_module;
+
+typedef struct {
+ char name[20];
+ int idx;
+} param_tuple;
+
+static const param_tuple AMD_PARAM_LIST[] = {
+ {"AMD_DENSE", AMD_DENSE},
+ {"AMD_AGGRESSIVE", AMD_AGGRESSIVE}
+}; /* 2 parameters */
+
+static int get_param_idx(char *str, int *idx)
+{
+ int i;
+
+ for (i=0; i<2; i++) if (!strcmp(AMD_PARAM_LIST[i].name, str)) {
+ *idx = AMD_PARAM_LIST[i].idx;
+ return 1;
+ }
+ return 0;
+}
+
+static int set_defaults(double *control)
+{
+ int_compat pos=0;
+ int param_id;
+ PyObject *param, *key, *value;
+ char *keystr, err_str[100];
+
+ amd_defaults(control);
+
+ if (!(param = PyObject_GetAttrString(amd_module, "options")) ||
+ !PyDict_Check(param)){
+ PyErr_SetString(PyExc_AttributeError, "missing amd.options"
+ "dictionary");
+ return 0;
+ }
+ while (PyDict_Next(param, &pos, &key, &value))
+ if ((keystr = PyString_AsString(key)) && get_param_idx(keystr,
+ ¶m_id)) {
+ if (!PyInt_Check(value) && !PyFloat_Check(value)){
+ sprintf(err_str, "invalid value for AMD parameter: "
+ "%-.20s", keystr);
+ PyErr_SetString(PyExc_ValueError, err_str);
+ Py_DECREF(param);
+ return 0;
+ }
+ control[param_id] = PyFloat_AsDouble(value);
+ }
+ Py_DECREF(param);
+ return 1;
+}
+
+
+static char doc_order[] =
+ "Computes the approximate minimum degree ordering of a square "
+ "matrix.\n\n"
+ "p = order(A, uplo='L')\n\n"
+ "PURPOSE\n"
+ "Computes a permutation p that reduces fill-in in the Cholesky\n"
+ "factorization of A[p,p].\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix\n\n"
+ "uplo 'L' or 'U'. If uplo is 'L', the lower triangular part\n"
+ " of A is used and the upper triangular is ignored. If\n"
+ " uplo is 'U', the upper triangular part is used and the\n"
+ " lower triangular part is ignored.\n\n"
+ "p 'i' matrix of length equal to the order of A";
+
+
+static PyObject* order_c(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ spmatrix *A;
+ matrix *perm;
+ char uplo='L';
+ int j, k, n, nnz, alloc=0, info;
+ int_t *rowind=NULL, *colptr=NULL;
+ double control[AMD_CONTROL];
+ char *kwlist[] = {"A", "uplo", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|c", kwlist, &A,
+ &uplo)) return NULL;
+ if (!set_defaults(control)) return NULL;
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A)){
+ PyErr_SetString(PyExc_TypeError, "A must be a square sparse "
+ "matrix");
+ return NULL;
+ }
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (!(perm = (matrix *) Matrix_New(SP_NROWS(A),1,INT)))
+ return PyErr_NoMemory();
+ n = SP_NROWS(A);
+ for (nnz=0, j=0; j<n; j++) {
+ if (uplo == 'L'){
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] && SP_ROW(A)[k]<j;
+ k++);
+ nnz += SP_COL(A)[j+1] - k;
+ }
+ else {
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] && SP_ROW(A)[k] <= j;
+ k++);
+ nnz += k - SP_COL(A)[j];
+ }
+ }
+ if (nnz == SP_NNZ(A)){
+ colptr = (int_t *) SP_COL(A);
+ rowind = (int_t *) SP_ROW(A);
+ }
+ else {
+ alloc = 1;
+ colptr = (int_t *) calloc(n+1, sizeof(int_t));
+ rowind = (int_t *) calloc(nnz, sizeof(int_t));
+ if (!colptr || !rowind) {
+ Py_XDECREF(perm); free(colptr); free(rowind);
+ return PyErr_NoMemory();
+ }
+ colptr[0] = 0;
+ for (j=0; j<n; j++) {
+ if (uplo == 'L'){
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] &&
+ SP_ROW(A)[k] < j; k++);
+ nnz = SP_COL(A)[j+1] - k;
+ colptr[j+1] = colptr[j] + nnz;
+ memcpy(rowind + colptr[j], (int_t *) SP_ROW(A) + k,
+ nnz*sizeof(int_t));
+ }
+ else {
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] &&
+ SP_ROW(A)[k] <= j; k++);
+ nnz = k - SP_COL(A)[j];
+ colptr[j+1] = colptr[j] + nnz;
+ memcpy(rowind + colptr[j], (int_t *) (SP_ROW(A) +
+ SP_COL(A)[j]), nnz*sizeof(int_t));
+ }
+ }
+ }
+ info = amd_order(n, colptr, rowind, MAT_BUFI(perm), control, NULL);
+ if (alloc){
+ free(colptr);
+ free(rowind);
+ }
+ switch (info) {
+ case AMD_OUT_OF_MEMORY:
+ Py_XDECREF(perm);
+ return PyErr_NoMemory();
+
+ case AMD_INVALID:
+ Py_XDECREF(perm);
+ return Py_BuildValue("");
+
+ case AMD_OK:
+ return (PyObject *) perm;
+ }
+ return Py_BuildValue("");
+}
+
+static PyMethodDef amd_functions[] = {
+{"order", (PyCFunction) order_c, METH_VARARGS|METH_KEYWORDS, doc_order},
+{NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC initamd(void)
+{
+ amd_module = Py_InitModule3("cvxopt.amd", amd_functions,
+ amd__doc__);
+ PyModule_AddObject(amd_module, "options", PyDict_New());
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/base.c b/src/C/base.c
new file mode 100644
index 0000000..7834906
--- /dev/null
+++ b/src/C/base.c
@@ -0,0 +1,950 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#define BASE_MODULE
+
+#include "Python.h"
+#include "cvxopt.h"
+#include "misc.h"
+
+#include <complexobject.h>
+
+PyDoc_STRVAR(base__doc__,"Convex optimization package");
+
+PyTypeObject matrix_tp ;
+matrix * Matrix_New(int, int, int) ;
+matrix * Matrix_NewFromMatrix(matrix *, int) ;
+matrix * Matrix_NewFromSequence(PyObject *, int) ;
+matrix * Matrix_NewFromArrayStruct(PyObject *, int, int *) ;
+
+PyTypeObject spmatrix_tp ;
+spmatrix * SpMatrix_New(int_t, int_t, int, int ) ;
+spmatrix * SpMatrix_NewFromMatrix(matrix *, int) ;
+spmatrix * SpMatrix_NewFromSpMatrix(spmatrix *, int, int) ;
+spmatrix * SpMatrix_NewFromIJV(matrix *, matrix *, matrix *,
+ int_t, int_t, int, int) ;
+void free_ccs(ccs *) ;
+
+extern int (*sp_axpy[])(number, void *, void *, int, int, int, void **) ;
+
+extern int (*sp_gemm[])(char, char, number, void *, void *, number, void *,
+ int, int, int, int, void **, int, int, int);
+
+extern int (*sp_gemv[])(char, int, int, number, void *, int, void *, int,
+ number, void *, int) ;
+
+extern int (*sp_symv[])(char, int, number, ccs *, int, void *, int,
+ number, void *, int) ;
+
+extern int (*sp_syrk[])(char, char, number, void *, number,
+ void *, int, int, int, int, void **) ;
+
+const int E_SIZE[] = { sizeof(int_t), sizeof(double), sizeof(complex) };
+const char TC_CHAR[][2] = {"i","d","z"} ;
+const char PRINTOPT[][15] = {"iformat","dformat","zformat"} ;
+
+PyObject *base_mod;
+
+/*
+ * Helper routines and definitions to implement type transparency.
+ */
+
+number One[3], MinusOne[3], Zero[3];
+
+static void write_inum(void *dest, int i, void *src, int j) {
+ ((int_t *)dest)[i] = ((int_t *)src)[j];
+}
+
+static void write_dnum(void *dest, int i, void *src, int j) {
+ ((double *)dest)[i] = ((double *)src)[j];
+}
+
+static void write_znum(void *dest, int i, void *src, int j) {
+ ((complex *)dest)[i] = ((complex *)src)[j];
+}
+
+void (*write_num[])(void *, int, void *, int) = {
+ write_inum, write_dnum, write_znum };
+
+static PyObject * inum2PyObject(void *src, int i) {
+ return Py_BuildValue("l", ((int_t *)src)[i]);
+}
+
+static PyObject * dnum2PyObject(void *src, int i) {
+ return Py_BuildValue("d", ((double *)src)[i]);
+}
+
+static PyObject * znum2PyObject(void *src, int i) {
+ Py_complex z;
+ z.real = creal (((complex *)src)[i]);
+ z.imag = cimag (((complex *)src)[i]);
+ return Py_BuildValue("D", &z);
+}
+
+PyObject * (*num2PyObject[])(void *, int) = {
+ inum2PyObject, dnum2PyObject, znum2PyObject };
+
+/* val_id: 0 = matrix, 1 = PyNumber */
+static int
+convert_inum(void *dest, void *val, int val_id, int offset)
+{
+ if (val_id==0) { /* 1x1 matrix */
+ switch (MAT_ID(val)) {
+ case INT:
+ *(int_t *)dest = MAT_BUFI(val)[offset]; return 0;
+ //case DOUBLE:
+ //*(int_t *)dest = (int_t)round(MAT_BUFD(val)[offset]); return 0;
+ default: PY_ERR_INT(PyExc_TypeError,"cannot cast argument as integer");
+ }
+ } else { /* PyNumber */
+ if (PyInt_Check((PyObject *)val)) {
+ *(int_t *)dest = PyInt_AS_LONG((PyObject *)val); return 0;
+ }
+ //else if (PyFloat_Check((PyObject *)val)) {
+ // *(int_t *)dest = roundl(PyFloat_AS_DOUBLE((PyObject *)val)); return 0;
+ //}
+ else PY_ERR_INT(PyExc_TypeError,"cannot cast argument as integer");
+ }
+}
+
+static int
+convert_dnum(void *dest, void *val, int val_id, int offset)
+{
+ if (val_id==0) { /* matrix */
+ switch (MAT_ID(val)) {
+ case INT: *(double *)dest = MAT_BUFI(val)[offset]; return 0;
+ case DOUBLE: *(double *)dest = MAT_BUFD(val)[offset]; return 0;
+ default: PY_ERR_INT(PyExc_TypeError, "cannot cast argument as double");
+ }
+ } else { /* PyNumber */
+ if (PyInt_Check((PyObject *)val) || PyFloat_Check((PyObject *)val)) {
+ *(double *)dest = PyFloat_AsDouble((PyObject *)val);
+ return 0;
+ }
+ else PY_ERR_INT(PyExc_TypeError,"cannot cast argument as double");
+ }
+}
+
+static int
+convert_znum(void *dest, void *val, int val_id, int offset)
+{
+ if (val_id==0) { /* 1x1 matrix */
+ switch (MAT_ID(val)) {
+ case INT:
+ *(complex *)dest = MAT_BUFI(val)[offset]; return 0;
+ case DOUBLE:
+ *(complex *)dest = MAT_BUFD(val)[offset]; return 0;
+ case COMPLEX:
+ *(complex *)dest = MAT_BUFZ(val)[offset]; return 0;
+ default: return -1;
+ }
+ } else { /* PyNumber */
+ Py_complex c = PyComplex_AsCComplex((PyObject *)val);
+ *(complex *)dest = c.real + I*c.imag;
+ return 0;
+ }
+}
+
+int (*convert_num[])(void *, void *, int, int) = {
+ convert_inum, convert_dnum, convert_znum };
+
+extern void daxpy_(int *, void *, void *, int *, void *, int *) ;
+extern void zaxpy_(int *, void *, void *, int *, void *, int *) ;
+
+static void i_axpy(int *n, void *a, void *x, int *incx, void *y, int *incy) {
+ int i;
+ for (i=0; i < *n; i++) {
+ ((int_t *)y)[i*(*incy)] += *((int_t *)a)*((int_t *)x)[i*(*incx)];
+ }
+}
+
+void (*axpy[])(int *, void *, void *, int *, void *, int *) = {
+ i_axpy, daxpy_, zaxpy_ };
+
+extern void dscal_(int *, void *, void *, int *) ;
+extern void zscal_(int *, void *, void *, int *) ;
+
+/* we dont implement a BLAS iscal */
+static void i_scal(int *n, void *a, void *x, int *incx) {
+ int i;
+ for (i=0; i < *n; i++) {
+ ((int_t *)x)[i*(*incx)] *= *((int_t *)a);
+ }
+}
+
+void (*scal[])(int *, void *, void *, int *) = { i_scal, dscal_, zscal_ };
+
+extern void dgemm_(char *, char *, int *, int *, int *, void *, void *,
+ int *, void *, int *, void *, void *, int *) ;
+extern void zgemm_(char *, char *, int *, int *, int *, void *, void *,
+ int *, void *, int *, void *, void *, int *) ;
+
+/* we dont implement a BLAS igemm */
+static void i_gemm(char *transA, char *transB, int *m, int *n, int *k,
+ void *alpha, void *A, int *ldA, void *B, int *ldB, void *beta,
+ void *C, int *ldC)
+{
+ int i, j, l;
+ for (j=0; j<*n; j++) {
+ for (i=0; i<*m; i++) {
+ ((int_t *)C)[i+j*(*m)] = 0;
+ for (l=0; l<*k; l++)
+ ((int_t *)C)[i+j*(*m)]+=((int_t *)A)[i+l*(*m)]*((int_t *)B)[j*(*k)+l];
+ }
+ }
+}
+
+void (*gemm[])(char *, char *, int *, int *, int *, void *, void *, int *,
+ void *, int *, void *, void *, int *) = { i_gemm, dgemm_, zgemm_ };
+
+extern void dgemv_(char *, int *, int *, void *, void *, int *, void *,
+ int *, void *, void *, int *);
+extern void zgemv_(char *, int *, int *, void *, void *, int *, void *,
+ int *, void *, void *, int *);
+static void (*gemv[])(char *, int *, int *, void *, void *, int *, void *,
+ int *, void *, void *, int *) = { NULL, dgemv_, zgemv_ };
+
+extern void dsyrk_(char *, char *, int *, int *, void *, void *,
+ int *, void *, void *, int *);
+extern void zsyrk_(char *, char *, int *, int *, void *, void *,
+ int *, void *, void *, int *);
+void (*syrk[])(char *, char *, int *, int *, void *, void *,
+ int *, void *, void *, int *) = { NULL, dsyrk_, zsyrk_ };
+
+extern void dsymv_(char *, int *, void *, void *, int *, void *, int *,
+ void *, void *, int *);
+extern void zsymv_(char *, int *, void *, void *, int *, void *, int *,
+ void *, void *, int *);
+void (*symv[])(char *, int *, void *, void *, int *, void *, int *,
+ void *, void *, int *) = { NULL, dsymv_, zsymv_ };
+
+static void mtx_iabs(void *src, void *dest, int n) {
+ int i;
+ for (i=0; i<n; i++)
+ ((int_t *)dest)[i] = labs(((int_t *)src)[i]);
+}
+
+static void mtx_dabs(void *src, void *dest, int n) {
+ int i;
+ for (i=0; i<n; i++)
+ ((double *)dest)[i] = fabs(((double *)src)[i]);
+}
+
+static void mtx_zabs(void *src, void *dest, int n) {
+ int i;
+ for (i=0; i<n; i++)
+ ((double *)dest)[i] = cabs(((complex *)src)[i]);
+}
+
+void (*mtx_abs[])(void *, void *, int) = { mtx_iabs, mtx_dabs, mtx_zabs };
+
+static int idiv(void *dest, number a, int n) {
+ if (a.i==0) PY_ERR_INT(PyExc_ZeroDivisionError, "division by zero");
+ int i;
+ for (i=0; i<n; i++)
+ ((int_t *)dest)[i] /= a.i;
+
+ return 0;
+}
+
+static int ddiv(void *dest, number a, int n) {
+ if (a.d==0.0) PY_ERR_INT(PyExc_ZeroDivisionError, "division by zero");
+ int _n = n, int1 = 1;
+ double _a = 1/a.d;
+ dscal_(&_n, (void *)&_a, dest, &int1);
+ return 0;
+}
+
+static int zdiv(void *dest, number a, int n) {
+ if (cabs(a.z) == 0.0)
+ PY_ERR_INT(PyExc_ZeroDivisionError, "division by zero");
+
+ int _n = n, int1 = 1;
+ complex _a = 1.0/a.z;
+ zscal_(&_n, (void *)&_a, dest, &int1);
+ return 0;
+}
+
+int (*div_array[])(void *, number, int) = { idiv, ddiv, zdiv };
+
+static int mtx_irem(void *dest, number a, int n) {
+ if (a.i==0) PY_ERR_INT(PyExc_ZeroDivisionError, "division by zero");
+ int i;
+ for (i=0; i<n; i++)
+ ((int_t *)dest)[i] %= a.i;
+
+ return 0;
+}
+
+static int mtx_drem(void *dest, number a, int n) {
+ if (a.d==0.0) PY_ERR_INT(PyExc_ZeroDivisionError, "division by zero");
+ int i;
+ for (i=0; i<n; i++)
+ ((double *)dest)[i] -= floor(((double *)dest)[i]/a.d)*a.d;
+
+ return 0;
+}
+
+int (*mtx_rem[])(void *, number, int) = { mtx_irem, mtx_drem };
+
+/* val_type = 0: (sp)matrix if type = 0, PY_NUMBER if type = 1 */
+int get_id(void *val, int val_type) {
+ if (!val_type) {
+ if Matrix_Check((PyObject *)val)
+ return MAT_ID((matrix *)val);
+ else
+ return SP_ID((spmatrix *)val);
+ }
+ else if (PyInt_Check((PyObject *)val))
+ return INT;
+ else if (PyFloat_Check((PyObject *)val))
+ return DOUBLE;
+ else
+ return COMPLEX;
+}
+
+
+
+static int Matrix_Check_func(void *o) {
+ return Matrix_Check((PyObject*)o);
+}
+
+static int SpMatrix_Check_func(void *o) {
+ return SpMatrix_Check((PyObject *)o);
+}
+
+
+static char doc_axpy[] =
+ "Constant times a vector plus a vector (y := alpha*x+y).\n\n"
+ "axpy(x, y, n=None, alpha=1.0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' (sp)matrix\n\n"
+ "y 'd' or 'z' (sp)matrix. Must have the same type as x.\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offsetx+1) ? 1+(len(x)-offsetx-1)/incx : 0.\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if x is complex";
+
+PyObject * base_axpy(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *x, *y, *partial = NULL;
+ PyObject *ao=NULL;
+ number a;
+ char *kwlist[] = {"x", "y", "alpha", "partial", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|OO", kwlist,
+ &x, &y, &ao, &partial)) return NULL;
+
+ if (!Matrix_Check(x) && !SpMatrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y) && !SpMatrix_Check(y)) err_mtrx("y");
+ if (partial && !PyBool_Check(partial)) err_bool("partial");
+
+ if (X_ID(x) != X_ID(y)) err_conflicting_ids;
+ int id = X_ID(x);
+
+ if (X_NROWS(x) != X_NROWS(y) || X_NCOLS(x) != X_NCOLS(y))
+ PY_ERR_TYPE("dimensions of x and y do not match");
+
+ if (ao && convert_num[id](&a, ao, 1, 0)) err_type("alpha");
+
+ if (Matrix_Check(x) && Matrix_Check(y)) {
+ int n = X_NROWS(x)*X_NCOLS(x);
+ axpy[id](&n, (ao ? &a : &One[id]), MAT_BUF(x), (int *)&One[INT],
+ MAT_BUF(y), (int *)&One[INT]);
+ }
+ else {
+
+ void *z = NULL;
+ if (sp_axpy[id]((ao ? a : One[id]),
+ Matrix_Check(x) ? MAT_BUF(x): ((spmatrix *)x)->obj,
+ Matrix_Check(y) ? MAT_BUF(y): ((spmatrix *)y)->obj,
+ SpMatrix_Check(x), SpMatrix_Check(y),
+ partial ? PyInt_AS_LONG(partial) : 0, &z))
+ return PyErr_NoMemory();
+
+ if (z) {
+ free_ccs( ((spmatrix *)y)->obj );
+ ((spmatrix *)y)->obj = z;
+ }
+ }
+
+ return Py_BuildValue("");
+}
+
+static char doc_gemm[] =
+ "General matrix-matrix product.\n\n"
+ "gemm(A, B, C, transA='N', transB='N', alpha=1.0, beta=0.0, \n"
+ " partial=False) \n\n"
+ "PURPOSE\n"
+ "Computes \n"
+ "C := alpha*A*B + beta*C if transA = 'N' and transB = 'N'.\n"
+ "C := alpha*A^T*B + beta*C if transA = 'T' and transB = 'N'.\n"
+ "C := alpha*A^H*B + beta*C if transA = 'C' and transB = 'N'.\n"
+ "C := alpha*A*B^T + beta*C if transA = 'N' and transB = 'T'.\n"
+ "C := alpha*A^T*B^T + beta*C if transA = 'T' and transB = 'T'.\n"
+ "C := alpha*A^H*B^T + beta*C if transA = 'C' and transB = 'T'.\n"
+ "C := alpha*A*B^H + beta*C if transA = 'N' and transB = 'C'.\n"
+ "C := alpha*A^T*B^H + beta*C if transA = 'T' and transB = 'C'.\n"
+ "C := alpha*A^H*B^H + beta*C if transA = 'C' and transB = 'C'.\n"
+ "If k=0, this reduces to C := beta*C.\n\n"
+ "ARGUMENTS\n\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "transA 'N', 'T' or 'C'\n\n"
+ "transB 'N', 'T' or 'C'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "partial boolean. If C is sparse and partial is True, then only the\n"
+ " nonzero elements of C are updated irrespective of the\n"
+ " sparsity patterns of A and B.";
+
+PyObject* base_gemm(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A, *B, *C, *partial=NULL;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m, n, k;
+ char transA='N', transB='N';
+ char *kwlist[] = {"A", "B", "C", "transA", "transB", "alpha", "beta",
+ "partial", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ccOOO",
+ kwlist, &A, &B, &C, &transA, &transB, &ao, &bo, &partial))
+ return NULL;
+
+ if (!(Matrix_Check(A) || SpMatrix_Check(A)))
+ PY_ERR_TYPE("A must a matrix or spmatrix");
+ if (!(Matrix_Check(B) || SpMatrix_Check(B)))
+ PY_ERR_TYPE("B must a matrix or spmatrix");
+ if (!(Matrix_Check(C) || SpMatrix_Check(C)))
+ PY_ERR_TYPE("C must a matrix or spmatrix");
+ if (partial && !PyBool_Check(partial)) err_bool("partial");
+
+ if (X_ID(A) != X_ID(B) || X_ID(A) != X_ID(C) ||
+ X_ID(B) != X_ID(C)) err_conflicting_ids;
+
+ if (transA != 'N' && transA != 'T' && transA != 'C')
+ err_char("transA", "'N', 'T', 'C'");
+ if (transB != 'N' && transB != 'T' && transB != 'C')
+ err_char("transB", "'N', 'T', 'C'");
+
+ m = (transA == 'N') ? X_NROWS(A) : X_NCOLS(A);
+ n = (transB == 'N') ? X_NCOLS(B) : X_NROWS(B);
+ k = (transA == 'N') ? X_NCOLS(A) : X_NROWS(A);
+ if (k != ((transB == 'N') ? X_NROWS(B) : X_NCOLS(B)))
+ PY_ERR_TYPE("dimensions of A and B do not match");
+
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ao && convert_num[X_ID(A)](&a, ao, 1, 0)) err_type("alpha");
+ if (bo && convert_num[X_ID(A)](&b, bo, 1, 0)) err_type("beta");
+
+ int id = X_ID(A);
+ if (Matrix_Check(A) && Matrix_Check(B) && Matrix_Check(C)) {
+
+ int ldA = MAX(1,MAT_NROWS(A));
+ int ldB = MAX(1,MAT_NROWS(B));
+ int ldC = MAX(1,MAT_NROWS(C));
+ if (id == INT) err_invalid_id;
+ gemm[id](&transA, &transB, &m, &n, &k, (ao ? &a : &One[id]),
+ MAT_BUF(A), &ldA, MAT_BUF(B), &ldB, (bo ? &b : &Zero[id]),
+ MAT_BUF(C), &ldC);
+ } else {
+
+ void *z = NULL;
+ if (sp_gemm[id](transA, transB, (ao ? a : One[id]),
+ Matrix_Check(A) ? MAT_BUF(A) : ((spmatrix *)A)->obj,
+ Matrix_Check(B) ? MAT_BUF(B) : ((spmatrix *)B)->obj,
+ (bo ? b : Zero[id]),
+ Matrix_Check(C) ? MAT_BUF(C) : ((spmatrix *)C)->obj,
+ SpMatrix_Check(A), SpMatrix_Check(B), SpMatrix_Check(C),
+ partial ? PyInt_AS_LONG(partial) : 0, &z, m, n, k))
+ return PyErr_NoMemory();
+
+ if (z) {
+ free_ccs( ((spmatrix *)C)->obj );
+ ((spmatrix *)C)->obj = z;
+ }
+ }
+
+ return Py_BuildValue("");
+}
+
+static char doc_gemv[] =
+ "General matrix-vector product for sparse and dense matrices. \n\n"
+ "gemv(A, x, y, trans='N', alpha=1.0, beta=0.0, m=A.size[0],\n"
+ " n=A.size[1], incx=1, incy=1, offsetA=0, offsetx=0, offsety=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes y := alpha*A*x + beta*y.\n"
+ "If trans is 'T', computes y := alpha*A^T*x + beta*y.\n"
+ "If trans is 'C', computes y := alpha*A^H*x + beta*y.\n"
+ "The matrix A is m by n.\n"
+ "Returns immediately if n=0 and trans is 'T' or 'C', or if m=0 \n"
+ "and trans is 'N'.\n"
+ "Computes y := beta*y if n=0, m>0 and trans is 'N', or if m=0, \n"
+ "n>0 and trans is 'T' or 'C'.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' (sp)matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ " If zero, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "This sparse version of GEMV requires that\n"
+ " m <= A.size[0] - (offsetA % A.size[0])";
+
+static PyObject* base_gemv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x, *y;
+ PyObject *A;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m=-1, n=-1, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char trans='N';
+ char *kwlist[] = {"A", "x", "y", "trans", "alpha", "beta", "m", "n",
+ "incx", "incy", "offsetA", "offsetx",
+ "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiiii",
+ kwlist, &A, &x, &y, &trans, &ao, &bo, &m, &n, &ix, &iy,
+ &oA, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A) && !SpMatrix_Check(A))
+ PY_ERR(PyExc_TypeError, "A must be a dense or sparse matrix");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+
+ if (MAT_ID(x) == INT || MAT_ID(y) == INT || X_ID(A) == INT)
+ PY_ERR_TYPE("invalid matrix types");
+
+ if (X_ID(A) != MAT_ID(x) || X_ID(A) != MAT_ID(y))
+ err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N','T','C'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ int id = MAT_ID(x);
+ if (m < 0) m = X_NROWS(A);
+ if (n < 0) n = X_NCOLS(A);
+ if ((!m && trans == 'N') || (!n && (trans == 'T' || trans == 'C')))
+ return Py_BuildValue("");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (n > 0 && m > 0 && oA + (n-1)*MAX(1,X_NROWS(A)) + m >
+ X_NROWS(A)*X_NCOLS(A))
+ err_buf_len("A");
+
+ if (ox < 0) err_nn_int("offsetx");
+ if ((trans == 'N' && n > 0 && ox + (n-1)*abs(ix) + 1 > MAT_LGT(x)) ||
+ ((trans == 'T' || trans == 'C') && m > 0 &&
+ ox + (m-1)*abs(ix) + 1 > MAT_LGT(x))) err_buf_len("x");
+
+ if (oy < 0) err_nn_int("offsety");
+ if ((trans == 'N' && oy + (m-1)*abs(iy) + 1 > MAT_LGT(y)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oy + (n-1)*abs(iy) + 1 > MAT_LGT(y))) err_buf_len("y");
+
+ if (ao && convert_num[MAT_ID(x)](&a, ao, 1, 0)) err_type("alpha");
+ if (bo && convert_num[MAT_ID(x)](&b, bo, 1, 0)) err_type("beta");
+
+ if (Matrix_Check(A)) {
+ int ldA = MAX(1,X_NROWS(A));
+ if (trans == 'N' && n == 0)
+ scal[id](&m, (bo ? &b : &Zero[id]), MAT_BUF(y)+oy*E_SIZE[id], &iy);
+ else if ((trans == 'T' || trans == 'C') && m == 0)
+ scal[id](&n, (bo ? &b : &Zero[id]), MAT_BUF(y)+oy*E_SIZE[id], &iy);
+ else
+ gemv[id](&trans, &m, &n, (ao ? &a : &One[id]),
+ MAT_BUF(A) + oA*E_SIZE[id], &ldA,
+ MAT_BUF(x) + ox*E_SIZE[id], &ix, (bo ? &b : &Zero[id]),
+ MAT_BUF(y) + oy*E_SIZE[id], &iy);
+ } else {
+ if (sp_gemv[id](trans, m, n, (ao ? a : One[id]), ((spmatrix *)A)->obj,
+ oA, MAT_BUF(x) + ox*E_SIZE[id], ix, (bo ? b : Zero[id]),
+ MAT_BUF(y) + oy*E_SIZE[id], iy))
+ return PyErr_NoMemory();
+ }
+
+ return Py_BuildValue("");
+}
+
+static char doc_syrk[] =
+ "Rank-k update of symmetric sparse or dense matrix.\n\n"
+ "syrk(A, C, uplo='L', trans='N', alpha=1.0, beta=0.0, partial=False)\n\n"
+ "PURPOSE \n"
+ "If trans is 'N', computes C := alpha*A*A^T + beta*C.\n"
+ "If trans is 'T', computes C := alpha*A^T*A + beta*C.\n"
+ "C is symmetric (real or complex) of order n. \n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' (sp)matrix\n\n"
+ "C 'd' or 'z' (sp)matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N' or 'T'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "partial boolean. If C is sparse and partial is True, then only the\n"
+ " nonzero elements of C are updated irrespective of the\n"
+ " sparsity patterns of A.";
+
+static PyObject* base_syrk(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A, *C, *partial=NULL, *ao=NULL, *bo=NULL;
+ number a, b;
+ char trans='N', uplo='L';
+ char *kwlist[] = {"A", "C", "uplo", "trans", "alpha", "beta", "partial",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccOOO", kwlist,
+ &A, &C, &uplo, &trans, &ao, &bo, &partial))
+ return NULL;
+
+ if (!(Matrix_Check(A) || SpMatrix_Check(A)))
+ PY_ERR_TYPE("A must be a dense or sparse matrix");
+ if (!(Matrix_Check(C) || SpMatrix_Check(C)))
+ PY_ERR_TYPE("C must be a dense or sparse matrix");
+
+ int id = X_ID(A);
+ if (id == INT) PY_ERR_TYPE("invalid matrix types");
+ if (id != X_ID(C)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (id == DOUBLE && trans != 'N' && trans != 'T' &&
+ trans != 'C') err_char("trans", "'N', 'T', 'C'");
+ if (id == COMPLEX && trans != 'N' && trans != 'T')
+ err_char("trans", "'N', 'T'");
+
+ if (partial && !PyBool_Check(partial)) err_bool("partial");
+
+ int n = (trans == 'N') ? X_NROWS(A) : X_NCOLS(A);
+ int k = (trans == 'N') ? X_NCOLS(A) : X_NROWS(A);
+ if (n == 0) return Py_BuildValue("");
+
+ if (ao && convert_num[id](&a, ao, 1, 0)) err_type("alpha");
+ if (bo && convert_num[id](&b, bo, 1, 0)) err_type("beta");
+
+ if (Matrix_Check(A) && Matrix_Check(C)) {
+
+ int ldA = MAX(1,MAT_NROWS(A));
+ int ldC = MAX(1,MAT_NROWS(C));
+
+ syrk[id](&uplo, &trans, &n, &k, (ao ? &a : &One[id]),
+ MAT_BUF(A), &ldA, (bo ? &b : &Zero[id]), MAT_BUF(C), &ldC);
+ } else {
+
+ void *z = NULL;
+ if (sp_syrk[id](uplo, trans,
+ (ao ? a : One[id]),
+ Matrix_Check(A) ? MAT_BUF(A) : ((spmatrix *)A)->obj,
+ (bo ? b : Zero[id]),
+ Matrix_Check(C) ? MAT_BUF(C) : ((spmatrix *)C)->obj,
+ SpMatrix_Check(A), SpMatrix_Check(C),
+ partial ? PyInt_AS_LONG(partial) : 0,
+ (trans == 'N' ? X_NCOLS(A) : X_NROWS(A)), &z))
+ return PyErr_NoMemory();
+
+ if (z) {
+ free_ccs( ((spmatrix *)C)->obj );
+ ((spmatrix *)C)->obj = z;
+ }
+ }
+
+ return Py_BuildValue("");
+}
+
+static char doc_symv[] =
+ "Matrix-vector product with a real symmetric dense or sparse matrix.\n\n"
+ "symv(A, x, y, uplo='L', alpha=1.0, beta=0.0, n=A.size[0], \n"
+ " ldA=max(1,A.size[0]), incx=1, incy=1, offsetA=0, offsetx=0,\n"
+ " offsety=0)\n\n"
+ "PURPOSE\n"
+ "Computes y := alpha*A*x + beta*y with A real symmetric of order n."
+ "n\n"
+ "ARGUMENTS\n"
+ "A 'd' (sp)matrix\n\n"
+ "x 'd' matrix\n\n"
+ "y 'd' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha real number (int or float)\n\n"
+ "beta real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used, we require that\n"
+ " A.size[0]=A.size[1].\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "This sparse version of SYMV requires that\n"
+ " m <= A.size[0] - (offsetA % A.size[0])";
+
+static PyObject* base_symv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A, *ao=NULL, *bo=NULL;
+ matrix *x, *y;
+ number a, b;
+ int n=-1, ix=1, iy=1, oA=0, ox=0, oy=0, ldA;
+ char uplo='L';
+ char *kwlist[] = {"A", "x", "y", "uplo", "alpha", "beta", "n",
+ "incx", "incy", "offsetA", "offsetx", "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiii", kwlist, &A,
+ &x, &y, &uplo, &ao, &bo, &n, &ix, &iy, &oA, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A) && !SpMatrix_Check(A))
+ PY_ERR_TYPE("A must be a dense or sparse matrix");
+
+ ldA = MAX(1,X_NROWS(A));
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (X_ID(A) != MAT_ID(x) || X_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ int id = X_ID(A);
+ if (id == INT) PY_ERR_TYPE("invalid matrix types");
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0) {
+ if (X_NROWS(A) != X_NCOLS(A)) {
+ PyErr_SetString(PyExc_ValueError, "A is not square");
+ return NULL;
+ }
+ n = X_NROWS(A);
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && convert_num[id](&a, ao, 1, 0)) err_type("alpha");
+ if (bo && convert_num[id](&b, bo, 1, 0)) err_type("beta");
+
+ if (Matrix_Check(A)) {
+
+ symv[id](&uplo, &n, (ao ? &a : &One[id]),
+ MAT_BUF(A) + oA*E_SIZE[id], &ldA, MAT_BUF(x) + ox*E_SIZE[id],
+ &ix, (bo ? &b : &Zero[id]), MAT_BUF(y) + oy*E_SIZE[id], &iy);
+ }
+ else {
+
+ if (sp_symv[id](uplo, n, (ao ? a : One[id]), ((spmatrix *)A)->obj,
+ oA, MAT_BUF(x) + ox*E_SIZE[id], ix,
+ (bo ? b : Zero[id]), MAT_BUF(y) + oy*E_SIZE[id], iy))
+ return PyErr_NoMemory();
+ }
+
+ return Py_BuildValue("");
+}
+
+spmatrix * sparse_concat(PyObject *L, int id_arg) ;
+
+static PyObject *
+sparse(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+ PyObject *Objx = NULL;
+ static char *kwlist[] = { "x", "tc", NULL};
+ char tc = 0;
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|c:matrix", kwlist,
+ &Objx, &tc))
+ return NULL;
+
+ if (tc && !(VALID_TC_SP(tc))) PY_ERR_TYPE("tc must be 'd' or 'z'");
+ int id = (tc ? TC2ID(tc) : -1);
+
+ spmatrix *ret = NULL;
+ /* a matrix */
+ if (Matrix_Check(Objx)) {
+
+ int m = MAT_NROWS(Objx), n = MAT_NCOLS(Objx);
+ ret = SpMatrix_NewFromMatrix((matrix *)Objx,
+ (id == -1 ? MAX(DOUBLE,MAT_ID(Objx)) : id));
+
+ MAT_NROWS(Objx) = m; MAT_NCOLS(Objx) = n;
+ }
+
+ /* sparse matrix */
+ else if (SpMatrix_Check(Objx)) {
+
+ int nnz=0, ik, jk;
+
+ for (jk=0; jk<SP_NCOLS(Objx); jk++) {
+ for (ik=SP_COL(Objx)[jk]; ik<SP_COL(Objx)[jk+1]; ik++) {
+ if (((SP_ID(Objx) == DOUBLE) && (SP_VALD(Objx)[ik] != 0.0)) ||
+ ((SP_ID(Objx) == COMPLEX) && (SP_VALZ(Objx)[ik] != 0.0)))
+ nnz++;
+ }
+ }
+
+ ret = SpMatrix_New(SP_NROWS(Objx), SP_NCOLS(Objx), nnz, SP_ID(Objx));
+ if (!ret) return PyErr_NoMemory();
+
+ nnz = 0;
+ for (jk=0; jk<SP_NCOLS(Objx); jk++) {
+ for (ik=SP_COL(Objx)[jk]; ik<SP_COL(Objx)[jk+1]; ik++) {
+ if ((SP_ID(Objx) == DOUBLE) && (SP_VALD(Objx)[ik] != 0.0)) {
+ SP_VALD(ret)[nnz] = SP_VALD(Objx)[ik];
+ SP_ROW(ret)[nnz++] = SP_ROW(Objx)[ik];
+ SP_COL(ret)[jk+1]++;
+ }
+ else if ((SP_ID(Objx) == COMPLEX) && (SP_VALZ(Objx)[ik] != 0.0)) {
+ SP_VALZ(ret)[nnz] = SP_VALZ(Objx)[ik];
+ SP_ROW(ret)[nnz++] = SP_ROW(Objx)[ik];
+ SP_COL(ret)[jk+1]++;
+ }
+ }
+ }
+
+ for (jk=0; jk<SP_NCOLS(Objx); jk++)
+ SP_COL(ret)[jk+1] += SP_COL(ret)[jk];
+
+ /*
+ ret = SpMatrix_NewFromSpMatrix((spmatrix *)Objx, 0,
+ (id == -1 ? SP_ID(Objx) : id));
+ */
+ }
+
+ /* x is a list of lists */
+ else if (PyList_Check(Objx))
+ ret = sparse_concat(Objx, id);
+
+ else PY_ERR_TYPE("invalid matrix initialization");
+
+ return (PyObject *)ret;
+}
+
+extern PyObject * matrix_exp(matrix *, PyObject *, PyObject *) ;
+extern PyObject * matrix_log(matrix *, PyObject *, PyObject *) ;
+extern PyObject * matrix_sqrt(matrix *, PyObject *, PyObject *) ;
+extern PyObject * matrix_cos(matrix *, PyObject *, PyObject *) ;
+extern PyObject * matrix_sin(matrix *, PyObject *, PyObject *) ;
+extern PyObject * matrix_elem_mul(matrix *, PyObject *, PyObject *) ;
+extern PyObject * matrix_elem_div(matrix *, PyObject *, PyObject *) ;
+
+static PyMethodDef base_functions[] = {
+ {"exp", (PyCFunction)matrix_exp, METH_VARARGS|METH_KEYWORDS,
+ "Computes the element-wise expontial of a matrix"},
+ {"log", (PyCFunction)matrix_log, METH_VARARGS|METH_KEYWORDS,
+ "Computes the element-wise logarithm of a matrix"},
+ {"sqrt", (PyCFunction)matrix_sqrt, METH_VARARGS|METH_KEYWORDS,
+ "Computes the element-wise square-root of a matrix"},
+ {"cos", (PyCFunction)matrix_cos, METH_VARARGS|METH_KEYWORDS,
+ "Computes the element-wise cosine of a matrix"},
+ {"sin", (PyCFunction)matrix_sin, METH_VARARGS|METH_KEYWORDS,
+ "Computes the element-wise sine of a matrix"},
+ {"axpy", (PyCFunction)base_axpy, METH_VARARGS|METH_KEYWORDS, doc_axpy},
+ {"gemm", (PyCFunction)base_gemm, METH_VARARGS|METH_KEYWORDS, doc_gemm},
+ {"gemv", (PyCFunction)base_gemv, METH_VARARGS|METH_KEYWORDS, doc_gemv},
+ {"syrk", (PyCFunction)base_syrk, METH_VARARGS|METH_KEYWORDS, doc_syrk},
+ {"symv", (PyCFunction)base_symv, METH_VARARGS|METH_KEYWORDS, doc_symv},
+ {"mul", (PyCFunction)matrix_elem_mul, METH_VARARGS|METH_KEYWORDS,
+ "elementwise product of two matrices"},
+ {"div", (PyCFunction)matrix_elem_div, METH_VARARGS|METH_KEYWORDS,
+ "elementwise division between two matrices"},
+ {"sparse", (PyCFunction)sparse, METH_VARARGS|METH_KEYWORDS,
+ "convenience function for creating sparse matrices"},
+ {NULL} /* sentinel */
+};
+
+PyMODINIT_FUNC
+initbase(void)
+{
+ static void *base_API[8];
+ PyObject *c_api_object;
+
+ if (!(base_mod = Py_InitModule3("base", base_functions, base__doc__)))
+ return;
+
+ /* for MS VC++ compatibility */
+ matrix_tp.tp_alloc = PyType_GenericAlloc;
+ matrix_tp.tp_free = PyObject_Del;
+ if (PyType_Ready(&matrix_tp) < 0)
+ return;
+
+ if (PyType_Ready(&matrix_tp) < 0)
+ return;
+
+ Py_INCREF(&matrix_tp);
+ if (PyModule_AddObject(base_mod, "matrix", (PyObject *) &matrix_tp) < 0)
+ return;
+
+ spmatrix_tp.tp_alloc = PyType_GenericAlloc;
+ spmatrix_tp.tp_free = PyObject_Del;
+ if (PyType_Ready(&spmatrix_tp) < 0)
+ return;
+
+ Py_INCREF(&spmatrix_tp);
+ if (PyModule_AddObject(base_mod, "spmatrix", (PyObject *) &spmatrix_tp) < 0)
+ return;
+
+ /* Create the print_options dictionary */
+ PyObject *printopt = PyDict_New();
+ PyObject *dstr = PyString_FromString("5.4e");
+ PyObject *istr = PyString_FromString("5li");
+ PyObject *zstr = PyString_FromString("5.4e");
+ if (PyDict_SetItemString(printopt, "dformat", dstr) ||
+ PyDict_SetItemString(printopt, "iformat", istr) ||
+ PyDict_SetItemString(printopt, "zformat", zstr))
+ {
+ Py_XDECREF(printopt);
+ Py_XDECREF(dstr); Py_XDECREF(istr); Py_XDECREF(zstr);
+ return;
+ }
+ Py_DECREF(dstr); Py_DECREF(istr); Py_DECREF(zstr);
+
+ if (PyModule_AddObject(base_mod, "print_options", printopt) < 0)
+ return;
+
+ One[INT].i = 1; One[DOUBLE].d = 1.0; One[COMPLEX].z = 1.0;
+
+ MinusOne[INT].i = -1; MinusOne[DOUBLE].d = -1.0; MinusOne[COMPLEX].z = -1.0;
+
+ Zero[INT].i = 0; Zero[DOUBLE].d = 0.0; Zero[COMPLEX].z = 0.0;
+
+ /* initialize the C API object */
+ base_API[0] = (void *)Matrix_New;
+ base_API[1] = (void *)Matrix_NewFromMatrix;
+ base_API[2] = (void *)Matrix_NewFromSequence;
+ base_API[3] = (void *)Matrix_Check_func;
+ base_API[4] = (void *)SpMatrix_New;
+ base_API[5] = (void *)SpMatrix_NewFromSpMatrix;
+ base_API[6] = (void *)SpMatrix_NewFromIJV;
+ base_API[7] = (void *)SpMatrix_Check_func;
+
+ /* Create a CObject containing the API pointer array's address */
+ c_api_object = PyCObject_FromVoidPtr((void *)base_API, NULL);
+
+ if (c_api_object != NULL)
+ PyModule_AddObject(base_mod, "_C_API", c_api_object);
+}
diff --git a/src/C/blas.c b/src/C/blas.c
new file mode 100644
index 0000000..825b48c
--- /dev/null
+++ b/src/C/blas.c
@@ -0,0 +1,3316 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "Python.h"
+#include "cvxopt.h"
+#include "misc.h"
+
+#define USE_CBLAS_ZDOT 0
+
+PyDoc_STRVAR(blas__doc__,"Interface to the double-precision real and "
+ "complex BLAS.\n\n"
+ "Double and complex matrices and vectors are stored in CVXOPT \n"
+ "matrices using the conventional BLAS storage schemes, with the\n"
+ "CVXOPT matrix buffers interpreted as one-dimensional arrays.\n"
+ "For each matrix argument X, an additional integer argument\n"
+ "offsetX specifies the start of the array, i.e., the pointer\n"
+ "X->buffer + offsetX is passed to the BLAS function. The other \n"
+ "arguments (dimensions and options) have the same meaning as in\n"
+ "the BLAS definition. Default values of the dimension arguments\n"
+ "are derived from the CVXOPT matrix sizes.");
+
+
+/* BLAS 1 prototypes */
+extern void dswap_(int *n, double *x, int *incx, double *y, int *incy);
+extern void zswap_(int *n, complex *x, int *incx, complex *y,
+ int *incy);
+extern void dscal_(int *n, double *alpha, double *x, int *incx);
+extern void zscal_(int *n, complex *alpha, complex *x, int *incx);
+extern void zdscal_(int *n, double *alpha, complex *x, int *incx);
+extern void dcopy_(int *n, double *x, int *incx, double *y, int *incy);
+extern void zcopy_(int *n, complex *x, int *incx, complex *y,
+ int *incy);
+extern void daxpy_(int *n, double *alpha, double *x, int *incx,
+ double *y, int *incy);
+extern void zaxpy_(int *n, complex *alpha, complex *x, int *incx,
+ complex *y, int *incy);
+extern double ddot_(int *n, double *x, int *incx, double *y, int *incy);
+#if USE_CBLAS_ZDOT
+extern void cblas_zdotc_sub(int n, void *x, int incx, void *y,
+ int incy, void *result);
+extern void cblas_zdotu_sub(int n, void *x, int incx, void *y, int incy,
+ void *result);
+#endif
+extern double dnrm2_(int *n, double *x, int *incx);
+extern double dznrm2_(int *n, complex *x, int *incx);
+extern double dasum_(int *n, double *x, int *incx);
+extern double dzasum_(int *n, complex *x, int *incx);
+extern int idamax_(int *n, double *x, int *incx);
+extern int izamax_(int *n, complex *x, int *incx);
+
+
+/* BLAS 2 prototypes */
+extern void dgemv_(char* trans, int *m, int *n, double *alpha,
+ double *A, int *lda, double *x, int *incx, double *beta, double *y,
+ int *incy);
+extern void zgemv_(char* trans, int *m, int *n, complex *alpha,
+ complex *A, int *lda, complex *x, int *incx, complex *beta,
+ complex *y, int *incy);
+extern void dgbmv_(char* trans, int *m, int *n, int *kl, int *ku,
+ double *alpha, double *A, int *lda, double *x, int *incx,
+ double *beta, double *y, int *incy);
+extern void zgbmv_(char* trans, int *m, int *n, int *kl, int *ku,
+ complex *alpha, complex *A, int *lda, complex *x, int *incx,
+ complex *beta, complex *y, int *incy);
+extern void dsymv_(char *uplo, int *n, double *alpha, double *A,
+ int *lda, double *x, int *incx, double *beta, double *y, int *incy);
+extern void zhemv_(char *uplo, int *n, complex *alpha, complex *A,
+ int *lda, complex *x, int *incx, complex *beta, complex *y,
+ int *incy);
+extern void dsbmv_(char *uplo, int *n, int *k, double *alpha, double *A,
+ int *lda, double *x, int *incx, double *beta, double *y, int *incy);
+extern void zhbmv_(char *uplo, int *n, int *k, complex *alpha,
+ complex *A, int *lda, complex *x, int *incx, complex *beta,
+ complex *y, int *incy);
+extern void dtrmv_(char *uplo, char *trans, char *diag, int *n,
+ double *A, int *lda, double *x, int *incx);
+extern void ztrmv_(char *uplo, char *trans, char *diag, int *n,
+ complex *A, int *lda, complex *x, int *incx);
+extern void dtbmv_(char *uplo, char *trans, char *diag, int *n, int *k,
+ double *A, int *lda, double *x, int *incx);
+extern void ztbmv_(char *uplo, char *trans, char *diag, int *n, int *k,
+ complex *A, int *lda, complex *x, int *incx);
+extern void dtrsv_(char *uplo, char *trans, char *diag, int *n,
+ double *A, int *lda, double *x, int *incx);
+extern void ztrsv_(char *uplo, char *trans, char *diag, int *n,
+ complex *A, int *lda, complex *x, int *incx);
+extern void dtbsv_(char *uplo, char *trans, char *diag, int *n, int *k,
+ double *A, int *lda, double *x, int *incx);
+extern void ztbsv_(char *uplo, char *trans, char *diag, int *n, int *k,
+ complex *A, int *lda, complex *x, int *incx);
+extern void dger_(int *m, int *n, double *alpha, double *x, int *incx,
+ double *y, int *incy, double *A, int *lda);
+extern void zgerc_(int *m, int *n, complex *alpha, complex *x,
+ int *incx, complex *y, int *incy, complex *A, int *lda);
+extern void zgeru_(int *m, int *n, complex *alpha, complex *x,
+ int *incx, complex *y, int *incy, complex *A, int *lda);
+extern void dsyr_(char *uplo, int *n, double *alpha, double *x,
+ int *incx, double *A, int *lda);
+extern void zher_(char *uplo, int *n, double *alpha, complex *x,
+ int *incx, complex *A, int *lda);
+extern void dsyr2_(char *uplo, int *n, double *alpha, double *x,
+ int *incx, double *y, int *incy, double *A, int *lda);
+extern void zher2_(char *uplo, int *n, complex *alpha, complex *x,
+ int *incx, complex *y, int *incy, complex *A, int *lda);
+
+
+/* BLAS 3 prototypes */
+extern void dgemm_(char *transa, char *transb, int *m, int *n, int *k,
+ double *alpha, double *A, int *lda, double *B, int *ldb,
+ double *beta, double *C, int *ldc);
+extern void zgemm_(char *transa, char *transb, int *m, int *n, int *k,
+ complex *alpha, complex *A, int *lda, complex *B, int *ldb,
+ complex *beta, complex *C, int *ldc);
+extern void dsymm_(char *side, char *uplo, int *m, int *n,
+ double *alpha, double *A, int *lda, double *B, int *ldb,
+ double *beta, double *C, int *ldc);
+extern void zsymm_(char *side, char *uplo, int *m, int *n,
+ complex *alpha, complex *A, int *lda, complex *B, int *ldb,
+ complex *beta, complex *C, int *ldc);
+extern void zhemm_(char *side, char *uplo, int *m, int *n,
+ complex *alpha, complex *A, int *lda, complex *B, int *ldb,
+ complex *beta, complex *C, int *ldc);
+extern void dsyrk_(char *uplo, char *trans, int *n, int *k,
+ double *alpha, double *A, int *lda, double *beta, double *B,
+ int *ldb);
+extern void zsyrk_(char *uplo, char *trans, int *n, int *k,
+ complex *alpha, complex *A, int *lda, complex *beta, complex *B,
+ int *ldb);
+extern void zherk_(char *uplo, char *trans, int *n, int *k,
+ double *alpha, complex *A, int *lda, double *beta, complex *B,
+ int *ldb);
+extern void dsyr2k_(char *uplo, char *trans, int *n, int *k,
+ double *alpha, double *A, int *lda, double *B, int *ldb,
+ double *beta, double *C, int *ldc);
+extern void zsyr2k_(char *uplo, char *trans, int *n, int *k,
+ complex *alpha, complex *A, int *lda, complex *B, int *ldb,
+ complex *beta, complex *C, int *ldc);
+extern void zher2k_(char *uplo, char *trans, int *n, int *k,
+ complex *alpha, complex *A, int *lda, complex *B, int *ldb,
+ double *beta, complex *C, int *ldc);
+extern void dtrmm_(char *side, char *uplo, char *transa, char *diag,
+ int *m, int *n, double *alpha, double *A, int *lda, double *B,
+ int *ldb);
+extern void ztrmm_(char *side, char *uplo, char *transa, char *diag,
+ int *m, int *n, complex *alpha, complex *A, int *lda, complex *B,
+ int *ldb);
+extern void dtrsm_(char *side, char *uplo, char *transa, char *diag,
+ int *m, int *n, double *alpha, double *A, int *lda, double *B,
+ int *ldb);
+extern void ztrsm_(char *side, char *uplo, char *transa, char *diag,
+ int *m, int *n, complex *alpha, complex *A, int *lda, complex *B,
+ int *ldb);
+
+
+static int number_from_pyobject(PyObject *o, number *a, int id)
+{
+ switch (id){
+ case DOUBLE:
+ if (!PyInt_Check(o) && !PyLong_Check(o) &&
+ !PyFloat_Check(o)) return -1;
+ (*a).d = PyFloat_AsDouble(o);
+ return 0;
+
+ case COMPLEX:
+ if (!PyInt_Check(o) && !PyLong_Check(o) &&
+ !PyFloat_Check(o) && !PyComplex_Check(o)) return -1;
+ (*a).z = PyComplex_RealAsDouble(o) +
+ I*PyComplex_ImagAsDouble(o);
+ return 0;
+ }
+ return -1;
+}
+
+
+static char doc_swap[] =
+ "Interchanges two vectors (x <-> y).\n\n"
+ "swap(x, y, n=None, incx=1, incy=1, offsetx=0, offsety=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " len(x)>=offsetx+1 ? 1+(len(x)-offsetx-1)/|incx| : 0.\n"
+ " If the default value is used, it must be equal to\n"
+ " len(y)>=offsety+1 ? 1+(len(y)-offsetx-1)/|incy| : 0.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+static PyObject* swap(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x, *y;
+ int n=-1, ix=1, iy=1, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "n", "incx", "incy", "offsetx",
+ "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiiii", kwlist,
+ &x, &y, &n, &ix, &iy, &ox, &oy)) return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (ox < 0) err_nn_int("offsetx");
+ if (oy < 0) err_nn_int("offsety");
+
+ if (n<0){
+ n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/abs(ix) : 0;
+ if (n != ((len(y) >= oy+1) ? 1+(len(y)-oy-1)/abs(iy) : 0)){
+ PyErr_SetString(PyExc_ValueError, "arrays have unequal "
+ "default lengths");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (len(x) < ox+1+(n-1)*abs(ix)) err_buf_len("x");
+ if (len(y) < oy+1+(n-1)*abs(iy)) err_buf_len("y");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dswap_(&n, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ case COMPLEX:
+ zswap_(&n, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_scal[] =
+ "Scales a vector by a constant (x := alpha*x).\n\n"
+ "scal(alpha, x, n=None, inc=1, offset=0)\n\n"
+ "ARGUMENTS\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if x is complex.\n\n"
+ "x 'd' or 'z' matrix\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offset+1) ? 1+(len-offset-1)/inc : 0.\n\n"
+ "inc positive integer\n\n"
+ "offset nonnegative integer";
+
+static PyObject* scal(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x;
+ PyObject *ao;
+ number a;
+ int n=-1, ix=1, ox=0;
+ char *kwlist[] = {"alpha", "x", "n", "inc", "offset", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iii", kwlist,
+ &ao, &x, &n, &ix, &ox)) return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (ix <= 0) err_p_int("inc");
+ if (ox < 0) err_nn_int("offset");
+ if (n < 0) n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/ix : 0;
+ if (n == 0) return Py_BuildValue("");
+ if (len(x) < ox+1+(n-1)*ix) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ dscal_(&n, &a.d, MAT_BUFD(x)+ox, &ix);
+ break;
+
+ case COMPLEX:
+ if (!number_from_pyobject(ao, &a, DOUBLE))
+ zdscal_(&n, &a.d, MAT_BUFZ(x)+ox, &ix);
+ else if (!number_from_pyobject(ao, &a, COMPLEX))
+ zscal_(&n, &a.z, MAT_BUFZ(x)+ox, &ix);
+ else
+ err_type("alpha");
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_copy[] =
+ "Copies a vector x to a vector y (y := x).\n\n"
+ "copy(x, y, n=None, incx=1, incy=1, offsetx=0, offsety=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is given by\n"
+ " (len(x)>=offsetx+1) ? 1+(len(x)-offsetx-1)/incx : 0\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+static PyObject* copy(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x, *y;
+ int n=-1, ix=1, iy=1, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "n", "incx", "incy", "offsetx",
+ "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiiii", kwlist,
+ &x, &y, &n, &ix, &iy, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (ox < 0 ) err_nn_int("offsetx");
+ if (oy < 0 ) err_nn_int("offsety");
+
+ if (n < 0) n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/abs(ix) : 0;
+ if (n == 0) return Py_BuildValue("");
+
+ if (len(x) < ox+1+(n-1)*abs(ix)) err_buf_len("x");
+ if (len(y) < oy+1+(n-1)*abs(iy)) err_buf_len("y");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dcopy_(&n, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ case COMPLEX:
+ zcopy_(&n, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_axpy[] =
+ "Constant times a vector plus a vector (y := alpha*x+y).\n\n"
+ "axpy(x, y, alpha=1.0, n=None, incx=1, incy=1, offsetx=0, "
+ "offsety=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if x is complex.\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offsetx+1) ? 1+(len(x)-offsetx-1)/incx : 0.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+static PyObject* axpy(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x, *y;
+ PyObject *ao=NULL;
+ number a;
+ int n=-1, ix=1, iy=1, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "alpha", "n", "incx", "incy", "offsetx",
+ "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|Oiiiii", kwlist,
+ &x, &y, &ao, &n, &ix, &iy, &ox, &oy)) return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (ox < 0) err_nn_int("offsetx");
+ if (oy < 0) err_nn_int("offsety");
+
+ if (n < 0) n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/abs(ix) : 0;
+ if (n == 0) return Py_BuildValue("");
+
+ if (len(x) < ox + 1+(n-1)*abs(ix)) err_buf_len("x");
+ if (len(y) < oy + 1+(n-1)*abs(iy)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ daxpy_(&n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z=1.0;
+ zaxpy_(&n, &a.z, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_dot[] =
+ "Returns x^H*y for real or complex x, y.\n\n"
+ "dot(x, y, n=None, incx=1, incy=1, offsetx=0, offsety=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offsetx+1) ? 1+(len(x)-offsetx-1)/incx : 0.\n"
+ " If the default value is used, it must be equal to\n"
+ " len(y)>=offsety+1 ? 1+(len(y)-offsetx-1)/|incy| : 0.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "Returns 0 if n=0.";
+
+static PyObject* dot(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x, *y;
+ number val;
+ int n=-1, ix=1, iy=1, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "n", "incx", "incy", "offsetx",
+ "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiiii", kwlist,
+ &x, &y, &n, &ix, &iy, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (ox < 0) err_nn_int("offsetx");
+ if (oy < 0) err_nn_int("offsety");
+
+ if (n<0){
+ n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/abs(ix) : 0;
+ if (n != ((len(y) >= oy+1) ? 1+(len(y)-oy-1)/abs(iy) : 0)){
+ PyErr_SetString(PyExc_ValueError, "arrays have unequal "
+ "default lengths");
+ return NULL;
+ }
+ }
+
+ if (n && len(x) < ox + 1 + (n-1)*abs(ix)) err_buf_len("x");
+ if (n && len(y) < oy + 1 + (n-1)*abs(iy)) err_buf_len("y");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ val.d = (n==0) ? 0.0 : ddot_(&n, MAT_BUFD(x)+ox, &ix,
+ MAT_BUFD(y)+oy, &iy);
+ return Py_BuildValue("d", val.d);
+
+ case COMPLEX:
+ if (n==0) val.z = 0.0;
+ else
+#if USE_CBLAS_ZDOT
+ cblas_zdotc_sub(n, MAT_BUFZ(x)+ox, ix, MAT_BUFZ(y)+oy,
+ iy, &val.z);
+#else
+ ix *= 2;
+ iy *= 2;
+ val.z = (ddot_(&n, MAT_BUFD(x)+2*ox, &ix,
+ MAT_BUFD(y)+2*oy, &iy) +
+ ddot_(&n, MAT_BUFD(x)+2*ox + 1, &ix,
+ MAT_BUFD(y)+2*oy + 1, &iy)) +
+ I*(ddot_(&n, MAT_BUFD(x)+2*ox, &ix,
+ MAT_BUFD(y)+2*oy + 1, &iy) -
+ ddot_(&n, MAT_BUFD(x)+2*ox + 1, &ix,
+ MAT_BUFD(y)+2*oy, &iy));
+#endif
+ return PyComplex_FromDoubles(creal(val.z),cimag(val.z));
+
+ default:
+ err_invalid_id;
+ }
+}
+
+
+static char doc_dotu[] =
+ "Returns x^T*y for real or complex x, y.\n\n"
+ "dotu(x, y, n=None, incx=1, incy=1, offsetx=0, offsety=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offsetx+1) ? 1+(len(x)-offsetx-1)/incx : 0.\n"
+ " If the default value is used, it must be equal to\n"
+ " len(y)>=offsety+1 ? 1+(len(y)-offsetx-1)/|incy| : 0.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "Returns 0 if n=0.";
+
+static PyObject* dotu(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x, *y;
+ number val;
+ int n=-1, ix=1, iy=1, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "n", "incx", "incy", "offsetx",
+ "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiiii", kwlist,
+ &x, &y, &n, &ix, &iy, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (ox < 0) err_nn_int("offsetx");
+ if (oy < 0) err_nn_int("offsety");
+
+ if (n<0){
+ n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/abs(ix) : 0;
+ if (n != ((len(y) >= oy+1) ? 1+(len(y)-oy-1)/abs(iy) : 0)){
+ PyErr_SetString(PyExc_ValueError, "arrays have unequal "
+ "default lengths");
+ return NULL;
+ }
+ }
+
+ if (n && len(x) < ox + 1 + (n-1)*abs(ix)) err_buf_len("x");
+ if (n && len(y) < oy + 1 + (n-1)*abs(iy)) err_buf_len("y");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ val.d = (n==0) ? 0.0 : ddot_(&n, MAT_BUFD(x)+ox, &ix,
+ MAT_BUFD(y)+oy, &iy);
+ return Py_BuildValue("d", val.d);
+
+ case COMPLEX:
+ if (n==0) val.z = 0.0;
+ else
+#if USE_CBLAS_ZDOT
+ cblas_zdotu_sub(n, MAT_BUFZ(x)+ox, ix, MAT_BUFZ(y)+oy,
+ iy, &val.z);
+#else
+ ix *= 2;
+ iy *= 2;
+ val.z = (ddot_(&n, MAT_BUFD(x)+2*ox, &ix,
+ MAT_BUFD(y)+2*oy, &iy) -
+ ddot_(&n, MAT_BUFD(x)+2*ox + 1, &ix,
+ MAT_BUFD(y)+2*oy + 1, &iy)) +
+ I*(ddot_(&n, MAT_BUFD(x)+2*ox, &ix,
+ MAT_BUFD(y)+2*oy + 1, &iy) +
+ ddot_(&n, MAT_BUFD(x)+2*ox + 1, &ix,
+ MAT_BUFD(y)+2*oy, &iy));
+#endif
+ return PyComplex_FromDoubles(creal(val.z),cimag(val.z));
+
+ default:
+ err_invalid_id;
+ }
+}
+
+
+static char doc_nrm2[] =
+ "Returns the Euclidean norm of a vector (returns ||x||_2).\n\n"
+ "nrm2(x, n=None, inc=1, offset=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offsetx+1) ? 1+(len(x)-offsetx-1)/incx : 0.\n\n"
+ "inc positive integer\n\n"
+ "offset nonnegative integer\n\n"
+ "Returns 0 if n=0.";
+
+static PyObject* nrm2(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x;
+ int n=-1, ix=1, ox=0;
+ char *kwlist[] = {"x", "n", "inc", "offset", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|iii", kwlist, &x,
+ &n, &ix, &ox)) return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (ix <= 0) err_p_int("incx");
+ if (ox < 0) err_nn_int("offsetx");
+ if (n < 0) n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/ix : 0;
+ if (n == 0) return Py_BuildValue("d", 0.0);
+ if (len(x) < ox + 1+(n-1)*ix) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ return Py_BuildValue("d", dnrm2_(&n, MAT_BUFD(x)+ox, &ix));
+
+ case COMPLEX:
+ return Py_BuildValue("d", dznrm2_(&n, MAT_BUFZ(x)+ox, &ix));
+
+ default:
+ err_invalid_id;
+ }
+}
+
+
+static char doc_asum[] =
+ "Returns ||Re x||_1 + ||Im x||_1.\n\n"
+ "asum(x, n=None, inc=1, offset=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " n = (len(x)>=offset+1) ? 1+(len(x)-offset-1)/inc : 0.\n"
+ "\n"
+ "inc positive integer\n\n"
+ "offset nonnegative integer\n\n"
+ "Returns 0 if n=0.";
+
+static PyObject* asum(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x;
+ int n=-1, ix=1, ox=0;
+ char *kwlist[] = {"x", "n", "inc", "offset", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|iii", kwlist,
+ &x, &n, &ix, &ox))
+ return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (ix <= 0) err_p_int("inc");
+ if (ox < 0) err_nn_int("offset");
+ if (n < 0) n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/ix : 0;
+ if (n == 0) return Py_BuildValue("d", 0.0);
+ if (len(x) < ox + 1+(n-1)*ix) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ return Py_BuildValue("d", dasum_(&n, MAT_BUFD(x)+ox, &ix));
+
+ case COMPLEX:
+ return Py_BuildValue("d", dzasum_(&n, MAT_BUFZ(x)+ox, &ix));
+
+ default:
+ err_invalid_id;
+ }
+}
+
+
+static char doc_iamax[] =
+ "Returns the index (in {0,...,n-1}) of the coefficient with \n"
+ "maximum value of |Re x_k| + |Im x_k|.\n\n"
+ "iamax(x, n=None, inc=1, offset=0)\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "n integer. If n<0, the default value of n is used.\n"
+ " The default value is equal to\n"
+ " (len(x)>=offset+1) ? 1+(len(x)-offset-1)/inc : 0.\n\n"
+ "inc positive integer\n\n"
+ "offset nonnegative integer\n\n"
+ "In the case of ties, the index of the first maximizer is \n"
+ "returned. If n=0, iamax returns 0.";
+
+static PyObject* iamax(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *x;
+ int n=-1, ix=1, ox=0;
+ char *kwlist[] = {"x", "n", "inc", "offset", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|iii", kwlist,
+ &x, &n, &ix, &ox))
+ return NULL;
+
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (ix <= 0) err_p_int("inc");
+ if (ox < 0) err_nn_int("offset");
+ if (n < 0) n = (len(x) >= ox+1) ? 1+(len(x)-ox-1)/ix : 0;
+ if (n == 0) return Py_BuildValue("i", 0);
+ if (len(x) < ox + 1+(n-1)*ix) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ return Py_BuildValue("i",
+ idamax_(&n, MAT_BUFD(x)+ox, &ix)-1);
+
+ case COMPLEX:
+ return Py_BuildValue("i",
+ izamax_(&n, MAT_BUFZ(x)+ox, &ix)-1);
+
+ default:
+ err_invalid_id;
+ }
+}
+
+
+static char doc_gemv[] =
+ "General matrix-vector product. \n\n"
+ "gemv(A, x, y, trans='N', alpha=1.0, beta=0.0, m=A.size[0],\n"
+ " n=A.size[1], ldA=max(1,A.size[0]), incx=1, incy=1, \n"
+ " offsetA=0, offsetx=0, offsety=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes y := alpha*A*x + beta*y.\n"
+ "If trans is 'T', computes y := alpha*A^T*x + beta*y.\n"
+ "If trans is 'C', computes y := alpha*A^H*x + beta*y.\n"
+ "The matrix A is m by n.\n"
+ "Returns immediately if n=0 and trans is 'T' or 'C', or if m=0 \n"
+ "and trans is 'N'.\n"
+ "Computes y := beta*y if n=0, m>0 and trans is 'N', or if m=0, \n"
+ "n>0 and trans is 'T' or 'C'.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+static PyObject* gemv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m=-1, n=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char trans='N';
+ char *kwlist[] = {"A", "x", "y", "trans", "alpha", "beta", "m", "n",
+ "ldA", "incx", "incy", "offsetA", "offsetx", "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiiiii",
+ kwlist, &A, &x, &y, &trans, &ao, &bo, &m, &n, &ldA, &ix, &iy,
+ &oA, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N','T','C'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if ((!m && trans == 'N') || (!n && (trans == 'T' || trans == 'C')))
+ return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (n > 0 && m > 0 && oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+
+ if (ox < 0) err_nn_int("offsetx");
+ if ((trans == 'N' && n > 0 && ox + (n-1)*abs(ix) + 1 > len(x)) ||
+ ((trans == 'T' || trans == 'C') && m > 0 &&
+ ox + (m-1)*abs(ix) + 1 > len(x))) err_buf_len("x");
+
+ if (oy < 0) err_nn_int("offsety");
+ if ((trans == 'N' && oy + (m-1)*abs(iy) + 1 > len(y)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oy + (n-1)*abs(iy) + 1 > len(y))) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(x)))
+ err_type("beta");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ if (!bo) b.d=0.0;
+ if (trans == 'N' && n == 0)
+ dscal_(&m, &b.d, MAT_BUFD(y)+oy, &iy);
+ else if ((trans == 'T' || trans == 'C') && m == 0)
+ dscal_(&n, &b.d, MAT_BUFD(y)+oy, &iy);
+ else
+ dgemv_(&trans, &m, &n, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix, &b.d, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z=1.0;
+ if (!bo) b.z=0.0;
+ if (trans == 'N' && n == 0)
+ zscal_(&m, &b.z, MAT_BUFZ(y)+oy, &iy);
+ else if ((trans == 'T' || trans == 'C') && m == 0)
+ zscal_(&n, &b.z, MAT_BUFZ(y)+oy, &iy);
+ else
+ zgemv_(&trans, &m, &n, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix, &b.z, MAT_BUFZ(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_gbmv[] =
+ "Matrix-vector product with a general banded matrix.\n\n"
+ "gbmv(A, m, kl, x, y, trans='N', alpha=1.0, beta=0.0, n=A.size[1],\n"
+ " ku=A.size[0]-kl-1, ldA=max(1,A.size[0]), incx=1, incy=1, \n"
+ " offsetA=0, offsetx=0, offsety=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes y := alpha*A*x + beta*y.\n"
+ "If trans is 'T', computes y := alpha*A^T*x + beta*y.\n"
+ "If trans is 'C', computes y := alpha*A^H*x + beta*y.\n"
+ "The matrix A is m by n with upper bandwidth ku and lower\n"
+ "bandwidth kl.\n"
+ "Returns immediately if n=0 and trans is 'T' or 'C', or if m=0 \n"
+ "and trans is 'N'.\n"
+ "Computes y := beta*y if n=0, m>0, and trans is 'N', or if m=0, n>0,\n"
+ "and trans is 'T' or 'C'.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "m nonnegative integer\n\n"
+ "kl nonnegative integer\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ku nonnegative integer. If negative, the default value is\n"
+ " used.\n"
+ "ldA positive integer. ldA >= kl+ku+1. If zero, the default\n"
+ " value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+static PyObject* gbmv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m, kl, ku=-1, n=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char trans='N';
+ char *kwlist[] = {"A", "m", "kl", "x", "y", "trans", "alpha", "beta",
+ "n", "ku", "ldA", "incx", "incy", "offsetA", "offsetx", "offsety",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OiiOO|cOOiiiiiiii",
+ kwlist, &A, &m, &kl, &x, &y, &trans, &ao, &bo, &n, &ku, &ldA, &ix,
+ &iy, &oA, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+ if (n < 0) n = A->ncols;
+ if ((!m && trans == 'N') || (!n && (trans == 'T' || trans == 'C')))
+ return Py_BuildValue("");
+
+ if (kl < 0) err_nn_int("kl");
+ if (ku < 0) ku = A->nrows - 1 - kl;
+ if (ku < 0) err_nn_int("ku");
+
+ if (ldA == 0) ldA = A->nrows;
+ if (ldA < kl+ku+1) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (m>0 && n>0 && oA + (n-1)*ldA + kl + ku + 1 > len(A))
+ err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if ((trans == 'N' && n > 0 && ox + (n-1)*abs(ix) + 1 > len(x)) ||
+ ((trans == 'T' || trans == 'C') && m > 0 &&
+ ox + (m-1)*abs(ix) + 1 > len(x))) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if ((trans == 'N' && oy + (m-1)*abs(iy) + 1 > len(y)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oy + (n-1)*abs(iy) + 1 > len(y))) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(x)))
+ err_type("beta");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ if (!bo) b.d=0.0;
+ if (trans == 'N' && n == 0)
+ dscal_(&m, &b.d, MAT_BUFD(y)+oy, &iy);
+ else if ((trans == 'T' || trans == 'C') && m == 0)
+ dscal_(&n, &b.d, MAT_BUFD(y)+oy, &iy);
+ else
+ dgbmv_(&trans, &m, &n, &kl, &ku, &a.d, MAT_BUFD(A)+oA,
+ &ldA, MAT_BUFD(x)+ox, &ix, &b.d, MAT_BUFD(y)+oy,
+ &iy);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z=1.0;
+ if (!bo) b.z=0.0;
+ if (trans == 'N' && n == 0)
+ zscal_(&m, &b.z, MAT_BUFZ(y)+oy, &iy);
+ else if ((trans == 'T' || trans == 'C') && m == 0)
+ zscal_(&n, &b.z, MAT_BUFZ(y)+oy, &iy);
+ else
+ zgbmv_(&trans, &m, &n, &kl, &ku, &a.z, MAT_BUFZ(A)+oA,
+ &ldA, MAT_BUFZ(x)+ox, &ix, &b.z, MAT_BUFZ(y)+oy,
+ &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_symv[] =
+ "Matrix-vector product with a real symmetric matrix.\n\n"
+ "symv(A, x, y, uplo='L', alpha=1.0, beta=0.0, n=A.size[0], \n"
+ " ldA=max(1,A.size[0]), incx=1, incy=1, offsetA=0, offsetx=0,\n"
+ " offsety=0)\n\n"
+ "PURPOSE\n"
+ "Computes y := alpha*A*x + beta*y with A real symmetric of order n."
+ "n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "x 'd' matrix\n\n"
+ "y 'd' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha real number (int or float)\n\n"
+ "beta real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used, we require that\n"
+ " A.size[0]=A.size[1].\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+static PyObject* symv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char uplo='L';
+ char *kwlist[] = {"A", "x", "y", "uplo", "alpha", "beta", "n",
+ "ldA", "incx", "incy", "offsetA", "offsetx", "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiiii",
+ kwlist, &A, &x, &y, &uplo, &ao, &bo, &n, &ldA, &ix, &iy, &oA,
+ &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_ValueError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(x)))
+ err_type("beta");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ if (!bo) b.d=0.0;
+ dsymv_(&uplo, &n, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix, &b.d, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+
+static char doc_hemv[] =
+ "Matrix-vector product with a real symmetric or complex Hermitian\n"
+ "matrix.\n\n"
+ "hemv(A, x, y, uplo='L', alpha=1.0, beta=0.0, n=A.size[0],\n"
+ " ldA=max(1,A.size[0]), incx=1, incy=1, offsetA=0, offsetx=0,\n"
+ " offsety=0)\n\n"
+ "PURPOSE\n"
+ "Computes y := alpha*A*x + beta*y, with A real symmetric or\n"
+ "complex Hermitian of order n.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used, we require that\n"
+ " A.size[0]=A.size[1].\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer";
+
+
+static PyObject* hemv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char uplo='L';
+ char *kwlist[] = {"A", "x", "y", "uplo", "alpha", "beta", "n",
+ "ldA", "incx", "incy", "offsetA", "offsetx", "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiiii",
+ kwlist, &A, &x, &y, &uplo, &ao, &bo, &n, &ldA, &ix, &iy, &oA,
+ &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_ValueError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(x)))
+ err_type("beta");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ if (!bo) b.d=0.0;
+ dsymv_(&uplo, &n, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix, &b.d, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z=1.0;
+ if (!bo) b.z=0.0;
+ zhemv_(&uplo, &n, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix, &b.z, MAT_BUFZ(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_sbmv[] =
+ "Matrix-vector product with a real symmetric band matrix.\n\n"
+ "sbmv(A, x, y, uplo='L', alpha=1.0, beta=0.0, n=A.size[1], \n"
+ " k=None, ldA=A.size[0], incx=1, incy=1, offsetA=0,\n"
+ " offsetx=0, offsety=0)\n\n"
+ "PURPOSE\n"
+ "Computes y := alpha*A*x + beta*y with A real symmetric and \n"
+ "banded of order n and with bandwidth k.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "x 'd' matrix\n\n"
+ "y 'd' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha real number (int or float)\n\n"
+ "beta real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is k = max(0,A.size[0]-1).\n\n"
+ "ldA nonnegative integer. ldA >= k+1.\n"
+ " If zero, the default vaule is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n";
+
+static PyObject* sbmv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, k=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char uplo='L';
+ char *kwlist[] = {"A", "x", "y", "uplo", "alpha", "beta", "n", "k",
+ "ldA", "incx", "incy", "offsetA", "offsetx", "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiiiii",
+ kwlist, &A, &x, &y, &uplo, &ao, &bo, &n, &k, &ldA, &ix, &iy,
+ &oA, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0) n = A->ncols;
+ if (n == 0) return Py_BuildValue("");
+
+ if (k < 0) k = MAX(0, A->nrows-1);
+ if (ldA == 0) ldA = A->nrows;
+ if (ldA < 1+k) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + k+1 > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(x)))
+ err_type("beta");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ if (!bo) b.d=0.0;
+ dsbmv_(&uplo, &n, &k, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix, &b.d, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_hbmv[] =
+ "Matrix-vector product with a real symmetric or complex Hermitian\n"
+ "band matrix.\n\n"
+ "hbmv(A, x, y, uplo='L', alpha=1.0, beta=0.0, n=A.size[1], \n"
+ " k=None, ldA=A.size[0], incx=1, incy=1, offsetA=0, \n"
+ " offsetx=0, offsety=0)\n\n"
+ "PURPOSE\n"
+ "Computes y := alpha*A*x + beta*y with A real symmetric or \n"
+ "complex Hermitian and banded of order n and with bandwidth k.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is k = max(0,A.size[0]-1).\n\n"
+ "ldA nonnegative integer. ldA >= k+1.\n"
+ " If zero, the default vaule is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "offsetA nonnegative integer.\n\n"
+ "offsetx nonnegative integer.\n\n"
+ "offsety nonnegative integer.\n\n";
+
+static PyObject* hbmv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, k=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char uplo='L';
+ char *kwlist[] = {"A", "x", "y", "uplo", "alpha", "beta", "n", "k",
+ "ldA", "incx", "incy", "offsetA", "offsetx", "offsety", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOOiiiiiiii",
+ kwlist, &A, &x, &y, &uplo, &ao, &bo, &n, &k, &ldA, &ix, &iy,
+ &oA, &ox, &oy))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0) n = A->ncols;
+ if (n == 0) return Py_BuildValue("");
+
+ if (k < 0) k = MAX(0, A->nrows-1);
+ if (ldA == 0) ldA = A->nrows;
+ if (ldA < 1+k) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + k+1 > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(x)))
+ err_type("beta");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d=1.0;
+ if (!bo) b.d=0.0;
+ dsbmv_(&uplo, &n, &k, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix, &b.d, MAT_BUFD(y)+oy, &iy);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z=1.0;
+ if (!bo) b.z=0.0;
+ zhbmv_(&uplo, &n, &k, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix, &b.z, MAT_BUFZ(y)+oy, &iy);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_trmv[] =
+ "Matrix-vector product with a triangular matrix.\n\n"
+ "trmv(A, x, uplo='L', trans='N', diag='N', n=A.size[0],\n"
+ " ldA=max(1,A.size[0]), incx=1, offsetA=0, offsetx=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes x := A*x.\n"
+ "If trans is 'T', computes x := A^T*x.\n"
+ "If trans is 'C', computes x := A^H*x.\n"
+ "A is triangular of order n.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N' or 'T'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used, we require that\n"
+ " A.size[0] = A.size[1].\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer";
+
+static PyObject* trmv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x;
+ int n=-1, ldA=0, ix=1, oA=0, ox=0;
+ char uplo='L', trans='N', diag='N';
+ char *kwlist[] = {"A", "x", "uplo", "trans", "diag", "n", "ldA",
+ "incx", "offsetA", "offsetx", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccciiiii",
+ kwlist, &A, &x, &uplo, &trans, &diag, &n, &ldA, &ix, &oA, &ox))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (MAT_ID(A) != MAT_ID(x)) err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'U', 'N'");
+
+ if (ix == 0) err_nz_int("incx");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("offsetx");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dtrmv_(&uplo, &trans, &diag, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix);
+ break;
+
+ case COMPLEX:
+ ztrmv_(&uplo, &trans, &diag, &n, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_tbmv[] =
+ "Matrix-vector product with a triangular band matrix.\n\n"
+ "tbmv(A, x, uplo='L', trans='N', diag='N', n=A.size[1],\n"
+ " k=max(0,A.size[0]-1), ldA=A.size[0], incx=1, offsetA=0,\n"
+ " offsetx=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes x := A*x.\n"
+ "If trans is 'T', computes x := A^T*x.\n"
+ "If trans is 'C', computes x := A^H*x.\n"
+ "A is banded triangular of order n and with bandwith k.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value\n"
+ " is used.\n\n"
+ "k nonnegative integer. If negative, the default value\n"
+ " is used.\n\n"
+ "ldA nonnegative integer. lda >= 1+k.\n"
+ " If zero the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer";
+
+static PyObject* tbmv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x;
+ int n=-1, k=-1, ldA=0, ix=1, oA=0, ox=0;
+ char uplo='L', trans='N', diag='N';
+ char *kwlist[] = {"A", "x", "uplo", "trans", "diag", "n", "k",
+ "ldA", "incx", "offsetA", "offsetx", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccciiiiii",
+ kwlist, &A, &x, &uplo, &trans, &diag, &n, &k, &ldA, &ix, &oA,
+ &ox))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (MAT_ID(A) != MAT_ID(x)) err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'U', 'N'");
+
+ if (ix == 0) err_nz_int("incx");
+
+ if (n < 0) n = A->ncols;
+ if (n == 0) return Py_BuildValue("");
+ if (k < 0) k = MAX(0,A->nrows-1);
+
+ if (ldA == 0) ldA = A->nrows;
+ if (ldA < k+1) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + k + 1 > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dtbmv_(&uplo, &trans, &diag, &n, &k, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix);
+ break;
+
+ case COMPLEX:
+ ztbmv_(&uplo, &trans, &diag, &n, &k, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_trsv[] =
+ "Solution of a triangular set of equations with one righthand side."
+ "\n\n"
+ "trsv(A, x, uplo='L', trans='N', diag='N', n=A.size[0],\n"
+ " ldA=max(1,A.size[0]), incx=1, offsetA=0, offsetx=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes x := A^{-1}*x.\n"
+ "If trans is 'T', computes x := A^{-T}*x.\n"
+ "If trans is 'C', computes x := A^{-H}*x.\n"
+ "A is triangular of order n. The code does not verify whether A\n"
+ "is nonsingular.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used, we require that\n"
+ " A.size[0] = A.size[1].\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer";
+
+static PyObject* trsv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x;
+ int n=-1, ldA=0, ix=1, oA=0, ox=0;
+ char uplo='L', trans='N', diag='N';
+ char *kwlist[] = {"A", "x", "uplo", "trans", "diag", "n", "ldA",
+ "incx", "offsetA", "offsetx", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccciiiii",
+ kwlist, &A, &x, &uplo, &trans, &diag, &n, &ldA, &ix, &oA, &ox))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (MAT_ID(A) != MAT_ID(x)) err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dtrsv_(&uplo, &trans, &diag, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix);
+ break;
+
+ case COMPLEX:
+ ztrsv_(&uplo, &trans, &diag, &n, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_tbsv[] =
+ "Solution of a triangular and banded set of equations.\n\n"
+ "tbsv(A, x, uplo='L', trans='N', diag='N', n=A.size[1],\n"
+ " k=max(0,A.size[0]-1), ldA=A.size[0], incx=1, offsetA=0,\n"
+ " offsetx=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes x := A^{-1}*x.\n"
+ "If trans is 'T', computes x := A^{-T}*x.\n"
+ "If trans is 'C', computes x := A^{-H}*x.\n"
+ "A is banded triangular of order n and with bandwidth k.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "x 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value\n"
+ " is used.\n\n"
+ "k nonnegative integer. If negative, the default value\n"
+ " is used.\n\n"
+ "ldA nonnegative integer. ldA >= 1+k.\n"
+ " If zero the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetx nonnegative integer";
+
+static PyObject* tbsv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x;
+ int n=-1, k=-1, ldA=0, ix=1, oA=0, ox=0;
+ char uplo='L', trans='N', diag='N';
+ char *kwlist[] = {"A", "x", "uplo", "trans", "diag", "n", "k",
+ "ldA", "incx", "offsetA", "offsetx", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccciiiiii",
+ kwlist, &A, &x, &uplo, &trans, &diag, &n, &k, &ldA, &ix, &oA,
+ &ox))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (MAT_ID(A) != MAT_ID(x)) err_conflicting_ids;
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+
+ if (ix == 0) err_nz_int("incx");
+
+ if (n < 0) n = A->ncols;
+ if (n == 0) return Py_BuildValue("");
+ if (k < 0) k = MAX(0, A->nrows-1);
+
+ if (ldA == 0) ldA = A->nrows;
+ if (ldA < k+1) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + k + 1 > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dtbsv_(&uplo, &trans, &diag, &n, &k, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(x)+ox, &ix);
+ break;
+
+ case COMPLEX:
+ ztbsv_(&uplo, &trans, &diag, &n, &k, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(x)+ox, &ix);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_ger[] =
+ "General rank-1 update.\n\n"
+ "ger(x, y, A, alpha=1.0, m=A.size[0], n=A.size[1], incx=1,\n"
+ " incy=1, ldA=max(1,A.size[0]), offsetx=0, offsety=0,\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes A := A + alpha*x*y^H with A m by n, real or complex.\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "A 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* ger(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL;
+ number a;
+ int m=-1, n=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "A", "alpha", "m", "n", "incx", "incy",
+ "ldA", "offsetx", "offsety", "offsetZ", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|Oiiiiiiii",
+ kwlist, &x, &y, &A, &ao, &m, &n, &ix, &iy, &ldA, &ox, &oy, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (m-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dger_(&m, &n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy,
+ &iy, MAT_BUFD(A)+oA, &ldA);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ zgerc_(&m, &n, &a.z, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(y)+oy,
+ &iy, MAT_BUFZ(A)+oA, &ldA);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_geru[] =
+ "General rank-1 update.\n\n"
+ "geru(x, y, A, m=A.size[0], n=A.size[1], alpha=1.0, incx=1,\n"
+ " incy=1, ldA=max(1,A.size[0]), offsetx=0, offsety=0,\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes A := A + alpha*x*y^T with A m by n, real or complex.\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "A 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* geru(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL;
+ number a;
+ int m=-1, n=-1, ldA=0, ix=1, iy=1, oA=0, ox=0, oy=0;
+ char *kwlist[] = {"x", "y", "A", "alpha", "m", "n", "incx", "incy",
+ "ldA", "offsetx", "offsety", "offsetZ", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|Oiiiiiiii",
+ kwlist, &x, &y, &A, &ao, &m, &n, &ix, &iy, &ldA, &ox, &oy, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (m-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dger_(&m, &n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy,
+ &iy, MAT_BUFD(A)+oA, &ldA);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ zgeru_(&m, &n, &a.z, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(y)+oy,
+ &iy, MAT_BUFZ(A)+oA, &ldA);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_syr[] =
+ "Symmetric rank-1 update.\n\n"
+ "syr(x, A, uplo='L', alpha=1.0, n=A.size[0], incx=1,\n"
+ " ldA=max(1,A.size[0]), offsetx=0, offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes A := A + alpha*x*x^T with A real symmetric of order n."
+ "\n\n"
+ "ARGUMENTS\n"
+ "x 'd' matrix\n\n"
+ "A 'd' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+
+static PyObject* syr(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x;
+ PyObject *ao=NULL;
+ number a;
+ int n=-1, ldA=0, ix=1, oA=0, ox=0;
+ char uplo='L';
+ char *kwlist[] = {"x", "A", "uplo", "alpha", "n", "incx", "ldA",
+ "offsetx", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cOiiiii", kwlist,
+ &x, &A, &uplo, &ao, &n, &ix, &ldA, &ox, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (MAT_ID(A) != MAT_ID(x)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ao && number_from_pyobject(ao, &a, DOUBLE)) err_type("alpha");
+ if (!ao) a.d = 1.0;
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dsyr_(&uplo, &n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(A)+oA,
+ &ldA);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_her[] =
+ "Hermitian rank-1 update.\n\n"
+ "her(x, A, uplo='L', alpha=1.0, n=A.size[0], incx=1,\n"
+ " ldA=max(1,A.size[0]), offsetx=0, offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes A := A + alpha*x*x^H with A real symmetric or complex\n"
+ "Hermitian of order n.\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "A 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+
+static PyObject* her(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x;
+ PyObject *ao=NULL;
+ number a;
+ int n=-1, ldA=0, ix=1, oA=0, ox=0;
+ char uplo='L';
+ char *kwlist[] = {"x", "A", "uplo", "alpha", "n", "incx", "ldA",
+ "offsetx", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cOiiiii",
+ kwlist, &x, &A, &uplo, &ao, &n, &ix, &ldA, &ox, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (MAT_ID(A) != MAT_ID(x)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (ao && number_from_pyobject(ao, &a, DOUBLE)) err_type("alpha");
+ if (!ao) a.d = 1.0;
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ dsyr_(&uplo, &n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(A)+oA,
+ &ldA);
+ break;
+
+ case COMPLEX:
+ zher_(&uplo, &n, &a.d, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(A)+oA,
+ &ldA);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+
+static char doc_syr2[] =
+ "Symmetric rank-2 update.\n\n"
+ "syr2(x, y, A, uplo='L', alpha=1.0, n=A.size[0], incx=1, incy=1,\n"
+ " ldA=max(1,A.size[0]), offsetx=0, offsety=0, offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes A := A + alpha*(x*y^T + y*x^T) with A real symmetric.\n\n"
+ "ARGUMENTS\n"
+ "x 'd' matrix\n\n"
+ "y 'd' matrix\n\n"
+ "A 'd' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero the default value is used.\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* syr2(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL;
+ number a;
+ int n=-1, ldA=0, ix=1, iy=1, ox=0, oy=0, oA=0;
+ char uplo='L';
+ char *kwlist[] = {"x", "y", "A", "uplo", "alpha", "n", "incx",
+ "incy", "ldA", "offsetx", "offsety", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOiiiiiii",
+ kwlist, &x, &y, &A, &uplo, &ao, &n, &ix, &iy, &ldA, &ox, &oy,
+ &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L','U'");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dsyr2_(&uplo, &n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy,
+ &iy, MAT_BUFD(A)+oA, &ldA);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_her2[] =
+ "Hermitian rank-2 update.\n\n"
+ "her2(x, y, A, uplo='L', alpha=1.0, n=A.size[0], incx=1, incy=1,\n"
+ " ldA=max(1,A.size[0]), offsetx=0, offsety=0, offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes A := A + alpha*x*y^H + conj(alpha)*y*x^H with A \n"
+ "real symmetric or complex Hermitian of order n.\n\n"
+ "ARGUMENTS\n"
+ "x 'd' or 'z' matrix\n\n"
+ "y 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "A 'd' or 'z' matrix. Must have the same type as x.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "incx nonzero integer\n\n"
+ "incy nonzero integer\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero the default value is used.\n\n"
+ "offsetx nonnegative integer\n\n"
+ "offsety nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* her2(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *x, *y;
+ PyObject *ao=NULL;
+ number a;
+ int n=-1, ldA=0, ix=1, iy=1, ox=0, oy=0, oA=0;
+ char uplo='L';
+ char *kwlist[] = {"x", "y", "A", "uplo", "alpha", "n", "incx",
+ "incy", "ldA", "offsetx", "offsety", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cOiiiiiii",
+ kwlist, &x, &y, &A, &uplo, &ao, &n, &ix, &iy, &ldA, &ox, &oy,
+ &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(x)) err_mtrx("x");
+ if (!Matrix_Check(y)) err_mtrx("y");
+ if (MAT_ID(A) != MAT_ID(x) || MAT_ID(A) != MAT_ID(y) ||
+ MAT_ID(x) != MAT_ID(y)) err_conflicting_ids;
+
+ if (ix == 0) err_nz_int("incx");
+ if (iy == 0) err_nz_int("incy");
+
+ if (n < 0){
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ n = A->nrows;
+ }
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (ox < 0) err_nn_int("offsetx");
+ if (ox + (n-1)*abs(ix) + 1 > len(x)) err_buf_len("x");
+ if (oy < 0) err_nn_int("offsety");
+ if (oy + (n-1)*abs(iy) + 1 > len(y)) err_buf_len("y");
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L','U'");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(x)))
+ err_type("alpha");
+
+ switch (MAT_ID(x)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dsyr2_(&uplo, &n, &a.d, MAT_BUFD(x)+ox, &ix, MAT_BUFD(y)+oy,
+ &iy, MAT_BUFD(A)+oA, &ldA);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ zher2_(&uplo, &n, &a.z, MAT_BUFZ(x)+ox, &ix, MAT_BUFZ(y)+oy,
+ &iy, MAT_BUFZ(A)+oA, &ldA);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_gemm[] =
+ "General matrix-matrix product.\n\n"
+ "gemm(A, B, C, transA='N', transB='N', alpha=1.0, beta=0.0, \n"
+ " m=None, n=None, k=None, ldA=max(1,A.size[0]), \n"
+ " ldB=max(1,B.size[0]), ldC=max(1,C.size[0]), offsetA=0, \n"
+ " offsetB=0, offsetC=0) \n\n"
+ "PURPOSE\n"
+ "Computes \n"
+ "C := alpha*A*B + beta*C if transA = 'N' and transB = 'N'.\n"
+ "C := alpha*A^T*B + beta*C if transA = 'T' and transB = 'N'.\n"
+ "C := alpha*A^H*B + beta*C if transA = 'C' and transB = 'N'.\n"
+ "C := alpha*A*B^T + beta*C if transA = 'N' and transB = 'T'.\n"
+ "C := alpha*A^T*B^T + beta*C if transA = 'T' and transB = 'T'.\n"
+ "C := alpha*A^H*B^T + beta*C if transA = 'C' and transB = 'T'.\n"
+ "C := alpha*A*B^H + beta*C if transA = 'N' and transB = 'C'.\n"
+ "C := alpha*A^T*B^H + beta*C if transA = 'T' and transB = 'C'.\n"
+ "C := alpha*A^H*B^H + beta*C if transA = 'C' and transB = 'C'.\n"
+ "If k=0, this reduces to C := beta*C.\n\n"
+ "ARGUMENTS\n\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "transA 'N', 'T' or 'C'\n\n"
+ "transB 'N', 'T' or 'C'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " m = (transA == 'N') ? A.size[0] : A.size[1].\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (transB == 'N') ? B.size[1] : B.size[0].\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " (transA == 'N') ? A.size[1] : A.size[0], transA='N'.\n"
+ " If the default value is used it should also be equal to\n"
+ " (transB == 'N') ? B.size[0] : B.size[1].\n\n"
+ "ldA nonnegative integer. ldA >= max(1,(transA == 'N') ? m : k).\n"
+ " If zero, the default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,(transB == 'N') ? k : n).\n"
+ " If zero, the default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* gemm(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m=-1, n=-1, k=-1, ldA=0, ldB=0, ldC=0, oA=0, oB=0, oC=0;
+ char transA='N', transB='N';
+ char *kwlist[] = {"A", "B", "C", "transA", "transB", "alpha",
+ "beta", "m", "n", "k", "ldA", "ldB", "ldC", "offsetA",
+ "offsetB", "offsetC", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ccOOiiiiiiiii",
+ kwlist, &A, &B, &C, &transA, &transB, &ao, &bo, &m, &n, &k,
+ &ldA, &ldB, &ldC, &oA, &oB, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(B) || MAT_ID(A) != MAT_ID(C) ||
+ MAT_ID(B) != MAT_ID(C)) err_conflicting_ids;
+
+ if (transA != 'N' && transA != 'T' && transA != 'C')
+ err_char("transA", "'N', 'T', 'C'");
+ if (transB != 'N' && transB != 'T' && transB != 'C')
+ err_char("transB", "'N', 'T', 'C'");
+
+ if (m < 0) m = (transA == 'N') ? A->nrows : A->ncols;
+ if (n < 0) n = (transB == 'N') ? B->ncols : B->nrows;
+ if (k < 0){
+ k = (transA == 'N') ? A->ncols : A->nrows;
+ if (k != ((transB == 'N') ? B->nrows : B->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (k > 0 && ldA < MAX(1, (transA == 'N') ? m : k)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (k > 0 && ldB < MAX(1, (transB == 'N') ? k : n)) err_ld("ldB");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,m)) err_ld("ldB");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (k > 0 && ((transA == 'N' && oA + (k-1)*ldA + m > len(A)) ||
+ ((transA == 'T' || transA == 'C') &&
+ oA + (m-1)*ldA + k > len(A)))) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (k > 0 && ((transB == 'N' && oB + (n-1)*ldB + k > len(B)) ||
+ ((transB == 'T' || transB == 'C') &&
+ oB + (k-1)*ldB + n > len(B)))) err_buf_len("B");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + m > len(C)) err_buf_len("C");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(A)))
+ err_type("beta");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ if (!bo) b.d = 0.0;
+ dgemm_(&transA, &transB, &m, &n, &k, &a.d,
+ MAT_BUFD(A)+oA, &ldA, MAT_BUFD(B)+oB, &ldB, &b.d,
+ MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ if (!bo) b.z = 0.0;
+ zgemm_(&transA, &transB, &m, &n, &k, &a.z,
+ MAT_BUFZ(A)+oA, &ldA, MAT_BUFZ(B)+oB, &ldB, &b.z,
+ MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_symm[] =
+ "Matrix-matrix product where one matrix is symmetric."
+ "\n\n"
+ "symm(A, B, C, side='L', uplo='L', alpha=1.0, beta=0.0, \n"
+ " m=B.size[0], n=B.size[1], ldA=max(1,A.size[0]), \n"
+ " ldB=max(1,B.size[0]), ldC=max(1,C.size[0]), offsetA=0, \n"
+ " offsetB=0, offsetC=0)\n\n"
+ "PURPOSE\n"
+ "If side is 'L', computes C := alpha*A*B + beta*C.\n"
+ "If side is 'R', computes C := alpha*B*A + beta*C.\n"
+ "C is m by n and A is real or complex symmetric. (Use hemm for\n"
+ "Hermitian A).\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "side 'L' or 'R'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n"
+ " If the default value is used and side = 'L', then m\n"
+ " must be equal to A.size[0] and A.size[1].\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used and side = 'R', then \n\n"
+ " must be equal to A.size[0] and A.size[1].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (side == 'L') ? m : n). If zero, the\n"
+ " default value is used.\n\n"
+ "ldB nonnegative integer.\n"
+ " ldB >= max(1, (side == 'L') ? n : m). If zero, the\n"
+ " default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* symm(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m=-1, n=-1, ldA=0, ldB=0, ldC=0, oA=0, oB=0, oC = 0;
+ char side='L', uplo='L';
+ char *kwlist[] = {"A", "B", "C", "side", "uplo", "alpha", "beta",
+ "m", "n", "ldA", "ldB", "ldC", "offsetA", "offsetB", "offsetC",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ccOOiiiiiiii",
+ kwlist, &A, &B, &C, &side, &uplo, &ao, &bo, &m, &n, &ldA, &ldB,
+ &ldC, &oA, &oB, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(B) || MAT_ID(A) != MAT_ID(C) ||
+ MAT_ID(B) != MAT_ID(C)) err_conflicting_ids;
+
+ if (side != 'L' && side != 'R') err_char("side", "'L', 'R'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (m < 0){
+ m = B->nrows;
+ if (side == 'L' && (m != A->nrows || m != A->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (n < 0){
+ n = B->ncols;
+ if (side == 'R' && (n != A->nrows || n != A->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1, (side == 'L') ? m : n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,m)) err_ld("ldB");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,m)) err_ld("ldC");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if ((side == 'L' && oA + (m-1)*ldA + m > len(A)) ||
+ (side == 'R' && oA + (n-1)*ldA + n > len(A))) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (n-1)*ldB + m > len(B)) err_buf_len("B");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + m > len(C)) err_buf_len("C");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(A)))
+ err_type("beta");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ if (!bo) b.d = 0.0;
+ dsymm_(&side, &uplo, &m, &n, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, &b.d, MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ if (!bo) b.z = 0.0;
+ zsymm_(&side, &uplo, &m, &n, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, &b.z, MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_hemm[] =
+ "Matrix-matrix product where one matrix is real symmetric or\n"
+ "complex Hermitian."
+ "\n\n"
+ "hemm(A, B, C, side='L', uplo='L', alpha=1.0, beta=0.0, \n"
+ " m=B.size[0], n=B.size[1], ldA=max(1,A.size[0]), \n"
+ " ldB=max(1,B.size[0]), ldC=max(1,C.size[0]), offsetA=0, \n"
+ " offsetB=0, offsetC=0)\n\n"
+ "PURPOSE\n"
+ "If side is 'L', computes C := alpha*A*B + beta*C.\n"
+ "If side is 'R', computes C := alpha*B*A + beta*C.\n"
+ "C is m by n and A is real symmetric or complex Hermitian.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "side 'L' or 'R'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n"
+ " If the default value is used and side = 'L', then m\n"
+ " must be equal to A.size[0] and A.size[1].\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " If the default value is used and side = 'R', then \n\n"
+ " must be equal to A.size[0] and A.size[1].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (side == 'L') ? m : n). If zero, the\n"
+ " default value is used.\n\n"
+ "ldB nonnegative integer.\n"
+ " ldB >= max(1, (side == 'L') ? n : m). If zero, the\n"
+ " default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* hemm(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int m=-1, n=-1, ldA=0, ldB=0, ldC=0, oA=0, oB=0, oC = 0;
+ char side='L', uplo='L';
+ char *kwlist[] = {"A", "B", "C", "side", "uplo", "alpha", "beta",
+ "m", "n", "ldA", "ldB", "ldC", "offsetA", "offsetB", "offsetC",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ccOOiiiiiiii",
+ kwlist, &A, &B, &C, &side, &uplo, &ao, &bo, &m, &n, &ldA, &ldB,
+ &ldC, &oA, &oB, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(B) || MAT_ID(A) != MAT_ID(C) ||
+ MAT_ID(B) != MAT_ID(C)) err_conflicting_ids;
+
+ if (side != 'L' && side != 'R') err_char("side", "'L', 'R'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+
+ if (m < 0){
+ m = B->nrows;
+ if (side == 'L' && (m != A->nrows || m != A->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (n < 0){
+ n = B->ncols;
+ if (side == 'R' && (n != A->nrows || n != A->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1, (side == 'L') ? m : n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,m)) err_ld("ldB");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,m)) err_ld("ldC");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if ((side == 'L' && oA + (m-1)*ldA + m > len(A)) ||
+ (side == 'R' && oA + (n-1)*ldA + n > len(A))) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (n-1)*ldB + m > len(B)) err_buf_len("B");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + m > len(C)) err_buf_len("C");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(A)))
+ err_type("beta");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ if (!bo) b.d = 0.0;
+ dsymm_(&side, &uplo, &m, &n, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, &b.d, MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ if (!bo) b.z = 0.0;
+ zhemm_(&side, &uplo, &m, &n, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, &b.z, MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+
+static char doc_syrk[] =
+ "Rank-k update of symmetric matrix.\n\n"
+ "syrk(A, C, uplo='L', trans='N', alpha=1.0, beta=0.0, n=None, \n"
+ " k=None, ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE \n"
+ "If trans is 'N', computes C := alpha*A*A^T + beta*C.\n"
+ "If trans is 'T', computes C := alpha*A^T*A + beta*C.\n"
+ "C is symmetric (real or complex) of order n. \n"
+ "The inner dimension of the matrix product is k. If k=0 this is\n"
+ "interpreted as C := beta*C.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N' or 'T'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (trans == N) ? A.size[0] : A.size[1].\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " k = (trans == 'N') ? A.size[1] : A.size[0].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (trans == 'N') ? n : k). If zero,\n"
+ " the default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* syrk(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, k=-1, ldA=0, ldC=0, oA = 0, oC = 0;
+ char trans='N', uplo='L';
+ char *kwlist[] = {"A", "C", "uplo", "trans", "alpha", "beta", "n",
+ "k", "ldA", "ldC", "offsetA", "offsetC", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccOOiiiiii",
+ kwlist, &A, &C, &uplo, &trans, &ao, &bo, &n, &k, &ldA, &ldC,
+ &oA, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(C)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (MAT_ID(A) == DOUBLE && trans != 'N' && trans != 'T' &&
+ trans != 'C') err_char("trans", "'N', 'T', 'C'");
+ if (MAT_ID(A) == COMPLEX && trans != 'N' && trans != 'T')
+ err_char("trans", "'N', 'T'");
+
+ if (n < 0) n = (trans == 'N') ? A->nrows : A->ncols;
+ if (k < 0) k = (trans == 'N') ? A->ncols : A->nrows;
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (k > 0 && ldA < MAX(1, (trans == 'N') ? n : k)) err_ld("ldA");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,n)) err_ld("ldC");
+ if (oA < 0) err_nn_int("offsetA");
+ if (k > 0 && ((trans == 'N' && oA + (k-1)*ldA + n > len(A)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oA + (n-1)*ldA + k > len(A))))
+ err_buf_len("A");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + n > len(C)) err_buf_len("C");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(A)))
+ err_type("beta");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ if (!bo) b.d = 0.0;
+ dsyrk_(&uplo, &trans, &n, &k, &a.d, MAT_BUFD(A)+oA, &ldA,
+ &b.d, MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ if (!bo) b.z = 0.0;
+ zsyrk_(&uplo, &trans, &n, &k, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ &b.z, MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_herk[] =
+ "Rank-k update of Hermitian matrix.\n\n"
+ "herk(A, C, uplo='L', trans='N', alpha=1.0, beta=0.0, n=None, \n"
+ " k=None, ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE \n"
+ "If trans is 'N', computes C := alpha*A*A^H + beta*C.\n"
+ "If trans is 'C', computes C := alpha*A^H*A + beta*C.\n"
+ "C is real symmetric or Hermitian of order n. The inner \n"
+ "dimension of the matrix product is k.\n"
+ "If k=0 this is interpreted as C := beta*C.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N' or 'C'\n\n"
+ "alpha real number (int or float)\n\n"
+ "beta number (int, float or complex)\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (trans == N) ? A.size[0] : A.size[1].\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " k = (trans == 'N') ? A.size[1] : A.size[0].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (trans == 'N') ? n : k). If zero,\n"
+ " the default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* herk(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, k=-1, ldA=0, ldC=0, oA = 0, oC = 0;
+ char trans='N', uplo='L';
+ char *kwlist[] = {"A", "C", "uplo", "trans", "alpha", "beta", "n",
+ "k", "ldA", "ldC", "offsetA", "offsetC", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccOOiiiiii",
+ kwlist, &A, &C, &uplo, &trans, &ao, &bo, &n, &k, &ldA, &ldC,
+ &oA, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(C)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (MAT_ID(A) == DOUBLE && trans != 'N' && trans != 'T' &&
+ trans != 'C') err_char("trans", "'N', 'T', 'C'");
+ if (MAT_ID(A) == COMPLEX && trans != 'N' && trans != 'C')
+ err_char("trans", "'N', 'C'");
+
+ if (n < 0) n = (trans == 'N') ? A->nrows : A->ncols;
+ if (k < 0) k = (trans == 'N') ? A->ncols : A->nrows;
+ if (n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (k > 0 && ldA < MAX(1, (trans == 'N') ? n : k)) err_ld("ldA");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,n)) err_ld("ldC");
+ if (oA < 0) err_nn_int("offsetA");
+ if (k > 0 && ((trans == 'N' && oA + (k-1)*ldA + n > len(A)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oA + (n-1)*ldA + k > len(A))))
+ err_buf_len("A");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + n > len(C)) err_buf_len("C");
+
+ if (ao && number_from_pyobject(ao, &a, DOUBLE)) err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, DOUBLE)) err_type("beta");
+ if (!ao) a.d = 1.0;
+ if (!bo) b.d = 0.0;
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dsyrk_(&uplo, &trans, &n, &k, &a.d, MAT_BUFD(A)+oA, &ldA,
+ &b.d, MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ zherk_(&uplo, &trans, &n, &k, &a.d, MAT_BUFZ(A)+oA, &ldA,
+ &b.d, MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_syr2k[] =
+ "Rank-2k update of symmetric matrix.\n\n"
+ "syr2k(A, B, C, uplo='L', trans='N', alpha=1.0, beta=0.0, n=None,\n"
+ " k=None, ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), \n"
+ " ldC=max(1,C.size[0])), offsetA=0, offsetB=0, offsetC=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', computes C := alpha*(A*B^T + B*A^T) + beta*C.\n"
+ "If trans is 'T', computes C := alpha*(A^T*B + B^T*A) + beta*C.\n"
+ "C is symmetric (real or complex) of order n.\n"
+ "The inner dimension of the matrix product is k. If k=0 this is\n"
+ "interpreted as C := beta*C.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N', 'T' or 'C' ('C' is only allowed when in the real\n"
+ " case and means the same as 'T')\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta number (int, float or complex). Complex beta is only\n"
+ " allowed if A is complex.\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (trans == 'N') ? A.size[0] : A.size[1].\n"
+ " If the default value is used, it should be equal to\n"
+ " (trans == 'N') ? B.size[0] : B.size[1].\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " k = (trans == 'N') ? A.size[1] : A.size[0].\n"
+ " If the default value is used, it should be equal to\n"
+ " (trans == 'N') ? B.size[1] : B.size[0].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (trans=='N') ? n : k).\n"
+ " If zero, the default value is used.\n\n"
+ "ldB nonnegative integer.\n"
+ " ldB >= max(1, (trans=='N') ? n : k).\n"
+ " If zero, the default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* syr2k(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, k=-1, ldA=0, ldB=0, ldC=0, oA = 0, oB = 0, oC = 0;
+ char trans='N', uplo='L';
+ char *kwlist[] = {"A", "B", "C", "uplo", "trans", "alpha", "beta",
+ "n", "k", "ldA", "ldB", "ldC", "offsetA", "offsetB", "offsetC",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ccOOiiiiiiii",
+ kwlist, &A, &B, &C, &uplo, &trans, &ao, &bo, &n, &k, &ldA, &ldB,
+ &ldC, &oA, &oB, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(B) || MAT_ID(A) != MAT_ID(C) ||
+ MAT_ID(B) != MAT_ID(C)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (MAT_ID(A) == DOUBLE && trans != 'N' && trans != 'T' &&
+ trans != 'C') err_char("trans", "'N', 'T', 'C'");
+ if (MAT_ID(A) == COMPLEX && trans != 'N' && trans != 'T')
+ err_char("trans", "'N', 'T'");
+
+ if (n < 0){
+ n = (trans == 'N') ? A->nrows : A->ncols;
+ if (n != ((trans == 'N') ? B->nrows : B->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (k < 0){
+ k = (trans == 'N') ? A->ncols : A->nrows;
+ if (k != ((trans == 'N') ? B->ncols : B->nrows)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (k > 0 && ldA < MAX(1, (trans == 'N') ? n : k)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (k > 0 && ldB < MAX(1, (trans == 'N') ? n : k)) err_ld("ldB");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,n)) err_ld("ldC");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (k > 0 && ((trans == 'N' && oA + (k-1)*ldA + n > len(A)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oA + (n-1)*ldA + k > len(A))))
+ err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (k > 0 && ((trans == 'N' && oB + (k-1)*ldB + n > len(B)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oB + (n-1)*ldB + k > len(B))))
+ err_buf_len("B");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + n > len(C)) err_buf_len("C");
+
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(A)))
+ err_type("beta");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ if (!bo) b.d = 0.0;
+ dsyr2k_(&uplo, &trans, &n, &k, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, &b.d, MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ if (!bo) b.z = 0.0;
+ zsyr2k_(&uplo, &trans, &n, &k, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, &b.z, MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+
+static char doc_her2k[] =
+ "Rank-2k update of Hermitian matrix.\n\n"
+ "her2k(A, B, C, alpha=1.0, beta=0.0, uplo='L', trans='N', n=None,\n"
+ " k=None, ldA=max(1,A.size[0]), ldB=max(1,B.size[0]),\n"
+ " ldC=max(1,C.size[0])), offsetA=0, offsetB=0, offsetC=0)\n\n"
+ "PURPOSE\n"
+ "Computes\n"
+ "C := alpha*A*B^H + conj(alpha)*B*A^H + beta*C (trans=='N')\n"
+ "C := alpha*A^H*B + conj(alpha)*B^H*A + beta*C (trans=='C')\n"
+ "C is real symmetric or complex Hermitian of order n. The inner\n"
+ "dimension of the matrix product is k. If k=0 this is interpreted\n"
+ "as C := beta*C.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N' or 'C'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "beta real number (int or float)\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (trans == 'N') ? A.size[0] : A.size[1].\n"
+ " If the default value is used, it should be equal to\n"
+ " (trans == 'N') ? B.size[0] : B.size[1].\n\n"
+ "k integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " k = (trans == 'N') ? A.size[1] : A.size[0].\n"
+ " If the default value is used, it should be equal to\n"
+ " (trans == 'N') ? B.size[1] : B.size[0].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (trans=='N') ? n : k).\n"
+ " If zero, the default value is used.\n\n"
+ "ldB nonnegative integer.\n"
+ " ldB >= max(1, (trans=='N') ? n : k).\n"
+ " If zero, the default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer\n\n"
+ "offsetC nonnegative integer";
+
+static PyObject* her2k(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *C;
+ PyObject *ao=NULL, *bo=NULL;
+ number a, b;
+ int n=-1, k=-1, ldA=0, ldB=0, ldC=0, oA = 0, oB = 0, oC = 0;
+ char trans='N', uplo='L';
+ char *kwlist[] = {"A", "B", "C", "uplo", "trans", "alpha", "beta",
+ "n", "k", "ldA", "ldB", "ldC", "offsetA", "offsetB", "offsetC",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ccOOiiiiiiii",
+ kwlist, &A, &B, &C, &uplo, &trans, &ao, &bo, &n, &k, &ldA, &ldB,
+ &ldC, &oA, &oB, &oC))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(B) || MAT_ID(A) != MAT_ID(C) ||
+ MAT_ID(B) != MAT_ID(C)) err_conflicting_ids;
+
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (MAT_ID(A) == DOUBLE && trans != 'N' && trans != 'T' &&
+ trans != 'C') err_char("trans", "'N', 'T', 'C'");
+ if (MAT_ID(A) == COMPLEX && trans != 'N' && trans != 'C')
+ err_char("trans", "'N', 'C'");
+
+ if (n < 0){
+ n = (trans == 'N') ? A->nrows : A->ncols;
+ if (n != ((trans == 'N') ? B->nrows : B->ncols)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (k < 0){
+ k = (trans == 'N') ? A->ncols : A->nrows;
+ if (k != ((trans == 'N') ? B->ncols : B->nrows)){
+ PyErr_SetString(PyExc_TypeError, "dimensions of A and B "
+ "do not match");
+ return NULL;
+ }
+ }
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (k > 0 && ldA < MAX(1, (trans == 'N') ? n : k)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (k > 0 && ldB < MAX(1, (trans == 'N') ? n : k)) err_ld("ldB");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,n)) err_ld("ldC");
+
+ if (oA < 0) err_nn_int("offsetA");
+ if (k > 0 && ((trans == 'N' && oA + (k-1)*ldA + n > len(A)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oA + (n-1)*ldA + k > len(A))))
+ err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (k > 0 && ((trans == 'N' && oB + (k-1)*ldB + n > len(B)) ||
+ ((trans == 'T' || trans == 'C') &&
+ oB + (n-1)*ldB + k > len(B))))
+ err_buf_len("B");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + n > len(C)) err_buf_len("C");
+
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+ if (bo && number_from_pyobject(bo, &b, MAT_ID(A)))
+ err_type("beta");
+ if (!bo) b.d = 0.0;
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dsyr2k_(&uplo, &trans, &n, &k, &a.d, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, &b.d, MAT_BUFD(C)+oC, &ldC);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ zher2k_(&uplo, &trans, &n, &k, &a.z, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, &b.d, MAT_BUFZ(C)+oC, &ldC);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_trmm[] =
+ "Matrix-matrix product where one matrix is triangular.\n\n"
+ "trmm(A, B, side='L', uplo='L', transA='N', diag='N', alpha=1.0,\n"
+ " m=None, n=None, ldA=max(1,A.size[0]), ldB=max(1,B.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Computes\n"
+ "B := alpha*A*B if transA is 'N' and side = 'L'.\n"
+ "B := alpha*B*A if transA is 'N' and side = 'R'.\n"
+ "B := alpha*A^T*B if transA is 'T' and side = 'L'.\n"
+ "B := alpha*B*A^T if transA is 'T' and side = 'R'.\n"
+ "B := alpha*A^H*B if transA is 'C' and side = 'L'.\n"
+ "B := alpha*B*A^H if transA is 'C' and side = 'R'.\n"
+ "B is m by n and A is triangular.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "side 'L' or 'R'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "transA 'N' or 'T'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " m = (side == 'L') ? A.size[0] : B.size[0].\n"
+ " If the default value is used and side is 'L', m must\n"
+ " be equal to A.size[1].\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (side == 'L') ? B.size[1] : A.size[0].\n"
+ " If the default value is used and side is 'R', n must\n"
+ " be equal to A.size[1].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (side == 'L') ? m : n).\n"
+ " If zero, the default value is used. \n\n"
+ "ldB nonnegative integer. ldB >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* trmm(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ PyObject *ao=NULL;
+ number a;
+ int m=-1, n=-1, ldA=0, ldB=0, oA=0, oB=0;
+ char side='L', uplo='L', transA='N', diag='N';
+ char *kwlist[] = {"A", "B", "side", "uplo", "transA", "diag",
+ "alpha", "m", "n", "ldA", "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccccOiiiiii",
+ kwlist, &A, &B, &side, &uplo, &transA, &diag, &ao, &m, &n, &ldA,
+ &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+
+ if (side != 'L' && side != 'R') err_char("side", "'L', 'R'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+ if (transA != 'N' && transA != 'T' && transA != 'C')
+ err_char("transA", "'N', 'T', 'C'");
+
+ if (n < 0){
+ n = (side == 'L') ? B->ncols : A->nrows;
+ if (side != 'L' && n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (m < 0){
+ m = (side == 'L') ? A->nrows: B->nrows;
+ if (side == 'L' && m != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (m == 0 || n == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1, (side == 'L') ? m : n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, m)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if ((side == 'L' && oA + (m-1)*ldA + m > len(A)) ||
+ (side == 'R' && oA + (n-1)*ldA + n > len(A))) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (n-1)*ldB + m > len(B)) err_buf_len("B");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dtrmm_(&side, &uplo, &transA, &diag, &m, &n, &a.d,
+ MAT_BUFD(A)+oA, &ldA, MAT_BUFD(B)+oB, &ldB);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ ztrmm_(&side, &uplo, &transA, &diag, &m, &n, &a.z,
+ MAT_BUFZ(A)+oA, &ldA, MAT_BUFZ(B)+oB, &ldB);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+
+static char doc_trsm[] =
+ "Solution of a triangular system of equations with multiple \n"
+ "righthand sides.\n\n"
+ "trsm(A, B, side='L', uplo='L', transA='N', diag='N', alpha=1.0,\n"
+ " m=None, n=None, ldA=max(1,A.size[0]), ldB=max(1,B.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Computes\n"
+ "B := alpha*A^{-1}*B if transA is 'N' and side = 'L'.\n"
+ "B := alpha*B*A^{-1} if transA is 'N' and side = 'R'.\n"
+ "B := alpha*A^{-T}*B if transA is 'T' and side = 'L'.\n"
+ "B := alpha*B*A^{-T} if transA is 'T' and side = 'R'.\n"
+ "B := alpha*A^{-H}*B if transA is 'C' and side = 'L'.\n"
+ "B := alpha*B*A^{-H} if transA is 'C' and side = 'R'.\n"
+ "B is m by n and A is triangular. The code does not verify \n"
+ "whether A is nonsingular.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "side 'L' or 'R'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "transA 'N' or 'T'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "alpha number (int, float or complex). Complex alpha is only\n"
+ " allowed if A is complex.\n\n"
+ "m integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " m = (side == 'L') ? A.size[0] : B.size[0].\n"
+ " If the default value is used and side is 'L', m must\n"
+ " be equal to A.size[1].\n\n"
+ "n integer. If negative, the default value is used.\n"
+ " The default value is\n"
+ " n = (side == 'L') ? B.size[1] : A.size[0].\n"
+ " If the default value is used and side is 'R', n must\n"
+ " be equal to A.size[1].\n\n"
+ "ldA nonnegative integer.\n"
+ " ldA >= max(1, (side == 'L') ? m : n).\n"
+ " If zero, the default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* trsm(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ PyObject *ao=NULL;
+ number a;
+ int m=-1, n=-1, ldA=0, ldB=0, oA=0, oB=0;
+ char side='L', uplo='L', transA='N', diag='N';
+ char *kwlist[] = {"A", "B", "side", "uplo", "transA", "diag",
+ "alpha", "m", "n", "ldA", "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccccOiiiiii",
+ kwlist, &A, &B, &side, &uplo, &transA, &ao, &diag, &m, &n, &ldA,
+ &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+
+ if (side != 'L' && side != 'R') err_char("side", "'L', 'R'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+ if (transA != 'N' && transA != 'T' && transA != 'C')
+ err_char("transA", "'N', 'T', 'C'");
+
+ if (n < 0){
+ n = (side == 'L') ? B->ncols : A->nrows;
+ if (side != 'L' && n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (m < 0){
+ m = (side == 'L') ? A->nrows: B->nrows;
+ if (side == 'L' && m != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0 || m == 0) return Py_BuildValue("");
+
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1, (side == 'L') ? m : n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,m)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if ((side == 'L' && oA + (m-1)*ldA + m > len(A)) ||
+ (side == 'R' && oA + (n-1)*ldA + n > len(A))) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB < 0 || oB + (n-1)*ldB + m > len(B)) err_buf_len("B");
+
+ if (ao && number_from_pyobject(ao, &a, MAT_ID(A)))
+ err_type("alpha");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!ao) a.d = 1.0;
+ dtrsm_(&side, &uplo, &transA, &diag, &m, &n, &a.d,
+ MAT_BUFD(A)+oA, &ldA, MAT_BUFD(B)+oB, &ldB);
+ break;
+
+ case COMPLEX:
+ if (!ao) a.z = 1.0;
+ ztrsm_(&side, &uplo, &transA, &diag, &m, &n, &a.z,
+ MAT_BUFZ(A)+oA, &ldA, MAT_BUFZ(B)+oB, &ldB);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static PyMethodDef blas_functions[] = {
+ {"swap", (PyCFunction) swap, METH_VARARGS|METH_KEYWORDS, doc_swap},
+ {"scal", (PyCFunction) scal, METH_VARARGS|METH_KEYWORDS, doc_scal},
+ {"copy", (PyCFunction) copy, METH_VARARGS|METH_KEYWORDS, doc_copy},
+ {"axpy", (PyCFunction) axpy, METH_VARARGS|METH_KEYWORDS, doc_axpy},
+ {"dot", (PyCFunction) dot, METH_VARARGS|METH_KEYWORDS, doc_dot},
+ {"dotu", (PyCFunction) dotu, METH_VARARGS|METH_KEYWORDS, doc_dotu},
+ {"nrm2", (PyCFunction) nrm2, METH_VARARGS|METH_KEYWORDS, doc_nrm2},
+ {"asum", (PyCFunction) asum, METH_VARARGS|METH_KEYWORDS, doc_asum},
+ {"iamax",(PyCFunction) iamax, METH_VARARGS|METH_KEYWORDS, doc_iamax},
+ {"gemv", (PyCFunction) gemv, METH_VARARGS|METH_KEYWORDS, doc_gemv},
+ {"gbmv", (PyCFunction) gbmv, METH_VARARGS|METH_KEYWORDS, doc_gbmv},
+ {"symv", (PyCFunction) symv, METH_VARARGS|METH_KEYWORDS, doc_symv},
+ {"hemv", (PyCFunction) hemv, METH_VARARGS|METH_KEYWORDS, doc_hemv},
+ {"sbmv", (PyCFunction) sbmv, METH_VARARGS|METH_KEYWORDS, doc_sbmv},
+ {"hbmv", (PyCFunction) hbmv, METH_VARARGS|METH_KEYWORDS, doc_hbmv},
+ {"trmv", (PyCFunction) trmv, METH_VARARGS|METH_KEYWORDS, doc_trmv},
+ {"tbmv", (PyCFunction) tbmv, METH_VARARGS|METH_KEYWORDS, doc_tbmv},
+ {"trsv", (PyCFunction) trsv, METH_VARARGS|METH_KEYWORDS, doc_trsv},
+ {"tbsv", (PyCFunction) tbsv, METH_VARARGS|METH_KEYWORDS, doc_tbsv},
+ {"ger", (PyCFunction) ger, METH_VARARGS|METH_KEYWORDS, doc_ger},
+ {"geru", (PyCFunction) geru, METH_VARARGS|METH_KEYWORDS, doc_geru},
+ {"syr", (PyCFunction) syr, METH_VARARGS|METH_KEYWORDS, doc_syr},
+ {"her", (PyCFunction) her, METH_VARARGS|METH_KEYWORDS, doc_her},
+ {"syr2", (PyCFunction) syr2, METH_VARARGS|METH_KEYWORDS, doc_syr2},
+ {"her2", (PyCFunction) her2, METH_VARARGS|METH_KEYWORDS, doc_her2},
+ {"gemm", (PyCFunction) gemm, METH_VARARGS|METH_KEYWORDS, doc_gemm},
+ {"symm", (PyCFunction) symm, METH_VARARGS|METH_KEYWORDS, doc_symm},
+ {"hemm", (PyCFunction) hemm, METH_VARARGS|METH_KEYWORDS, doc_hemm},
+ {"syrk", (PyCFunction) syrk, METH_VARARGS|METH_KEYWORDS, doc_syrk},
+ {"herk", (PyCFunction) herk, METH_VARARGS|METH_KEYWORDS, doc_herk},
+ {"syr2k",(PyCFunction) syr2k, METH_VARARGS|METH_KEYWORDS, doc_syr2k},
+ {"her2k",(PyCFunction) her2k, METH_VARARGS|METH_KEYWORDS, doc_her2k},
+ {"trmm", (PyCFunction) trmm, METH_VARARGS|METH_KEYWORDS, doc_trmm},
+ {"trsm", (PyCFunction) trsm, METH_VARARGS|METH_KEYWORDS, doc_trsm},
+ {NULL} /* Sentinel */
+};
+
+
+PyMODINIT_FUNC initblas(void)
+{
+ PyObject *m;
+ m = Py_InitModule3("cvxopt.blas", blas_functions, blas__doc__);
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/blas_redefines.h b/src/C/blas_redefines.h
new file mode 100644
index 0000000..7b60c44
--- /dev/null
+++ b/src/C/blas_redefines.h
@@ -0,0 +1,140 @@
+#ifdef BLAS_NO_UNDERSCORE
+
+#define dswap_ dswap
+#define zswap_ zswap
+#define dscal_ dscal
+#define zscal_ zscal
+#define zdscal_ zdscal
+#define dcopy_ dcopy
+#define zcopy_ zcopy
+#define daxpy_ daxpy
+#define zaxpy_ zaxpy
+#define ddot_ ddot
+#define dnrm2_ dnrm2
+#define dznrm2_ dznrm2
+#define dasum_ dasum
+#define dzasum_ dzasum
+#define idamax_ idamax
+#define izamax_ izamax
+#define dgemv_ dgemv
+#define zgemv_ zgemv
+#define dgbmv_ dgbmv
+#define zgbmv_ zgbmv
+#define dsymv_ dsymv
+#define zsymv_ zsymv
+#define zhemv_ zhemv
+#define dsbmv_ dsbmv
+#define zhbmv_ zhbmv
+#define dtrmv_ dtrmv
+#define ztrmv_ ztrmv
+#define dtbmv_ dtbmv
+#define ztbmv_ ztbmv
+#define dtrsv_ dtrsv
+#define ztrsv_ ztrsv
+#define dtbsv_ dtbsv
+#define ztbsv_ ztbsv
+#define dger_ dger
+#define zgerc_ zgerc
+#define zgeru_ zgeru
+#define dsyr_ dsyr
+#define zher_ zher
+#define dsyr2_ dsyr2
+#define zher2_ zher2
+#define dgemm_ dgemm
+#define zgemm_ zgemm
+#define dsymm_ dsymm
+#define zsymm_ zsymm
+#define zhemm_ zhemm
+#define dsyrk_ dsyrk
+#define zsyrk_ zsyrk
+#define zherk_ zherk
+#define dsyr2k_ dsyr2k
+#define zsyr2k_ zsyr2k
+#define zher2k_ zher2k
+#define dtrmm_ dtrmm
+#define ztrmm_ ztrmm
+#define dtrsm_ dtrsm
+#define ztrsm_ ztrsm
+#define dgetrf_ dgetrf
+#define zgetrf_ zgetrf
+#define dgetrs_ dgetrs
+#define zgetrs_ zgetrs
+#define dgetri_ dgetri
+#define zgetri_ zgetri
+#define dgesv_ dgesv
+#define zgesv_ zgesv
+#define dpotrf_ dpotrf
+#define dpotri_ dpotri
+#define zpotri_ zpotri
+#define zpotrf_ zpotrf
+#define dpotrs_ dpotrs
+#define zpotrs_ zpotrs
+#define dposv_ dposv
+#define zposv_ zposv
+#define dsytrf_ dsytrf
+#define zsytrf_ zsytrf
+#define zhetrf_ zhetrf
+#define dsytri_ dsytri
+#define zsytri_ zsytri
+#define dsytrs_ dsytrs
+#define zsytrs_ zsytrs
+#define zhetrs_ zhetrs
+#define zhetri_ zhetri
+#define dsysv_ dsysv
+#define zsysv_ zsysv
+#define dsygv_ dsygv
+#define zhesv_ zhesv
+#define dgels_ dgels
+#define zgels_ zgels
+#define dsyev_ dsyev
+#define zheev_ zheev
+#define dsyevx_ dsyevx
+#define zheevx_ zheevx
+#define dsyevd_ dsyevd
+#define zheevd_ zheevd
+#define dsyevr_ dsyevr
+#define zheevr_ zheevr
+#define ilaenv_ ilaenv
+#define zhegv_ zhegv
+#define dgesvd_ dgesvd
+#define zgesvd_ zgesvd
+#define dgesdd_ dgesdd
+#define zgesdd_ zgesdd
+#define dgeqrf_ dgeqrf
+#define zgeqrf_ zgeqrf
+#define dormqr_ dormqr
+#define zunmqr_ zunmqr
+#define dtrtrs_ dtrtrs
+#define ztrtrs_ ztrtrs
+#define dgbtrf_ dgbtrf
+#define zgbtrf_ zgbtrf
+#define dgbtrs_ dgbtrs
+#define zgbtrs_ zgbtrs
+#define dgbsv_ dgbsv
+#define zgbsv_ zgbsv
+#define dgtsv_ dgtsv
+#define zgtsv_ zgtsv
+#define dpbsv_ dpbsv
+#define zpbsv_ zpbsv
+#define dptsv_ dptsv
+#define zptsv_ zptsv
+#define dgttrf_ dgttrf
+#define zgttrf_ zgttrf
+#define dgttrs_ dgttrs
+#define zgttrs_ zgttrs
+#define dtrtri_ dtrtri
+#define ztrtri_ ztrtri
+#define dpbtrf_ dpbtrf
+#define zpbtrf_ zpbtrf
+#define dtbtrs_ dtbtrs
+#define ztbtrs_ ztbtrs
+#define dtbtrf_ dtbtrf
+#define ztbtrf_ ztbtrf
+#define dpttrf_ dpttrf
+#define zpttrf_ zpttrf
+#define dpbtrs_ dpbtrs
+#define zpbtrs_ zpbtrs
+#define dpttrs_ dpttrs
+#define zpttrs_ zpttrs
+
+#endif
diff --git a/src/C/cholmod.c b/src/C/cholmod.c
new file mode 100644
index 0000000..5a2c8a1
--- /dev/null
+++ b/src/C/cholmod.c
@@ -0,0 +1,947 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#define NO_ANSI99_COMPLEX
+
+#include "cvxopt.h"
+#include "misc.h"
+#include "cholmod.h"
+#include "complex.h"
+
+const int E_SIZE[] = { sizeof(int_t), sizeof(double), sizeof(complex) };
+
+/* defined in pyconfig.h */
+#if (SIZEOF_INT < SIZEOF_LONG)
+#define CHOL(name) cholmod_l_ ## name
+#else
+#define CHOL(name) cholmod_ ## name
+#endif
+
+PyDoc_STRVAR(cholmod__doc__, "Interface to the CHOLMOD library.\n\n"
+"Routines for sparse Cholesky factorization.\n\n"
+"The default values of the control parameters in the CHOLMOD 'Common'\n"
+"object are used, except Common->print, which is set to 0, and \n"
+"Common->supernodal, which is set to 2.\n"
+"The parameters Common->supernodal, Common->print, Common->nmethods, \n"
+"Common->postorder and Common->dbound can be modified by making an\n"
+"entry in the dictionary cholmod.options, with key value 'supernodal', "
+"\n'print', 'nmethods', 'postorder', or 'dbound', respectively.\n \n"
+"These parameters have the following meaning.\n\n"
+"options['supernodal']: If equal to 0, an LDL^T or LDL^H factorization"
+"\n is computed using a simplicial algorithm. If equal to 2, an\n"
+" LL^T or LL^H factorization is computed using a supernodal\n"
+" algorithm. If equal to 1, the most efficient of the two\n"
+" factorizations is selected, based on the sparsity pattern.\n\n"
+"options['print']: A nonnegative integer that controls the amount of\n"
+" output printed to the screen.\n\n"
+"options['nmethods']: A nonnegative integer that specifies how many\n"
+" orderings are attempted prior to factorization. If equal to 0,\n"
+" the AMD ordering and the user-provided permutation (if any) are\n"
+" compared, and the best one is used. If equal to 1, the AMD\n"
+" ordering is used when no permutation is provided by the user,\n"
+" and the user-provided permutation is used otherwise. Default: 0."
+"\n\noptions['postorder']: True or False. If True the symbolic\n"
+" analysis is followed by a postordering. Default: True.\n\n"
+"options['dbound']: Smallest absolute value for the diagonal\n"
+" elements of D in an LDL^T factorization, or the diagonal\n"
+" elements of L in a Cholesky factorization. Default: 0.0.\n\n"
+"CHOLMOD is available from http://www.cise.ufl.edu/research/sparse.");
+
+
+static PyObject *cholmod_module;
+static cholmod_common Common;
+
+static int set_options(void)
+{
+ int_compat pos=0;
+ PyObject *param, *key, *value;
+ char *keystr, err_str[100];
+
+ CHOL(defaults)(&Common);
+ Common.print = 0;
+ Common.supernodal = 2;
+
+ if (!(param = PyObject_GetAttrString(cholmod_module, "options")) ||
+ ! PyDict_Check(param)) {
+ PyErr_SetString(PyExc_AttributeError, "missing cholmod.options"
+ "dictionary");
+ return 0;
+ }
+ while (PyDict_Next(param, &pos, &key, &value))
+ if ((keystr = PyString_AsString(key))) {
+
+ if (!strcmp("supernodal", keystr) && PyInt_Check(value))
+ Common.supernodal = (int) PyInt_AsLong(value);
+ else if (!strcmp("print", keystr) && PyInt_Check(value)){
+ Common.print = (int) PyInt_AsLong(value);
+ }
+ else if (!strcmp("nmethods", keystr) && PyInt_Check(value))
+ Common.nmethods = (int) PyInt_AsLong(value);
+ else if (!strcmp("postorder", keystr) &&
+ PyBool_Check(value))
+ Common.postorder = (int) PyInt_AsLong(value);
+ else if (!strcmp("dbound", keystr) && PyFloat_Check(value))
+ Common.dbound = (double) PyFloat_AsDouble(value);
+ else {
+ sprintf(err_str, "invalid value for CHOLMOD parameter: "
+ "%-.20s", keystr);
+ PyErr_SetString(PyExc_ValueError, err_str);
+ Py_DECREF(param);
+ return 0;
+ }
+ }
+ Py_DECREF(param);
+ return 1;
+}
+
+
+static cholmod_sparse *pack(spmatrix *A, char uplo)
+{
+ int j, k, n = SP_NROWS(A), nnz = 0, cnt = 0;
+ cholmod_sparse *B;
+
+ if (uplo == 'L'){
+ for (j=0; j<n; j++){
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] && SP_ROW(A)[k] < j;
+ k++);
+ nnz += SP_COL(A)[j+1] - k;
+ }
+ if (!(B = CHOL(allocate_sparse)(n, n, nnz, 1, 1, -1,
+ (SP_ID(A) == DOUBLE ? CHOLMOD_REAL : CHOLMOD_COMPLEX),
+ &Common))) return 0;
+ for (j=0; j<n; j++){
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] && SP_ROW(A)[k] < j;
+ k++);
+ for (; k<SP_COL(A)[j+1]; k++) {
+ if (SP_ID(A) == DOUBLE)
+ ((double *)B->x)[cnt] = SP_VALD(A)[k];
+ else
+ ((complex *)B->x)[cnt] = SP_VALZ(A)[k];
+ ((int_t *)B->p)[j+1]++;
+ ((int_t *)B->i)[cnt++] = SP_ROW(A)[k];
+ }
+ }
+ }
+ else {
+ for (j=0; j<n; j++)
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] && SP_ROW(A)[k] <= j;
+ k++)
+ nnz++;
+ if (!(B = CHOL(allocate_sparse)(n, n, nnz, 1, 1, 1,
+ (SP_ID(A) == DOUBLE ? CHOLMOD_REAL : CHOLMOD_COMPLEX),
+ &Common))) return 0;
+
+ for (j=0; j<n; j++)
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1] && SP_ROW(A)[k] <= j;
+ k++) {
+ if (SP_ID(A) == DOUBLE)
+ ((double *)B->x)[cnt] = SP_VALD(A)[k];
+ else
+ ((complex *)B->x)[cnt] = SP_VALZ(A)[k];
+ ((int_t *)B->p)[j+1]++;
+ ((int_t *)B->i)[cnt++] = SP_ROW(A)[k];
+ }
+ }
+ for (j=0; j<n; j++) ((int_t *)B->p)[j+1] += ((int_t *)B->p)[j];
+ return B;
+}
+
+
+static cholmod_sparse * create_matrix(spmatrix *A)
+{
+ cholmod_sparse *B;
+
+ if (!(B = CHOL(allocate_sparse)(SP_NROWS(A), SP_NCOLS(A), 0,
+ 1, 0, 0, (SP_ID(A) == DOUBLE ? CHOLMOD_REAL : CHOLMOD_COMPLEX),
+ &Common))) return NULL;
+
+ int i;
+ for (i=0; i<SP_NCOLS(A); i++)
+ ((int_t *)B->nz)[i] = SP_COL(A)[i+1] - SP_COL(A)[i];
+ B->x = SP_VAL(A);
+ B->i = SP_ROW(A);
+ B->nzmax = SP_NNZ(A);
+ memcpy(B->p, SP_COL(A), (SP_NCOLS(A)+1)*sizeof(int_t));
+ return B;
+}
+
+
+static void free_matrix(cholmod_sparse *A)
+{
+ A->x = NULL;
+ A->i = NULL;
+ CHOL(free_sparse)(&A, &Common);
+}
+
+static void cvxopt_free_cholmod_factor(void *L, void *descr)
+{
+ CHOL(free_factor) ((cholmod_factor **) &L, &Common) ;
+}
+
+
+static char doc_symbolic[] =
+ "Symbolic Cholesky factorization of a real symmetric or Hermitian\n"
+ "sparse matrix.\n\n"
+ "F = symbolic(A, p=None, uplo='L')\n\n"
+ "PURPOSE\n"
+ "If cholmod.options['supernodal'] = 2, factors A as\n"
+ "P*A*P^T = L*L^T or P*A*P^T = L*L^H. This is the default value.\n"
+ "If cholmod.options['supernodal'] = 0, factors A as\n"
+ "P*A*P^T = L*D*L^T or P*A*P^T = L*D*L^H with D diagonal and \n"
+ "possibly nonpositive.\n"
+ "If cholmod.options['supernodal'] = 1, the most efficient of the\n"
+ "two factorizations is used.\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix of order n.\n\n"
+ "p None, or an 'i' matrix of length n that contains a \n"
+ " permutation vector. If p is not provided, CHOLMOD\n"
+ " uses a permutation from the AMD library.\n\n"
+ "uplo 'L' or 'U'. If uplo is 'L', only the lower triangular\n"
+ " part of A is used and the upper triangular part is\n"
+ " ignored. If uplo is 'U', only the upper triangular\n"
+ " part of A is used and the lower triangular part is\n"
+ " ignored.\n\n"
+ "F the symbolic factorization, including the permutation,\n"
+ " as an opaque C object that can be passed to\n"
+ " cholmod.numeric\n\n";
+
+static PyObject* symbolic(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ spmatrix *A;
+ cholmod_sparse *Ac = NULL;
+ cholmod_factor *L;
+ matrix *P=NULL;
+ char uplo='L';
+ int n;
+ char *kwlist[] = {"A", "p", "uplo", NULL};
+
+ if (!set_options()) return NULL;
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|Oc", kwlist, &A,
+ &P, &uplo)) return NULL;
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A))
+ PY_ERR_TYPE("A is not a square sparse matrix");
+ n = SP_NROWS(A);
+
+ if (P) {
+ if (!Matrix_Check(P) || MAT_ID(P) != INT) err_int_mtrx("p");
+ if (MAT_LGT(P) != n) err_buf_len("p");
+ if (!CHOL(check_perm)(P->buffer, n, n, &Common))
+ PY_ERR(PyExc_ValueError, "p is not a valid permutation");
+ }
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (!(Ac = pack(A, uplo))) return PyErr_NoMemory();
+ L = CHOL(analyze_p)(Ac, P ? MAT_BUFI(P): NULL, NULL, 0, &Common);
+ CHOL(free_sparse)(&Ac, &Common);
+
+ if (Common.status != CHOLMOD_OK){
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY)
+ return PyErr_NoMemory();
+ else
+ PyErr_SetString(PyExc_ValueError, "symbolic factorization "
+ "failed");
+ return NULL;
+ }
+ return (PyObject *) PyCObject_FromVoidPtrAndDesc((void *) L,
+ SP_ID(A)==DOUBLE ? (uplo == 'L' ?
+ "CHOLMOD FACTOR D L" : "CHOLMOD FACTOR D U") :
+ (uplo == 'L' ?
+ "CHOLMOD FACTOR Z L" : "CHOLMOD FACTOR Z U"),
+ cvxopt_free_cholmod_factor);
+}
+
+
+static char doc_numeric[] =
+ "Numeric Cholesky factorization of a real symmetric or Hermitian\n"
+ "sparse matrix.\n\n"
+ "numeric(A, F)\n\n"
+ "PURPOSE\n"
+ "If cholmod.options['supernodal'] = 2, factors A as\n"
+ "P*A*P^T = L*L^T or P*A*P^T = L*L^H. This is the default value.\n"
+ "If cholmod.options['supernodal'] = 0, factors A as\n"
+ "P*A*P^T = L*D*L^T or P*A*P^T = L*D*L^H with D diagonal and \n"
+ "possibly nonpositive.\n"
+ "If cholmod.options['supernodal'] = 1, the most efficient of the\n"
+ "two factorizations is used. \n"
+ "On entry, F is the symbolic factorization computed by \n"
+ "cholmod.symbolic. On exit, F contains the numeric\n"
+ "factorization. If the matrix is singular, an ArithmeticError\n"
+ "exception is raised, with as its first argument the index of the\n"
+ "column at which the factorization failed.\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix. If F was created by calling\n"
+ " cholmod.symbolic with uplo='L', then only the lower\n"
+ " triangular part of A is used. If F was created with\n"
+ " uplo='U', then only the upper triangular part is used.\n"
+ "\n"
+ "F symbolic factorization computed by cholmod.symbolic\n"
+ " applied to a matrix with the same sparsity patter and\n"
+ " type as A. After a successful call, F contains the\n"
+ " numeric factorization.";
+
+static PyObject* numeric(PyObject *self, PyObject *args)
+{
+ spmatrix *A;
+ PyObject *F;
+ cholmod_factor *Lc;
+ cholmod_sparse *Ac = NULL;
+ char *descr, uplo;
+
+ if (!set_options()) return NULL;
+
+ if (!PyArg_ParseTuple(args, "OO", &A, &F)) return NULL;
+
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A))
+ PY_ERR_TYPE("A is not a sparse matrix");
+
+ if (!PyCObject_Check(F)) err_CO("F");
+ descr = PyCObject_GetDesc(F);
+ if (!descr) PY_ERR_TYPE("F is not a CHOLMOD factor");
+ if (SP_ID(A) == DOUBLE){
+ if (!strcmp(descr, "CHOLMOD FACTOR D L"))
+ uplo = 'L';
+ else if (!strcmp(descr, "CHOLMOD FACTOR D U"))
+ uplo = 'U';
+ else
+ PY_ERR_TYPE("F is not the CHOLMOD factor of a 'd' matrix");
+ } else {
+ if (!strcmp(descr, "CHOLMOD FACTOR Z L"))
+ uplo = 'L';
+ else if (!strcmp(descr, "CHOLMOD FACTOR Z U"))
+ uplo = 'U';
+ else
+ PY_ERR_TYPE("F is not the CHOLMOD factor of a 'z' matrix");
+ }
+ Lc = (cholmod_factor *) PyCObject_AsVoidPtr(F);
+ if (!(Ac = pack(A, uplo))) return PyErr_NoMemory();
+ CHOL(factorize) (Ac, Lc, &Common);
+ CHOL(free_sparse)(&Ac, &Common);
+
+ if (Common.status < 0) switch (Common.status) {
+ case CHOLMOD_OUT_OF_MEMORY:
+ return PyErr_NoMemory();
+
+ default:
+ PyErr_SetString(PyExc_ValueError, "factorization failed");
+ return NULL;
+ }
+
+ if (Common.status > 0) switch (Common.status) {
+ case CHOLMOD_NOT_POSDEF:
+ PyErr_SetObject(PyExc_ArithmeticError, Py_BuildValue("i",
+ Lc->minor));
+ return NULL;
+ break;
+
+ case CHOLMOD_DSMALL:
+ /* This never happens unless we change the default value
+ * of Common.dbound (0.0). */
+ if (Lc->is_ll)
+ PyErr_Warn(PyExc_RuntimeWarning, "tiny diagonal "\
+ "elements in L");
+ else
+ PyErr_Warn(PyExc_RuntimeWarning, "tiny diagonal "\
+ "elements in D");
+ break;
+
+ default:
+ PyErr_Warn(PyExc_UserWarning, "");
+ }
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_solve[] =
+ "Solves a sparse set of linear equations with a factored\n"
+ "coefficient matrix and an dense matrix as right-hand side.\n\n"
+ "solve(F, B, sys=0, nrhs=B.size[1], ldB=max(1,B.size[0], "
+ "offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves one of the following systems using the factorization\n"
+ "computed by cholmod.numeric:\n\n"
+ " sys System sys System\n"
+ " 0 A*X = B 5 L'*X = B\n"
+ " 1 L*D*L'*X = B 6 D*X = B\n"
+ " 2 L*D*X = B 7 P'*X = B\n"
+ " 3 D*L'*X = B 8 P*X = B\n"
+ " 4 L*X = B\n\n"
+ "If A was factored as P*A*P' = L*L', then D = I in this table.\n"
+ "B is stored using the LAPACK and BLAS conventions. On exit it\n"
+ "is overwritten with the solution.\n\n"
+ "ARGUMENTS\n"
+ "F the factorization object of A computed by\n"
+ " cholmod.numeric\n\n"
+ "B dense 'd' or 'z' matrix. Must have the same type\n"
+ " as A.\n\n"
+ "sys integer (0 <= sys <= 8)\n\n"
+ "nrhs integer. If negative, the default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* solve(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *B;
+ PyObject *F;
+ int i, n, oB=0, ldB=0, nrhs=-1, sys=0;
+ char *descr;
+ char *kwlist[] = {"F", "B", "sys", "nrhs", "ldB", "offsetB", NULL};
+ int sysvalues[] = { CHOLMOD_A, CHOLMOD_LDLt, CHOLMOD_LD,
+ CHOLMOD_DLt, CHOLMOD_L, CHOLMOD_Lt, CHOLMOD_D, CHOLMOD_P,
+ CHOLMOD_Pt };
+
+ if (!set_options()) return NULL;
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiii", kwlist,
+ &F, &B, &sys, &nrhs, &ldB, &oB)) return NULL;
+
+ if (!PyCObject_Check(F)) err_CO("F");
+ descr = PyCObject_GetDesc(F);
+ if (!descr || strncmp(descr, "CHOLMOD FACTOR", 14))
+ PY_ERR_TYPE("F is not a CHOLMOD factor");
+ cholmod_factor *L = (cholmod_factor *) PyCObject_AsVoidPtr(F);
+ if (L->xtype == CHOLMOD_PATTERN)
+ PY_ERR(PyExc_ValueError, "called with symbolic factor");
+
+ n = L->n;
+ if (L->minor<n) PY_ERR(PyExc_ArithmeticError, "singular matrix");
+
+ if (sys < 0 || sys > 8)
+ PY_ERR(PyExc_ValueError, "invalid value for sys");
+
+ if (!Matrix_Check(B) || MAT_ID(B) == INT ||
+ (MAT_ID(B) == DOUBLE && L->xtype == CHOLMOD_COMPLEX) ||
+ (MAT_ID(B) == COMPLEX && L->xtype == CHOLMOD_REAL))
+ PY_ERR_TYPE("B must a dense matrix of the same numerical "
+ "type as F");
+
+ if (nrhs < 0) nrhs = MAT_NCOLS(B);
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldB == 0) ldB = MAX(1,MAT_NROWS(B));
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > MAT_LGT(B)) err_buf_len("B");
+
+ cholmod_dense *x;
+ cholmod_dense *b = CHOL(allocate_dense)(n, 1, n,
+ (MAT_ID(B) == DOUBLE ? CHOLMOD_REAL : CHOLMOD_COMPLEX),
+ &Common);
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY) return PyErr_NoMemory();
+
+ void *b_old = b->x;
+ for (i=0; i<nrhs; i++){
+ b->x = MAT_BUF(B) + (i*ldB + oB)*E_SIZE[MAT_ID(B)];
+ x = CHOL(solve) (sysvalues[sys], L, b, &Common);
+ if (Common.status != CHOLMOD_OK){
+ PyErr_SetString(PyExc_ValueError, "solve step failed");
+ CHOL(free_dense)(&x, &Common);
+ CHOL(free_dense)(&b, &Common);
+ return NULL;
+ }
+ memcpy(b->x, x->x, n*E_SIZE[MAT_ID(B)]);
+ CHOL(free_dense)(&x, &Common);
+ }
+ b->x = b_old;
+ CHOL(free_dense)(&b, &Common);
+
+ return Py_BuildValue("");
+}
+
+
+static char doc_spsolve[] =
+ "Solves a sparse set of linear equations with a factored\n"
+ "coefficient matrix and sparse righthand side.\n\n"
+ "X = spsolve(F, B, sys=0)\n\n"
+ "PURPOSE\n"
+ "Solves one of the following systems using the factorization F\n"
+ "computed by cholmod.numeric:\n\n"
+ " sys System sys System\n"
+ " 0 A*X = B 5 L'*X = B\n"
+ " 1 L*D*L'*X = B 6 D*X = B\n"
+ " 2 L*D*X = B 7 P'*X = B\n"
+ " 3 D*L'*X = B 8 P*X = B\n"
+ " 4 L*X = B\n\n"
+ "If A was factored as P*A*P^T = L*L^T, then D = I in this table.\n"
+ "On exit B is overwritten with the solution.\n\n"
+ "ARGUMENTS\n"
+ "F the factorization object of A computed by\n"
+ " cholmod.numeric\n\n"
+ "B sparse unsymmetric matrix\n\n"
+ "sys integer (0 <= sys <= 8)\n\n"
+ "X sparse unsymmetric matrix";
+
+static PyObject* spsolve(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ spmatrix *B, *X=NULL;
+ cholmod_sparse *Bc=NULL, *Xc=NULL;
+ PyObject *F;
+ cholmod_factor *L;
+ int n, sys=0;
+ char *descr;
+ char *kwlist[] = {"F", "B", "sys", NULL};
+ int sysvalues[] = {CHOLMOD_A, CHOLMOD_LDLt, CHOLMOD_LD,
+ CHOLMOD_DLt, CHOLMOD_L, CHOLMOD_Lt, CHOLMOD_D, CHOLMOD_P,
+ CHOLMOD_Pt };
+
+ if (!set_options()) return NULL;
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|i", kwlist, &F,
+ &B, &sys)) return NULL;
+
+ if (!PyCObject_Check(F)) err_CO("F");
+ descr = PyCObject_GetDesc(F);
+ if (!descr || strncmp(descr, "CHOLMOD FACTOR", 14))
+ PY_ERR_TYPE("F is not a CHOLMOD factor");
+ L = (cholmod_factor *) PyCObject_AsVoidPtr(F);
+ if (L->xtype == CHOLMOD_PATTERN)
+ PY_ERR(PyExc_ValueError, "called with symbolic factor");
+ n = L->n;
+ if (L->minor<n) PY_ERR(PyExc_ArithmeticError, "singular matrix");
+
+ if (sys < 0 || sys > 8)
+ PY_ERR(PyExc_ValueError, "invalid value for sys");
+
+ if (!SpMatrix_Check(B) ||
+ (SP_ID(B) == DOUBLE && L->xtype == CHOLMOD_COMPLEX) ||
+ (SP_ID(B) == COMPLEX && L->xtype == CHOLMOD_REAL))
+ PY_ERR_TYPE("B must a sparse matrix of the same "
+ "numerical type as F");
+ if (SP_NROWS(B) != n)
+ PY_ERR(PyExc_ValueError, "incompatible dimensions for B");
+
+ if (!(Bc = create_matrix(B))) return PyErr_NoMemory();
+ Xc = CHOL(spsolve)(sysvalues[sys], L, Bc, &Common);
+ free_matrix(Bc);
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY) return PyErr_NoMemory();
+ if (Common.status != CHOLMOD_OK)
+ PY_ERR(PyExc_ValueError, "solve step failed");
+
+ if (!(X = SpMatrix_New(Xc->nrow, Xc->ncol,
+ ((int_t*)Xc->p)[Xc->ncol], (L->xtype == CHOLMOD_REAL ? DOUBLE :
+ COMPLEX)))) {
+ CHOL(free_sparse)(&Xc, &Common);
+ return PyErr_NoMemory();
+ }
+ memcpy(SP_COL(X), Xc->p, (Xc->ncol+1)*sizeof(int_t));
+ memcpy(SP_ROW(X), Xc->i, ((int_t *)Xc->p)[Xc->ncol]*sizeof(int_t));
+ memcpy(SP_VAL(X), Xc->x,
+ ((int_t *) Xc->p)[Xc->ncol]*E_SIZE[SP_ID(X)]);
+ CHOL(free_sparse)(&Xc, &Common);
+ return (PyObject *) X;
+}
+
+
+static char doc_linsolve[] =
+ "Solves a sparse positive definite set of linear equations.\n\n"
+ "linsolve(A, B, p=None, uplo='L', nrhs=B.size[1], \n"
+ " ldB=max(1,B.size[0]), offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B using a sparse Cholesky factorization. On exit\n"
+ "B is overwritten with the solution. The argument p specifies\n"
+ "an optional permutation matrix. If it is not provided, CHOLMOD\n"
+ "uses a permutation from the AMD library. An ArithmeticError\n"
+ "exception is raised if the matrix is singular, with as its first\n"
+ "argument the index of the column at which the factorization\n"
+ "failed.\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix\n\n"
+ "B dense 'd' or 'z' matrix. Must have the same type\n"
+ " as A.\n\n"
+ "p None, or an 'i' matrix of length n that contains\n"
+ " a permutation vector\n\n"
+ "uplo 'L' or 'U'. If uplo is 'L', only the lower triangular\n"
+ " part of A is used and the upper triangular part is\n"
+ " ignored. If uplo is 'U', only the upper triangular\n"
+ " part is used, and the lower triangular part is ignored."
+ "\n\n"
+ "nrhs integer. If negative, the default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* linsolve(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ spmatrix *A;
+ matrix *B, *P=NULL;
+ int i, n, nnz, oB=0, ldB=0, nrhs=-1;
+ cholmod_sparse *Ac=NULL;
+ cholmod_factor *L=NULL;
+ cholmod_dense *x=NULL, *b=NULL;
+ void *b_old;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "p", "uplo", "nrhs", "ldB", "offsetB",
+ NULL};
+
+ if (!set_options()) return NULL;
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|Ociii", kwlist,
+ &A, &B, &P, &uplo, &nrhs, &ldB, &oB)) return NULL;
+
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A))
+ PY_ERR_TYPE("A is not a sparse matrix");
+ n = SP_NROWS(A);
+ nnz = SP_NNZ(A);
+
+ if (!Matrix_Check(B) || MAT_ID(B) != SP_ID(A))
+ PY_ERR_TYPE("B must be a dense matrix of the same numerical "
+ "type as A");
+ if (nrhs < 0) nrhs = MAT_NCOLS(B);
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldB == 0) ldB = MAX(1,MAT_NROWS(B));
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > MAT_LGT(B)) err_buf_len("B");
+
+ if (P) {
+ if (!Matrix_Check(P) || MAT_ID(P) != INT) err_int_mtrx("p");
+ if (MAT_LGT(P) != n) err_buf_len("p");
+ if (!CHOL(check_perm)(P->buffer, n, n, &Common))
+ PY_ERR(PyExc_ValueError, "not a valid permutation");
+ }
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+
+ if (!(Ac = pack(A, uplo))) return PyErr_NoMemory();
+ L = CHOL(analyze_p)(Ac, P ? MAT_BUFI(P): NULL, NULL, 0, &Common);
+ if (Common.status != CHOLMOD_OK){
+ free_matrix(Ac);
+ CHOL(free_sparse)(&Ac, &Common);
+ CHOL(free_factor)(&L, &Common);
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY)
+ return PyErr_NoMemory();
+ else {
+ PyErr_SetString(PyExc_ValueError, "symbolic factorization "
+ "failed");
+ return NULL;
+ }
+ }
+
+ CHOL(factorize) (Ac, L, &Common);
+ CHOL(free_sparse)(&Ac, &Common);
+ if (Common.status < 0) {
+ CHOL(free_factor)(&L, &Common);
+ switch (Common.status) {
+ case CHOLMOD_OUT_OF_MEMORY:
+ return PyErr_NoMemory();
+
+ default:
+ PyErr_SetString(PyExc_ValueError, "factorization "
+ "failed");
+ return NULL;
+ }
+ }
+ if (Common.status > 0) switch (Common.status) {
+ case CHOLMOD_NOT_POSDEF:
+ PyErr_SetObject(PyExc_ArithmeticError,
+ Py_BuildValue("i", L->minor));
+ CHOL(free_factor)(&L, &Common);
+ return NULL;
+ break;
+
+ case CHOLMOD_DSMALL:
+ /* This never happens unless we change the default value
+ * of Common.dbound (0.0). */
+ if (L->is_ll)
+ PyErr_Warn(PyExc_RuntimeWarning, "tiny diagonal "
+ "elements in L");
+ else
+ PyErr_Warn(PyExc_RuntimeWarning, "tiny diagonal "
+ "elements in D");
+ break;
+
+ default:
+ PyErr_Warn(PyExc_UserWarning, "");
+ }
+
+ if (L->minor<n) {
+ CHOL(free_factor)(&L, &Common);
+ PY_ERR(PyExc_ArithmeticError, "singular matrix");
+ }
+ b = CHOL(allocate_dense)(n, 1, n, (MAT_ID(B) == DOUBLE ?
+ CHOLMOD_REAL : CHOLMOD_COMPLEX) , &Common);
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY) {
+ CHOL(free_factor)(&L, &Common);
+ CHOL(free_dense)(&b, &Common);
+ return PyErr_NoMemory();
+ }
+ b_old = b->x;
+ for (i=0; i<nrhs; i++) {
+ b->x = MAT_BUF(B) + (i*ldB + oB)*E_SIZE[MAT_ID(B)];
+ x = CHOL(solve) (CHOLMOD_A, L, b, &Common);
+ if (Common.status != CHOLMOD_OK){
+ PyErr_SetString(PyExc_ValueError, "solve step failed");
+ CHOL(free_factor)(&L, &Common);
+ b->x = b_old;
+ CHOL(free_dense)(&b, &Common);
+ CHOL(free_dense)(&x, &Common);
+ return NULL;
+ }
+ memcpy(b->x, x->x, SP_NROWS(A)*E_SIZE[MAT_ID(B)]);
+ CHOL(free_dense)(&x, &Common);
+ }
+ b->x = b_old;
+ CHOL(free_dense)(&b, &Common);
+ CHOL(free_factor)(&L, &Common);
+ return Py_BuildValue("");
+}
+
+
+
+static char doc_splinsolve[] =
+ "Solves a sparse positive definite set of linear equations with\n"
+ "sparse righthand side.\n\n"
+ "X = splinsolve(A, B, p=None, uplo='L')\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B using a sparse Cholesky factorization.\n"
+ "The argument p specifies an optional permutation matrix. If it\n"
+ "is not provided, CHOLMOD uses a permutation from the AMD\n"
+ "library. An ArithmeticError exception is raised if the\n"
+ "factorization does not exist.\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix. Only the lower triangular part\n"
+ " of A is used; the upper triangular part is ignored.\n\n"
+ "B sparse matrix of the same type as A\n\n"
+ "p None, or an 'i' matrix of length n that contains\n"
+ " a permutation vector";
+
+static PyObject* splinsolve(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ spmatrix *A, *B, *X;
+ matrix *P=NULL;
+ int n, nnz;
+ cholmod_sparse *Ac=NULL, *Bc=NULL, *Xc=NULL;
+ cholmod_factor *L=NULL;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "p", "uplo", NULL};
+
+ if (!set_options()) return NULL;
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|Oc", kwlist, &A,
+ &B, &P, &uplo)) return NULL;
+
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A))
+ PY_ERR_TYPE("A is not a square sparse matrix");
+ n = SP_NROWS(A);
+ nnz = SP_NNZ(A);
+
+ if (!SpMatrix_Check(B) || SP_ID(A) != SP_ID(B))
+ PY_ERR_TYPE("B must be a sparse matrix of the same type as A");
+ if (SP_NROWS(B) != n)
+ PY_ERR(PyExc_ValueError, "incompatible dimensions for B");
+
+ if (P) {
+ if (!Matrix_Check(P) || MAT_ID(P) != INT) err_int_mtrx("p");
+ if (MAT_LGT(P) != n) err_buf_len("p");
+ if (!CHOL(check_perm)(P->buffer, n, n, &Common))
+ PY_ERR(PyExc_ValueError, "not a valid permutation");
+ }
+
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (!(Ac = pack(A, uplo))) return PyErr_NoMemory();
+
+ L = CHOL(analyze_p) (Ac, P ? MAT_BUFI(P): NULL, NULL, 0, &Common);
+ if (Common.status != CHOLMOD_OK){
+ CHOL(free_factor)(&L, &Common);
+ CHOL(free_sparse)(&Ac, &Common);
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY)
+ return PyErr_NoMemory();
+ else
+ PyErr_SetString(PyExc_ValueError, "symbolic factorization "
+ "failed");
+ return NULL;
+ }
+
+ CHOL(factorize) (Ac, L, &Common);
+ CHOL(free_sparse)(&Ac, &Common);
+ if (Common.status > 0) switch (Common.status) {
+ case CHOLMOD_NOT_POSDEF:
+ PyErr_SetObject(PyExc_ArithmeticError, Py_BuildValue("i",
+ L->minor));
+ CHOL(free_factor)(&L, &Common);
+ return NULL;
+ break;
+
+ case CHOLMOD_DSMALL:
+ /* This never happens unless we change the default value
+ * of Common.dbound (0.0). */
+ if (L->is_ll)
+ PyErr_Warn(PyExc_RuntimeWarning, "tiny diagonal "
+ "elements in L");
+ else
+ PyErr_Warn(PyExc_RuntimeWarning, "tiny diagonal "
+ "elements in D");
+ break;
+
+ default:
+ PyErr_Warn(PyExc_UserWarning, "");
+ }
+
+ if (L->minor<n) {
+ CHOL(free_factor)(&L, &Common);
+ PY_ERR(PyExc_ArithmeticError, "singular matrix");
+ }
+ if (!(Bc = create_matrix(B))) {
+ CHOL(free_factor)(&L, &Common);
+ return PyErr_NoMemory();
+ }
+
+ Xc = CHOL(spsolve)(0, L, Bc, &Common);
+ free_matrix(Bc);
+ CHOL(free_factor)(&L, &Common);
+ if (Common.status != CHOLMOD_OK){
+ CHOL(free_sparse)(&Xc, &Common);
+ if (Common.status == CHOLMOD_OUT_OF_MEMORY)
+ return PyErr_NoMemory();
+ else
+ PY_ERR(PyExc_ValueError, "solve step failed");
+ }
+
+ if (!(X = SpMatrix_New(Xc->nrow, Xc->ncol,
+ ((int_t*)Xc->p)[Xc->ncol], SP_ID(A)))) {
+ CHOL(free_sparse)(&Xc, &Common);
+ return PyErr_NoMemory();
+ }
+ memcpy(SP_COL(X), (int_t *) Xc->p, (Xc->ncol+1)*sizeof(int_t));
+ memcpy(SP_ROW(X), (int_t *) Xc->i,
+ ((int_t *) Xc->p)[Xc->ncol]*sizeof(int_t));
+ memcpy(SP_VAL(X), (double *) Xc->x,
+ ((int_t *) Xc->p)[Xc->ncol]*E_SIZE[SP_ID(X)]);
+ CHOL(free_sparse)(&Xc, &Common);
+ return (PyObject *) X;
+}
+
+
+static char doc_diag[] =
+ "Returns the diagonal of a Cholesky factor.\n\n"
+ "D = diag(F)\n\n"
+ "PURPOSE\n"
+ "Returns the diagonal of the Cholesky factor L in a \n"
+ "factorization P*A*P^T = L*L^T or P*A*P^T = L*L^H.\n\n"
+ "ARGUMENTS\n"
+ "D an nx1 'd' matrix with the diagonal elements of L.\n"
+ " Note that the permutation P is not returned, so the\n"
+ " order of the diagonal elements is unknown.\n\n"
+ "F a numeric Cholesky factor obtained by a call to\n"
+ " cholmod.numeric computed with options['supernodal'] = 2";
+
+extern void dcopy_(int *n, double *x, int *incx, double *y, int *incy);
+extern void zcopy_(int *n, complex *x, int *incx, complex *y, int *incy);
+
+static PyObject* diag(PyObject *self, PyObject *args)
+{
+ PyObject *F;
+ matrix *d=NULL;
+ cholmod_factor *L;
+ char *descr;
+ int k, strt, incx=1, incy, nrows, ncols;
+
+ if (!set_options()) return NULL;
+ if (!PyArg_ParseTuple(args, "O", &F)) return NULL;
+
+ if (!PyCObject_Check(F)) err_CO("F");
+ descr = PyCObject_GetDesc(F);
+ if (!descr || strncmp(descr, "CHOLMOD FACTOR", 14))
+ PY_ERR_TYPE("F is not a CHOLMOD factor");
+ L = (cholmod_factor *) PyCObject_AsVoidPtr(F);
+
+ /* Check factorization */
+ if (L->xtype == CHOLMOD_PATTERN || L->minor<L->n || !L->is_ll
+ || !L->is_super)
+ PY_ERR(PyExc_ValueError, "F must be a nonsingular supernodal "
+ "Cholesky factor");
+ if (!(d = Matrix_New(L->n,1,L->xtype == CHOLMOD_REAL ? DOUBLE :
+ COMPLEX))) return PyErr_NoMemory();
+
+ strt = 0;
+ for (k=0; k<L->nsuper; k++){
+ /* x[L->px[k], .... ,L->px[k+1]-1] is a dense lower-triangular
+ * nrowx times ncols matrix. We copy its diagonal to
+ * d[strt, ..., strt+ncols-1] */
+
+ ncols = (int)((int_t *) L->super)[k+1] -
+ ((int_t *) L->super)[k];
+ nrows = (int)((int_t *) L->pi)[k+1] - ((int_t *) L->pi)[k];
+ incy = nrows+1;
+ if (MAT_ID(d) == DOUBLE)
+ dcopy_(&ncols, ((double *) L->x) + ((int_t *) L->px)[k],
+ &incy, MAT_BUFD(d)+strt, &incx);
+ else
+ zcopy_(&ncols, ((complex *) L->x) + ((int_t *) L->px)[k],
+ &incy, MAT_BUFZ(d)+strt, &incx);
+ strt += ncols;
+ }
+ return (PyObject *)d;
+}
+
+
+static PyObject* getfactor(PyObject *self, PyObject *args)
+{
+ PyObject *F;
+ cholmod_factor *Lf;
+ cholmod_sparse *Ls;
+ char *descr;
+
+ if (!set_options()) return NULL;
+ if (!PyArg_ParseTuple(args, "O", &F)) return NULL;
+
+ if (!PyCObject_Check(F)) err_CO("F");
+ descr = PyCObject_GetDesc(F);
+ if (!descr || strncmp(descr, "CHOLMOD FACTOR", 14))
+ PY_ERR_TYPE("F is not a CHOLMOD factor");
+ Lf = (cholmod_factor *) PyCObject_AsVoidPtr(F);
+
+ /* Check factorization */
+ if (Lf->xtype == CHOLMOD_PATTERN)
+ PY_ERR(PyExc_ValueError, "F must be a numeric Cholesky factor");
+
+ if (!(Ls = CHOL(factor_to_sparse)(Lf, &Common)))
+ return PyErr_NoMemory();
+
+ spmatrix *ret = SpMatrix_New(Ls->nrow, Ls->ncol, Ls->nzmax,
+ (Ls->xtype == CHOLMOD_REAL ? DOUBLE : COMPLEX));
+ if (!ret) {
+ CHOL(free_sparse)(&Ls, &Common);
+ return PyErr_NoMemory();
+ }
+
+ memcpy(SP_COL(ret), Ls->p, (Ls->ncol+1)*sizeof(int_t));
+ memcpy(SP_ROW(ret), Ls->i, (Ls->nzmax)*sizeof(int_t));
+ memcpy(SP_VAL(ret), Ls->x, (Ls->nzmax)*E_SIZE[SP_ID(ret)]);
+ CHOL(free_sparse)(&Ls, &Common);
+
+ return (PyObject *)ret;
+}
+
+
+static PyMethodDef cholmod_functions[] = {
+ {"symbolic", (PyCFunction) symbolic, METH_VARARGS|METH_KEYWORDS,
+ doc_symbolic},
+ {"numeric", (PyCFunction) numeric, METH_VARARGS|METH_KEYWORDS,
+ doc_numeric},
+ {"solve", (PyCFunction) solve, METH_VARARGS|METH_KEYWORDS,
+ doc_solve},
+ {"spsolve", (PyCFunction) spsolve, METH_VARARGS|METH_KEYWORDS,
+ doc_spsolve},
+ {"linsolve", (PyCFunction) linsolve, METH_VARARGS|METH_KEYWORDS,
+ doc_linsolve},
+ {"splinsolve", (PyCFunction) splinsolve, METH_VARARGS|METH_KEYWORDS,
+ doc_splinsolve},
+ {"diag", (PyCFunction) diag, METH_VARARGS|METH_KEYWORDS, doc_diag},
+ {"getfactor", (PyCFunction) getfactor, METH_VARARGS|METH_KEYWORDS,
+ ""},
+ {NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC initcholmod(void)
+{
+ CHOL(start) (&Common);
+
+ cholmod_module = Py_InitModule3("cvxopt.cholmod", cholmod_functions,
+ cholmod__doc__);
+ PyModule_AddObject(cholmod_module, "options", PyDict_New());
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/cvxopt.h b/src/C/cvxopt.h
new file mode 100644
index 0000000..f37f7a8
--- /dev/null
+++ b/src/C/cvxopt.h
@@ -0,0 +1,127 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "Python.h"
+#include "structmember.h"
+#include "blas_redefines.h"
+
+/* ANSI99 complex is disabled during build of CHOLMOD */
+
+#ifndef NO_ANSI99_COMPLEX
+#include "complex.h"
+#define MAT_BUFZ(O) ((complex *)((matrix *)O)->buffer)
+#endif
+
+
+#ifndef __CVXOPT__
+#define __CVXOPT__
+
+#define INT 0
+#define DOUBLE 1
+#define COMPLEX 2
+
+/* compatibility between Python2.5 and lower versions */
+#if PY_VERSION_HEX < 0x02050000
+#define int_t Py_intptr_t
+#define lenfunc inquiry
+#define int_compat int
+#else
+#define int_t Py_ssize_t
+#define int_compat Py_ssize_t
+#endif
+
+typedef struct {
+ PyObject_HEAD
+ void *buffer; /* in column-major-mode array of type 'id' */
+ int nrows, ncols; /* number of rows and columns */
+ int id; /* DOUBLE, INT, COMPLEX */
+} matrix;
+
+typedef struct {
+ void *values; /* value list */
+ int_t *colptr; /* column pointer list */
+ int_t *rowind; /* row index list */
+ int_t nrows, ncols; /* number of rows and columns */
+ int nzmax; /* number of allocated elements */
+ int id; /* DOUBLE, COMPLEX */
+} ccs;
+
+typedef struct {
+ PyObject_HEAD
+ ccs *obj;
+} spmatrix;
+
+#ifdef BASE_MODULE
+
+#define Matrix_Check(v) ((v)->ob_type == &matrix_tp)
+#define SpMatrix_Check(v) ((v)->ob_type == &spmatrix_tp)
+
+#else
+
+static void **cvxopt_API;
+
+#define Matrix_New (*(matrix * (*)(int, int, int)) cvxopt_API[0])
+#define Matrix_NewFromMatrix (*(matrix * (*)(matrix *, int)) cvxopt_API[1])
+#define Matrix_NewFromList (*(matrix * (*)(PyObject *, int)) cvxopt_API[2])
+#define Matrix_Check (*(int * (*)(void *)) cvxopt_API[3])
+
+#define SpMatrix_New (*(spmatrix * (*)(int, int, int, int)) cvxopt_API[4])
+#define SpMatrix_NewFromSpMatrix \
+ (*(spmatrix * (*)(spmatrix *, int)) cvxopt_API[5])
+#define SpMatrix_NewFromIJV \
+ (*(spmatrix * (*)(matrix *, matrix *, matrix *, int, int, int, int)) \
+ cvxopt_API[6])
+#define SpMatrix_Check (*(int * (*)(void *)) cvxopt_API[7])
+
+/* Return -1 and set exception on error, 0 on success. */
+static int
+import_cvxopt(void)
+{
+ PyObject *module = PyImport_ImportModule("cvxopt.base");
+
+ if (module != NULL) {
+ PyObject *c_api_object = PyObject_GetAttrString(module, "_C_API");
+ if (c_api_object == NULL)
+ return -1;
+ if (PyCObject_Check(c_api_object))
+ cvxopt_API = (void **)PyCObject_AsVoidPtr(c_api_object);
+ Py_DECREF(c_api_object);
+ }
+ return 0;
+}
+
+#endif
+
+/*
+ * Below this line are non-essential convenience macros
+ */
+
+#define MAT_BUF(O) ((matrix *)O)->buffer
+#define MAT_BUFI(O) ((int_t *)((matrix *)O)->buffer)
+#define MAT_BUFD(O) ((double *)((matrix *)O)->buffer)
+#define MAT_BUFZ(O) ((complex *)((matrix *)O)->buffer)
+
+#define MAT_NROWS(O) ((matrix *)O)->nrows
+#define MAT_NCOLS(O) ((matrix *)O)->ncols
+#define MAT_LGT(O) (MAT_NROWS(O)*MAT_NCOLS(O))
+#define MAT_ID(O) ((matrix *)O)->id
+
+#define SP_NCOLS(O) ((spmatrix *)O)->obj->ncols
+#define SP_NROWS(O) ((spmatrix *)O)->obj->nrows
+#define SP_LGT(O) (SP_NROWS(O)*SP_NCOLS(O))
+#define SP_NNZ(O) ((spmatrix *)O)->obj->colptr[SP_NCOLS(O)]
+#define SP_NZMAX(O) ((spmatrix *)O)->obj->nzmax
+#define SP_ID(O) ((spmatrix *)O)->obj->id
+#define SP_COL(O) ((spmatrix *)O)->obj->colptr
+#define SP_ROW(O) ((spmatrix *)O)->obj->rowind
+#define SP_VAL(O) ((spmatrix *)O)->obj->values
+#define SP_VALD(O) ((double *)((spmatrix *)O)->obj->values)
+#define SP_VALZ(O) ((complex *)((spmatrix *)O)->obj->values)
+
+#define CCS_NROWS(O) ((ccs *)O)->nrows
+#define CCS_NCOLS(O) ((ccs *)O)->ncols
+#define CCS_NNZ(O) ((ccs *)O)->colptr[CCS_NCOLS(O)]
+
+#endif
diff --git a/src/C/dense.c b/src/C/dense.c
new file mode 100644
index 0000000..882cbc4
--- /dev/null
+++ b/src/C/dense.c
@@ -0,0 +1,2129 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#define BASE_MODULE
+
+#include "Python.h"
+#include "cvxopt.h"
+#include "misc.h"
+
+#include <complexobject.h>
+
+
+/* NumPy array protocol */
+typedef struct {
+ int version;
+ int nd;
+ char typekind;
+ int itemsize;
+ int flags;
+ int_t *shape;
+ int_t *strides;
+ void *data;
+ } PyArrayInterface;
+
+static const char PY_ARRAY_TC[3] = { 'i', 'f', 'c' };
+
+/* prototyping and forward declarations */
+PyObject *base_mod;
+extern void (*axpy[])(int *, number *, void *, int *, void *, int *) ;
+extern void (*scal[])(int *, number *, void *, int *) ;
+extern void (*gemm[])(char *, char *, int *, int *, int *, void *, void *,
+ int *, void *, int *, void *, void *, int *) ;
+extern void (*mtx_abs[])(void *, void *, int) ;
+extern int (*div_array[])(void *, number, int) ;
+extern int (*mtx_rem[])(void *, number, int) ;
+
+extern void (*write_num[])(void *, int, void *, int) ;
+extern int (*convert_num[])(void *, void *, int, int_t) ;
+extern PyObject * (*num2PyObject[])(void *, int) ;
+int get_id(void *, int ) ;
+
+extern const int E_SIZE[];
+extern const char TC_CHAR[][2];
+extern const char PRINTOPT[][15];
+extern number One[3], MinusOne[3], Zero[3];
+
+
+PyTypeObject spmatrix_tp ;
+/*
+spmatrix * SpMatrix_New(int_t, int_t, int, int ) ;
+spmatrix * SpMatrix_NewFromSpMatrix(spmatrix *, int, int) ;
+spmatrix * SpMatrix_NewFromIJV(matrix *, matrix *, matrix *,
+ int_t, int_t, int, int) ;
+*/
+
+PyTypeObject matrix_tp ;
+matrix * Matrix_NewFromNumber(int , int , int , void *, int ) ;
+static PyNumberMethods matrix_as_number ;
+static PyObject * matrix_iter(matrix *) ;
+
+
+void dscal_(int *, double *, double *, int *) ;
+void zscal_(int *, complex *, complex *, int *) ;
+void daxpy_(int *, double *, double *, int *, double *, int *) ;
+void zaxpy_(int *, complex *, complex *, int *, complex *, int *) ;
+void dgemm_(char *, char *, int *, int *, int *, double *, double *,
+ int *, double *, int *, double *, double *, int *) ;
+void zgemm_(char *, char *, int *, int *, int *, complex *, complex *,
+ int *, complex *, int *, complex *, complex *, int *) ;
+
+
+
+static const char err_mtx_list2matrix[][35] =
+ {"not an integer list",
+ "not a floating point list",
+ "not a complex floating point list" };
+
+#define free_convert_mtx_alloc(O1, O2, id) { \
+if (MAT_BUF(O1) != O2) { \
+ free(MAT_BUF(O1)); MAT_BUF(O1) = O2; MAT_ID(O1) = id; \
+ } \
+}
+
+#define free_lists_exit(argI,argJ,I,J,ret) { \
+ if (argI && !Matrix_Check(argI)) { Py_XDECREF(I); } \
+ if (argJ && !Matrix_Check(argJ)) { Py_XDECREF(J); } \
+ return ret; }
+
+
+static int convert_mtx(matrix *src, void *dest, int id)
+{
+ if (PY_NUMBER((PyObject *)src))
+ return convert_num[id](dest, src, 1, 0);
+
+ if (MAT_ID(src) == id) {
+ memcpy(dest, src->buffer, E_SIZE[src->id]*MAT_LGT(src) );
+ return 0;
+ }
+
+ int_t i;
+ for (i=0; i<MAT_LGT(src); i++)
+ if (convert_num[id](dest + i*E_SIZE[id], src, 0,i)) return -1;
+
+ return 0;
+}
+
+void * convert_mtx_alloc(matrix *src, int id)
+{
+ void *ptr;
+ if (MAT_ID(src) == id) return MAT_BUF(src);
+
+ if (!(ptr = malloc(E_SIZE[id]*MAT_LGT(src)))) return NULL;
+
+ int_t i;
+ for (i=0; i<MAT_LGT(src); i++)
+ if (convert_num[id](ptr + i*E_SIZE[id], src, 0,i))
+ { free(ptr); return NULL; }
+
+ return ptr;
+}
+
+
+/*
+ Creates an unpopulated "empty" matrix. In API
+*/
+matrix * Matrix_New(int nrows, int ncols, int id)
+{
+ matrix *a;
+ if ((nrows < 0) || (ncols < 0) || (id < INT) || (id > COMPLEX)) {
+ PyErr_BadInternalCall();
+ return NULL;
+ }
+
+ if (!(a = (matrix *)matrix_tp.tp_alloc(&matrix_tp, 0)))
+ return NULL;
+
+ a->id = id; a->nrows = nrows; a->ncols = ncols;
+ if (!(a->buffer = malloc(E_SIZE[id]*nrows*ncols))) {
+ a->ob_type->tp_free((PyObject*)a);
+ return (matrix *)PyErr_NoMemory();
+ }
+
+ int i;
+ for (i=0; i<MAT_LGT(a); i++)
+ write_num[MAT_ID(a)](MAT_BUF(a), i, &Zero[MAT_ID(a)], 0);
+
+ return a;
+}
+
+/*
+ Creates a copy of matrix as a new object. In API.
+*/
+matrix *Matrix_NewFromMatrix(matrix *src, int id)
+{
+ matrix *a;
+
+ if (PY_NUMBER((PyObject *)src))
+ return Matrix_NewFromNumber(1, 1, id, src, 1);
+
+ if (!(a = Matrix_New(src->nrows, src->ncols, id)))
+ return (matrix *)PyErr_NoMemory();
+
+ if (convert_mtx(src, a->buffer, id)) {
+ Py_DECREF(a); PY_ERR_TYPE("illegal type conversion");
+ }
+
+ return a;
+}
+
+/*
+ Creates a matrix from a PyArrayInterface.
+*/
+matrix *Matrix_NewFromArrayStruct(PyObject *obj, int id, int_t *ndim)
+{
+ PyObject *cobj = PyObject_GetAttrString(obj, "__array_struct__");
+ PyArrayInterface *src = (PyArrayInterface *)PyCObject_AsVoidPtr(cobj);
+
+ if (src->version != 2)
+ PY_ERR(PyExc_AssertionError, "unexpected format in array structure");
+
+ if (src->nd != 1 && src->nd != 2)
+ PY_ERR(PyExc_TypeError, "imported array must have 1 or 2 dimensions");
+
+ int src_id;
+ switch (src->typekind) {
+ case 'i' : src_id = INT; break;
+ case 'f' : src_id = DOUBLE; break;
+ case 'c' : src_id = COMPLEX; break;
+ default:
+ Py_DECREF(cobj); PY_ERR_TYPE("invalid array type");
+ }
+
+ if (id == -1) id = src_id;
+ if ((src_id > id) || (src->itemsize != E_SIZE[src_id])) {
+ Py_DECREF(cobj);
+ PY_ERR_TYPE("invalid array type");
+ }
+
+ /* XXX: revise flags check */
+ //if (src->flags != 0x701) {
+ if (!(src->flags & 0x001)) {
+ Py_DECREF(cobj);
+ PY_ERR_TYPE("array not contiguous)");
+ }
+
+ *ndim = src->nd;
+ matrix *a = Matrix_New(src->shape[0], src->nd == 2 ? src->shape[1] : 1, id);
+ if (!a) {
+ Py_DECREF(cobj); return (matrix *)PyErr_NoMemory();
+ }
+
+ int i, j, cnt;
+
+ for (j=0, cnt=0; j<MAT_NCOLS(a); j++) {
+ for (i=0; i<src->shape[0]; i++, cnt++) {
+
+ number n;
+ switch (id) {
+ case INT :
+ MAT_BUFI(a)[cnt] =
+ *(int_t *)(src->data+i*src->strides[0]+j*src->strides[1]);
+ break;
+ case DOUBLE:
+ switch (src_id) {
+ case INT:
+ n.d = *(int_t *)(src->data + i*src->strides[0]+j*src->strides[1]);
+ break;
+ case DOUBLE:
+ n.d = *(double *)(src->data + i*src->strides[0]+j*src->strides[1]);
+ break;
+ }
+ MAT_BUFD(a)[cnt] = n.d;
+ break;
+ case COMPLEX:
+ switch (src_id) {
+ case INT:
+ n.z = *(int_t *)(src->data+i*src->strides[0]+j*src->strides[1]);
+ break;
+ case DOUBLE:
+ n.z = *(double *)(src->data+i*src->strides[0]+j*src->strides[1]);
+ break;
+ case COMPLEX:
+ n.z = *(complex *)(src->data+i*src->strides[0]+j*src->strides[1]);
+ break;
+ }
+ MAT_BUFZ(a)[cnt] = n.z;
+ break;
+ }
+ }
+ }
+
+ Py_DECREF(cobj);
+ return a;
+}
+
+/*
+ Generates a matrix with all entries equal.
+*/
+matrix *
+Matrix_NewFromNumber(int nrows, int ncols, int id, void *val, int val_id)
+{
+
+ int i;
+ matrix *a = Matrix_New(nrows, ncols, id);
+ if (!a) return (matrix *)PyErr_NoMemory();
+
+ number n;
+ if (convert_num[id](&n, val, val_id, 0)) { Py_DECREF(a); return NULL; }
+ for (i=0; i<MAT_LGT(a); i++) write_num[id](MAT_BUF(a), i, &n, 0);
+
+ return a;
+}
+
+/*
+ Converts a Python list to a matrix. Part of API
+*/
+matrix * Matrix_NewFromSequence(PyObject *x, int id)
+{
+ int i, len = PySequence_Size(x);
+ PyObject *seq = PySequence_Fast(x, "list is not iterable");
+ if (!seq) return NULL;
+
+ if (id == -1) {
+ for (i=0; i<len; i++) {
+ PyObject *item = PySequence_Fast_GET_ITEM(seq, i);
+
+ if (!PY_NUMBER(item)) {
+ Py_DECREF(seq); PY_ERR_TYPE("non-numeric element in list");
+ }
+
+ id = MAX(id, get_id(item, 1));
+ }
+ }
+
+ if (!len) return Matrix_New(0, 0, (id < 0 ? INT : id));
+
+ matrix *L = Matrix_New(len,1,id);
+ if (!L) { Py_DECREF(seq); return (matrix *)PyErr_NoMemory(); }
+
+ for (i=0; i<len; i++) {
+ PyObject *item = PySequence_Fast_GET_ITEM(seq, i);
+
+ if (!PY_NUMBER(item)) {
+ Py_DECREF(seq); Py_DECREF(L);
+ PY_ERR_TYPE("non-numeric type in list");
+ }
+
+ number n;
+ if (convert_num[id](&n, item, 1, 0)) {
+ Py_DECREF(L); Py_DECREF(seq);
+ PY_ERR(PyExc_TypeError, err_mtx_list2matrix[id]);
+ }
+ write_num[id](L->buffer, i, &n, 0);
+ }
+ Py_DECREF(seq);
+ return L;
+}
+
+matrix * dense(spmatrix *self)
+{
+ matrix *A;
+ int_t i, j, k;
+
+ if (!(A = Matrix_New(SP_NROWS(self),SP_NCOLS(self),SP_ID(self))))
+ return (matrix *)PyErr_NoMemory();
+
+ for (i=0; i<SP_LGT(self); i++)
+ write_num[SP_ID(self)](MAT_BUF(A),i,&Zero,0);
+
+ for (k=0; k<SP_NCOLS(self); k++)
+ for (j=SP_COL(self)[k]; j<SP_COL(self)[k+1]; j++) {
+ write_num[SP_ID(self)](MAT_BUF(A),k*SP_NROWS(self)+SP_ROW(self)[j],
+ SP_VAL(self), j);
+ }
+ return A;
+}
+
+int convert_array(void *dest, void *src, int dest_id, int src_id, int n);
+
+matrix * dense_concat(PyObject *L, int id_arg)
+{
+ int m=0, n=0, mk=0, nk=0, i=0, j, id = 0;
+ PyObject *col;
+
+ int single_col = (PyList_GET_SIZE(L) > 0 &&
+ !PyList_Check(PyList_GET_ITEM(L, 0)));
+
+ for (j=0; j<(single_col ? 1 : PyList_GET_SIZE(L)); j++) {
+
+ col = (single_col ? L : PyList_GET_ITEM(L, j));
+ if (!PyList_Check(col))
+ PY_ERR_TYPE("invalid type in list");
+
+ mk = 0;
+ for (i=0; i<PyList_GET_SIZE(col); i++) {
+ PyObject *Lij = PyList_GET_ITEM(col, i);
+ if (!Matrix_Check(Lij) && !SpMatrix_Check(Lij) && !PY_NUMBER(Lij))
+ PY_ERR_TYPE("invalid type in list");
+
+ int blk_nrows, blk_ncols;
+ if (Matrix_Check(Lij) || SpMatrix_Check(Lij)) {
+ blk_nrows = X_NROWS(Lij); blk_ncols = X_NCOLS(Lij);
+ id = MAX(id, X_ID(Lij));
+ } else {
+ blk_nrows = 1; blk_ncols = 1;
+ id = MAX(id, get_id(Lij,1));
+ }
+
+ if (i==0) {
+ nk = blk_ncols; n += nk;
+ mk = blk_nrows;
+ } else {
+ if (blk_ncols != nk)
+ PY_ERR_TYPE("incompatible dimensions of subblocks");
+ mk += blk_nrows;
+ }
+ }
+ if (j==0)
+ m = mk;
+ else if (m != mk) PY_ERR_TYPE("incompatible dimensions of subblocks");
+ }
+
+ if ((id_arg >= 0) && (id_arg < id))
+ PY_ERR_TYPE("illegal type conversion");
+
+ id = MAX(id, id_arg);
+
+ matrix *A = Matrix_New(m, n, id);
+ if (!A) return (matrix *)PyErr_NoMemory();
+
+ nk = 0;
+ for (j=0; j<(single_col ? 1 : PyList_GET_SIZE(L)); j++) {
+ col = (single_col ? L : PyList_GET_ITEM(L, j));
+
+ mk = 0;
+ int blk_nrows = 0, blk_ncols = 0;
+ for (i=0; i<PyList_GET_SIZE(col); i++) {
+ PyObject *Lij = PyList_GET_ITEM(col, i);
+
+ if (Matrix_Check(Lij) || SpMatrix_Check(Lij)) {
+ blk_nrows = X_NROWS(Lij); blk_ncols = X_NCOLS(Lij);
+ } else {
+ blk_nrows = 1; blk_ncols = 1;
+ }
+
+ int ik, jk;
+ for (jk=0; jk<blk_ncols; jk++) {
+
+ if (Matrix_Check(Lij)) {
+ for (ik=0; ik<blk_nrows; ik++)
+ convert_num[id](MAT_BUF(A) + (mk+ik+(nk+jk)*m)*E_SIZE[id],
+ Lij, 0, ik + jk*blk_nrows);
+
+ } else if (SpMatrix_Check(Lij)) {
+ for (ik=SP_COL(Lij)[jk]; ik<SP_COL(Lij)[jk+1]; ik++)
+ convert_array(MAT_BUF(A) + ((nk+jk)*m+mk+SP_ROW(Lij)[ik])*
+ E_SIZE[id], SP_VAL(Lij) + ik*E_SIZE[SP_ID(Lij)],
+ id, SP_ID(Lij), 1);
+
+ } else {
+
+ convert_num[id](MAT_BUF(A) + (mk+(nk+jk)*m)*E_SIZE[id],
+ Lij, 1, 0);
+ }
+ }
+ mk += blk_nrows;
+ }
+ nk += blk_ncols;
+ }
+ return A;
+}
+
+static void
+matrix_dealloc(matrix* self)
+{
+ free(self->buffer);
+ self->ob_type->tp_free((PyObject*)self);
+}
+
+static PyObject *
+matrix_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+ PyObject *Objx = NULL, *size = NULL;
+ static char *kwlist[] = { "x", "size", "tc", NULL};
+
+ int nrows=0, ncols=0;
+ char tc = 0;
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|Oc:matrix", kwlist,
+ &Objx, &size, &tc))
+ return NULL;
+
+ if (size && !PyArg_ParseTuple(size, "ii", &nrows, &ncols))
+ PY_ERR_TYPE("invalid dimension tuple") ;
+
+ if (nrows < 0 || ncols < 0)
+ PY_ERR_TYPE("dimensions must be non-negative");
+
+ if (tc && !(VALID_TC_MAT(tc))) PY_ERR_TYPE("tc must be 'i', 'd' or 'z'");
+ int id = (tc ? TC2ID(tc) : -1);
+
+ matrix *ret = NULL;
+ /* x is a number */
+ if (PY_NUMBER(Objx))
+ return (PyObject *)
+ Matrix_NewFromNumber(MAX(nrows, size ? 0 : 1),
+ MAX(ncols, size ? 0 : 1), (id == -1 ? get_id(Objx,1):id),Objx,1);
+
+ /* a matrix */
+ else if (Matrix_Check(Objx))
+ ret = Matrix_NewFromMatrix((matrix *)Objx, (id == -1 ?MAT_ID(Objx):id));
+
+ /* sparse matrix */
+ else if (SpMatrix_Check(Objx)) {
+ matrix *tmp = dense((spmatrix *)Objx);
+ if (!tmp) return PyErr_NoMemory();
+ ret = Matrix_NewFromMatrix(tmp, (id == -1 ? SP_ID(Objx) : id));
+ Py_DECREF(tmp);
+ }
+
+ /* PyArrayStructure */
+ else if (PyObject_HasAttrString(Objx,"__array_struct__")) {
+ int_t ndim = 0;
+ ret = Matrix_NewFromArrayStruct(Objx, id, &ndim);
+ }
+
+ /* x is a list */
+ else if (PyList_Check(Objx)) {
+
+ /* first try a regular list */
+ if (!(ret = Matrix_NewFromSequence(Objx, id))) {
+ PyErr_Clear();
+ /* try concatenation */
+ ret = dense_concat(Objx, id);
+ }
+ }
+
+ /* x is a sequence */
+ else if (PySequence_Check(Objx)) {
+ ret = Matrix_NewFromSequence(Objx, id);
+ }
+ else PY_ERR_TYPE("invalid matrix initialization");
+
+ if (ret && size) {
+ if (nrows*ncols == MAT_LGT(ret)) {
+ ret->nrows=nrows; ret->ncols=ncols;
+ } else {
+ Py_DECREF(ret); PY_ERR_TYPE("wrong matrix dimensions");
+ }
+ }
+
+ return (PyObject *)ret;
+}
+
+static PyObject *
+matrix_str(matrix *self)
+{
+ PyObject *printopt;
+
+ /* these PyObject variables will all be borrowed references */
+ PyObject *opt, *s, *stmp=NULL;
+
+ if (self->nrows == 0 || self->ncols == 0)
+ return Py_BuildValue("s","");
+
+ if (!(printopt = PyObject_GetAttrString(base_mod, "print_options")) ||
+ !PyDict_Check(printopt)) {
+ PY_ERR(PyExc_AttributeError, "cannot access 'print_options' dictionary");
+ }
+
+ if (!(opt = PyDict_GetItemString(printopt, PRINTOPT[self->id]))) {
+ Py_DECREF(printopt);
+ PY_ERR(PyExc_KeyError, "missing print format key in 'base_options'");
+ }
+
+ char tmp[50], format[20] = "%- ", format_im[20] = "%";
+ strncat(format, PyString_AsString(opt), 18);
+ if (MAT_ID(self)==COMPLEX)
+ strncat(format_im, PyString_AsString(opt), 18);
+
+ if (!(s = PyString_FromString(""))) {
+ Py_DECREF(printopt);
+ return PyErr_NoMemory();
+ }
+
+ int i, j;
+ for (i=0; i<self->nrows; i++) {
+
+ for (j=0; j<self->ncols; j++) {
+ PyString_ConcatAndDel(&s, PyString_FromString(" "));
+ switch (MAT_ID(self)) {
+ case DOUBLE:
+ if ((snprintf(tmp,50,format, MAT_BUFD(self)[j*self->nrows+i])<0) ||
+ !(stmp = PyString_FromString(tmp)))
+ goto fail;
+ break;
+ case INT:
+ if ((snprintf(tmp,50,format,MAT_BUFI(self)[j*self->nrows+i])<0) ||
+ !(stmp = PyString_FromString(tmp)))
+ goto fail;
+ break;
+ case COMPLEX:
+ if ((snprintf(tmp,50,format,
+ creal(MAT_BUFZ(self)[j*self->nrows+i]))<0) ||
+ !(stmp = PyString_FromString(tmp)))
+ goto fail;
+
+ if (snprintf(tmp,50,format_im,
+ fabs(cimag(MAT_BUFZ(self)[j*self->nrows+i])))<0)
+ goto fail;
+
+ PyString_ConcatAndDel(&stmp, cimag(MAT_BUFZ(self)[j*self->nrows+i])>0 ?
+ PyString_FromString("+j") : PyString_FromString("-j"));
+ PyString_ConcatAndDel(&stmp, PyString_FromString(tmp));
+ break;
+ }
+ PyString_ConcatAndDel(&s, stmp);
+ }
+ PyString_ConcatAndDel(&s, PyString_FromString("\n"));
+ }
+
+ Py_DECREF(printopt);
+ return s;
+
+ fail:
+ Py_DECREF(printopt);
+ Py_DECREF(s); return PyErr_NoMemory();
+}
+
+static PyObject *
+matrix_repr(matrix *self) {
+
+ PyObject *s = PyString_FromFormat("<%ldx%ld matrix, tc='%s'>",
+ (long)self->nrows,(long)self->ncols,TC_CHAR[self->id]);
+
+ return s;
+}
+
+/*
+ * This method converts different index sets into a matrix indexlist
+ */
+matrix * create_indexlist(int dim, PyObject *A)
+{
+ matrix *x;
+ int_t i, j;
+
+ /* integer */
+ if (PyInt_Check(A)) {
+ i = PyInt_AS_LONG(A);
+ if (OUT_RNG(i,dim)) PY_ERR(PyExc_IndexError, "index out of range");
+
+ if ((x = Matrix_New(1,1,INT))) MAT_BUFI(x)[0] = i;
+ return x;
+ }
+ /* slice */
+ else if (PySlice_Check(A)) {
+ int_compat start, stop, step, lgt;
+
+ if (PySlice_GetIndicesEx((PySliceObject*)A, dim,
+ &start, &stop, &step, &lgt) < 0) return NULL;
+
+ if ((x = Matrix_New(lgt, 1, INT)))
+ for (i=start, j=0; j<lgt; i += step, j++) MAT_BUFI(x)[j] = i;
+
+ return x;
+ }
+ /* Matrix index list */
+ else if (Matrix_Check(A)) {
+ if (MAT_ID(A) != INT) PY_ERR_TYPE("not an integer index list");
+
+ for (i=0; i<MAT_LGT(A); i++)
+ if ( OUT_RNG(MAT_BUFI(A)[i], dim) )
+ PY_ERR(PyExc_IndexError, "index out of range");
+
+ return (matrix *)A;
+ }
+ /* List */
+ else if (PyList_Check(A)) {
+ if (!(x = (matrix *)Matrix_NewFromSequence(A, INT))) return NULL;
+
+ return create_indexlist(dim, (PyObject *)x);
+ }
+ else PY_ERR(PyExc_TypeError, "invalid index argument");
+}
+
+static int
+matrix_length(matrix *self)
+{
+ return MAT_LGT(self);
+}
+
+static PyObject *
+matrix_subscr(matrix* self, PyObject* args)
+{
+ matrix *Il = NULL, *Jl = NULL, *ret;
+ if (PyInt_Check(args)) {
+ int_t i = PyInt_AS_LONG(args);
+ if (OUT_RNG(i,MAT_LGT(self)))
+ PY_ERR(PyExc_IndexError, "index out of range");
+
+ return num2PyObject[self->id](self->buffer, CWRAP(i,MAT_LGT(self)));
+ }
+
+ else if (PyList_Check(args) || Matrix_Check(args) || PySlice_Check(args)) {
+
+ if (!(Il = create_indexlist(MAT_LGT(self), args))) return NULL;
+
+ int i;
+ if (!(ret = Matrix_New(MAT_LGT(Il), 1, self->id) ))
+ free_lists_exit(args,(PyObject *)NULL,Il,(PyObject *)NULL,
+ PyErr_NoMemory());
+
+ for (i=0; i<MAT_LGT(Il); i++)
+ write_num[self->id](ret->buffer, i, self->buffer,
+ CWRAP(MAT_BUFI(Il)[i],MAT_LGT(self)));
+
+ free_lists_exit(args,(PyObject *)NULL,Il,(PyObject *)NULL,(PyObject *)ret);
+ }
+
+ /* remainding cases are different two argument indexing */
+ PyObject *argI = NULL, *argJ = NULL;
+ if (!PyArg_ParseTuple(args, "OO", &argI,&argJ))
+ PY_ERR_TYPE("invalid index arguments");
+
+ /* handle normal subscripts (two integers) separately */
+ if (PyInt_Check(argI) && PyInt_Check(argJ)) {
+
+ int i = PyInt_AS_LONG(argI), j = PyInt_AS_LONG(argJ);
+ if ( OUT_RNG(i, self->nrows) || OUT_RNG(j, self->ncols))
+ PY_ERR(PyExc_IndexError, "index out of range");
+
+ return num2PyObject[self->id](self->buffer,
+ CWRAP(i,self->nrows) + CWRAP(j,self->ncols)*self->nrows);
+ }
+
+ /* two slices, handled separately for speed */
+ if (PySlice_Check(argI) && PySlice_Check(argJ)) {
+ int_compat rowstart, rowstop, rowstep, rowlgt;
+ int_compat colstart, colstop, colstep, collgt;
+
+ if ( (PySlice_GetIndicesEx((PySliceObject*)argI, MAT_NROWS(self),
+ &rowstart, &rowstop, &rowstep, &rowlgt) < 0) ||
+ (PySlice_GetIndicesEx((PySliceObject*)argJ, MAT_NCOLS(self),
+ &colstart, &colstop, &colstep, &collgt) < 0)) return NULL;
+
+ if (!(ret = Matrix_New(rowlgt, collgt, self->id)))
+ return PyErr_NoMemory();
+
+ int i, j, icnt, jcnt, cnt=0;
+ for (j=colstart, jcnt=0; jcnt<collgt; jcnt++, j+=colstep)
+ for (i=rowstart, icnt=0; icnt<rowlgt; icnt++, i+=rowstep) {
+ switch (self->id) {
+ case INT:
+ MAT_BUFI(ret)[cnt++] = MAT_BUFI(self)[j*self->nrows+i];
+ break;
+ case DOUBLE:
+ MAT_BUFD(ret)[cnt++] = MAT_BUFD(self)[j*self->nrows+i];
+ break;
+ case COMPLEX:
+ MAT_BUFZ(ret)[cnt++] = MAT_BUFZ(self)[j*self->nrows+i];
+ break;
+ }
+ }
+
+ return (PyObject *)ret;
+ }
+
+ /* remaining two indexing cases */
+ if (!(Il = create_indexlist(self->nrows, argI)) ||
+ !(Jl = create_indexlist(self->ncols, argJ)))
+ free_lists_exit(argI, argJ, Il, Jl, (PyObject *)NULL);
+
+ int i, j, cnt;
+ if (!(ret = Matrix_New(MAT_LGT(Il), MAT_LGT(Jl), self->id)))
+ free_lists_exit(argI, argJ, Il, Jl, PyErr_NoMemory());
+
+ for (j=0, cnt=0; j < MAT_LGT(Jl); j++)
+ for (i=0; i < MAT_LGT(Il); i++) {
+ write_num[self->id](ret->buffer, cnt++, self->buffer,
+ CWRAP(MAT_BUFI(Il)[i],self->nrows) +
+ CWRAP(MAT_BUFI(Jl)[j],self->ncols)*self->nrows);
+ }
+
+ free_lists_exit(argI, argJ, Il, Jl, (PyObject *)ret);
+}
+
+#define spmatrix_getitem_i(O,i,v) \
+ spmatrix_getitem_ij(O,i%SP_NROWS(O),i/SP_NROWS(O),v)
+
+int spmatrix_getitem_ij(spmatrix *, int_t, int_t, number *) ;
+
+static int
+matrix_ass_subscr(matrix* self, PyObject* args, PyObject* val)
+{
+ matrix *Il = NULL, *Jl = NULL;
+ int_t i, j, id = self->id, decref_val = 0, arraystruct_nd = 0;
+
+ if (!val) PY_ERR_INT(PyExc_NotImplementedError,
+ "cannot delete matrix entries");
+
+ if (!(PY_NUMBER(val) || Matrix_Check(val) || SpMatrix_Check(val))) {
+
+ if (PyObject_HasAttrString(val,"__array_struct__"))
+ val = (PyObject *)Matrix_NewFromArrayStruct(val, -1, &arraystruct_nd);
+ else
+ val = (PyObject *)Matrix_NewFromSequence(val, MAT_ID(self));
+
+ if (!val)
+ PY_ERR_INT(PyExc_NotImplementedError, "invalid type in assignment");
+
+ decref_val = 1;
+ }
+
+ if (get_id(val, (PY_NUMBER(val) ? 1 : 0)) > id)
+ PY_ERR_INT(PyExc_TypeError, "invalid type in assignment");
+
+ if (PyInt_Check(args) || PyList_Check(args) ||
+ Matrix_Check(args) || PySlice_Check(args)) {
+
+ if (!(Il = create_indexlist(MAT_LGT(self), args))) {
+ if (decref_val) { Py_DECREF(val); }
+ return -1;
+ }
+ number n;
+ if (PY_NUMBER(val) || (Matrix_Check(val) && MAT_LGT(val)==1)) {
+ convert_num[id](&n, val, (Matrix_Check(val) ? 0 : 1), 0);
+
+ for (i=0; i<MAT_LGT(Il); i++)
+ write_num[id](self->buffer,CWRAP(MAT_BUFI(Il)[i],MAT_LGT(self)),&n,0);
+ }
+ else {
+
+ if (Matrix_Check(val)) {
+ if (MAT_LGT(val) != MAT_LGT(Il) || MAT_NCOLS(val) > 1) {
+ if (!Matrix_Check(args)) { Py_DECREF(Il); }
+ if (decref_val) { Py_DECREF(val); }
+ PY_ERR_INT(PyExc_TypeError, "argument has wrong size");
+ }
+
+ for (i=0; i < MAT_LGT(Il); i++) {
+ convert_num[id](&n, val, 0, i);
+ write_num[id](self->buffer,
+ CWRAP(MAT_BUFI(Il)[i], MAT_LGT(self)), &n, 0);
+ }
+ }
+ else { /* spmatrix */
+
+ if (SP_NROWS(val) != MAT_LGT(Il) || SP_NCOLS(val) > 1) {
+ if (!Matrix_Check(args)) { Py_DECREF(Il); }
+ if (decref_val) { Py_DECREF(val); }
+ PY_ERR_INT(PyExc_TypeError, "argument has wrong size");
+ }
+
+ for (i=0; i < MAT_LGT(Il); i++) {
+ spmatrix_getitem_i((spmatrix *)val, i, &n);
+ write_num[id](self->buffer,
+ CWRAP(MAT_BUFI(Il)[i], MAT_LGT(self)), &n, 0);
+ }
+ }
+ }
+
+ if (decref_val) { Py_DECREF(val); }
+ free_lists_exit(args,(PyObject *)NULL,Il,(PyObject *)NULL,0);
+ }
+
+ /* remainding cases are different two argument indexing */
+ PyObject *argI = NULL, *argJ = NULL;
+ if (!PyArg_ParseTuple(args, "OO", &argI,&argJ))
+ PY_ERR_INT(PyExc_TypeError, "invalid index arguments");
+
+ /* two slices, RHS of same type, handled separately for speed */
+ if (PySlice_Check(argI) && PySlice_Check(argJ) &&
+ Matrix_Check(val) && MAT_ID(val) == MAT_ID(self)) {
+
+ int_compat rowstart, rowstop, rowstep, rowlgt;
+ int_compat colstart, colstop, colstep, collgt;
+
+ if ( (PySlice_GetIndicesEx((PySliceObject*)argI, MAT_NROWS(self),
+ &rowstart, &rowstop, &rowstep, &rowlgt) < 0) ||
+ (PySlice_GetIndicesEx((PySliceObject*)argJ, MAT_NCOLS(self),
+ &colstart, &colstop, &colstep, &collgt) < 0)) return -1;
+
+ if (decref_val && MAT_LGT(val) == rowlgt*collgt) {
+ MAT_NROWS(val) = rowlgt; MAT_NCOLS(val) = collgt;
+ }
+
+ if (MAT_NROWS(val)!=rowlgt || MAT_NCOLS(val)!=collgt)
+ PY_ERR_INT(PyExc_TypeError, "argument has wrong size");
+
+ int i, j, icnt, jcnt, cnt=0;
+ for (j=colstart, jcnt=0; jcnt<collgt; jcnt++, j+=colstep)
+ for (i=rowstart, icnt=0; icnt<rowlgt; icnt++, i+=rowstep) {
+ switch (self->id) {
+ case INT:
+ MAT_BUFI(self)[j*self->nrows+i] = MAT_BUFI(val)[cnt++];
+ break;
+ case DOUBLE:
+ MAT_BUFD(self)[j*self->nrows+i] = MAT_BUFD(val)[cnt++];
+ break;
+ case COMPLEX:
+ MAT_BUFZ(self)[j*self->nrows+i] = MAT_BUFZ(val)[cnt++];
+ break;
+ }
+ }
+
+ return 0;
+ }
+
+ if (!(Il = create_indexlist(self->nrows, argI)) ||
+ !(Jl = create_indexlist(self->ncols, argJ))) {
+ if (decref_val) { Py_DECREF(val); }
+ free_lists_exit(argI,argJ,Il,Jl,-1);
+ }
+
+ if (decref_val && arraystruct_nd < 2 &&
+ MAT_LGT(val) == MAT_LGT(Il)*MAT_LGT(Jl)) {
+ MAT_NROWS(val) = MAT_LGT(Il); MAT_NCOLS(val) = MAT_LGT(Jl);
+ }
+
+ number n;
+ if (PY_NUMBER(val) || (Matrix_Check(val) && MAT_LGT(val)==1)) {
+ if (convert_num[id](&n, val, (Matrix_Check(val) ? 0 : 1), 0)) {
+ if (decref_val) { Py_DECREF(val); }
+ free_lists_exit(Il,Jl,argI,argJ,-1);
+ }
+
+ for (j=0; j < MAT_LGT(Jl); j++)
+ for (i=0; i < MAT_LGT(Il); i++) {
+ write_num[id](self->buffer,CWRAP(MAT_BUFI(Il)[i],self->nrows) +
+ CWRAP(MAT_BUFI(Jl)[j],self->ncols)*self->nrows, &n, 0);
+ }
+ }
+ else if (Matrix_Check(val)) {
+ if (MAT_LGT(Il) != MAT_NROWS(val) || MAT_LGT(Jl) != MAT_NCOLS(val) ) {
+ if (!Matrix_Check(argI)) { Py_DECREF(Il); }
+ if (!Matrix_Check(argJ)) { Py_DECREF(Jl); }
+ if (decref_val) { Py_DECREF(val); }
+ PY_ERR_INT(PyExc_TypeError, "argument has wrong size");
+ }
+
+ int cnt = 0;
+ for (j=0; j < MAT_LGT(Jl); j++)
+ for (i=0; i < MAT_LGT(Il); i++, cnt++) {
+ if (convert_num[id](&n, val, 0, cnt))
+ free_lists_exit(argI,argJ,Il,Jl,-1);
+
+ write_num[id](self->buffer,CWRAP(MAT_BUFI(Il)[i],self->nrows) +
+ CWRAP(MAT_BUFI(Jl)[j],self->ncols)*self->nrows, &n, 0);
+ }
+ }
+ else { /* spmatrix */
+ if (MAT_LGT(Il) != SP_NROWS(val) || MAT_LGT(Jl) != SP_NCOLS(val) ) {
+ if (!Matrix_Check(argI)) { Py_DECREF(Il); }
+ if (!Matrix_Check(argJ)) { Py_DECREF(Jl); }
+ if (decref_val) { Py_DECREF(val); }
+ PY_ERR_INT(PyExc_TypeError, "argument has wrong size");
+ }
+
+ int cnt = 0;
+ for (j=0; j < MAT_LGT(Jl); j++)
+ for (i=0; i < MAT_LGT(Il); i++, cnt++) {
+
+ spmatrix_getitem_i((spmatrix *)val, cnt, &n);
+ write_num[id](self->buffer,CWRAP(MAT_BUFI(Il)[i],self->nrows) +
+ CWRAP(MAT_BUFI(Jl)[j],self->ncols)*self->nrows, &n, 0);
+ }
+ }
+
+ if (decref_val) { Py_DECREF(val); }
+ free_lists_exit(argI,argJ,Il,Jl,0);
+}
+
+static PyMappingMethods matrix_as_mapping = {
+ (lenfunc)matrix_length,
+ (binaryfunc)matrix_subscr,
+ (objobjargproc)matrix_ass_subscr
+};
+
+static PyObject * matrix_transpose(matrix *self) {
+
+ matrix *ret = Matrix_New(self->ncols, self->nrows, self->id);
+ if (!ret) return PyErr_NoMemory();
+
+ int i, j, cnt = 0;
+ for (i=0; i < ret->nrows; i++)
+ for (j=0; j < ret->ncols; j++)
+ write_num[self->id](ret->buffer, i + j*ret->nrows, self->buffer, cnt++);
+
+ return (PyObject *)ret;
+}
+
+static PyObject * matrix_ctranspose(matrix *self) {
+
+ if (self->id != COMPLEX) return matrix_transpose(self);
+
+ matrix *ret = Matrix_New(self->ncols, self->nrows, self->id);
+ if (!ret) return PyErr_NoMemory();
+
+ int i, j, cnt = 0;
+ for (i=0; i < ret->nrows; i++)
+ for (j=0; j < ret->ncols; j++)
+ MAT_BUFZ(ret)[i + j*ret->nrows] = conj(MAT_BUFZ(self)[cnt++]);
+
+ return (PyObject *)ret;
+}
+
+static PyObject * matrix_real(matrix *self) {
+
+ if (self->id != COMPLEX)
+ return (PyObject *)Matrix_NewFromMatrix(self,self->id);
+
+ matrix *ret = Matrix_New(self->nrows, self->ncols, DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i < MAT_LGT(self); i++)
+ MAT_BUFD(ret)[i] = creal(MAT_BUFZ(self)[i]);
+
+ return (PyObject *)ret;
+}
+
+static PyObject * matrix_imag(matrix *self) {
+
+ matrix *ret;
+ if (self->id != COMPLEX) {
+ PyObject *a = PyFloat_FromDouble(0);
+ ret = Matrix_NewFromNumber(self->nrows, self->ncols, self->id, a, 2);
+ Py_DECREF(a);
+ if (!ret) return PyErr_NoMemory();
+
+ return (PyObject *)ret;
+ }
+
+ if (!(ret = Matrix_New(self->nrows, self->ncols, DOUBLE)))
+ return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i < MAT_LGT(self); i++)
+ MAT_BUFD(ret)[i] = cimag(MAT_BUFZ(self)[i]);
+
+ return (PyObject *)ret;
+}
+
+static char doc_tofile[] =
+ "Writes a matrix to file\n\n"
+ "ARGUMENTS\n"
+ "fo a Python file object prevously obtained by open()\n\n";
+static PyObject *
+matrix_tofile(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *file_obj;
+ FILE *fp;
+ char *kwlist[] = {"fo", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O", kwlist, &file_obj))
+ return NULL;
+
+ if (!PyFile_Check(file_obj))
+ PY_ERR_TYPE("argument must a file object");
+
+ if (!(fp = PyFile_AsFile(file_obj)))
+ PY_ERR(PyExc_IOError,"file not open for writing");
+
+ fwrite(self->buffer, E_SIZE[self->id], MAT_LGT(self), fp);
+ return Py_BuildValue("");
+}
+
+static char doc_fromfile[] =
+ "Reads a matrix from file\n\n"
+ "ARGUMENTS\n"
+ "fo a Python file object prevously obtained by open()\n\n";
+static PyObject *
+matrix_fromfile(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *file_obj;
+ FILE *fp;
+ char *kwlist[] = {"fo", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O", kwlist, &file_obj))
+ return NULL;
+
+ if (!PyFile_Check(file_obj))
+ PY_ERR_TYPE("argument must a file object");
+ if (!(fp = PyFile_AsFile(file_obj)))
+ PY_ERR(PyExc_IOError,"file not open for reading");
+
+ int n = fread(self->buffer, E_SIZE[self->id], MAT_LGT(self), fp);
+
+ if (n < MAT_LGT(self))
+ PY_ERR(PyExc_IOError, "could not read entire matrix");
+ return Py_BuildValue("");
+}
+
+static PyObject *
+matrix_getstate(matrix *self)
+{
+ PyObject *list = PyList_New(MAT_LGT(self));
+ PyObject *size = PyTuple_New(2);
+ if (!list || !size) {
+ Py_XDECREF(list); Py_XDECREF(size); return NULL;
+ }
+
+ PyTuple_SET_ITEM(size, 0, PyInt_FromLong(MAT_NROWS(self)));
+ PyTuple_SET_ITEM(size, 1, PyInt_FromLong(MAT_NCOLS(self)));
+
+ int i;
+ for (i=0; i<MAT_LGT(self); i++) {
+ PyList_SET_ITEM(list, i, num2PyObject[MAT_ID(self)](MAT_BUF(self), i));
+ }
+
+ return Py_BuildValue("NNs", list, size, TC_CHAR[MAT_ID(self)]);
+}
+
+static PyObject *
+matrix_reduce(matrix* self)
+{
+ return Py_BuildValue("ON", self->ob_type, matrix_getstate(self));
+}
+
+static PyMethodDef matrix_methods[] = {
+ {"trans", (PyCFunction)matrix_transpose, METH_NOARGS,
+ "Returns the matrix transpose"},
+ {"ctrans", (PyCFunction)matrix_ctranspose, METH_NOARGS,
+ "Returns the matrix conjugate transpose"},
+ {"real", (PyCFunction)matrix_real, METH_NOARGS,
+ "Returns real part of matrix"},
+ {"imag", (PyCFunction)matrix_imag, METH_NOARGS,
+ "Returns imaginary part of matrix"},
+ {"tofile", (PyCFunction)matrix_tofile, METH_VARARGS|METH_KEYWORDS,
+ doc_tofile},
+ {"fromfile", (PyCFunction)matrix_fromfile, METH_VARARGS|METH_KEYWORDS,
+ doc_fromfile},
+ {"__reduce__", (PyCFunction)matrix_reduce, METH_NOARGS,
+ "__reduce__() -> (cls, state)"},
+ {NULL} /* Sentinel */
+};
+
+static PyObject *
+matrix_get_size(matrix *self, void *closure)
+{
+ PyObject *t = PyTuple_New(2);
+
+ PyTuple_SET_ITEM(t, 0, PyInt_FromLong(self->nrows));
+ PyTuple_SET_ITEM(t, 1, PyInt_FromLong(self->ncols));
+
+ return t;
+}
+
+static PyObject * matrix_get_typecode(matrix *self, void *closure)
+{
+ return PyString_FromStringAndSize(TC_CHAR[self->id], 1);
+}
+
+
+static void matrix_free_array_struct(void *a_struct, void *descr)
+{
+ free(((PyArrayInterface *)a_struct)->shape);
+ free(((PyArrayInterface *)a_struct)->strides);
+ free(a_struct);
+}
+
+static PyObject * matrix_array_struct(matrix *self, void *closure) {
+
+ PyArrayInterface *a = malloc(sizeof(PyArrayInterface));
+ if (!a) return PyErr_NoMemory();
+
+ a->shape = malloc(2*sizeof(int_t));
+ a->strides = malloc(2*sizeof(int_t));
+ if (!a->shape || !a->strides) {
+ free(a->shape); free(a->strides); free(a);
+ return PyErr_NoMemory();
+ }
+
+ a->version = 2;
+ a->nd = 2;
+ a->typekind = PY_ARRAY_TC[self->id];
+ a->itemsize = E_SIZE[self->id];
+ a->flags = 0x001 + 0x002 + 0x100 + 0x200 + 0x400;
+ a->shape[0] = self->nrows;
+ a->shape[1] = self->ncols;
+ a->strides[0] = E_SIZE[self->id];
+ a->strides[1] = self->nrows*E_SIZE[self->id];
+ a->data = self->buffer;
+
+ return (PyObject *) PyCObject_FromVoidPtrAndDesc((void *) a,
+ "CVXOPT ARRAY STRUCT", matrix_free_array_struct);
+
+}
+
+static PyObject * matrix_get_T(matrix *self, void *closure)
+{
+ return matrix_transpose(self);
+}
+
+static PyObject * matrix_get_H(matrix *self, void *closure)
+{
+ return matrix_ctranspose(self);
+}
+
+static PyGetSetDef matrix_getsets[] = {
+ {"size", (getter) matrix_get_size, NULL, "matrix dimensions"},
+ {"typecode", (getter) matrix_get_typecode, NULL, "typecode character"},
+ {"__array_struct__", (getter) matrix_array_struct, NULL,
+ "C object implementing the NumPy array protocol"},
+ {"T", (getter) matrix_get_T, NULL, "transpose"},
+ {"H", (getter) matrix_get_H, NULL, "conjugate transpose"},
+ {NULL} /* Sentinel */
+};
+
+PyTypeObject matrix_tp = {
+ PyObject_HEAD_INIT(NULL)
+ 0,
+ "cvxopt.base.matrix",
+ sizeof(matrix),
+ 0,
+ (destructor)matrix_dealloc, /* tp_dealloc */
+ 0, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ 0, /* tp_compare */
+ (reprfunc)matrix_repr, /* tp_repr */
+ &matrix_as_number, /* tp_as_number */
+ 0, /* tp_as_sequence */
+ &matrix_as_mapping, /* tp_as_mapping */
+ 0, /* tp_hash */
+ 0, /* tp_call */
+ (reprfunc)matrix_str, /* tp_str */
+ 0, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE |
+ Py_TPFLAGS_CHECKTYPES, /* tp_flags */
+ 0, /* tp_doc */
+ 0, /* tp_traverse */
+ 0, /* tp_clear */
+ 0, /* tp_richcompare */
+ 0, /* tp_weaklistoffset */
+ (getiterfunc)matrix_iter, /* tp_iter */
+ 0, /* tp_iternext */
+ matrix_methods, /* tp_methods */
+ 0, /* tp_members */
+ matrix_getsets, /* tp_getset */
+ 0, /* tp_base */
+ 0, /* tp_dict */
+ 0, /* tp_descr_get */
+ 0, /* tp_descr_set */
+ 0, /* tp_dictoffset */
+ 0, /* tp_init */
+ 0, /* tp_alloc */
+ matrix_new, /* tp_new */
+ 0, /* tp_free */
+};
+
+/**************************************************************************/
+
+static PyObject *
+matrix_add_generic(PyObject *self, PyObject *other, int inplace)
+{
+ if (!(Matrix_Check(self) || PY_NUMBER(self)) ||
+ !(Matrix_Check(other) || PY_NUMBER(other))) {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ int id_self = get_id(self, (Matrix_Check(self) ? 0 : 1));
+ int id_other = get_id(other, (Matrix_Check(other) ? 0 : 1));
+ int id = MAX(id_self,id_other);
+
+ if (inplace && (id != id_self || (MAT_LGT(self)==1 &&
+ (Matrix_Check(other) && MAT_LGT(other)!=1))))
+ PY_ERR_TYPE("invalid inplace operation");
+
+ /* first operand is a scalar */
+ if (PY_NUMBER(self) || (Matrix_Check(self) && MAT_LGT(self)==1))
+ {
+ number n;
+ if (!inplace) {
+ convert_num[id](&n,self,(Matrix_Check(self) ? 0 : 1),0);
+
+ matrix *ret = Matrix_NewFromMatrix((matrix *)other, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(ret), int1 = 1, int0 = 0;
+ axpy[id](&lgt, &One[id], &n, &int0, ret->buffer, &int1);
+ return (PyObject *)ret;
+ }
+ else {
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ int int1 = 1, int0 = 0;
+ axpy[id](&int1, &One[id], &n, &int0, MAT_BUF(self), &int1);
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+ /* second operand is a scalar */
+ else if (PY_NUMBER(other) || (Matrix_Check(other) &&
+ MAT_LGT(other)==1))
+ {
+ number n;
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(self), int1 = 1, int0 = 0;
+ axpy[id](&lgt, &One[id], &n, &int0, ret->buffer, &int1);
+
+ return (PyObject *)ret;
+ }
+ else {
+ int lgt = MAT_LGT(self), int1 = 1, int0 = 0;
+ axpy[id](&lgt, &One[id], &n, &int0, MAT_BUF(self), &int1);
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+ else { /* adding two matrices */
+ if (MAT_NROWS(self) != MAT_NROWS(other) ||
+ MAT_NCOLS(self) != MAT_NCOLS(other))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ void *other_coerce = convert_mtx_alloc((matrix *)other, id);
+ if (!other_coerce) return PyErr_NoMemory();
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(self), int1 = 1;
+ axpy[id](&lgt, &One[id], other_coerce, &int1, MAT_BUF(ret), &int1);
+
+ if (MAT_BUF(other) != other_coerce) { free(other_coerce); }
+ return (PyObject *)ret;
+ }
+ else {
+ int lgt = MAT_LGT(self), int1 = 1;
+ axpy[id](&lgt, &One[id], other_coerce, &int1, MAT_BUF(self), &int1);
+
+ if (MAT_BUF(other) != other_coerce) { free(other_coerce); }
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+}
+
+PyObject * matrix_add(PyObject *self, PyObject *other)
+{
+ return matrix_add_generic(self, other, 0);
+}
+
+static PyObject * matrix_iadd(PyObject *self,PyObject *other)
+{
+ return matrix_add_generic(self, other, 1);
+}
+
+static PyObject *
+matrix_sub_generic(PyObject *self, PyObject *other, int inplace)
+{
+ if (!(Matrix_Check(self) || PY_NUMBER(self)) ||
+ !(Matrix_Check(other) || PY_NUMBER(other))) {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ int id_self = get_id(self, (Matrix_Check(self) ? 0 : 1));
+ int id_other = get_id(other, (Matrix_Check(other) ? 0 : 1));
+ int id = MAX(id_self,id_other);
+
+ if (inplace && (id != id_self || (MAT_LGT(self)==1 &&
+ (Matrix_Check(other) && MAT_LGT(other)!=1))))
+ PY_ERR_TYPE("invalid inplace operation");
+
+ /* first operand is a scalar */
+ if (PY_NUMBER(self) || (Matrix_Check(self) && MAT_LGT(self)==1))
+ {
+
+ number n;
+ if (!inplace) {
+ convert_num[id](&n,self,(Matrix_Check(self) ? 0 : 1),0);
+
+ matrix *ret = Matrix_NewFromMatrix((matrix *)other, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(ret), int1 = 1, int0 = 0;
+ scal[id](&lgt, &MinusOne[id], ret->buffer, &int1);
+ axpy[id](&lgt, &One[id], &n, &int0, ret->buffer, &int1);
+ return (PyObject *)ret;
+ }
+ else {
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ int int1 = 1, int0 = 0;
+ axpy[id](&int1, &MinusOne[id], &n, &int0, MAT_BUF(self), &int1);
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+ /* second operand is a scalar */
+ else if (PY_NUMBER(other) || (Matrix_Check(other) && MAT_LGT(other)==1))
+ {
+ number n;
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(self), int1 = 1, int0 = 0;
+ axpy[id](&lgt, &MinusOne[id], &n, &int0, ret->buffer, &int1);
+
+ return (PyObject *)ret;
+ }
+ else {
+ int lgt = MAT_LGT(self), int1 = 1, int0 = 0;
+ axpy[id](&lgt, &MinusOne[id], &n, &int0, MAT_BUF(self), &int1);
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+ else { /* subtracting two matrices */
+ if (MAT_NROWS(self) != MAT_NROWS(other) ||
+ MAT_NCOLS(self) != MAT_NCOLS(other))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ void *other_coerce = convert_mtx_alloc((matrix *)other, id);
+ if (!other_coerce) return PyErr_NoMemory();
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(self), int1 = 1;
+ axpy[id](&lgt, &MinusOne[id], other_coerce, &int1, MAT_BUF(ret), &int1);
+
+ if (MAT_BUF(other) != other_coerce) { free(other_coerce); }
+ return (PyObject *)ret;
+ }
+ else {
+ int lgt = MAT_LGT(self), int1 = 1;
+ axpy[id](&lgt,&MinusOne[id],other_coerce,&int1,MAT_BUF(self),&int1);
+
+ if (MAT_BUF(other) != other_coerce) { free(other_coerce); }
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+}
+
+PyObject * matrix_sub(PyObject *self, PyObject *other)
+{
+ return matrix_sub_generic(self, other, 0);
+}
+
+static PyObject * matrix_isub(PyObject *self,PyObject *other)
+{
+ return matrix_sub_generic(self, other, 1);
+}
+
+static PyObject *
+matrix_mul_generic(PyObject *self, PyObject *other, int inplace)
+{
+
+ if (!(Matrix_Check(self) || PY_NUMBER(self)) ||
+ !(Matrix_Check(other) || PY_NUMBER(other))) {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ int id_self = get_id(self, (Matrix_Check(self) ? 0 : 1));
+ int id_other = get_id(other, (Matrix_Check(other) ? 0 : 1));
+ int id = MAX(id_self,id_other);
+
+ if (inplace && (id != id_self || (MAT_LGT(self)==1 &&
+ (Matrix_Check(other) && MAT_LGT(other)!=1)) ||
+ (MAT_LGT(self)>1 && (Matrix_Check(other) && MAT_LGT(other)>1))) )
+ PY_ERR_TYPE("invalid inplace operation");
+
+ /* first operand is a scalar */
+ if (PY_NUMBER(self) || (Matrix_Check(self) && MAT_LGT(self)==1))
+ {
+ number n;
+ if (!inplace) {
+ convert_num[id](&n,self,(Matrix_Check(self) ? 0 : 1),0);
+
+ matrix *ret = Matrix_NewFromMatrix((matrix *)other, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(ret), int1 = 1;
+ scal[id](&lgt, &n, ret->buffer, &int1);
+ return (PyObject *)ret;
+ }
+ else {
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ int int1 = 1;
+ scal[id](&int1, &n, MAT_BUF(self), &int1);
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+ /* second operand is a scalar */
+ else if (PY_NUMBER(other) || (Matrix_Check(other) &&
+ MAT_LGT(other)==1))
+ {
+ number n;
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(self), int1 = 1;
+ scal[id](&lgt, &n, ret->buffer, &int1);
+ return (PyObject *)ret;
+ }
+ else {
+ int lgt = MAT_LGT(self), int1 = 1;
+ scal[id](&lgt, &n, MAT_BUF(self), &int1);
+
+ Py_INCREF(self);
+ return self;
+ }
+ }
+ else { /* multiplying two matrices */
+ if (MAT_NCOLS(self) != MAT_NROWS(other))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ int m = MAT_NROWS(self), n = MAT_NCOLS(other), k = MAT_NCOLS(self);
+
+ int ldA = MAX(1,MAT_NROWS(self));
+ int ldB = MAX(1,MAT_NROWS(other));
+ int ldC = MAX(1,MAT_NROWS(self));
+ char transA='N', transB='N';
+
+ void *self_coerce = convert_mtx_alloc((matrix *)self, id);
+ if (!self_coerce) return PyErr_NoMemory();
+
+ void *other_coerce = convert_mtx_alloc((matrix *)other, id);
+ if (!other_coerce) {
+ if (MAT_ID(self) != id) { free(self_coerce); }
+ return PyErr_NoMemory();
+ }
+
+ matrix *c = Matrix_New(m, n, id);
+ if (!c) {
+ if (MAT_ID(self) != id) { free(self_coerce); }
+ if (MAT_ID(other) != id) { free(other_coerce); }
+ return PyErr_NoMemory();
+ }
+
+ gemm[id](&transA, &transB, &m, &n, &k, &One[id], self_coerce,
+ &ldA, other_coerce, &ldB, &Zero[id], MAT_BUF(c), &ldC);
+
+ if (MAT_ID(self) != id) { free(self_coerce); }
+ if (MAT_ID(other) != id) { free(other_coerce); }
+ return (PyObject *)c;
+ }
+}
+
+static PyObject * matrix_mul(PyObject *self, PyObject *other)
+{
+ return matrix_mul_generic(self, other, 0);
+}
+
+static PyObject * matrix_imul(PyObject *self,PyObject *other)
+{
+ return matrix_mul_generic(self, other, 1);
+}
+
+static PyObject *
+matrix_div_generic(PyObject *self, PyObject *other, int inplace)
+{
+ if (!((Matrix_Check(other) && MAT_LGT(other)==1) || PY_NUMBER(other))) {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ int id_self = get_id(self, (Matrix_Check(self) ? 0 : 1));
+ int id_other = get_id(other, (Matrix_Check(other) ? 0 : 1));
+ int id = MAX(id_self,id_other);
+
+ number n;
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(ret);
+ if (div_array[id](ret->buffer, n, lgt)) { Py_DECREF(ret); return NULL; }
+ return (PyObject *)ret;
+ }
+ else {
+ if (id != id_self) PY_ERR_TYPE("invalid inplace operation");
+
+ if (div_array[id](MAT_BUF(self), n, MAT_LGT(self)))
+ return NULL;
+
+ Py_INCREF(self);
+ return self;
+ }
+}
+
+static PyObject * matrix_div(PyObject *self, PyObject *other)
+{
+ return matrix_div_generic(self, other, 0);
+}
+
+static PyObject * matrix_idiv(PyObject *self,PyObject *other)
+{
+ return matrix_div_generic(self, other, 1);
+}
+
+static PyObject *
+matrix_rem_generic(PyObject *self, PyObject *other, int inplace)
+{
+ if (!((Matrix_Check(other) && MAT_LGT(other)==1) || PY_NUMBER(other))) {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ int id_self = get_id(self, (Matrix_Check(self) ? 0 : 1));
+ int id_other = get_id(other, (Matrix_Check(other) ? 0 : 1));
+ int id = MAX(id_self,id_other);
+
+ if (id == COMPLEX) PY_ERR(PyExc_NotImplementedError, "complex modulo");
+
+ number n;
+ convert_num[id](&n,other,(Matrix_Check(other) ? 0 : 1),0);
+
+ if (!inplace) {
+ matrix *ret = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!ret) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(ret);
+ if (mtx_rem[id](ret->buffer, n, lgt)) { Py_DECREF(ret); return NULL; }
+ return (PyObject *)ret;
+ }
+ else {
+ void *ptr = convert_mtx_alloc((matrix *)self, id);
+ if (!ptr) return PyErr_NoMemory();
+
+ int lgt = MAT_LGT(self);
+ if (mtx_rem[id](ptr,n,lgt)) { free(ptr); return NULL; }
+
+ free_convert_mtx_alloc(self, ptr, id);
+ Py_INCREF(self);
+ return self;
+ }
+}
+
+static PyObject * matrix_rem(PyObject *self, PyObject *other)
+{
+ return matrix_rem_generic(self, other, 0);
+}
+
+static PyObject * matrix_irem(PyObject *self, PyObject *other)
+{
+ return matrix_rem_generic(self, other, 1);
+}
+
+static PyObject * matrix_neg(matrix *self)
+{
+ matrix *x = Matrix_NewFromMatrix(self,self->id);
+ if (!x) return PyErr_NoMemory();
+
+ int n = MAT_LGT(x), int1 = 1;
+ scal[x->id](&n, &MinusOne[x->id], x->buffer, &int1);
+
+ return (PyObject *)x;
+}
+
+static PyObject * matrix_pos(matrix *self)
+{
+ matrix *x = Matrix_NewFromMatrix(self, self->id);
+ if (!x) return PyErr_NoMemory();
+
+ return (PyObject *)x;
+}
+
+static PyObject * matrix_abs(matrix *self)
+{
+ matrix *ret = Matrix_New(self->nrows, self->ncols,
+ (self->id == COMPLEX ? DOUBLE : self->id));
+
+ if (!ret) return PyErr_NoMemory();
+
+ mtx_abs[self->id](MAT_BUF(self), MAT_BUF(ret), MAT_LGT(self));
+ return (PyObject *)ret;
+}
+
+static PyObject * matrix_pow(PyObject *self, PyObject *other)
+{
+ if (!PY_NUMBER(other)) PY_ERR_TYPE("exponent must be a number");
+
+ number val;
+ int id = MAX(DOUBLE, MAX(MAT_ID(self), get_id(other, 1)));
+ convert_num[id](&val, other, 1, 0);
+ matrix *Y = Matrix_NewFromMatrix((matrix *)self, id);
+ if (!Y) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i<MAT_LGT(Y); i++) {
+ if (id == DOUBLE) {
+ if ((MAT_BUFD(Y)[i] == 0.0 && val.d < 0.0) ||
+ (MAT_BUFD(Y)[i] < 0.0 && val.d < 1.0 && val.d > 0.0)) {
+ Py_DECREF(Y);
+ PY_ERR(PyExc_ValueError, "domain error");
+ }
+
+
+ MAT_BUFD(Y)[i] = pow(MAT_BUFD(Y)[i], val.d);
+ } else {
+ if (MAT_BUFZ(Y)[i] == 0.0 && (cimag(val.z) != 0.0 || creal(val.z)<0.0)) {
+ Py_DECREF(Y);
+ PY_ERR(PyExc_ValueError, "domain error");
+ }
+ MAT_BUFZ(Y)[i] = cpow(MAT_BUFZ(Y)[i], val.z);
+ }
+ }
+
+ return (PyObject *)Y;
+}
+
+
+static PyNumberMethods matrix_as_number = {
+ (binaryfunc)matrix_add, /*nb_add*/
+ (binaryfunc)matrix_sub, /*nb_subtract*/
+ (binaryfunc)matrix_mul, /*nb_multiply*/
+ (binaryfunc)matrix_div, /*nb_divide*/
+ (binaryfunc)matrix_rem, /*nb_remainder*/
+ 0, /*nb_divmod*/
+ (ternaryfunc)matrix_pow, /*nb_power*/
+ (unaryfunc)matrix_neg, /*nb_negative*/
+ (unaryfunc)matrix_pos, /*nb_positive*/
+ (unaryfunc)matrix_abs, /*nb_absolute*/
+ 0, /*nb_nonzero*/
+ 0, /*nb_invert*/
+ 0, /*nb_lshift*/
+ 0, /*nb_rshift*/
+ 0, /*nb_and*/
+ 0, /*nb_xor*/
+ 0, /*nb_or*/
+ 0, /*nb_coerce*/
+ 0, /*nb_int*/
+ 0, /*nb_long*/
+ 0, /*nb_float*/
+ 0, /*nb_oct*/
+ 0, /*nb_hex*/
+ (binaryfunc)matrix_iadd,/*nb_inplace_add*/
+ (binaryfunc)matrix_isub,/*nb_inplace_subtract*/
+ (binaryfunc)matrix_imul,/*nb_inplace_multiply*/
+ (binaryfunc)matrix_idiv,/*nb_inplace_divide*/
+ (binaryfunc)matrix_irem,/*nb_inplace_remainder*/
+ 0, /*nb_inplace_power*/
+ 0, /*nb_inplace_lshift*/
+ 0, /*nb_inplace_rshift*/
+ 0, /*nb_inplace_and*/
+ 0, /*nb_inplace_xor*/
+ 0, /*nb_inplace_or*/
+ 0, /*nb_floor_divide*/
+ 0, /*nb_true_divide*/
+ 0, /*nb_inplace_floor_divide*/
+ 0, /*nb_inplace_true_divide*/
+};
+
+
+/*********************** Iterator **************************/
+
+typedef struct {
+ PyObject_HEAD
+ long index;
+ matrix *mObj;
+} matrixiter;
+
+static PyTypeObject matrixiter_tp;
+
+#define MatrixIter_Check(O) PyObject_TypeCheck(O, &matrixiter_tp)
+
+static PyObject *
+matrix_iter(matrix *obj)
+{
+ matrixiter *it;
+
+ if (!Matrix_Check(obj)) {
+ PyErr_BadInternalCall();
+ return NULL;
+ }
+
+ it = PyObject_GC_New(matrixiter, &matrixiter_tp);
+ if (!it) return NULL;
+
+ matrixiter_tp.tp_iter = PyObject_SelfIter;
+ matrixiter_tp.tp_getattro = PyObject_GenericGetAttr;
+
+ Py_INCREF(obj);
+ it->index = 0;
+ it->mObj = obj;
+ PyObject_GC_Track(it);
+
+ return (PyObject *)it;
+}
+
+static void
+matrixiter_dealloc(matrixiter *it)
+{
+ PyObject_GC_UnTrack(it);
+ Py_XDECREF(it->mObj);
+ PyObject_GC_Del(it);
+}
+
+static int
+matrixiter_traverse(matrixiter *it, visitproc visit, void *arg)
+{
+ if (it->mObj == NULL)
+ return 0;
+
+ return visit((PyObject *)(it->mObj), arg);
+}
+
+static PyObject *
+matrixiter_next(matrixiter *it)
+{
+ assert(MatrixIter_Check(it));
+ if (it->index >= MAT_LGT(it->mObj))
+ return NULL;
+
+ return num2PyObject[it->mObj->id](it->mObj->buffer, it->index++);
+}
+
+static PyTypeObject matrixiter_tp = {
+ PyObject_HEAD_INIT(NULL)
+ 0, /* ob_size */
+ "matrixiter", /* tp_name */
+ sizeof(matrixiter), /* tp_basicsize */
+ 0, /* tp_itemsize */
+ (destructor)matrixiter_dealloc, /* tp_dealloc */
+ 0, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ 0, /* tp_compare */
+ 0, /* tp_repr */
+ 0, /* tp_as_number */
+ 0, /* tp_as_sequence */
+ 0, /* tp_as_mapping */
+ 0, /* tp_hash */
+ 0, /* tp_call */
+ 0, /* tp_str */
+ 0, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,/* tp_flags */
+ 0, /* tp_doc */
+ (traverseproc)matrixiter_traverse, /* tp_traverse */
+ 0, /* tp_clear */
+ 0, /* tp_richcompare */
+ 0, /* tp_weaklistoffset */
+ 0, /* tp_iter */
+ (iternextfunc)matrixiter_next, /* tp_iternext */
+ 0, /* tp_methods */
+};
+
+
+
+PyObject * matrix_log(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A;
+
+ if (!PyArg_ParseTuple(args, "O", &A)) return NULL;
+
+ if (PyInt_Check(A) || PyFloat_Check(A)) {
+ double f = PyFloat_AsDouble(A);
+ if (f>0.0)
+ return Py_BuildValue("d",log(f));
+ else
+ PY_ERR(PyExc_ValueError, "domain error");
+ }
+ else if (PyComplex_Check(A)) {
+ number n;
+ convert_num[COMPLEX](&n, A, 1, 0);
+
+ if (n.z == 0) PY_ERR(PyExc_ValueError, "domain error");
+
+ n.z = clog(n.z);
+ return num2PyObject[COMPLEX](&n, 0);
+ }
+
+ else if (Matrix_Check(A) && (MAT_ID(A) == INT || MAT_ID(A) == DOUBLE)) {
+ if (MAT_LGT(A) == 0)
+ return (PyObject *)Matrix_New(MAT_NROWS(A),MAT_NCOLS(A),DOUBLE);
+
+ double val = (MAT_ID(A) == INT ? MAT_BUFI(A)[0] : MAT_BUFD(A)[0]);
+
+ int i;
+ for (i=1; i<MAT_LGT(A); i++) {
+ if (MAT_ID(A) == INT)
+ val = MIN(val,(MAT_BUFI(A)[i]));
+ else
+ val = MIN(val,(MAT_BUFD(A)[i]));
+ }
+
+ if (val > 0.0) {
+ matrix *ret = Matrix_New(MAT_NROWS(A), MAT_NCOLS(A), DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ for (i=0; i<MAT_LGT(A); i++)
+ MAT_BUFD(ret)[i] = log((MAT_ID(A)== INT ?
+ MAT_BUFI(A)[i] : MAT_BUFD(A)[i]));
+
+ return (PyObject *)ret;
+ }
+ else PY_ERR(PyExc_ValueError, "domain error");
+
+ }
+ else if (Matrix_Check(A) && MAT_ID(A) == COMPLEX) {
+ matrix *ret = Matrix_New(MAT_NROWS(A), MAT_NCOLS(A), COMPLEX);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i<MAT_LGT(A); i++) {
+ if (MAT_BUFZ(A)[i] == 0) {
+ Py_DECREF(ret);
+ PY_ERR(PyExc_ValueError, "domain error");
+ }
+ MAT_BUFZ(ret)[i] = clog(MAT_BUFZ(A)[i]);
+ }
+ return (PyObject *)ret;
+ }
+ else PY_ERR_TYPE("argument must a be a number or dense matrix");
+}
+
+PyObject * matrix_exp(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A;
+
+ if (!PyArg_ParseTuple(args, "O", &A)) return NULL;
+
+ if (PyInt_Check(A) || PyFloat_Check(A))
+ return Py_BuildValue("d",exp(PyFloat_AsDouble(A)));
+
+ else if (PyComplex_Check(A)) {
+ number n;
+ convert_num[COMPLEX](&n, A, 1, 0);
+ n.z = cexp(n.z);
+ return num2PyObject[COMPLEX](&n, 0);
+ }
+
+ else if (Matrix_Check(A)) {
+ matrix *ret = Matrix_New(MAT_NROWS(A),MAT_NCOLS(A),
+ (MAT_ID(A) == COMPLEX ? COMPLEX : DOUBLE));
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ if (MAT_ID(ret) == DOUBLE)
+ for (i=0; i<MAT_LGT(ret); i++)
+ MAT_BUFD(ret)[i] = exp(MAT_ID(A) == DOUBLE ? MAT_BUFD(A)[i] :
+ MAT_BUFI(A)[i]);
+ else
+ for (i=0; i<MAT_LGT(ret); i++)
+ MAT_BUFZ(ret)[i] = cexp(MAT_BUFZ(A)[i]);
+
+ return (PyObject *)ret;
+ }
+ else PY_ERR_TYPE("argument must a be a number or dense matrix");
+}
+
+PyObject * matrix_sqrt(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A;
+
+ if (!PyArg_ParseTuple(args, "O", &A)) return NULL;
+
+ if (PyInt_Check(A) || PyFloat_Check(A)) {
+ double f = PyFloat_AsDouble(A);
+ if (f >= 0.0)
+ return Py_BuildValue("d",sqrt(f));
+ else PY_ERR(PyExc_ValueError, "domain error");
+ }
+ else if (PyComplex_Check(A)) {
+ number n;
+ convert_num[COMPLEX](&n, A, 1, 0);
+ n.z = csqrt(n.z);
+ return num2PyObject[COMPLEX](&n, 0);
+ }
+ else if (Matrix_Check(A) && (MAT_ID(A) == INT || MAT_ID(A) == DOUBLE)) {
+ if (MAT_LGT(A) == 0)
+ return (PyObject *)Matrix_New(MAT_NROWS(A),MAT_NCOLS(A),DOUBLE);
+
+ double val = (MAT_ID(A) == INT ? MAT_BUFI(A)[0] : MAT_BUFD(A)[0]);
+
+ int i;
+ for (i=1; i<MAT_LGT(A); i++) {
+ if (MAT_ID(A) == INT)
+ val = MIN(val,(MAT_BUFI(A)[i]));
+ else
+ val = MIN(val,(MAT_BUFD(A)[i]));
+ }
+
+ if (val >= 0.0) {
+ matrix *ret = Matrix_New(MAT_NROWS(A), MAT_NCOLS(A), DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ for (i=0; i<MAT_LGT(A); i++)
+ MAT_BUFD(ret)[i] = sqrt((MAT_ID(A)== INT ?
+ MAT_BUFI(A)[i] : MAT_BUFD(A)[i]));
+
+ return (PyObject *)ret;
+
+ }
+ else PY_ERR(PyExc_ValueError, "domain error");
+ }
+ else if (Matrix_Check(A) && MAT_ID(A) == COMPLEX) {
+ matrix *ret = Matrix_New(MAT_NROWS(A), MAT_NCOLS(A), COMPLEX);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i<MAT_LGT(A); i++)
+ MAT_BUFZ(ret)[i] = csqrt(MAT_BUFZ(A)[i]);
+
+ return (PyObject *)ret;
+ }
+ else PY_ERR_TYPE("argument must a be a number or dense matrix");
+}
+
+PyObject * matrix_cos(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A;
+
+ if (!PyArg_ParseTuple(args, "O", &A)) return NULL;
+
+ if (PyInt_Check(A) || PyFloat_Check(A))
+ return Py_BuildValue("d",cos(PyFloat_AsDouble(A)));
+
+ else if (PyComplex_Check(A)) {
+ number n;
+ convert_num[COMPLEX](&n, A, 1, 0);
+ n.z = ccos(n.z);
+ return num2PyObject[COMPLEX](&n, 0);
+ }
+
+ else if (Matrix_Check(A)) {
+ matrix *ret = Matrix_New(MAT_NROWS(A),MAT_NCOLS(A),
+ (MAT_ID(A) == COMPLEX ? COMPLEX : DOUBLE));
+ if (!ret) return PyErr_NoMemory();
+
+ int_t i;
+ if (MAT_ID(ret) == DOUBLE)
+ for (i=0; i<MAT_LGT(ret); i++)
+ MAT_BUFD(ret)[i] = cos(MAT_ID(A) == DOUBLE ? MAT_BUFD(A)[i] :
+ MAT_BUFI(A)[i]);
+ else
+ for (i=0; i<MAT_LGT(ret); i++)
+ MAT_BUFZ(ret)[i] = ccos(MAT_BUFZ(A)[i]);
+
+ return (PyObject *)ret;
+ }
+ else PY_ERR_TYPE("argument must a be a number or dense matrix");
+}
+
+PyObject * matrix_sin(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ PyObject *A;
+
+ if (!PyArg_ParseTuple(args, "O", &A)) return NULL;
+
+ if (PyInt_Check(A) || PyFloat_Check(A))
+ return Py_BuildValue("d",sin(PyFloat_AsDouble(A)));
+
+ else if (PyComplex_Check(A)) {
+ number n;
+ convert_num[COMPLEX](&n, A, 1, 0);
+ n.z = csin(n.z);
+ return num2PyObject[COMPLEX](&n, 0);
+ }
+
+ else if (Matrix_Check(A)) {
+ matrix *ret = Matrix_New(MAT_NROWS(A),MAT_NCOLS(A),
+ (MAT_ID(A) == COMPLEX ? COMPLEX : DOUBLE));
+ if (!ret) return PyErr_NoMemory();
+
+ int_t i;
+ if (MAT_ID(ret) == DOUBLE)
+ for (i=0; i<MAT_LGT(ret); i++)
+ MAT_BUFD(ret)[i] = sin(MAT_ID(A) == DOUBLE ? MAT_BUFD(A)[i] :
+ MAT_BUFI(A)[i]);
+ else
+ for (i=0; i<MAT_LGT(ret); i++)
+ MAT_BUFZ(ret)[i] = csin(MAT_BUFZ(A)[i]);
+
+ return (PyObject *)ret;
+ }
+ else PY_ERR_TYPE("argument must a be a number or dense matrix");
+}
+
+PyObject * matrix_elem_mul(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+
+ if (!PyArg_ParseTuple(args, "OO", &A, &B)) return NULL;
+
+ if (!Matrix_Check(A) || !Matrix_Check(B) || MAT_ID(A) != MAT_ID(B))
+ PY_ERR_TYPE("arguments must be matrices of same type");
+
+ if (MAT_NROWS(A) != MAT_NROWS(B) || MAT_NCOLS(A) != MAT_NCOLS(B))
+ PY_ERR_TYPE("arguments must have same dimensions");
+
+ matrix *ret = Matrix_New(MAT_NROWS(A), MAT_NCOLS(A), MAT_ID(A));
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i<MAT_LGT(A); i++) {
+ switch (MAT_ID(A)) {
+ case INT: MAT_BUFI(ret)[i] = MAT_BUFI(A)[i]*MAT_BUFI(B)[i]; break;
+ case DOUBLE: MAT_BUFD(ret)[i] = MAT_BUFD(A)[i]*MAT_BUFD(B)[i]; break;
+ case COMPLEX: MAT_BUFZ(ret)[i] = MAT_BUFZ(A)[i]*MAT_BUFZ(B)[i]; break;
+ }
+ }
+
+ return (PyObject *)ret;
+}
+
+PyObject * matrix_elem_div(matrix *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+
+ if (!PyArg_ParseTuple(args, "OO", &A, &B)) return NULL;
+
+ if (!Matrix_Check(A) || !Matrix_Check(B) || MAT_ID(A) != MAT_ID(B))
+ PY_ERR_TYPE("arguments must be matrices of same type");
+
+ if (MAT_NROWS(A) != MAT_NROWS(B) || MAT_NCOLS(A) != MAT_NCOLS(B))
+ PY_ERR_TYPE("arguments must have same dimensions");
+
+ matrix *ret = Matrix_New(MAT_NROWS(A), MAT_NCOLS(A), MAT_ID(A));
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i<MAT_LGT(A); i++) {
+ switch (MAT_ID(A)) {
+ case INT:
+ if (MAT_BUFI(B)[i] == 0) goto divzero;
+ MAT_BUFI(ret)[i] = MAT_BUFI(A)[i]/MAT_BUFI(B)[i]; break;
+ case DOUBLE:
+ if (MAT_BUFD(B)[i] == 0.0) goto divzero;
+ MAT_BUFD(ret)[i] = MAT_BUFD(A)[i]/MAT_BUFD(B)[i]; break;
+ case COMPLEX:
+ if (MAT_BUFZ(B)[i] == 0.0) goto divzero;
+ MAT_BUFZ(ret)[i] = MAT_BUFZ(A)[i]/MAT_BUFZ(B)[i]; break;
+ }
+ }
+
+ return (PyObject *)ret;
+
+ divzero:
+ Py_DECREF(ret);
+ PY_ERR(PyExc_ArithmeticError, "division by zero");
+}
+
diff --git a/src/C/dsdp.c b/src/C/dsdp.c
new file mode 100644
index 0000000..0f120d9
--- /dev/null
+++ b/src/C/dsdp.c
@@ -0,0 +1,437 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "cvxopt.h"
+#include "misc.h"
+#include "dsdp5.h"
+#include "math.h"
+
+PyDoc_STRVAR(dsdp__doc__,"Interface to DSDP version 5.8.\n\n"
+ "Software for Semidefinite Programming.\n\n"
+ "Three control parameters can be modified by making an entry in \n"
+ "dictionary dsdp.options:\n"
+ " options['DSDP_Monitor']: set to k in order to show \n"
+ " progress after every kth iteration (default: 0). \n"
+ " options['DSDP_MaxIts']: maximum number of iterations\n"
+ " options['DSDP_GapTolerance']: the relative tolerance used\n"
+ " in the exit condition (default: 1e-5).\n\n"
+ "DSDSP is available from www-unix.mcs.anl.gov/DSDP.");
+
+static PyObject *dsdp_module;
+
+static char doc_dsdp[] =
+ "Solves a semidefinite program using DSDP.\n\n"
+ "(status, x, r, zl, zs) = sdp(c, Gl=None, hl=None, Gs=None, hs=None"
+ ",\n"
+ " gamma=1e8, beta=1e7)"
+ "\n\n"
+ "PURPOSE\n"
+ "Solves the SDP\n\n"
+ " minimize c'*x + gamma*r\n"
+ " subject to Gl*x <= hl + r\n"
+ " mat(Gs[k]*x) <= hs[k] + r*I, k=1,...,L\n"
+ " -beta <= x <= beta, r >= 0\n\n"
+ "and its dual\n\n"
+ " maximize -hl'*zl - sum_k tr(hs[k]*zs[k]) - beta*||zb||_1\n"
+ " subject to Gl'*zl + sum_k Gs[k]'*vec(zs[k]) + zb + c = 0\n"
+ " sum(zl) + sum_k tr(zs[k]) <= gamma \n"
+ " zl >= 0, zs[k] >=0, k=1,...,L. \n\n"
+ "For an mxm matrix y, vec(y) denotes the m^2-vector with the\n"
+ "entries of y stored columnwise. mat(y) is the inverse\n"
+ "operation.\n\n"
+ "ARGUMENTS\n"
+ "c n by 1 dense 'd' matrix\n\n"
+ "Gl ml by n dense or sparse 'd' matrixi. The default\n"
+ " value is a matrix with zero rows.\n\n"
+ "hl ml by 1 dense 'd' matrix. The default value is a\n"
+ " vector of length zero.\n\n"
+ "Gs list of L dense or sparse 'd' matrices. If the kth\n"
+ " linear matrix inequality has size mk, then Gs[k] is a\n"
+ " matrix of size mk**2 by n, and mat(Gs[k][:,i]) is the\n"
+ " coefficient of the ith variable i in inequality k.\n"
+ " Only the lower triangular entries in mat(Gs[k][:,i])\n"
+ " are accessed. The default value of Gs is an empty list."
+ "\n\n"
+ "hs list of L square dense 'd' matrices. hs[k] is the\n"
+ " righthand side in the kth linear matrix inequality.\n"
+ " Only the lower triangular entries of hs[k] are\n"
+ " accessed. The default value of hs is an empty list.\n\n"
+ "beta positive double\n\n"
+ "gamma positive double\n\n"
+ "status the DSDP solution status: 'DSDP_PDFEASIBLE', \n"
+ " 'DSDP_UNBOUNDED', 'DSDP_INFEASIBLE', or\n"
+ " 'DSDP_UNKNOWN'.\n\n"
+ "x the primal solution, as a dense 'd' matrix of size\n"
+ " n by 1\n\n"
+ "r the optimal value of the variable r\n\n"
+ "zl the dual solution as a dense 'd' matrix of size\n"
+ " ml by 1\n\n"
+ "zs the dual solution as a list of L square dense 'd'\n"
+ " matrices. Each matrix represents a symmetric matrix\n"
+ " in unpacked lower triangular format.";
+
+
+typedef struct { /* symmetric matrix X in DSDP packed storage */
+ int n; /* order of X */
+ char issparse;
+ double *val; /* lower triangular nonzeros of X. Stored in row
+ * major order as an n*(n+1)/2-array if X is dense,
+ * and in arbitrary order if X is sparse.*/
+ int *ind; /* NULL if X is dense; otherwise, the indices of
+ * the elements of val in the n*(n+1)/2 array of
+ * the lower triangular entries of X stored
+ * rowwise. */
+ int nnz; /* length of val */
+} dsdp_matrix;
+
+extern void dcopy_(int *n, double *x, int *incx, double *y, int *incy);
+
+static PyObject* solvesdp(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ matrix *c, *hl=NULL, *hk, *x=NULL, *zl=NULL, *zsk=NULL;
+ PyObject *Gl=NULL, *Gs=NULL, *hs=NULL, *Gk, *t=NULL, *zs=NULL,
+ *param, *key, *value;
+ int i, j, k, n, ml, l, mk, nnz, *lp_colptr=NULL, *lp_rowind=NULL,
+ incx, incy, lngth, maxm;
+ int_compat pos=0;
+ double *lp_values=NULL, *zlvals=NULL, *zk=NULL, r, beta=-1.0,
+ gamma=-1.0, tol;
+ dsdp_matrix **lmis=NULL;
+ div_t qr;
+ DSDP sdp;
+ LPCone lpcone;
+ SDPCone sdpcone;
+ DSDPTerminationReason info;
+ DSDPSolutionType status;
+ char *keystr, err_str[100];
+ char *kwlist[] = {"c", "Gl", "hl", "Gs", "hs", "gamma", "beta",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|OOOOdd", kwlist,
+ &c, &Gl, &hl, &Gs, &hs, &gamma, &beta)) return NULL;
+
+
+
+ if (!Matrix_Check(c) || MAT_NCOLS(c) != 1 || MAT_ID(c) != DOUBLE)
+ PY_ERR_TYPE("c must be a dense 'd' matrix with one column");
+ n = MAT_NROWS(c);
+
+ if (Gl && ((!Matrix_Check(Gl) && !SpMatrix_Check(Gl)) ||
+ X_NCOLS(Gl) != n || X_ID(Gl) != DOUBLE))
+ PY_ERR_TYPE("invalid type or dimensions for Gl");
+ ml = Gl ? X_NROWS(Gl) : 0;
+ if ((!hl && ml) || (hl && (!Matrix_Check(hl) || MAT_NCOLS(hl) != 1
+ || MAT_NROWS(hl) != ml || MAT_ID(hl) != DOUBLE)))
+ PY_ERR_TYPE("invalid type or dimensions for hl");
+
+ if (Gs && !PyList_Check(Gs)) PY_ERR_TYPE("Gs must be a list");
+ l = Gs ? PyList_Size(Gs) : 0;
+ if (hs && !PyList_Check(hs)) PY_ERR_TYPE("hs must be a list");
+ if ((!hs && l) || (hs && PyList_Size(hs) != l))
+ PY_ERR_TYPE("Gs and hs must be lists of equal length");
+ for (maxm=0, k=0; k<l; k++) {
+ Gk = PyList_GetItem(Gs, k);
+ hk = (matrix *) PyList_GetItem(hs, k);
+ if ((!Matrix_Check(Gk) && !SpMatrix_Check(Gk)) ||
+ X_ID(Gk) != DOUBLE)
+ PY_ERR_TYPE("Gs must be a list of 'd' matrices with n "
+ "columns");
+ if (!Matrix_Check(hk) || MAT_ID(hk) != DOUBLE ||
+ ((mk = MAT_NCOLS(hk)) != MAT_NROWS(hk)))
+ PY_ERR_TYPE("hs must be a list of square dense 'd' "
+ "matrices");
+ if (X_NROWS(Gk) != mk*mk || X_NCOLS(Gk) != n)
+ PY_ERR_TYPE("incompatible dimensions for elements of Gs");
+ maxm = MAX(mk, maxm);
+ }
+
+ if (DSDPCreate(n, &sdp) || DSDPCreateLPCone(sdp, &lpcone) ||
+ DSDPCreateSDPCone(sdp, l, &sdpcone)){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+
+ if (!(param = PyObject_GetAttrString(dsdp_module, "options")) ||
+ !PyDict_Check(param)){
+ PyErr_SetString(PyExc_AttributeError, "missing dsdp.options "
+ " dictionary");
+ t = NULL;
+ goto done;
+ }
+ while (PyDict_Next(param, &pos, &key, &value))
+ if ((keystr = PyString_AsString(key))){
+ if (!strcmp(keystr, "DSDP_Monitor")){
+ if (!PyInt_Check(value)) {
+ sprintf(err_str, "invalid value for integer "
+ "DSDP parameter: DSDP_Monitor");
+ PyErr_SetString(PyExc_ValueError, err_str);
+ t = NULL;
+ Py_DECREF(param);
+ goto done;
+ }
+ else
+ DSDPSetStandardMonitor(sdp, PyInt_AsLong(value));
+ }
+ if (!strcmp(keystr, "DSDP_MaxIts")){
+ if (!PyInt_Check(value) ||
+ (k = PyInt_AsLong(value)) < 0) {
+ sprintf(err_str, "invalid value for nonnegative "
+ "integer DSDP parameter: DSDP_MaxIts");
+ PyErr_SetString(PyExc_ValueError, err_str);
+ t = NULL;
+ Py_DECREF(param);
+ goto done;
+ }
+ else
+ DSDPSetMaxIts(sdp, k);
+ }
+ if (!strcmp(keystr, "DSDP_GapTolerance")){
+ if ((!PyFloat_Check(value) && !PyInt_Check(value)) ||
+ (tol = PyFloat_AsDouble(value)) <= 0.0) {
+ sprintf(err_str, "invalid value for float "
+ "DSDP parameter: DSDP_GapTolerance");
+ PyErr_SetString(PyExc_ValueError, err_str);
+ t = NULL;
+ Py_DECREF(param);
+ goto done;
+ }
+ else
+ DSDPSetGapTolerance(sdp, tol);
+ }
+ }
+ Py_DECREF(param);
+
+ if (gamma > 0) DSDPSetPenaltyParameter(sdp, gamma);
+ if (beta > 0) DSDPSetYBounds(sdp, -beta, beta);
+
+ /* cost function */
+ for (k=0; k<n; k++) DSDPSetDualObjective(sdp, k+1, -MAT_BUFD(c)[k]);
+
+ /* linear inequalities: store [Gl, hl] in CCS format */
+ nnz = ml ? ml + (Matrix_Check(Gl) ? ml*n : SP_NNZ(Gl)) : 0;
+ if (!(lp_colptr = (int *) calloc(n+2, sizeof(int))) ||
+ !(lp_rowind = (int *) calloc(nnz, sizeof(int))) ||
+ !(lp_values = (double *) calloc(nnz, sizeof(double)))){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ lp_colptr[0] = 0;
+ if (ml){
+ if (Matrix_Check(Gl)){
+ memcpy(lp_values, MAT_BUFD(Gl), ml*n*sizeof(double));
+ for (k=0; k<n; k++){
+ for (j=0; j<ml; j++) lp_rowind[ml*k+j] = j;
+ lp_colptr[k+1] = lp_colptr[k] + ml;
+ }
+ }
+ else {
+ memcpy(lp_values, SP_VALD(Gl), SP_NNZ(Gl)*sizeof(double));
+ for (k=0; k<n; k++){
+ for (j=SP_COL(Gl)[k]; j<SP_COL(Gl)[k+1]; j++)
+ lp_rowind[j] = (int) SP_ROW(Gl)[j];
+ lp_colptr[k+1] = lp_colptr[k] + (int) (SP_COL(Gl)[k+1] -
+ SP_COL(Gl)[k]);
+ }
+ }
+ memcpy(lp_values+lp_colptr[n], MAT_BUFD(hl), ml*sizeof(double));
+ for (k=0; k<ml; k++) lp_rowind[lp_colptr[n]+k] = k;
+ lp_colptr[n+1] = lp_colptr[n] + ml;
+ }
+ if (LPConeSetData2(lpcone, ml, lp_colptr, lp_rowind, lp_values)){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ /* LPConeView(lpcone); */
+
+ /* linear matrix inequalities: store mat(hs[k]), mat(Gs[k][:,i])
+ * as an lx(n+1) array of dsdp matrices. */
+ if (!(lmis = (dsdp_matrix **) calloc(l, sizeof(dsdp_matrix *)))){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ for (k=0; k<l; k++) lmis[k] = NULL;
+ for (k=0; k<l; k++){
+ Gk = PyList_GetItem(Gs, k);
+ hk = (matrix *) PyList_GetItem(hs, k);
+ if (!(lmis[k] = (dsdp_matrix *) calloc(n+1,
+ sizeof(dsdp_matrix)))){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+
+ /* lmis[k][0] is hs[k] as a dsdp matrix */
+ mk = MAT_NROWS(hk);
+ lmis[k][0].n = mk;
+ lmis[k][0].issparse = 0;
+ if (!(lmis[k][0].val = (double *) calloc(mk*(mk+1)/2,
+ sizeof(double)))){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ lmis[k][0].ind = NULL;
+ lmis[k][0].nnz = mk*(mk+1)/2;
+ for (j=0; j<mk; j++){
+ lngth = j+1; incx = mk; incy = 1;
+ dcopy_(&lngth, MAT_BUFD(hk)+j, &incx,
+ lmis[k][0].val+j*(j+1)/2, &incy);
+ }
+
+ /* lmis[k][i+1] is mat(Gs[k][i]) as a dsdp matrix */
+ for (i=0; i<n; i++){
+ lmis[k][i+1].n = mk;
+ if (Matrix_Check(Gk)){
+ lmis[k][i+1].issparse = 0;
+ if (!(lmis[k][i+1].val = (double *) calloc(mk*(mk+1)/2,
+ sizeof(double)))){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ lmis[k][i+1].ind = NULL;
+ lmis[k][i+1].nnz = mk*(mk+1)/2;
+ for (j=0; j<mk; j++){
+ lngth = j+1; incx = mk; incy = 1;
+ dcopy_(&lngth, MAT_BUFD(Gk)+i*mk*mk+j, &incx,
+ lmis[k][i+1].val+j*(j+1)/2, &incy);
+ }
+ } else {
+ lmis[k][i+1].issparse = 1;
+ /* nnz is number of lower triangular nonzeros in
+ * Gk[:,i] */
+ for (nnz=0, j=SP_COL(Gk)[i]; j<SP_COL(Gk)[i+1]; j++){
+ qr = div(SP_ROW(Gk)[j], mk);
+ if (qr.quot <= qr.rem) nnz++;
+ }
+ lmis[k][i+1].nnz = nnz;
+ if (!(lmis[k][i+1].val = (double *) calloc(nnz,
+ sizeof(double))) || !(lmis[k][i+1].ind = (int *)
+ calloc(nnz, sizeof(int)))){
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ /* lmis[k][i+1].val, lmis[k][i+1].ind are the lower
+ * triangular nonzeros/indices of Gk[:,i]. The indices
+ * refer to the postions in the lower triangular part
+ * stored in row major order as an mk*(mk+1)/2 array. */
+ for (nnz=0, j=SP_COL(Gk)[i]; j<SP_COL(Gk)[i+1]; j++){
+ qr = div(SP_ROW(Gk)[j], mk);
+ if (qr.quot <= qr.rem){
+ lmis[k][i+1].val[nnz] = SP_VALD(Gk)[j];
+ lmis[k][i+1].ind[nnz] = qr.rem*(qr.rem+1)/2 +
+ qr.quot;
+ nnz++;
+ }
+ }
+ }
+ }
+ }
+ for (k=0; k<l; k++) for(i=0; i<n+1; i++){
+ if (lmis[k][i].issparse){
+ SDPConeSetASparseVecMat(sdpcone, k, i, lmis[k][i].n, 1.0, 0,
+ lmis[k][i].ind, lmis[k][i].val, lmis[k][i].nnz);
+ }
+ else {
+ SDPConeSetADenseVecMat(sdpcone, k, i, lmis[k][i].n, 1.0,
+ lmis[k][i].val, lmis[k][i].nnz);
+ }
+ /* SDPConeViewDataMatrix(sdpcone, k, i); */
+ }
+
+ DSDPSetup(sdp);
+ if (DSDPSolve(sdp)){
+ PyErr_SetString(PyExc_ArithmeticError, "DSDP error");
+ t = NULL;
+ goto done;
+ }
+ DSDPStopReason(sdp, &info);
+ if (info != DSDP_CONVERGED){
+ PyErr_SetObject(PyExc_ArithmeticError, Py_BuildValue("i",info));
+ t = NULL;
+ goto done;
+ }
+
+ if (!(zs = PyList_New(l)) || !(x = (matrix *) Matrix_New(n, 1,
+ DOUBLE)) || !(zl = (matrix *) Matrix_New(ml, 1, DOUBLE)) ||
+ !(zk = (double *) calloc(maxm*(maxm+1)/2, sizeof(double))) ||
+ !(t = PyTuple_New(5))) {
+ Py_XDECREF(x); Py_XDECREF(zl); Py_XDECREF(zs); Py_XDECREF(t);
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ DSDPGetSolutionType(sdp, &status);
+
+ switch (status){
+ case DSDP_PDFEASIBLE:
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("DSDP_PDFEASIBLE"));
+ break;
+ case DSDP_UNBOUNDED:
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("DSDP_UNBOUNDED"));
+ break;
+ case DSDP_INFEASIBLE:
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("DSDP_INFEASIBLE"));
+ break;
+ case DSDP_PDUNKNOWN:
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("DSDP_UNKNOWN"));
+ break;
+ }
+
+ DSDPGetY(sdp, MAT_BUFD(x), n);
+ PyTuple_SET_ITEM(t, 1, (PyObject *) x);
+
+ DSDPGetR(sdp, &r);
+ PyTuple_SET_ITEM(t, 2, Py_BuildValue("d", r));
+
+ DSDPComputeX(sdp);
+ LPConeGetXArray(lpcone, &zlvals, &k);
+ memcpy(MAT_BUFD(zl), zlvals, ml*sizeof(double));
+ PyTuple_SET_ITEM(t, 3, (PyObject *) zl);
+
+ for (k=0; k<l; k++){
+ hk = (matrix *) PyList_GetItem(hs, k);
+ mk = MAT_NROWS(hk);
+ if (!(zsk = (matrix *) Matrix_New(mk, mk, DOUBLE))){
+ Py_XDECREF(x); Py_XDECREF(zl); Py_XDECREF(zs);
+ Py_XDECREF(t);
+ t = PyErr_NoMemory();
+ goto done;
+ }
+ SDPConeComputeX(sdpcone, k, mk, zk, maxm*(maxm+1)/2);
+ for (j=0; j<mk; j++){
+ lngth=j+1; incx=1; incy=mk;
+ dcopy_(&lngth, zk+j*(j+1)/2, &incx, MAT_BUFD(zsk)+j, &incy);
+ }
+ PyList_SetItem(zs, k, (PyObject *) zsk);
+ }
+ PyTuple_SET_ITEM(t, 4, (PyObject *) zs);
+
+ done:
+ free(lp_colptr); free(lp_rowind); free(lp_values); free(zk);
+ DSDPDestroy(sdp);
+ if (lmis) for (k=0; k<l; k++){
+ if (lmis[k]) for (i=0; i<n+1; i++){
+ if (lmis[k][i].issparse) free(lmis[k][i].ind);
+ free(lmis[k][i].val);
+ }
+ }
+ free(lmis);
+ return t;
+}
+
+static PyMethodDef dsdp_functions[] = {
+ {"sdp", (PyCFunction) solvesdp, METH_VARARGS|METH_KEYWORDS, doc_dsdp},
+ {NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC initdsdp(void)
+{
+ dsdp_module = Py_InitModule3("cvxopt.dsdp", dsdp_functions,
+ dsdp__doc__);
+ PyModule_AddObject(dsdp_module, "options", PyDict_New());
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/fftw.c b/src/C/fftw.c
new file mode 100644
index 0000000..65feadd
--- /dev/null
+++ b/src/C/fftw.c
@@ -0,0 +1,290 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "cvxopt.h"
+#include "misc.h"
+#include <fftw3.h>
+
+PyDoc_STRVAR(fftw__doc__,
+ "Interface to the FFTW3 library.\n");
+
+extern void zscal_(int *n, complex *alpha, complex *x, int *incx);
+extern void dscal_(int *n, double *alpha, double *x, int *incx);
+
+static char doc_dft[] =
+ "DFT of a matrix, X := dft(X)\n\n"
+ "PURPOSE\n"
+ "Computes the DFT of a dense matrix X column by column.\n\n"
+ "ARGUMENTS\n"
+ "X A dense matrix of typecode 'z'.";
+
+
+static PyObject *dft(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *X;
+ char *kwlist[] = {"X", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O", kwlist, &X))
+ return NULL;
+
+ if (!(Matrix_Check(X) && MAT_ID(X) == COMPLEX))
+ PY_ERR(PyExc_ValueError, "X must be a dense matrix with type 'z'");
+
+ int m = X->nrows, n = X->ncols;
+ if (m == 0) return Py_BuildValue("");
+
+ fftw_plan p = fftw_plan_many_dft(1, &m, n,
+ X->buffer, &m, 1, m,
+ X->buffer, &m, 1, m,
+ FFTW_FORWARD, FFTW_ESTIMATE);
+
+ fftw_execute(p);
+ fftw_destroy_plan(p);
+ return Py_BuildValue("");
+}
+
+static char doc_idft[] =
+ "IDFT of a matrix, X := idft(X)\n\n"
+ "PURPOSE\n"
+ "Computes the inverse DFT of a dense matrix X column by column.\n\n"
+ "ARGUMENTS\n"
+ "X A dense matrix of typecode 'z'.";
+
+static PyObject *idft(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *X;
+ char *kwlist[] = {"X", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O", kwlist, &X))
+ return NULL;
+
+ if (!(Matrix_Check(X) && MAT_ID(X) == COMPLEX))
+ PY_ERR(PyExc_ValueError, "X must be a dense matrix with type 'z'");
+
+ int m = X->nrows, n = X->ncols;
+ if (m == 0) return Py_BuildValue("");
+
+ fftw_plan p = fftw_plan_many_dft(1, &m, n,
+ X->buffer, &m, 1, m,
+ X->buffer, &m, 1, m,
+ FFTW_BACKWARD, FFTW_ESTIMATE);
+
+ fftw_execute(p);
+
+ number a;
+ a.z = 1.0/m;
+ int mn = m*n, ix = 1;
+ zscal_(&mn, &a.z, MAT_BUFZ(X), &ix);
+
+ fftw_destroy_plan(p);
+ return Py_BuildValue("");
+}
+
+static char doc_dct[] =
+ "DCT of a matrix.\n"
+ "X := dct(X, type=2)\n\n"
+ "PURPOSE\n"
+ "Computes the DCT of a dense matrix X column by column.\n\n"
+ "ARGUMENTS\n"
+ "X A dense matrix of typecode 'd'.\n\n"
+ "type integer from 1 to 4; chooses either DCT-I, DCT-II, \n"
+ " DCT-III or DCT-IV.";
+
+static PyObject *dct(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *X;
+ int type = 2;
+ char *kwlist[] = {"X", "type", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|i", kwlist, &X, &type))
+ return NULL;
+
+ if (!(Matrix_Check(X) && MAT_ID(X) == DOUBLE))
+ PY_ERR(PyExc_ValueError, "X must be a dense matrix with type 'd'");
+
+ int m = X->nrows, n = X->ncols;
+ if (m == 0) return Py_BuildValue("");
+
+ fftw_r2r_kind kind;
+ switch(type) {
+ case 1:
+ kind = FFTW_REDFT00;
+ if (m <= 1) PY_ERR(PyExc_ValueError, "m must be greater than 1 for DCT-I");
+ break;
+ case 2: kind = FFTW_REDFT10; break;
+ case 3: kind = FFTW_REDFT01; break;
+ case 4: kind = FFTW_REDFT11; break;
+ default: PY_ERR(PyExc_ValueError, "type must be between 1 and 4");
+ }
+ fftw_plan p = fftw_plan_many_r2r(1, &m, n,
+ X->buffer, &m, 1, m,
+ X->buffer, &m, 1, m,
+ &kind, FFTW_ESTIMATE);
+
+ fftw_execute(p);
+ fftw_destroy_plan(p);
+ return Py_BuildValue("");
+}
+
+static char doc_idct[] =
+ "IDCT of a matrix.\n"
+ "X := idct(X, type=2)\n\n"
+ "PURPOSE\n"
+ "Computes the IDCT of a dense matrix X column by column.\n\n"
+ "ARGUMENTS\n"
+ "X A dense matrix of typecode 'd'.\n\n"
+ "type integer from 1 to 4; chooses the inverse transform for\n"
+ " either DCT-I, DCT-II, DCT-III or DCT-IV.";
+
+static PyObject *idct(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *X;
+ int type = 2;
+ char *kwlist[] = {"X", "type", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|i", kwlist, &X, &type))
+ return NULL;
+
+ if (!(Matrix_Check(X) && MAT_ID(X) == DOUBLE))
+ PY_ERR(PyExc_ValueError, "X must be a dense matrix with type 'd'");
+
+ int m = X->nrows, n = X->ncols;
+ if (m == 0) return Py_BuildValue("");
+
+ fftw_r2r_kind kind;
+ switch(type) {
+ case 1: kind = FFTW_REDFT00;
+ if (m <= 1) PY_ERR(PyExc_ValueError, "m must be greater than 1 for DCT-I");
+ break;
+ case 2: kind = FFTW_REDFT01; break;
+ case 3: kind = FFTW_REDFT10; break;
+ case 4: kind = FFTW_REDFT11; break;
+ default: PY_ERR(PyExc_ValueError, "type must be between 1 and 4");
+ }
+ fftw_plan p = fftw_plan_many_r2r(1, &m, n,
+ X->buffer, &m, 1, m,
+ X->buffer, &m, 1, m,
+ &kind, FFTW_ESTIMATE);
+
+ fftw_execute(p);
+
+ double a = 1.0/(type == 1 ? MAX(1,2*(m-1)) : 2*m);
+ int mn = m*n, ix = 1;
+ dscal_(&mn, &a, MAT_BUFD(X), &ix);
+
+ fftw_destroy_plan(p);
+ return Py_BuildValue("");
+}
+
+static char doc_dst[] =
+ "DST of a matrix.\n"
+ "X := dst(X, type=1)\n\n"
+ "PURPOSE\n"
+ "Computes the DST of a dense matrix X column by column.\n\n"
+ "ARGUMENTS\n"
+ "X A dense matrix of typecode 'd'.\n\n"
+ "type integer from 1 to 4; chooses either DST-I, DST-II, \n"
+ " DST-III or DST-IV.";
+
+static PyObject *dst(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *X;
+ int type = 1;
+ char *kwlist[] = {"X", "type", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|i", kwlist, &X, &type))
+ return NULL;
+
+ if (!(Matrix_Check(X) && MAT_ID(X) == DOUBLE))
+ PY_ERR(PyExc_ValueError, "X must be a dense matrix with type 'd'");
+
+ int m = X->nrows, n = X->ncols;
+ if (m == 0) return Py_BuildValue("");
+
+ fftw_r2r_kind kind;
+ switch(type) {
+ case 1: kind = FFTW_RODFT00; break;
+ case 2: kind = FFTW_RODFT10; break;
+ case 3: kind = FFTW_RODFT01; break;
+ case 4: kind = FFTW_RODFT11; break;
+ default: PY_ERR(PyExc_ValueError, "type must be between 1 and 4");
+ }
+ fftw_plan p = fftw_plan_many_r2r(1, &m, n,
+ X->buffer, &m, 1, m,
+ X->buffer, &m, 1, m,
+ &kind, FFTW_ESTIMATE);
+
+ fftw_execute(p);
+ fftw_destroy_plan(p);
+ return Py_BuildValue("");
+}
+
+static char doc_idst[] =
+ "IDST of a matrix.\n"
+ "X := idst(X, type=1)\n\n"
+ "PURPOSE\n"
+ "Computes the IDST of a dense matrix X column by column.\n\n"
+ "ARGUMENTS\n"
+ "X A dense matrix of typecode 'd'.\n\n"
+ "type integer from 1 to 4; chooses the inverse transform for\n"
+ " either DST-I, DST-II, DST-III or DST-IV.";
+
+static PyObject *idst(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *X;
+ int type = 1;
+ char *kwlist[] = {"X", "type", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|i", kwlist, &X, &type))
+ return NULL;
+
+ if (!(Matrix_Check(X) && MAT_ID(X) == DOUBLE))
+ PY_ERR(PyExc_ValueError, "X must be a dense matrix with type 'd'");
+
+ int m = X->nrows, n = X->ncols;
+ if (m == 0) return Py_BuildValue("");
+
+ fftw_r2r_kind kind;
+ switch(type) {
+ case 1: kind = FFTW_RODFT00; break;
+ case 2: kind = FFTW_RODFT01; break;
+ case 3: kind = FFTW_RODFT10; break;
+ case 4: kind = FFTW_RODFT11; break;
+ default: PY_ERR(PyExc_ValueError, "type must be between 1 and 4");
+ }
+ fftw_plan p = fftw_plan_many_r2r(1, &m, n,
+ X->buffer, &m, 1, m,
+ X->buffer, &m, 1, m,
+ &kind, FFTW_ESTIMATE);
+
+ fftw_execute(p);
+
+ double a = 1.0/(type == 1 ? MAX(1,2*(m+1)) : 2*m);
+ int mn = m*n, ix = 1;
+ dscal_(&mn, &a, MAT_BUFD(X), &ix);
+
+ fftw_destroy_plan(p);
+ return Py_BuildValue("");
+}
+
+static PyMethodDef fftw_functions[] = {
+ {"dft", (PyCFunction) dft, METH_VARARGS|METH_KEYWORDS, doc_dft},
+ {"idft", (PyCFunction) idft, METH_VARARGS|METH_KEYWORDS, doc_idft},
+ {"dct", (PyCFunction) dct, METH_VARARGS|METH_KEYWORDS, doc_dct},
+ {"idct", (PyCFunction) idct, METH_VARARGS|METH_KEYWORDS, doc_idct},
+ {"dst", (PyCFunction) dst, METH_VARARGS|METH_KEYWORDS, doc_dst},
+ {"idst", (PyCFunction) idst, METH_VARARGS|METH_KEYWORDS, doc_idst},
+ {NULL} /* Sentinel */
+};
+
+
+PyMODINIT_FUNC initfftw(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("cvxopt.fftw", fftw_functions, fftw__doc__);
+
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/glpk.c b/src/C/glpk.c
new file mode 100644
index 0000000..d05dd31
--- /dev/null
+++ b/src/C/glpk.c
@@ -0,0 +1,358 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "cvxopt.h"
+#include "glpk.h"
+
+#define err_dbl_mtrx(s) {PyErr_SetString(PyExc_TypeError, \
+ s " must be a matrix with typecode 'd'"); \
+ return NULL;}
+
+#define err_p_int(s) {PyErr_SetString(PyExc_ValueError, \
+ s " must be a positive integer"); \
+ return NULL;}
+
+PyDoc_STRVAR(glpk__doc__,
+ "Interface to the simplex algorithm in GLPK.\n\n"
+ "The GLPK control parameters have the default values listed in \n"
+ "the GLPK documentation, except for 'LPX_K_PRESOL', which is set\n"
+ "to 1 and cannot be modified. The other parameters can be\n"
+ "modified by making an entry in the dictionary glpk.options.\n"
+ "For example, the command glpk.options['LPX_K_MSGLEV'] = 0 turns\n"
+ "off the printed output during execution of glpk.simplex().\n"
+ "See the documentation at www.gnu.org/software/glpk/glpk.html for\n"
+ "the list of GLPK control parameters and their default values.");
+
+static PyObject *glpk_module;
+
+typedef struct {
+ char name[20];
+ int idx;
+ char type;
+} param_tuple;
+
+static const param_tuple GLPK_PARAM_LIST[] = {
+ {"LPX_K_MSGLEV", 300, 'i'},
+ {"LPX_K_SCALE", 301, 'i'},
+ {"LPX_K_DUAL", 302, 'i'},
+ {"LPX_K_PRICE", 303, 'i'},
+ {"LPX_K_RELAX", 304, 'f'},
+ {"LPX_K_TOLBND", 305, 'f'},
+ {"LPX_K_TOLDJ", 306, 'f'},
+ {"LPX_K_TOLPIV", 307, 'f'},
+ {"LPX_K_ROUND", 308, 'i'},
+ {"LPX_K_OBJLL", 309, 'f'},
+ {"LPX_K_OBJUL", 310, 'f'},
+ {"LPX_K_ITLIM", 311, 'i'},
+ {"LPX_K_ITCNT", 312, 'i'},
+ {"LPX_K_TMLIM", 313, 'f'},
+ {"LPX_K_OUTFRQ", 314, 'i'},
+ {"LPX_K_OUTDLY", 315, 'f'},
+ {"LPX_K_BRANCH", 316, 'i'},
+ {"LPX_K_BTRACK", 317, 'i'},
+ {"LPX_K_TOLINT", 318, 'f'},
+ {"LPX_K_TOLOBJ", 319, 'f'},
+ {"LPX_K_MPSINFO",320, 'i'},
+ {"LPX_K_MPSOBJ", 321, 'i'},
+ {"LPX_K_MPSORIG",322, 'i'},
+ {"LPX_K_MPSWIDE",323, 'i'},
+ {"LPX_K_MPSFREE",324, 'i'},
+ {"LPX_K_MPSSKIP",325, 'i'},
+ {"LPX_K_LPTORIG",326, 'i'},
+ {"LPX_K_PRESOL", 327, 'i'}
+}; /* 28 paramaters */
+
+
+static int get_param_idx(char *str, int *idx, char *type)
+{
+ int i;
+
+ for (i=0; i<28; i++) {
+ if (!strcmp(GLPK_PARAM_LIST[i].name, str)) {
+ *idx = GLPK_PARAM_LIST[i].idx;
+ *type = GLPK_PARAM_LIST[i].type;
+ return 1;
+ }
+ }
+ return 0;
+}
+
+
+static char doc_simplex[] =
+ "Solves a linear program using GLPK.\n\n"
+ "(status, x, z, y) = solvelp(c, G, h, A, b)\n"
+ "(status, x, z) = solvelp(c, G, h)\n\n"
+ "PURPOSE\n"
+ "(status, x, z, y) = solvelp(c, G, h, A, b) solves the pair\n"
+ "of primal and dual LPs\n\n"
+ " minimize c'*x maximize -h'*z + b'*y\n"
+ " subject to G*x <= h subject to G'*z + A'*y + c = 0\n"
+ " A*x = b z >= 0.\n\n"
+ "(status, x, z) = solvelp(c, G, h) solves the pair of primal\n"
+ "and dual LPs\n\n"
+ " minimize c'*x maximize -h'*z \n"
+ " subject to G*x <= h subject to G'*z + c = 0\n"
+ " z >= 0.\n\n"
+ "ARGUMENTS\n"
+ "c nx1 dense 'd' matrix with n>=1\n\n"
+ "G mxn dense or sparse 'd' matrix with m>=1\n\n"
+ "h mx1 dense 'd' matrix\n\n"
+ "A pxn dense or sparse 'd' matrix with p>=0\n\n"
+ "b px1 dnese 'd' matrix\n\n"
+ "status 'optimal', 'primal infeasible', 'dual infeasible' \n"
+ " or 'unknown'\n\n"
+ "x if status is 'optimal', a primal optimal solution;\n"
+ " None otherwise\n\n"
+ "z,y if status is 'optimal', the dual optimal solution;\n"
+ " None otherwise";
+
+
+static PyObject *simplex(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ matrix *c, *h, *b=NULL, *x=NULL, *z=NULL, *y=NULL;
+ PyObject *G, *A=NULL, *t=NULL, *param, *key, *value;
+ LPX *lp;
+ int m, n, p, i, j, k, nnz, nnzmax, *rn=NULL, *cn=NULL, param_id;
+ int_compat pos=0;
+ double *a=NULL, val;
+ char param_type, err_str[100], *keystr;
+ char *kwlist[] = {"c", "G", "h", "A", "b", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|OO", kwlist, &c,
+ &G, &h, &A, &b)) return NULL;
+
+ if ((Matrix_Check(G) && MAT_ID(G) != DOUBLE) ||
+ (SpMatrix_Check(G) && SP_ID(G) != DOUBLE) ||
+ (!Matrix_Check(G) && !SpMatrix_Check(G))){
+ PyErr_SetString(PyExc_TypeError, "G must be a 'd' matrix");
+ return NULL;
+ }
+ if ((m = Matrix_Check(G) ? MAT_NROWS(G) : SP_NROWS(G)) <= 0)
+ err_p_int("m");
+ if ((n = Matrix_Check(G) ? MAT_NCOLS(G) : SP_NCOLS(G)) <= 0)
+ err_p_int("n");
+
+ if (!Matrix_Check(h) || h->id != DOUBLE) err_dbl_mtrx("h");
+ if (h->nrows != m || h->ncols != 1){
+ PyErr_SetString(PyExc_ValueError, "incompatible dimensions");
+ return NULL;
+ }
+
+ if (A){
+ if ((Matrix_Check(A) && MAT_ID(A) != DOUBLE) ||
+ (SpMatrix_Check(A) && SP_ID(A) != DOUBLE) ||
+ (!Matrix_Check(A) && !SpMatrix_Check(A))){
+ PyErr_SetString(PyExc_ValueError, "A must be a dense "
+ "'d' matrix or a general sparse matrix");
+ return NULL;
+ }
+ if ((p = Matrix_Check(A) ? MAT_NROWS(A) : SP_NROWS(A)) < 0)
+ err_p_int("p");
+ if ((Matrix_Check(A) ? MAT_NCOLS(A) : SP_NCOLS(A)) != n){
+ PyErr_SetString(PyExc_ValueError, "incompatible "
+ "dimensions");
+ return NULL;
+ }
+ }
+ else p = 0;
+
+ if (b && (!Matrix_Check(b) || b->id != DOUBLE)) err_dbl_mtrx("b");
+ if ((b && (b->nrows != p || b->ncols != 1)) || (!b && p !=0 )){
+ PyErr_SetString(PyExc_ValueError, "incompatible dimensions");
+ return NULL;
+ }
+
+ lp = lpx_create_prob();
+ lpx_add_rows(lp, m+p);
+ lpx_add_cols(lp, n);
+
+ for (i=0; i<n; i++){
+ lpx_set_obj_coef(lp, i+1, MAT_BUFD(c)[i]);
+ lpx_set_col_bnds(lp, i+1, LPX_FR, 0.0, 0.0);
+ }
+ for (i=0; i<m; i++)
+ lpx_set_row_bnds(lp, i+1, LPX_UP, 0.0, MAT_BUFD(h)[i]);
+ for (i=0; i<p; i++)
+ lpx_set_row_bnds(lp, i+m+1, LPX_FX, MAT_BUFD(b)[i],
+ MAT_BUFD(b)[i]);
+
+ nnzmax = (SpMatrix_Check(G) ? SP_NNZ(G) : m*n ) +
+ ((A && SpMatrix_Check(A)) ? SP_NNZ(A) : p*n);
+ a = (double *) calloc(nnzmax+1, sizeof(double));
+ rn = (int *) calloc(nnzmax+1, sizeof(int));
+ cn = (int *) calloc(nnzmax+1, sizeof(int));
+ if (!a || !rn || !cn){
+ free(a); free(rn); free(cn); lpx_delete_prob(lp);
+ return PyErr_NoMemory();
+ }
+
+ nnz = 0;
+ if (SpMatrix_Check(G)) {
+ for (j=0; j<n; j++) for (k=SP_COL(G)[j]; k<SP_COL(G)[j+1]; k++)
+ if ((val = SP_VALD(G)[k]) != 0.0){
+ a[1+nnz] = val;
+ rn[1+nnz] = SP_ROW(G)[k]+1;
+ cn[1+nnz] = j+1;
+ nnz++;
+ }
+ }
+ else for (j=0; j<n; j++) for (i=0; i<m; i++)
+ if ((val = MAT_BUFD(G)[i+j*m]) != 0.0){
+ a[1+nnz] = val;
+ rn[1+nnz] = i+1;
+ cn[1+nnz] = j+1;
+ nnz++;
+ }
+
+ if (A && SpMatrix_Check(A)){
+ for (j=0; j<n; j++) for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1]; k++)
+ if ((val = SP_VALD(A)[k]) != 0.0){
+ a[1+nnz] = val;
+ rn[1+nnz] = m+SP_ROW(A)[k]+1;
+ cn[1+nnz] = j+1;
+ nnz++;
+ }
+ }
+ else for (j=0; j<n; j++) for (i=0; i<p; i++)
+ if ((val = MAT_BUFD(A)[i+j*p]) != 0.0){
+ a[1+nnz] = val;
+ rn[1+nnz] = m+i+1;
+ cn[1+nnz] = j+1;
+ nnz++;
+ }
+
+ lpx_load_matrix(lp, nnz, rn, cn, a);
+ free(rn); free(cn); free(a);
+
+ if (!(t = PyTuple_New(A ? 4 : 3))){
+ lpx_delete_prob(lp);
+ return PyErr_NoMemory();
+ }
+
+ if (!(param = PyObject_GetAttrString(glpk_module, "options"))
+ || !PyDict_Check(param)){
+ lpx_delete_prob(lp);
+ PyErr_SetString(PyExc_AttributeError,
+ "missing glpk.options dictionary");
+ return NULL;
+ }
+
+ while (PyDict_Next(param, &pos, &key, &value))
+ if ((keystr = PyString_AsString(key)) && get_param_idx(keystr,
+ ¶m_id, ¶m_type)){
+ if (param_type == 'i'){
+ if (!PyInt_Check(value)){
+ sprintf(err_str, "invalid value for integer "
+ "GLPK parameter: %-.20s", keystr);
+ PyErr_SetString(PyExc_ValueError, err_str);
+ lpx_delete_prob(lp);
+ Py_DECREF(param);
+ return NULL;
+ }
+ if (!strcmp("LPX_K_PRESOL", keystr) &&
+ PyInt_AS_LONG(value) != 1){
+ PyErr_Warn(PyExc_UserWarning, "ignoring value of "
+ "GLPK parameter 'LPX_K_PRESOL'");
+ }
+ else lpx_set_int_parm(lp, param_id,
+ PyInt_AS_LONG(value));
+ }
+ else {
+ if (!PyInt_Check(value) && !PyFloat_Check(value)){
+ sprintf(err_str, "invalid value for floating point "
+ "GLPK parameter: %-.20s", keystr);
+ PyErr_SetString(PyExc_ValueError, err_str);
+ lpx_delete_prob(lp);
+ Py_DECREF(param);
+ return NULL;
+ }
+ lpx_set_real_parm(lp, param_id,
+ PyFloat_AsDouble(value));
+ }
+ }
+ lpx_set_int_parm(lp, LPX_K_PRESOL, 1);
+ Py_DECREF(param);
+
+ switch (lpx_simplex(lp)){
+
+ case LPX_E_OK:
+
+ x = (matrix *) Matrix_New(n,1,DOUBLE);
+ z = (matrix *) Matrix_New(m,1,DOUBLE);
+ if (A) y = (matrix *) Matrix_New(p,1,DOUBLE);
+ if (!x || !z || (A && !y)){
+ Py_XDECREF(x);
+ Py_XDECREF(z);
+ Py_XDECREF(y);
+ Py_XDECREF(t);
+ lpx_delete_prob(lp);
+ return PyErr_NoMemory();
+ }
+
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("optimal"));
+
+ for (i=0; i<n; i++)
+ MAT_BUFD(x)[i] = lpx_get_col_prim(lp, i+1);
+ PyTuple_SET_ITEM(t, 1, (PyObject *) x);
+
+ for (i=0; i<m; i++)
+ MAT_BUFD(z)[i] = -lpx_get_row_dual(lp, i+1);
+ PyTuple_SET_ITEM(t, 2, (PyObject *) z);
+
+ if (A){
+ for (i=0; i<p; i++)
+ MAT_BUFD(y)[i] = -lpx_get_row_dual(lp, m+i+1);
+ PyTuple_SET_ITEM(t, 3, (PyObject *) y);
+ }
+
+ lpx_delete_prob(lp);
+ return (PyObject *) t;
+
+ case LPX_E_NOPFS:
+
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("primal infeasible"));
+ break;
+
+ case LPX_E_NODFS:
+
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("dual infeasible"));
+ break;
+
+ default:
+
+ PyTuple_SET_ITEM(t, 0, (PyObject *)
+ PyString_FromString("unknown"));
+ }
+
+ lpx_delete_prob(lp);
+
+ PyTuple_SET_ITEM(t, 1, Py_BuildValue(""));
+ PyTuple_SET_ITEM(t, 2, Py_BuildValue(""));
+ if (A) PyTuple_SET_ITEM(t, 3, Py_BuildValue(""));
+
+ return (PyObject *) t;
+}
+
+
+static PyMethodDef glpk_functions[] = {
+ {"solvelp", (PyCFunction) simplex, METH_VARARGS|METH_KEYWORDS,
+ doc_simplex},
+ {NULL} /* Sentinel */
+};
+
+
+PyMODINIT_FUNC initglpk(void)
+{
+ glpk_module = Py_InitModule3("cvxopt.glpk", glpk_functions,
+ glpk__doc__);
+
+ PyModule_AddObject(glpk_module, "options", PyDict_New());
+
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/lapack.c b/src/C/lapack.c
new file mode 100644
index 0000000..469f694
--- /dev/null
+++ b/src/C/lapack.c
@@ -0,0 +1,5088 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "Python.h"
+#include "cvxopt.h"
+#include "misc.h"
+
+#define err_lapack { PyErr_SetObject( (info < 0) ? PyExc_ValueError :\
+ PyExc_ArithmeticError, Py_BuildValue("i",info) ); \
+ return NULL;}
+
+PyDoc_STRVAR(lapack__doc__, "Interface to the LAPACK library.\n\n"
+ "Double-precision real and complex LAPACK routines for solving\n"
+ "sets of linear equations, linear least-squares and least-norm\n"
+ "problems, symmetric and Hermitian eigenvalue problems, and \n"
+ "singular value decomposition.\n\n"
+ "For more details, see the LAPACK Users' Guide at \n"
+ "www.netlib.org/lapack/lug/lapack_lug.html.\n\n"
+ "Double and complex matrices and vectors are stored in CVXOPT \n"
+ "matrices using the conventional BLAS storage schemes, with the\n"
+ "CVXOPT matrix buffers interpreted as one-dimensional arrays.\n"
+ "For each matrix argument X, an additional integer argument offsetX\n"
+ "specifies the start of the array, i.e., the pointer \n"
+ "X->buffer + offsetX is passed to the LAPACK function. The other\n"
+ "arguments (dimensions and options) have the same meaning as in\n"
+ "the LAPACK definition. Default values of the dimension arguments\n"
+ "are derived from the CVXOPT matrix sizes.\n"
+ "If a routine from the LAPACK library returns with a positive \n"
+ "'info' value, an ArithmeticError is raised. If it returns with \n"
+ "a negative 'info' value, a ValueError is raised. In both cases\n"
+ "the value of 'info' is returned as an argument to the exception.");
+
+
+/* LAPACK prototypes */
+extern int ilaenv_(int *ispec, char **name, char **opts, int *n1,
+ int *n2, int *n3, int *n4);
+
+extern void dgetrf_(int *m, int *n, double *A, int *lda, int *ipiv,
+ int *info);
+extern void zgetrf_(int *m, int *n, complex *A, int *lda, int *ipiv,
+ int *info);
+extern void dgetrs_(char *trans, int *n, int *nrhs, double *A, int *lda,
+ int *ipiv, double *B, int *ldb, int *info);
+extern void zgetrs_(char *trans, int *n, int *nrhs, complex *A, int *lda,
+ int *ipiv, complex *B, int *ldb, int *info);
+extern void dgetri_(int *n, double *A, int *lda, int *ipiv, double *work,
+ int *lwork, int *info);
+extern void zgetri_(int *n, complex *A, int *lda, int *ipiv, complex *work,
+ int *lwork, int *info);
+extern void dgesv_(int *n, int *nrhs, double *A, int *lda, int *ipiv,
+ double *B, int *ldb, int *info);
+extern void zgesv_(int *n, int *nrhs, complex *A, int *lda, int *ipiv,
+ complex *B, int *ldb, int *info);
+
+extern void dgbtrf_(int *m, int *n, int *kl, int *ku, double *AB,
+ int *ldab, int *ipiv, int *info);
+extern void zgbtrf_(int *m, int *n, int *kl, int *ku, complex *AB,
+ int *ldab, int *ipiv, int *info);
+extern void dgbtrs_(char *trans, int *n, int *kl, int *ku, int *nrhs,
+ double *AB, int *ldab, int *ipiv, double *B, int *ldB, int *info);
+extern void zgbtrs_(char *trans, int *n, int *kl, int *ku, int *nrhs,
+ complex *AB, int *ldab, int *ipiv, complex *B, int *ldB, int *info);
+extern void dgbsv_(int *n, int *kl, int *ku, int *nrhs, double *ab,
+ int *ldab, int *ipiv, double *b, int *ldb, int *info);
+extern void zgbsv_(int *n, int *kl, int *ku, int *nrhs, complex *ab,
+ int *ldab, int *ipiv, complex *b, int *ldb, int *info);
+
+extern void dgttrf_(int *n, double *dl, double *d, double *du,
+ double *du2, int *ipiv, int *info);
+extern void zgttrf_(int *n, complex *dl, complex *d, complex *du,
+ complex *du2, int *ipiv, int *info);
+extern void dgttrs_(char *trans, int *n, int *nrhs, double *dl, double *d,
+ double *du, double *du2, int *ipiv, double *B, int *ldB, int *info);
+extern void zgttrs_(char *trans, int *n, int *nrhs, complex *dl,
+ complex *d, complex *du, complex *du2, int *ipiv, complex *B,
+ int *ldB, int *info);
+extern void dgtsv_(int *n, int *nrhs, double *dl, double *d, double *du,
+ double *B, int *ldB, int *info);
+extern void zgtsv_(int *n, int *nrhs, complex *dl, complex *d, complex *du,
+ complex *B, int *ldB, int *info);
+
+extern void dpotrf_(char *uplo, int *n, double *A, int *lda, int *info);
+extern void zpotrf_(char *uplo, int *n, complex *A, int *lda, int *info);
+extern void dpotrs_(char *uplo, int *n, int *nrhs, double *A, int *lda,
+ double *B, int *ldb, int *info);
+extern void zpotrs_(char *uplo, int *n, int *nrhs, complex *A, int *lda,
+ complex *B, int *ldb, int *info);
+extern void dpotri_(char *uplo, int *n, double *A, int *lda, int *info);
+extern void zpotri_(char *uplo, int *n, complex *A, int *lda, int *info);
+extern void dposv_(char *uplo, int *n, int *nrhs, double *A, int *lda,
+ double *B, int *ldb, int *info);
+extern void zposv_(char *uplo, int *n, int *nrhs, complex *A, int *lda,
+ complex *B, int *ldb, int *info);
+
+extern void dpbtrf_(char *uplo, int *n, int *kd, double *AB, int *ldab,
+ int *info);
+extern void zpbtrf_(char *uplo, int *n, int *kd, complex *AB, int *ldab,
+ int *info);
+extern void dpbtrs_(char *uplo, int *n, int *kd, int *nrhs, double *AB,
+ int *ldab, double *B, int *ldb, int *info);
+extern void zpbtrs_(char *uplo, int *n, int *kd, int *nrhs, complex *AB,
+ int *ldab, complex *B, int *ldb, int *info);
+extern void dpbsv_(char *uplo, int *n, int *kd, int *nrhs, double *A,
+ int *lda, double *B, int *ldb, int *info);
+extern void zpbsv_(char *uplo, int *n, int *kd, int *nrhs, complex *A,
+ int *lda, complex *B, int *ldb, int *info);
+
+extern void dpttrf_(int *n, double *d, double *e, int *info);
+extern void zpttrf_(int *n, double *d, complex *e, int *info);
+extern void dpttrs_(int *n, int *nrhs, double *d, double *e, double *B,
+ int *ldB, int *info);
+extern void zpttrs_(char *uplo, int *n, int *nrhs, double *d, complex *e,
+ complex *B, int *ldB, int *info);
+extern void dptsv_(int *n, int *nrhs, double *d, double *e, double *B,
+ int *ldB, int *info);
+extern void zptsv_(int *n, int *nrhs, double *d, complex *e, complex *B,
+ int *ldB, int *info);
+
+extern void dsytrf_(char *uplo, int *n, double *A, int *lda, int *ipiv,
+ double *work, int *lwork, int *info);
+extern void zsytrf_(char *uplo, int *n, complex *A, int *lda, int *ipiv,
+ complex *work, int *lwork, int *info);
+extern void zhetrf_(char *uplo, int *n, complex *A, int *lda, int *ipiv,
+ complex *work, int *lwork, int *info);
+extern void dsytrs_(char *uplo, int *n, int *nrhs, double *A, int *lda,
+ int *ipiv, double *B, int *ldb, int *info);
+extern void zsytrs_(char *uplo, int *n, int *nrhs, complex *A, int *lda,
+ int *ipiv, complex *B, int *ldb, int *info);
+extern void zhetrs_(char *uplo, int *n, int *nrhs, complex *A, int *lda,
+ int *ipiv, complex *B, int *ldb, int *info);
+extern void dsytri_(char *uplo, int *n, double *A, int *lda, int *ipiv,
+ double *work, int *info);
+extern void zsytri_(char *uplo, int *n, complex *A, int *lda, int *ipiv,
+ complex *work, int *info);
+extern void zhetri_(char *uplo, int *n, complex *A, int *lda, int *ipiv,
+ complex *work, int *info);
+extern void dsysv_(char *uplo, int *n, int *nrhs, double *A, int *lda,
+ int *ipiv, double *B, int *ldb, double *work, int *lwork,
+ int *info);
+extern void zsysv_(char *uplo, int *n, int *nrhs, complex *A, int *lda,
+ int *ipiv, complex *B, int *ldb, complex *work, int *lwork, int *info);
+extern void zhesv_(char *uplo, int *n, int *nrhs, complex *A, int *lda,
+ int *ipiv, complex *B, int *ldb, complex *work, int *lwork, int *info);
+
+extern void dtrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs,
+ double *a, int *lda, double *b, int *ldb, int *info);
+extern void ztrtrs_(char *uplo, char *trans, char *diag, int *n, int *nrhs,
+ complex *a, int *lda, complex *b, int *ldb, int *info);
+extern void dtrtri_(char *uplo, char *diag, int *n, double *a, int *lda,
+ int *info);
+extern void ztrtri_(char *uplo, char *diag, int *n, complex *a, int *lda,
+ int *info);
+extern void dtbtrs_(char *uplo, char *trans, char *diag, int *n, int *kd,
+ int *nrhs, double *ab, int *ldab, double *b, int *ldb, int *info);
+extern void ztbtrs_(char *uplo, char *trans, char *diag, int *n, int *kd,
+ int *nrhs, complex *ab, int *ldab, complex *b, int *ldb, int *info);
+
+extern void dgels_(char *trans, int *m, int *n, int *nrhs, double *a,
+ int *lda, double *b, int *ldb, double *work, int *lwork, int *info);
+extern void zgels_(char *trans, int *m, int *n, int *nrhs, complex *a,
+ int *lda, complex *b, int *ldb, complex *work, int *lwork, int *info);
+extern void dgeqrf_(int *m, int *n, double *a, int *lda, double *tau,
+ double *work, int *lwork, int *info);
+extern void zgeqrf_(int *m, int *n, complex *a, int *lda, complex *tau,
+ complex *work, int *lwork, int *info);
+extern void dormqr_(char *side, char *trans, int *m, int *n, int *k,
+ double *a, int *lda, double *tau, double *c, int *ldc, double *work,
+ int *lwork, int *info);
+extern void zunmqr_(char *side, char *trans, int *m, int *n, int *k,
+ complex *a, int *lda, complex *tau, complex *c, int *ldc,
+ complex *work, int *lwork, int *info);
+
+extern void dsyev_(char *jobz, char *uplo, int *n, double *A, int *lda,
+ double *W, double *work, int *lwork, int *info);
+extern void zheev_(char *jobz, char *uplo, int *n, complex *A, int *lda,
+ double *W, complex *work, int *lwork, double *rwork, int *info);
+extern void dsyevx_(char *jobz, char *range, char *uplo, int *n, double *A,
+ int *lda, double *vl, double *vu, int *il, int *iu, double *abstol,
+ int *m, double *W, double *Z, int *ldz, double *work, int *lwork,
+ int *iwork, int *ifail, int *info);
+extern void zheevx_(char *jobz, char *range, char *uplo, int *n,
+ complex *A, int *lda, double *vl, double *vu, int *il, int *iu,
+ double *abstol, int *m, double *W, complex *Z, int *ldz, complex *work,
+ int *lwork, double *rwork, int *iwork, int *ifail, int *info);
+extern void dsyevd_(char *jobz, char *uplo, int *n, double *A, int *ldA,
+ double *W, double *work, int *lwork, int *iwork, int *liwork,
+ int *info);
+extern void zheevd_(char *jobz, char *uplo, int *n, complex *A, int *ldA,
+ double *W, complex *work, int *lwork, double *rwork, int *lrwork,
+ int *iwork, int *liwork, int *info);
+extern void dsyevr_(char *jobz, char *range, char *uplo, int *n, double *A,
+ int *ldA, double *vl, double *vu, int *il, int *iu, double *abstol,
+ int *m, double *W, double *Z, int *ldZ, int *isuppz, double *work,
+ int *lwork, int *iwork, int *liwork, int *info);
+extern void zheevr_(char *jobz, char *range, char *uplo, int *n,
+ complex *A, int *ldA, double *vl, double *vu, int *il, int *iu,
+ double *abstol, int *m, double *W, complex *Z, int *ldZ, int *isuppz,
+ complex *work, int *lwork, double *rwork, int *lrwork, int *iwork,
+ int *liwork, int *info);
+
+extern void dsygv_(int *itype, char *jobz, char *uplo, int *n, double *A,
+ int *lda, double *B, int *ldb, double *W, double *work, int *lwork,
+ int *info);
+extern void zhegv_(int *itype, char *jobz, char *uplo, int *n, complex *A,
+ int *lda, complex *B, int *ldb, double *W, complex *work, int *lwork,
+ double *rwork, int *info);
+
+extern void dgesvd_(char *jobu, char *jobvt, int *m, int *n, double *A,
+ int *ldA, double *S, double *U, int *ldU, double *Vt, int *ldVt,
+ double *work, int *lwork, int *info);
+extern void dgesdd_(char *jobz, int *m, int *n, double *A, int *ldA,
+ double *S, double *U, int *ldU, double *Vt, int *ldVt, double *work,
+ int *lwork, int *iwork, int *info);
+extern void zgesvd_(char *jobu, char *jobvt, int *m, int *n, complex *A,
+ int *ldA, double *S, complex *U, int *ldU, complex *Vt, int *ldVt,
+ complex *work, int *lwork, double *rwork, int *info);
+extern void zgesdd_(char *jobz, int *m, int *n, complex *A, int *ldA,
+ double *S, complex *U, int *ldU, complex *Vt, int *ldVt, complex *work,
+ int *lwork, double *rwork, int *iwork, int *info);
+
+
+static char doc_getrf[] =
+ "LU factorization of a general real or complex m by n matrix.\n\n"
+ "getrf(A, ipiv, m=A.size[0], n=A.size[1], ldA=max(1,A.size[0]),\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "On exit, A is replaced with L, U in the factorization P*A = L*U\n"
+ "and ipiv contains the permutation:\n"
+ "P = P_min{m,n} * ... * P2 * P1 where Pi interchanges rows i and\n"
+ "ipiv[i] of A (using the Fortran convention, i.e., the first row\n"
+ "is numbered 1).\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix of length at least min(m,n)\n\n"
+ "m nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,m). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* getrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ int m=-1, n=-1, ldA=0, oA=0, info;
+ char *kwlist[] = {"A", "ipiv", "m", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiii", kwlist,
+ &A, &ipiv, &m, &n, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv ->id != INT) err_int_mtrx("ipiv");
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (len(ipiv) < MIN(n,m)) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(MIN(m,n)*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)) {
+ case DOUBLE:
+ dgetrf_(&m, &n, MAT_BUFD(A)+oA, &ldA, ipiv_ptr, &info);
+ break;
+
+ case COMPLEX:
+ zgetrf_(&m, &n, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int i; for (i=0; i<MIN(m,n); i++) MAT_BUFI(ipiv)[i] = ipiv_ptr[i];
+ free(ipiv_ptr);
+#endif
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_getrs[] =
+ "Solves a general real or complex set of linear equations,\n"
+ "given the LU factorization computed by getrf() or gesv().\n\n"
+ "getrs(A, ipiv, B, trans='N', n=A.size[0], nrhs=B.size[1],\n"
+ " ldA = max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X = B.\n"
+ "If trans is 'T', solves A^T*X = B.\n"
+ "If trans is 'C', solves A^H*X = B.\n"
+ "On entry, A and ipiv contain the LU factorization of an n by n\n"
+ "matrix A as computed by getrf() or gesv(). On exit B is replaced\n"
+ "by the solution X.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* getrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char trans='N';
+ char *kwlist[] = {"A", "ipiv", "B", "trans", "n", "nrhs", "ldA",
+ "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ciiiiii", kwlist,
+ &A, &ipiv, &B, &trans, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (trans == 'C') trans = 'T';
+ dgetrs_(&trans, &n, &nrhs, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zgetrs_(&trans, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_getri[] =
+ "Inverse of a real or complex matrix.\n\n"
+ "getri(A, ipiv, n=A.size[0], ldA = max(1,A.size[0]), offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes the inverse of real or complex matrix of order n. On\n"
+ "entry, A and ipiv contain the LU factorization, as returned by\n"
+ "gesv() or getrf(). On exit A is replaced by the inverse.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* getri(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ int n=-1, ldA=0, oA=0, info, lwork;
+ void *work;
+ number wl;
+ char *kwlist[] = {"A", "ipiv", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iii", kwlist, &A,
+ &ipiv, &n, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dgetri_(&n, NULL, &ldA, NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double)))) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ dgetri_(&n, MAT_BUFD(A)+oA, &ldA, ipiv_ptr, (double *) work,
+ &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zgetri_(&n, NULL, &ldA, NULL, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ zgetri_(&n, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ (complex *) work, &lwork, &info);
+ free(work);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gesv[] =
+ "Solves a general real or complex set of linear equations.\n\n"
+ "dgesv(A, B, ipiv=None, n=A.size[0], nrhs=B.size[1], \n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, \n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X=B with A n by n real or complex.\n"
+ "If ipiv is provided, then on exit A is overwritten with the details\n"
+ "of the LU factorization, and ipiv contains the permutation matrix.\n"
+ "If ipiv is not provided, then gesv() does not return the \n"
+ "factorization and does not modify A. On exit B is replaced with\n"
+ "the solution X.\n\n"
+ "ARGUMENTS.\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* gesv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv=NULL;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info, k;
+ void *Ac=NULL;
+ int *ipivc=NULL;
+ static char *kwlist[] = {"A", "B", "ipiv", "n", "nrhs", "ldA",
+ "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|Oiiiiii", kwlist,
+ &A, &B, &ipiv, &n, &nrhs, &ldA, &ldB, &oA, &oB)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (ipiv && (!Matrix_Check(ipiv) || ipiv->id != INT))
+ err_int_mtrx("ipiv");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (ipiv && len(ipiv) < n) err_buf_len("ipiv");
+
+ if (ipiv) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ if (!(ipivc = (int *) calloc(n, sizeof(int))))
+ return PyErr_NoMemory();
+#else
+ ipivc = MAT_BUFI(ipiv);
+#endif
+ }
+ else if (!(ipivc = (int *) calloc(n, sizeof(int))))
+ return PyErr_NoMemory();
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (ipiv)
+ dgesv_(&n, &nrhs, MAT_BUFD(A)+oA, &ldA, ipivc,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ else {
+ if (!(Ac = (void *) calloc(n*n, sizeof(double)))){
+ free(ipivc);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++) memcpy((double *) Ac + k*n,
+ MAT_BUFD(A)+oA+k*ldA, n*sizeof(double));
+ dgesv_(&n, &nrhs, (double *) Ac, &n, ipivc,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ free(Ac);
+ }
+ break;
+
+ case COMPLEX:
+ if (ipiv)
+ zgesv_(&n, &nrhs, MAT_BUFZ(A)+oA, &ldA, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ else {
+ if (!(Ac = (void *) calloc(n*n, sizeof(complex)))){
+ free(ipivc);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++) memcpy((complex *) Ac + k*n,
+ MAT_BUFZ(A)+oA+k*ldA, n*sizeof(complex));
+ zgesv_(&n, &nrhs, (complex *) Ac, &n, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ free(Ac);
+ }
+ break;
+
+ default:
+ if (ipiv){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipivc);
+#endif
+ }
+ else free(ipivc);
+ err_invalid_id;
+ }
+
+ if (ipiv){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ for (k=0; k<n; k++) MAT_BUFI(ipiv)[k] = ipivc[k];
+ free(ipivc);
+#endif
+ }
+ else free(ipivc);
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gbtrf[] =
+ "LU factorization of a real or complex m by n band matrix.\n\n"
+ "gbtrf(A, m, kl, ipiv, n=A.size[1], ku=A.size[0]-2*kl-1,\n"
+ " ldA=max(1,A.size[0]), offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes the LU factorization of an m by n band matrix with kl\n"
+ "subdiagonals and ku superdiagonals. On entry, the diagonals are\n"
+ "stored in rows kl+1 to 2*kl+ku+1 of the array A, in the BLAS format\n"
+ "for general band matrices. On exit A and ipiv contains the\n"
+ "factorization.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "m nonnegative integer\n\n"
+ "kl nonnegative integer.\n\n"
+ "ipiv 'i' matrix of length at least min(m,n)\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ku nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= 2*kl+ku+1. If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* gbtrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ int m, kl, n=-1, ku=-1, ldA=0, oA=0, info;
+ char *kwlist[] = {"A", "m", "kl", "ipiv", "n", "ku", "ldA", "offsetA",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OiiO|iiii", kwlist,
+ &A, &m, &kl, &ipiv, &n, &ku, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (m < 0) err_nn_int("m");
+ if (kl < 0) err_nn_int("kl");
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+ if (ku < 0) ku = A->nrows - 2*kl - 1;
+ if (ku < 0) err_nn_int("kl");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < 2*kl + ku + 1) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + 2*kl + ku + 1 > len(A)) err_buf_len("A");
+ if (!Matrix_Check(ipiv) || ipiv ->id != INT) err_int_mtrx("ipiv");
+ if (len(ipiv) < MIN(n,m)) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(MIN(m,n)*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)) {
+ case DOUBLE:
+ dgbtrf_(&m, &n, &kl, &ku, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ &info);
+ break;
+
+ case COMPLEX:
+ zgbtrf_(&m, &n, &kl, &ku, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int i; for (i=0; i<MIN(m,n); i++) MAT_BUFI(ipiv)[i] = ipiv_ptr[i];
+ free(ipiv_ptr);
+#endif
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gbtrs[] =
+ "Solves a real or complex set of linear equations with a banded\n"
+ "coefficient matrix, given the LU factorization computed by gbtrf()\n"
+ "or gbsv().\n\n"
+ "gbtrs(A, kl, ipiv, B, trans='N', n=A.size[1], ku=A.size[0]-2*kl-1,\n"
+ " nrhs=B.size[1], ldA=max(1,AB.size[0]), ldB=max(1,B.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X = B.\n"
+ "If trans is 'T', solves A^T*X = B.\n"
+ "If trans is 'C', solves A^H*X = B.\n"
+ "On entry, A and ipiv contain the LU factorization of an n by n\n"
+ "band matrix A as computed by getrf() or gbsv(). On exit B is\n"
+ "replaced by the solution X.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "kl nonnegative integer\n\n"
+ "ipiv 'i' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ku nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= 2*kl+ku+1. If zero, the\n"
+ " default value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* gbtrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv;
+ int kl, n=-1, ku=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char trans='N';
+ char *kwlist[] = {"A", "kl", "ipiv", "B", "trans", "n", "ku", "nrhs",
+ "ldA", "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OiOO|ciiiiiii", kwlist,
+ &A, &kl, &ipiv, &B, &trans, &n, &ku, &nrhs, &ldA, &ldB, &oA,
+ &oB)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (kl < 0) err_nn_int("kl");
+ if (ku < 0) ku = A->nrows - 2*kl - 1;
+ if (ku < 0) err_nn_int("kl");
+ if (n < 0) n = A->ncols;
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < 2*kl+ku+1) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + 2*kl + ku + 1 > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (trans == 'C') trans = 'T';
+ dgbtrs_(&trans, &n, &kl, &ku, &nrhs, MAT_BUFD(A)+oA, &ldA,
+ ipiv_ptr, MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zgbtrs_(&trans, &n, &kl, &ku, &nrhs, MAT_BUFZ(A)+oA, &ldA,
+ ipiv_ptr, MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gbsv[] =
+ "Solves a real or complex set of linear equations with a banded\n"
+ "coefficient matrix.\n\n"
+ "gbsv(A, kl, B, ipiv=None, ku=None, n=A.size[1], nrhs=B.size[1],\n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, \n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X=B with A an n by n real or complex band matrix with kl\n"
+ "subdiagonals and ku superdiagonals.\n"
+ "If ipiv is provided, then on entry the kl+ku+1 diagonals of the\n"
+ "matrix are stored in rows kl+1 to 2*kl+ku+1 of A, in the BLAS\n"
+ "format for general band matrices. On exit, A and ipiv contain the\n"
+ "details of the factorization. If ipiv is not provided, then on\n"
+ "entry the diagonals of the matrix are stored in rows 1 to kl+ku+1 \n"
+ "of A, and gbsv() does not return the factorization and does not\n"
+ "modify A. On exit B is replaced with solution X.\n\n"
+ "ARGUMENTS.\n"
+ "A 'd' or 'z' banded matrix\n\n"
+ "kl nonnegative integer\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "ku nonnegative integer. If negative, the default value is\n"
+ " used. The default value is A.size[0]-kl-1 if ipiv is\n"
+ " not provided, and A.size[0]-2*kl-1 otherwise.\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= kl+ku+1 if ipiv is not provided\n"
+ " and ldA >= 2*kl+ku+1 if ipiv is provided. If zero, the\n"
+ " default value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+
+static PyObject* gbsv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv=NULL;
+ void *Ac;
+ int kl, ku=-1, n=-1, nrhs=-1, ldA=0, oA=0, ldB=0, oB=0, info, k;
+ int *ipivc=NULL;
+ static char *kwlist[] = {"A", "kl", "B", "ipiv", "ku", "n", "nrhs",
+ "ldA", "ldB", "oA", "oB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OiO|Oiiiiiii", kwlist,
+ &A, &kl, &B, &ipiv, &ku, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (ipiv && (!Matrix_Check(ipiv) || ipiv->id != INT))
+ err_int_mtrx("ipiv");
+ if (n < 0) n = A->ncols;
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (kl < 0) err_nn_int("kl");
+ if (ku < 0) ku = A->nrows - kl - 1 - (ipiv ? kl : 0);
+ if (ku < 0) err_nn_int("ku");
+ if (ldA == 0) ldA = MAX(1, A->nrows);
+ if (ldA < ( ipiv ? 2*kl+ku+1 : kl+ku+1)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + (ipiv ? 2*kl+ku+1 : kl+ku+1) > len(A))
+ err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (ipiv && len(ipiv) < n) err_buf_len("ipiv");
+
+ if (ipiv) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ if (!(ipivc = (int *) calloc(n, sizeof(int))))
+ return PyErr_NoMemory();
+#else
+ ipivc = MAT_BUFI(ipiv);
+#endif
+ }
+ else if (!(ipivc = (int *) calloc(n, sizeof(int))))
+ return PyErr_NoMemory();
+
+ switch (MAT_ID(A)) {
+ case DOUBLE:
+ if (ipiv)
+ dgbsv_(&n, &kl, &ku, &nrhs, MAT_BUFD(A)+oA, &ldA, ipivc,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ else {
+ if (!(Ac = (void *) calloc((2*kl+ku+1)*n,
+ sizeof(double)))){
+ free(ipivc);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++)
+ memcpy((double *) Ac + kl + k*(2*kl+ku+1),
+ MAT_BUFD(A) + oA + k*ldA,
+ (kl+ku+1)*sizeof(double));
+ ldA = 2*kl+ku+1;
+ dgbsv_(&n, &kl, &ku, &nrhs, (double *) Ac, &ldA, ipivc,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ free(Ac);
+ }
+ break;
+
+ case COMPLEX:
+ if (ipiv)
+ zgbsv_(&n, &kl, &ku, &nrhs, MAT_BUFZ(A)+oA, &ldA, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ else {
+ if (!(Ac = (void *) calloc((2*kl+ku+1)*n,
+ sizeof(complex)))){
+ free(ipivc);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++)
+ memcpy((complex *) Ac + kl + k*(2*kl+ku+1),
+ MAT_BUFZ(A) + oA + k*ldA,
+ (kl+ku+1)*sizeof(complex));
+ ldA = 2*kl+ku+1;
+ zgbsv_(&n, &kl, &ku, &nrhs, (complex *) Ac, &ldA, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ free(Ac);
+ }
+ break;
+
+ default:
+ if (ipiv){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipivc);
+#endif
+ }
+ else free(ipivc);
+ err_invalid_id;
+ }
+
+ if (ipiv){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ for (k=0; k<n; k++) MAT_BUFI(ipiv)[k] = ipivc[k];
+ free(ipivc);
+#endif
+ }
+ else free(ipivc);
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gttrf[] =
+ "LU factorization of a real or complex tridiagonal matrix.\n\n"
+ "gttrf(dl, d, du, du2, ipiv, n=len(d)-offsetd, offsetdl=0, offsetd=0,"
+ "\n"
+ " offsetdu=0)\n\n"
+ "PURPOSE\n"
+ "Factors an n by n real or complex tridiagonal matrix A as A = P*L*U."
+ "\n A is specified by its lower diagonal dl, diagonal d, and upper\n"
+ "diagonal du. On exit dl, d, du, du2 and ipiv contain the details\n"
+ "of the factorization.\n\n"
+ "ARGUMENTS.\n"
+ "dl 'd' or 'z' matrix\n\n"
+ "d 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "du 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "du2 'd' or 'z' matrix of length at least n-2. Must have the\n"
+ " same type as dl.\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "offsetdl nonnegative integer\n\n"
+ "offsetd nonnegative integer\n\n"
+ "offsetdu nonnegative integer";
+
+static PyObject* gttrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *dl, *d, *du, *du2, *ipiv;
+ int n=-1, odl=0, od=0, odu=0, info;
+ static char *kwlist[] = {"dl", "d", "du", "du2", "ipiv", "n",
+ "offsetdl", "offsetd", "offsetdu", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOOOO|iiii", kwlist,
+ &dl, &d, &du, &du2, &ipiv, &n, &odl, &od, &odu))
+ return NULL;
+
+ if (!Matrix_Check(dl)) err_mtrx("dl");
+ if (!Matrix_Check(d)) err_mtrx("d");
+ if (!Matrix_Check(du)) err_mtrx("du");
+ if (!Matrix_Check(du2)) err_mtrx("du");
+ if ((MAT_ID(dl) != MAT_ID(d)) || (MAT_ID(dl) != MAT_ID(du)) ||
+ (MAT_ID(dl) != MAT_ID(du2))) err_conflicting_ids;
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (od < 0) err_nn_int("offsetd");
+ if (n < 0) n = len(d) - od;
+ if (n < 0) err_buf_len("d");
+ if (n == 0) return Py_BuildValue("");
+ if (odl < 0) err_nn_int("offsetdl");
+ if (odl + n - 1 > len(dl)) err_buf_len("dl");
+ if (od + n > len(d)) err_buf_len("d");
+ if (odu < 0) err_nn_int("offsetdu");
+ if (odu + n - 1 > len(du)) err_buf_len("du");
+ if (n - 2 > len(du2)) err_buf_len("du2");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+ if (n > len(ipiv)) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(dl)){
+ case DOUBLE:
+ dgttrf_(&n, MAT_BUFD(dl)+odl, MAT_BUFD(d)+od, MAT_BUFD(du)+odu,
+ MAT_BUFD(du2), ipiv_ptr, &info);
+ break;
+
+ case COMPLEX:
+ zgttrf_(&n, MAT_BUFZ(dl)+odl, MAT_BUFZ(d)+od, MAT_BUFZ(du)+odu,
+ MAT_BUFZ(du2), ipiv_ptr, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int i; for (i=0; i<n; i++) MAT_BUFI(ipiv)[i] = ipiv_ptr[i];
+ free(ipiv_ptr);
+#endif
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gttrs[] =
+ "Solves a real or complex tridiagonal set of linear equations, \n"
+ "given the LU factorization computed by gttrf().\n\n"
+ "gttrs(dl, d, du, du2, ipiv, B, trans='N', n=len(d)-offsetd,\n"
+ " nrhs=B.size[1], ldB=max(1,B.size[0]), offsetdl=0, offsetd=0,\n"
+ " offsetdu=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X=B.\n"
+ "If trans is 'T', solves A^T*X=B.\n"
+ "If trans is 'C', solves A^H*X=B.\n"
+ "On entry, dl, d, du, du2 and ipiv contain the LU factorization of \n"
+ "an n by n tridiagonal matrix A as computed by gttrf(). On exit B\n"
+ "is replaced by the solution X.\n\n"
+ "ARGUMENTS.\n"
+ "dl 'd' or 'z' matrix\n\n"
+ "d 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "du 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "du2 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "ipiv 'i' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type oas dl.\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetdl nonnegative integer\n\n"
+ "offsetd nonnegative integer\n\n"
+ "offsetdu nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* gttrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *dl, *d, *du, *du2, *ipiv, *B;
+ char trans='N';
+ int n=-1, nrhs=-1, ldB=0, odl=0, od=0, odu=0, oB=0, info;
+ static char *kwlist[] = {"dl", "d", "du", "du2", "ipiv", "B", "trans",
+ "n", "nrhs", "ldB", "offsetdl", "offsetd", "offsetdu", "offsetB",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOOOOO|ciiiiiii",
+ kwlist, &dl, &d, &du, &du2, &ipiv, &B, &trans, &n, &nrhs, &ldB,
+ &odl, &od, &odu, &oB)) return NULL;
+
+ if (!Matrix_Check(dl)) err_mtrx("dl");
+ if (!Matrix_Check(d)) err_mtrx("d");
+ if (!Matrix_Check(du)) err_mtrx("du");
+ if (!Matrix_Check(du2)) err_mtrx("du");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if ((MAT_ID(dl) != MAT_ID(d)) || (MAT_ID(dl) != MAT_ID(du)) ||
+ (MAT_ID(dl) != MAT_ID(du2)) || (MAT_ID(dl) != MAT_ID(B)))
+ err_conflicting_ids;
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (od < 0) err_nn_int("offsetd");
+ if (n < 0) n = len(d) - od;
+ if (n < 0) err_buf_len("d");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (odl < 0) err_nn_int("offsetdl");
+ if (odl + n - 1 > len(dl)) err_buf_len("dl");
+ if (od + n > len(d)) err_buf_len("d");
+ if (odu < 0) err_nn_int("offsetdu");
+ if (odu + n - 1 > len(du)) err_buf_len("du");
+ if (n - 2 > len(du2)) err_buf_len("du2");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (n > len(ipiv)) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(dl)){
+ case DOUBLE:
+ dgttrs_(&trans, &n, &nrhs, MAT_BUFD(dl)+odl, MAT_BUFD(d)+od,
+ MAT_BUFD(du)+odu, MAT_BUFD(du2), ipiv_ptr,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zgttrs_(&trans, &n, &nrhs, MAT_BUFZ(dl)+odl, MAT_BUFZ(d)+od,
+ MAT_BUFZ(du)+odu, MAT_BUFZ(du2), ipiv_ptr,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gtsv[] =
+ "Solves a real or complex set of linear equations with a tridiagonal\n"
+ "coefficient matrix.\n\n"
+ "gtsv(dl, d, du, B, n=len(d)-offsetd, nrhs=B.size[1], \n"
+ " ldB=max(1,B.size[0]), offsetdl=0, offsetd=0, offsetdu=0, \n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X=B with A n by n real or complex and tridiagonal.\n"
+ "A is specified by its lower diagonal dl, diagonal d and upper \n"
+ "diagonal du. On exit B is overwritten with the solution, and dl,\n"
+ "d, du are overwritten with the elements of the upper triangular\n"
+ "matrix in the LU factorization of A.\n\n"
+ "ARGUMENTS.\n"
+ "dl 'd' or 'z' matrix\n\n"
+ "d 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "du 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as dl.\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetdl nonnegative integer\n\n"
+ "offsetd nonnegative integer\n\n"
+ "offsetdu nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* gtsv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *dl, *d, *du, *B;
+ int n=-1, nrhs=-1, ldB=0, odl=0, od=0, odu=0, oB=0, info;
+ static char *kwlist[] = {"dl", "d", "du", "B", "n", "nrhs", "ldB",
+ "offsetdl", "offsetd", "offsetdu", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOOO|iiiiiii", kwlist,
+ &dl, &d, &du, &B, &n, &nrhs, &ldB, &odl, &od, &odu, &oB))
+ return NULL;
+
+ if (!Matrix_Check(dl)) err_mtrx("dl");
+ if (!Matrix_Check(d)) err_mtrx("d");
+ if (!Matrix_Check(du)) err_mtrx("du");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if ((MAT_ID(dl) != MAT_ID(B)) || (MAT_ID(dl) != MAT_ID(d)) ||
+ (MAT_ID(dl) != MAT_ID(du)) || (MAT_ID(dl) != MAT_ID(B)))
+ err_conflicting_ids;
+ if (od < 0) err_nn_int("offsetd");
+ if (n < 0) n = len(d) - od;
+ if (n < 0) err_buf_len("d");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (odl < 0) err_nn_int("offsetdl");
+ if (odl + n - 1 > len(dl)) err_buf_len("dl");
+ if (od + n > len(d)) err_buf_len("d");
+ if (odu < 0) err_nn_int("offsetdu");
+ if (odu + n - 1 > len(du)) err_buf_len("du");
+ if (oB < 0) err_nn_int("offsetB");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(dl)){
+ case DOUBLE:
+ dgtsv_(&n, &nrhs, MAT_BUFD(dl)+odl, MAT_BUFD(d)+od,
+ MAT_BUFD(du)+odu, MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zgtsv_(&n, &nrhs, MAT_BUFZ(dl)+odl, MAT_BUFZ(d)+od,
+ MAT_BUFZ(du)+odu, MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_potrf[] =
+ "Cholesky factorization of a real symmetric or complex Hermitian\n"
+ "positive definite matrix.\n\n"
+ "potrf(A, uplo='L', n=A.size[0], ldA = max(1,A.size[0]), offsetA=0)"
+ "\n\n"
+ "PURPOSE\n"
+ "Factors A as A=L*L^T or A = L*L^H, where A is n by n, real\n"
+ "symmetric or complex Hermitian, and positive definite.\n"
+ "On exit, if uplo='L', the lower triangular part of A is replaced\n"
+ "by L. If uplo='U', the upper triangular part is replaced by L^T\n"
+ "or L^H.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* potrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A;
+ int n=-1, ldA=0, oA=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "uplo", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|ciii", kwlist, &A,
+ &uplo, &n, &ldA, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A is not square");
+ return NULL;
+ }
+ }
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1, A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dpotrf_(&uplo, &n, MAT_BUFD(A)+oA, &ldA, &info);
+ break;
+
+ case COMPLEX:
+ zpotrf_(&uplo, &n, MAT_BUFZ(A)+oA, &ldA, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_potrs[] =
+ "Solves a real symmetric or complex Hermitian positive definite set\n"
+ "of linear equations, given the Cholesky factorization computed by\n"
+ "potrf() or posv().\n\n"
+ "potrs(A, B, uplo='L', n=A.size[0], nrhs=B.size[1],\n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B where A is n by n, real symmetric or complex\n"
+ "Hermitian and positive definite, and B is n by nrhs.\n"
+ "On entry, A contains the Cholesky factor, as returned by posv() or\n"
+ "potrf(). On exit B is replaced by the solution X.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* potrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "uplo", "n", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciiiiii", kwlist,
+ &A, &B, &uplo, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0) n = A->nrows;
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dpotrs_(&uplo, &n, &nrhs, MAT_BUFD(A)+oA, &ldA, MAT_BUFD(B)+oB,
+ &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zpotrs_(&uplo, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA, MAT_BUFZ(B)+oB,
+ &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_potri[] =
+ "Inverse of a real symmetric or complex Hermitian positive definite\n"
+ "matrix.\n\n"
+ "potri(A, uplo='L', n=A.size[0], ldA=max(1,A.size[0]), offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes the inverse of a real symmetric or complex Hermitian\n"
+ "positive definite matrix of order n. On entry, A contains the\n"
+ "Cholesky factor, as returned by posv() or potrf(). On exit it is\n"
+ "replaced by the inverse.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* potri(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A;
+ int n=-1, ldA=0, oA=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "uplo", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|ciii", kwlist,
+ &A, &uplo, &n, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0) n = A->nrows;
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dpotri_(&uplo, &n, MAT_BUFD(A)+oA, &ldA, &info);
+ break;
+
+ case COMPLEX:
+ zpotri_(&uplo, &n, MAT_BUFZ(A)+oA, &ldA, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_posv[] =
+ "Solves a real symmetric or complex Hermitian positive definite set\n"
+ "of linear equations.\n\n"
+ "posv(A, B, uplo='L', n=A.size[0], nrhs=B.size[1], \n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, \n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B with A n by n, real symmetric or complex Hermitian,\n"
+ "and positive definite, and B n by nrhs.\n"
+ "On exit, if uplo is 'L', the lower triangular part of A is\n"
+ "replaced by L. If uplo is 'U', the upper triangular part is\n"
+ "replaced by L^H. B is replaced by the solution.\n\n"
+ "ARGUMENTS.\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* posv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "uplo", "n", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciiiiii", kwlist,
+ &A, &B, &uplo, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0) n = A->nrows;
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dposv_(&uplo, &n, &nrhs, MAT_BUFD(A)+oA, &ldA, MAT_BUFD(B)+oB,
+ &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zposv_(&uplo, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA, MAT_BUFZ(B)+oB,
+ &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_pbtrf[] =
+ "Cholesky factorization of a real symmetric or complex Hermitian\n"
+ "positive definite band matrix.\n\n"
+ "pbtrf(A, uplo='L', n=A.size[1], kd=A.size[0]-1, ldA=max(1,A.size[0]),"
+ "\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Factors A as A=L*L^T or A = L*L^H, where A is an n by n real\n"
+ "symmetric or complex Hermitian positive definite band matrix with\n"
+ "kd subdiagonals and kd superdiagonals. A is stored in the BLAS \n"
+ "format for symmetric band matrices. On exit, A contains the\n"
+ "Cholesky factor in the BLAS format for triangular band matrices.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "kd nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= kd+1. If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* pbtrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A;
+ int n=-1, kd=-1, ldA=0, oA=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "uplo", "n", "kd", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|ciiii", kwlist, &A,
+ &uplo, &n, &kd, &ldA, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (n < 0) n = A->ncols;
+ if (n == 0) return Py_BuildValue("");
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (kd < 0) kd = A->nrows - 1;
+ if (kd < 0) err_nn_int("kd");
+ if (ldA == 0) ldA = MAX(1, A->nrows);
+ if (ldA < kd+1) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + kd + 1 > len(A)) err_buf_len("A");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dpbtrf_(&uplo, &n, &kd, MAT_BUFD(A)+oA, &ldA, &info);
+ break;
+
+ case COMPLEX:
+ zpbtrf_(&uplo, &n, &kd, MAT_BUFZ(A)+oA, &ldA, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_pbtrs[] =
+ "Solves a real symmetric or complex Hermitian positive definite set\n"
+ "of linear equations with a banded coefficient matrix, given the\n"
+ "Cholesky factorization computed by pbtrf() or pbsv().\n\n"
+ "pbtrs(A, B, uplo='L', n=A.size[1], kd=A.size[0]-1, nrhs=B.size[1],\n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B where A is an n by n real symmetric or complex \n"
+ "Hermitian positive definite band matrix with kd subdiagonals and kd\n"
+ "superdiagonals, and B is n by nrhs. A contains the Cholesky factor\n"
+ "of A, as returned by pbtrf() or pbtrs(). On exit, B is replaced by\n"
+ "the solution X.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix.\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "kd nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= kd+1. If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* pbtrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ int n=-1, kd=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "uplo", "n", "kd", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciiiiiii", kwlist,
+ &A, &B, &uplo, &n, &kd, &nrhs, &ldA, &ldB, &oA, oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (n < 0) n = A->ncols;
+ if (kd < 0) kd = A->nrows - 1;
+ if (kd < 0) err_nn_int("kd");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < kd+1) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + kd + 1 > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dpbtrs_(&uplo, &n, &kd, &nrhs, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zpbtrs_(&uplo, &n, &kd, &nrhs, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_pbsv[] =
+ "Solves a real symmetric or complex Hermitian positive definite set\n"
+ "of linear equations with a banded coefficient matrix.\n\n"
+ "pbsv(A, B, uplo='L', n=A.size[1], kd=A.size[0]-1, nrhs=B.size[1],\n"
+ " ldA=MAX(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B where A is an n by n real symmetric or complex\n"
+ "Hermitian positive definite band matrix with kd subdiagonals and kd\n"
+ "superdiagonals, and B is n by nrhs.\n"
+ "On entry, A contains A in the BLAS format for symmetric band\n"
+ "matrices. On exit, A is replaced with the Cholesky factors, stored\n"
+ "in the BLAS format for triangular band matrices. B is replaced\n"
+ "by the solution X.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix.\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "kd nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= kd+1. If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* pbsv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ int n=-1, kd=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "uplo", "n", "kd", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciiiiiii", kwlist,
+ &A, &B, &uplo, &n, &kd, &nrhs, &ldA, &ldB, &oA, oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'U' && uplo != 'L') err_char("uplo", "'L', 'U'");
+ if (n < 0) n = A->ncols;
+ if (kd < 0) kd = A->nrows - 1;
+ if (kd < 0) err_nn_int("kd");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < kd+1) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + kd + 1 > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dpbsv_(&uplo, &n, &kd, &nrhs, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zpbsv_(&uplo, &n, &kd, &nrhs, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_pttrf[] =
+ "Cholesky factorization of a real symmetric or complex Hermitian\n"
+ "positive definite tridiagonal matrix.\n\n"
+ "pttrf(d, e, n=len(d)-offsetd, offsetd=0, offsete=0)\n\n"
+ "PURPOSE\n"
+ "Factors A as A = L*D*L^T or A = L*D*L^H where A is n by n, real\n"
+ "symmetric or complex Hermitian, positive definite, and tridiagonal.\n"
+ "On entry, d is the subdiagonal of A and e is the diagonal. On \n"
+ "exit, d contains the diagonal of D and e contains the subdiagonal\n"
+ "of the unit bidiagonal matrix L.\n\n"
+ "ARGUMENTS.\n"
+ "d 'd' matrix\n\n"
+ "e 'd' or 'z' matrix.\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "offsetd nonnegative integer\n\n"
+ "offsete nonnegative integer";
+
+static PyObject* pttrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *d, *e;
+ int n=-1, od=0, oe=0, info;
+ static char *kwlist[] = {"d", "e", "n", "offsetd", "offsete", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iii", kwlist, &d,
+ &e, &n, &od, &oe)) return NULL;
+
+ if (!Matrix_Check(d)) err_mtrx("d");
+ if (MAT_ID(d) != DOUBLE) err_type("d");
+ if (!Matrix_Check(e)) err_mtrx("e");
+ if (od < 0) err_nn_int("offsetd");
+ if (n < 0) n = len(d) - od;
+ if (n < 0) err_buf_len("d");
+ if (od + n > len(d)) err_buf_len("d");
+ if (n == 0) return Py_BuildValue("");
+ if (oe < 0) err_nn_int("offsete");
+ if (oe + n - 1 > len(e)) err_buf_len("e");
+
+ switch (MAT_ID(e)){
+ case DOUBLE:
+ dpttrf_(&n, MAT_BUFD(d)+od, MAT_BUFD(e)+oe, &info);
+ break;
+
+ case COMPLEX:
+ zpttrf_(&n, MAT_BUFD(d)+od, MAT_BUFZ(e)+oe, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_pttrs[] =
+ "Solves a real symmetric or complex Hermitian positive definite set\n"
+ "of linear equations with a tridiagonal coefficient matrix, given \n"
+ "the factorization computed by pttrf().\n\n"
+ "pttrs(d, e, B, uplo='L', n=len(d)-offsetd, nrhs=B.size[1],\n"
+ " ldB=max(1,B.size[0], offsetd=0, offsete=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X=B with A n by n real or complex Hermitian positive\n"
+ "definite and tridiagonal, and B n by nrhs. On entry, d and e\n"
+ "contain the Cholesky factorization L*D*L^T or L*D*L^H, for example,\n"
+ "as returned by pttrf(). The argument d is the diagonal of the \n"
+ "diagonal matrix D. The argument uplo only matters in the complex\n"
+ "case. If uplo = 'L', then e is the subdiagonal of L. If uplo='U',\n"
+ "e is the superdiagonal of L^H. On exit B is overwritten with the\n"
+ "solution X. \n\n"
+ "ARGUMENTS.\n"
+ "d 'd' matrix\n\n"
+ "e 'd' or 'z' matrix.\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as e.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetd nonnegative integer\n\n"
+ "offsete nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* pttrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *d, *e, *B;
+ char uplo='L';
+ int n=-1, nrhs=-1, ldB=0, od=0, oe=0, oB=0, info;
+ static char *kwlist[] = {"d", "e", "B", "uplo", "n", "nrhs", "ldB",
+ "offsetd", "offsete", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ciiiiii", kwlist,
+ &d, &e, &B, &uplo, &n, &nrhs, &ldB, &od, &oe, &oB)) return NULL;
+
+ if (!Matrix_Check(d)) err_mtrx("d");
+ if (MAT_ID(d) != DOUBLE) err_type("d");
+ if (!Matrix_Check(e)) err_mtrx("e");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(e) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (od < 0) err_nn_int("offsetd");
+ if (n < 0) n = len(d) - od;
+ if (n < 0) err_buf_len("d");
+ if (od + n > len(d)) err_buf_len("d");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (oe < 0) err_nn_int("offsete");
+ if (oe + n - 1 > len(e)) err_buf_len("e");
+ if (oB < 0) err_nn_int("offsetB");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(e)){
+ case DOUBLE:
+ dpttrs_(&n, &nrhs, MAT_BUFD(d)+od, MAT_BUFD(e)+oe,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zpttrs_(&uplo, &n, &nrhs, MAT_BUFD(d)+od, MAT_BUFZ(e)+oe,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_ptsv[] =
+ "Solves a real symmetric or complex Hermitian positive definite set\n"
+ "of linear equations with a tridiagonal coefficient matrix.\n\n"
+ "ptsv(d, e, B, n=len(d)-offsetd, nrhs=B.size[1], ldB=max(1,B.size[0],"
+ "\n"
+ " offsetd=0, offsete=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X=B with A n by n real or complex Hermitian positive\n"
+ "definite and tridiagonal. A is specified by its diagonal d and\n"
+ "subdiagonal e. On exit B is overwritten with the solution, and d\n"
+ "and e are overwritten with the elements of Cholesky factorization\n"
+ "of A.\n\n"
+ "ARGUMENTS.\n"
+ "d 'd' matrix\n\n"
+ "e 'd' or 'z' matrix.\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as e.\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetd nonnegative integer\n\n"
+ "offsete nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* ptsv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *d, *e, *B;
+ int n=-1, nrhs=-1, ldB=0, od=0, oe=0, oB=0, info;
+ static char *kwlist[] = {"d", "e", "B", "n", "nrhs", "ldB", "offsetd",
+ "offsete", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|iiiiii", kwlist,
+ &d, &e, &B, &n, &nrhs, &ldB, &od, &oe, &oB)) return NULL;
+
+ if (!Matrix_Check(d)) err_mtrx("d");
+ if (MAT_ID(d) != DOUBLE) err_type("d");
+ if (!Matrix_Check(e)) err_mtrx("e");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(e) != MAT_ID(B)) err_conflicting_ids;
+ if (od < 0) err_nn_int("offsetd");
+ if (n < 0) n = len(d) - od;
+ if (n < 0) err_buf_len("d");
+ if (od + n > len(d)) err_buf_len("d");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (oe < 0) err_nn_int("offsete");
+ if (oe + n - 1 > len(e)) err_buf_len("e");
+ if (oB < 0) err_nn_int("offsetB");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(e)){
+ case DOUBLE:
+ dptsv_(&n, &nrhs, MAT_BUFD(d)+od, MAT_BUFD(e)+oe,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zptsv_(&n, &nrhs, MAT_BUFD(d)+od, MAT_BUFZ(e)+oe,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_sytrf[] =
+ "LDL^T factorization of a real or complex symmetric matrix.\n\n"
+ "sytrf(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]))\n\n"
+ "PURPOSE\n"
+ "Computes the LDL^T factorization of a real or complex symmetric\n"
+ "n by n matrix A. On exit, A and ipiv contain the details of the\n"
+ "factorization.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* sytrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ void *work;
+ number wl;
+ int n=-1, ldA=0, oA=0, info, lwork;
+ char uplo='L';
+ char *kwlist[] = {"A", "ipiv", "uplo", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciii", kwlist,
+ &A, &ipiv, &uplo, &n, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dsytrf_(&uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ dsytrf_(&uplo, &n, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ (double *) work, &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zsytrf_(&uplo, &n, NULL, &ldA, NULL, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ zsytrf_(&uplo, &n, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ (complex *) work, &lwork, &info);
+ free(work);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int i; for (i=0; i<n; i++) MAT_BUFI(ipiv)[i] = ipiv_ptr[i];
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_hetrf[] =
+ "LDL^H factorization of a real symmetric or complex Hermitian matrix."
+ "\n\n"
+ "hetrf(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]))\n\n"
+ "PURPOSE\n"
+ "Computes the LDL^H factorization of a real symmetric or complex\n"
+ "Hermitian n by n matrix A. On exit, A and ipiv contain the\n"
+ "details of the factorization.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* hetrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ void *work;
+ number wl;
+ int n=-1, ldA=0, oA=0, info, lwork;
+ char uplo='L';
+ char *kwlist[] = {"A", "ipiv", "uplo", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciii", kwlist,
+ &A, &ipiv, &uplo, &n, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dsytrf_(&uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ dsytrf_(&uplo, &n, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ (double *) work, &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zhetrf_(&uplo, &n, NULL, &ldA, NULL, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ zhetrf_(&uplo, &n, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ (complex *) work, &lwork, &info);
+ free(work);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int i; for (i=0; i<n; i++) MAT_BUFI(ipiv)[i] = ipiv_ptr[i];
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_sytrs[] =
+ "Solves a real or complex symmetric set of linear equations,\n"
+ "given the LDL^T factorization computed by sytrf() or sysv().\n\n"
+ "sytrs(A, ipiv, B, uplo='L', n=A.size[0], nrhs=B.size[1],\n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B where A is real or complex symmetric and n by n,\n"
+ "and B is n by nrhs. On entry, A and ipiv contain the\n"
+ "factorization of A as returned by sytrf() or sysv(). On exit, B is\n"
+ "replaced by the solution.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix \n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* sytrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "ipiv", "B", "uplo", "n", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ciiiiii", kwlist,
+ &A, &ipiv, &B, &uplo, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dsytrs_(&uplo, &n, &nrhs, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zsytrs_(&uplo, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_hetrs[] =
+ "Solves a real symmetric or complex Hermitian set of linear\n"
+ "equations, given the LDL^H factorization computed by hetrf() or "
+ "hesv().\n\n"
+ "hetrs(A, ipiv, B, uplo='L', n=A.size[0], nrhs=B.size[1],\n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B where A is real symmetric or complex Hermitian\n"
+ "and n by n, and B is n by nrhs. On entry, A and ipiv contain\n"
+ "the factorization of A as returned by hetrf or hesv. On exit, B\n"
+ "is replaced by the solution.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix \n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'U' or 'L'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* hetrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L';
+ char *kwlist[] = {"A", "ipiv", "B", "uplo", "n", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ciiiiii", kwlist,
+ &A, &ipiv, &B, &uplo, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dsytrs_(&uplo, &n, &nrhs, MAT_BUFD(A)+oA, &ldA,
+ ipiv_ptr, MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ zhetrs_(&uplo, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA,
+ ipiv_ptr, MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_sytri[] =
+ "Inverse of a real or complex symmetric matrix.\n\n"
+ "sytri(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]),\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes the inverse of a real or complex symmetric matrix of\n"
+ "order n. On entry, A and ipiv contain the LDL^T factorization,\n"
+ "as returned by sysv() or sytrf(). On exit A is replaced by the\n"
+ "inverse. \n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix \n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* sytri(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ int n=-1, ldA=0, oA=0, info;
+ char uplo='L';
+ void *work;
+ char *kwlist[] = {"A", "ipiv", "uplo", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciii", kwlist,
+ &A, &ipiv, &uplo, &n, &ldA, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!(work = (void *) calloc(n, sizeof(double)))) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ dsytri_(&uplo, &n, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ (double *) work, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ if (!(work = (void *) calloc(2*n, sizeof(complex)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ zsytri_(&uplo, &n, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ (complex *) work, &info);
+ free(work);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_hetri[] =
+ "Inverse of a real symmetric or complex Hermitian matrix.\n\n"
+ "hetri(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]),\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes the inverse of a real symmetric or complex Hermitian\n"
+ "matrix of order n. On entry, A and ipiv contain the LDL^T\n"
+ "factorization, as returned by hesv() or hetrf(). On exit A is\n"
+ "replaced by the inverse. \n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "ipiv 'i' matrix \n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* hetri(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *ipiv;
+ int n=-1, ldA=0, oA=0, info;
+ char uplo='L';
+ void *work;
+ char *kwlist[] = {"A", "ipiv", "uplo", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciii", kwlist,
+ &A, &ipiv, &uplo, &n, &ldA, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(ipiv) || ipiv->id != INT) err_int_mtrx("ipiv");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (len(ipiv) < n) err_buf_len("ipiv");
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ int *ipiv_ptr = malloc(n*sizeof(int));
+ if (!ipiv_ptr) return PyErr_NoMemory();
+ int i; for (i=0; i<n; i++) ipiv_ptr[i] = MAT_BUFI(ipiv)[i];
+#else
+ int *ipiv_ptr = MAT_BUFI(ipiv);
+#endif
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (!(work = (void *) calloc(n, sizeof(double)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ dsytri_(&uplo, &n, MAT_BUFD(A)+oA, &ldA, ipiv_ptr,
+ (double *) work, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ if (!(work = (void *) calloc(n, sizeof(complex)))){
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ return PyErr_NoMemory();
+ }
+ zhetri_(&uplo, &n, MAT_BUFZ(A)+oA, &ldA, ipiv_ptr,
+ (complex *) work, &info);
+ free(work);
+ break;
+
+ default:
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ err_invalid_id;
+ }
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+ free(ipiv_ptr);
+#endif
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_sysv[] =
+ "Solves a real or complex symmetric set of linear equations.\n\n"
+ "sysv(A, B, ipiv=None, uplo='L', n=A.size[0], nrhs=B.size[1],\n"
+ " ldA = max(1,A.size[0]), ldB = max(1,B.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X = B where A is real or complex symmetric and n by n.\n"
+ "If ipiv is provided, then on exit A and ipiv contain the details\n"
+ "of the LDL^T factorization of A. If ipiv is not provided, then\n"
+ "the factorization is not returned and A is not modified. On\n"
+ "exit, B contains the solution.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* sysv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv=NULL;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info, lwork, k,
+ *ipivc=NULL;
+ void *work=NULL, *Ac=NULL;
+ number wl;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "ipiv", "uplo", "n", "nrhs", "ldA",
+ "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|Ociiiiii", kwlist,
+ &A, &B, &ipiv, &uplo, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (ipiv && (!Matrix_Check(ipiv) || ipiv->id != INT))
+ err_int_mtrx("ipiv");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (ipiv && len(ipiv) < n) err_buf_len("ipiv");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dsytrf_(&uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ if (ipiv) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ if (!(ipivc = (int *) calloc(n, sizeof(int)))){
+ free(work);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++) ipivc[k] = MAT_BUFI(ipiv)[k];
+#else
+ ipivc = MAT_BUFI(ipiv);
+#endif
+ dsysv_(&uplo, &n, &nrhs, MAT_BUFD(A)+oA, &ldA, ipivc,
+ MAT_BUFD(B)+oB, &ldB, (double *) work, &lwork,
+ &info);
+#if (SIZEOF_INT < SIZEOF_LONG)
+ for (k=0; k<n; k++) MAT_BUFI(ipiv)[k] = ipivc[k];
+ free(ipivc);
+#endif
+ }
+ else {
+ ipivc = (int *) calloc(n, sizeof(int));
+ Ac = (void *) calloc(n*n, sizeof(double));
+ if (!ipivc || !Ac){
+ free(work); free(ipivc); free(Ac);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++)
+ memcpy((double *) Ac + k*n, MAT_BUFD(A) + oA + k*ldA,
+ n*sizeof(double));
+ dsysv_(&uplo, &n, &nrhs, (double *) Ac, &n, ipivc,
+ MAT_BUFD(B)+oB, &ldB, work, &lwork, &info);
+ free(ipivc); free(Ac);
+ }
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zsytrf_(&uplo, &n, NULL, &ldA, NULL, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex))))
+ return PyErr_NoMemory();
+ if (ipiv) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ if (!(ipivc = (int *) calloc(n, sizeof(int)))){
+ free(work);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++) ipivc[k] = MAT_BUFI(ipiv)[k];
+#else
+ ipivc = MAT_BUFI(ipiv);
+#endif
+ zsysv_(&uplo, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, (complex *) work, &lwork, &info);
+#if (SIZEOF_INT < SIZEOF_LONG)
+ for (k=0; k<n; k++) MAT_BUFI(ipiv)[k] = ipivc[k];
+ free(ipivc);
+#endif
+ }
+ else {
+ ipivc = (int *) calloc(n, sizeof(int));
+ Ac = (void *) calloc(n*n, sizeof(complex));
+ if (!ipivc || !Ac){
+ free(work); free(ipivc); free(Ac);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++)
+ memcpy((complex *) Ac + k*n, MAT_BUFZ(A) + oA + k*ldA,
+ n*sizeof(complex));
+ zsysv_(&uplo, &n, &nrhs, (complex *) Ac, &n, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, work, &lwork, &info);
+ free(ipivc); free(Ac);
+ }
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_hesv[] =
+ "Solves a real symmetric or complex Hermitian set of linear\n"
+ "equations.\n\n"
+ "herv(A, B, ipiv=None, uplo='L', n=A.size[0], nrhs=B.size[1],\n"
+ " ldA = max(1,A.size[0]), ldB = max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "Solves A*X=B where A is real symmetric or complex Hermitian and\n"
+ "n by n. If ipiv is provided, then on exit A and ipiv contain\n"
+ "the details of the LDL^H factorization of A. If ipiv is not\n"
+ "provided, then the factorization is not returned and A is not\n"
+ "modified. On exit, B contains the solution.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "ipiv 'i' matrix of length at least n\n\n"
+ "uplo 'U' or 'L'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* hesv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *ipiv=NULL;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info, lwork, k,
+ *ipivc=NULL;
+ void *work=NULL, *Ac=NULL;
+ number wl;
+ char uplo='L';
+ char *kwlist[] = {"A", "B", "ipiv", "uplo", "n", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|Ociiiiii", kwlist,
+ &A, &B, &ipiv, &uplo, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (ipiv && (!Matrix_Check(ipiv) || ipiv->id != INT))
+ err_int_mtrx("ipiv");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1, n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+ if (ipiv && len(ipiv) < n) err_buf_len("ipiv");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dsytrf_(&uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ if (ipiv) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ if (!(ipivc = (int *) calloc(n,sizeof(int)))){
+ free(work);
+ return PyErr_NoMemory();
+ }
+ int i; for (i=0; i<n; i++) ipivc[i] = MAT_BUFI(ipiv)[i];
+#else
+ ipivc = MAT_BUFI(ipiv);
+#endif
+ dsysv_(&uplo, &n, &nrhs, MAT_BUFD(A)+oA, &ldA, ipivc,
+ MAT_BUFD(B)+oB, &ldB, (double *) work, &lwork,
+ &info);
+#if (SIZEOF_INT < SIZEOF_LONG)
+ for (i=0; i<n; i++) MAT_BUFI(ipiv)[i] = ipivc[i];
+ free(ipivc);
+#endif
+ }
+ else {
+ ipivc = (int *) calloc(n, sizeof(int));
+ Ac = (void *) calloc(n*n, sizeof(double));
+ if (!ipivc || !Ac){
+ free(work); free(ipivc); free(Ac);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++)
+ memcpy((double *) Ac + k*n, MAT_BUFD(A) + oA + k*ldA,
+ n*sizeof(double));
+ dsysv_(&uplo, &n, &nrhs, (double *) Ac, &n, ipivc,
+ MAT_BUFD(B)+oB, &ldB, work, &lwork, &info);
+ free(ipivc); free(Ac);
+ }
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zhetrf_(&uplo, &n, NULL, &ldA, NULL, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex))))
+ return PyErr_NoMemory();
+ if (ipiv) {
+#if (SIZEOF_INT < SIZEOF_LONG)
+ if (!(ipivc = (int *) calloc(n,sizeof(int)))){
+ free(work);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++) ipivc[k] = MAT_BUFI(ipiv)[k];
+#else
+ ipivc = MAT_BUFI(ipiv);
+#endif
+ zhesv_(&uplo, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, (complex *) work, &lwork, &info);
+#if (SIZEOF_INT < SIZEOF_LONG)
+ for (k=0; k<n; k++) MAT_BUFI(ipiv)[k] = ipivc[k];
+ free(ipivc);
+#endif
+ }
+ else {
+ ipivc = (int *) calloc(n, sizeof(int));
+ Ac = (void *) calloc(n*n, sizeof(complex));
+ if (!ipivc || !Ac){
+ free(work); free(ipivc); free(Ac);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<n; k++)
+ memcpy((complex *) Ac + k*n, MAT_BUFZ(A) + oA + k*ldA,
+ n*sizeof(complex));
+ zhesv_(&uplo, &n, &nrhs, (complex *) Ac, &n, ipivc,
+ MAT_BUFZ(B)+oB, &ldB, work, &lwork, &info);
+ free(ipivc); free(Ac);
+ }
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_trtrs[] =
+ "Solution of a triangular set of equations with multiple righthand\n"
+ "sides.\n\n"
+ "trtrs(A, B, uplo='L', trans='N', diag='N', n=A.size[0],\n"
+ " nrhs=B.size[1], ldA=max(1,A.size[0]), ldB=max(1,B.size[0]),\n"
+ " offsetA=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X = B.\n"
+ "If trans is 'T', solves A^T*X = B.\n"
+ "If trans is 'C', solves A^H*X = B.\n"
+ "B is n by nrhs and A is triangular of order n.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* trtrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ int n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char uplo='L', trans='N', diag='N';
+ char *kwlist[] = {"A", "B", "uplo", "trans", "diag", "n", "nrhs",
+ "ldA", "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccciiiiii", kwlist,
+ &A, &B, &uplo, &trans, &diag, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (n < 0){
+ n = A->nrows;
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (trans == 'C') trans = 'T';
+ dtrtrs_(&uplo, &trans, &diag, &n, &nrhs, MAT_BUFD(A)+oA,
+ &ldA, MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ ztrtrs_(&uplo, &trans, &diag, &n, &nrhs, MAT_BUFZ(A)+oA,
+ &ldA, MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_trtri[] =
+ "Inverse of a triangular matrix.\n\n"
+ "trtri(A, uplo='L', diag='N', n=A.size[0], ldA=max(1,A.size[0]),\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "Computes the inverse of a triangular matrix of order n.\n"
+ "On exit, A is replaced with its inverse.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* trtri(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A;
+ int n=-1, ldA=0, oA=0, info;
+ char uplo='L', diag='N';
+ char *kwlist[] = {"A", "uplo", "diag", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "O|cciii", kwlist,
+ &A, &uplo, &diag, &n, &ldA, &oA)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (A->nrows != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ dtrtri_(&uplo, &diag, &n, MAT_BUFD(A)+oA, &ldA, &info);
+ break;
+
+ case COMPLEX:
+ ztrtri_(&uplo, &diag, &n, MAT_BUFZ(A)+oA, &ldA, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_tbtrs[] =
+ "Solution of a triangular set of equations with banded coefficient\n"
+ "matrix.\n\n"
+ "tbtrs(A, B, uplo='L', trans='N', diag='N', n=A.size[1], \n"
+ " kd=A.size[0]-1, nrhs=B.size[1], ldA=max(1,A.size[0]),\n"
+ " ldB=max(1,B.size[0]), offsetA=0, offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X = B.\n"
+ "If trans is 'T', solves A^T*X = B.\n"
+ "If trans is 'C', solves A^H*X = B.\n"
+ "B is n by nrhs and A is a triangular band matrix of order n with kd\n"
+ "subdiagonals (uplo is 'L') or superdiagonals (uplo is 'U').\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "diag 'N' or 'U'\n\n"
+ "n nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "kd nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "nrhs nonnegative integer. If negative, the default value is\n"
+ " used.\n\n"
+ "ldA positive integer. ldA >= kd+1. If zero, the default\n"
+ " value is used.\n\n"
+ "ldB positive integer. ldB >= max(1,n). If zero, the default\n"
+ " value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* tbtrs(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ char uplo='L', trans='N', diag='N';
+ int n=-1, kd=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info;
+ char *kwlist[] = {"A", "B", "uplo", "trans", "diag", "n", "kd", "nrhs",
+ "ldA", "ldB", "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccciiiiiii", kwlist,
+ &A, &B, &uplo, &trans, &diag, &n, &kd, &nrhs, &ldA, &ldB, &oA,
+ &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (diag != 'N' && diag != 'U') err_char("diag", "'N', 'U'");
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (n < 0) n = A->ncols;
+ if (kd < 0) kd = A->nrows - 1;
+ if (kd < 0) err_nn_int("kd");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < kd+1) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + kd + 1 > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > len(B)) err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (trans == 'C') trans = 'T';
+ dtbtrs_(&uplo, &trans, &diag, &n, &kd, &nrhs, MAT_BUFD(A)+oA,
+ &ldA, MAT_BUFD(B)+oB, &ldB, &info);
+ break;
+
+ case COMPLEX:
+ ztbtrs_(&uplo, &trans, &diag, &n, &kd, &nrhs, MAT_BUFZ(A)+oA,
+ &ldA, MAT_BUFZ(B)+oB, &ldB, &info);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gels[] =
+ "Solves least-squares and least-norm problems with full rank\n"
+ "matrices.\n\n"
+ "gels(A, B, trans='N', m=A.size[0], n=A.size[1], nrhs=B.size[1],\n"
+ " ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "1. If trans is 'N' and A and B are real/complex:\n"
+ "- if m >= n: minimizes ||A*X - B||_F.\n"
+ "- if m < n: minimizes ||X||_F subject to A*X = B.\n\n"
+ "2. If trans is 'N' or 'C' and A and B are real:\n"
+ "- if m >= n: minimizes ||X||_F subject to A^T*X = B.\n"
+ "- if m < n: minimizes ||X||_F subject to A^T*X = B.\n\n"
+ "3. If trans is 'C' and A and B are complex:\n"
+ "- if m >= n: minimizes ||X||_F subject to A^H*X = B.\n"
+ "- if m < n: minimizes ||X||_F subject to A^H*X = B.\n\n"
+ "A is an m by n matrix. B has nrhs columns. On exit, B is\n"
+ "replaced with the solution, and A is replaced with the details\n"
+ "of its QR or LQ factorization.\n\n"
+ "Note that gels does not check whether A has full rank.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "trans 'N', 'T' or 'C' if A is real. 'N' or 'C' if A is\n"
+ " complex.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "nrhs integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m). If zero, the\n"
+ " default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,m,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* gels(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B;
+ int m=-1, n=-1, nrhs=-1, ldA=0, ldB=0, oA=0, oB=0, info, lwork;
+ void *work;
+ number wl;
+ char trans='N';
+ char *kwlist[] = {"A", "B", "trans", "m", "n", "nrhs", "ldA", "ldB",
+ "offsetA", "offsetB", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciiiiiii",
+ kwlist, &A, &B, &trans, &m, &n, &nrhs, &ldA, &ldB, &oA, &oB))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B)) err_mtrx("B");
+ if (MAT_ID(A) != MAT_ID(B)) err_conflicting_ids;
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (nrhs < 0) nrhs = B->ncols;
+ if (m == 0 || n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(MAX(1,n),m)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + ((trans == 'N') ? m : n) > len(B))
+ err_buf_len("B");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (trans == 'C') trans = 'T';
+ lwork = -1;
+ dgels_(&trans, &m, &n, &nrhs, NULL, &ldA, NULL, &ldB, &wl.d,
+ &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dgels_(&trans, &m, &n, &nrhs, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, (double *) work, &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ if (trans == 'T') err_char("trans", "'N', 'C'");
+ lwork = -1;
+ zgels_(&trans, &m, &n, &nrhs, NULL, &ldA, NULL, &ldB, &wl.z,
+ &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex))))
+ return PyErr_NoMemory();
+ zgels_(&trans, &m, &n, &nrhs, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, (complex *) work, &lwork, &info);
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_geqrf[] =
+ "QR factorization.\n\n"
+ "geqrf(A, tau, m=A.size[0], n=A.size[1], ldA=max(1,A.size[0]),\n"
+ " offsetA=0)\n\n"
+ "PURPOSE\n"
+ "QR factorization of an m by n real or complex matrix A:\n"
+ "A = Q*R = [Q1 Q2] * [R1; 0] if m >= n\n"
+ "A = Q*R = Q * [R1 R2] if m <= n,\n"
+ "where Q is m by m and orthogonal/unitary and R is m by n with R1\n"
+ "upper triangular. On exit, R is stored in the upper triangular\n"
+ "part of A. Q is stored as a product of k=min(m,n) elementary\n"
+ "reflectors. The parameters of the reflectors are stored in the\n"
+ "first k entries of tau and in the lower triangular part of the\n"
+ "first k columns of A.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "tau 'd' or 'z' matrix of length at least min(m,n). Must\n"
+ " have the same type as A.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer";
+
+static PyObject* geqrf(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *tau;
+ int m=-1, n=-1, ldA=0, oA=0, info, lwork;
+ void *work;
+ number wl;
+ char *kwlist[] = {"A", "tau", "m", "n", "ldA", "offsetA", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|iiii", kwlist,
+ &A, &tau, &m, &n, &ldA, &oA))
+ return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(tau)) err_mtrx("tau");
+ if (MAT_ID(A) != MAT_ID(tau)) err_conflicting_ids;
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (len(tau) < MIN(m,n)) err_buf_len("tau");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dgeqrf_(&m, &n, NULL, &ldA, NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dgeqrf_(&m, &n, MAT_BUFD(A)+oA, &ldA, MAT_BUFD(tau),
+ (double *) work, &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zgeqrf_(&m, &n, NULL, &ldA, NULL, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex))))
+ return PyErr_NoMemory();
+ zgeqrf_(&m, &n, MAT_BUFZ(A)+oA, &ldA, MAT_BUFZ(tau),
+ (complex *) work, &lwork, &info);
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_ormqr[] =
+ "Product with a real orthogonal matrix.\n\n"
+ "ormqr(A, tau, C, side='L', trans='N', m=C.size[0], n=C.size[1],\n"
+ " k=min(A.size), ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),\n"
+ " offsetA=0, offsetC=0)\n\n"
+ "PURPOSE\n"
+ "Computes\n"
+ "C := Q*C if side = 'L' and trans = 'N'.\n"
+ "C := Q^T*C if side = 'L' and trans = 'T'.\n"
+ "C := C*Q if side = 'R' and trans = 'N'.\n"
+ "C := C*Q^T if side = 'R' and trans = 'T'.\n"
+ "C is m by n and Q is a square orthogonal matrix computed by geqrf."
+ "\n"
+ "Q is defined as a product of k elementary reflectors, stored as\n"
+ "the first k columns of A and the first k entries of tau.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "tau 'd' matrix of length at least k\n\n"
+ "C 'd' matrix\n\n"
+ "side 'L' or 'R'\n\n"
+ "trans 'N' or 'T'\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "k integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m) if side = 'L'\n"
+ " and ldA >= max(1,n) if side = 'R'. If zero, the\n"
+ " default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,m). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* ormqr(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *tau, *C;
+ int m=-1, n=-1, k=-1, ldA=0, ldC=0, oA=0, oC=0, info, lwork;
+ void *work;
+ number wl;
+ char side='L', trans='N';
+ char *kwlist[] = {"A", "tau", "C", "side", "trans", "m", "n", "k",
+ "ldA", "ldC", "offsetA", "offsetC", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cciiiiiii",
+ kwlist, &A, &tau, &C, &side, &trans, &m, &n, &k, &ldA, &ldC,
+ &oA, &oC)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(tau)) err_mtrx("tau");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(tau) || MAT_ID(A) != MAT_ID(C))
+ err_conflicting_ids;
+ if (side != 'L' && side != 'R') err_char("side", "'L', 'R'");
+ if (trans != 'N' && trans != 'T') err_char("trans", "'N', 'T'");
+ if (m < 0) m = C->nrows;
+ if (n < 0) n = C->ncols;
+ if (k < 0) k = MIN(A->nrows, A->ncols);
+ if (m == 0 || n == 0 || k == 0) return Py_BuildValue("");
+ if (k > ((side == 'L') ? m : n)) err_ld("k");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < ((side == 'L') ? MAX(1,m) : MAX(1,n))) err_ld("ldA");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,m)) err_ld("ldC");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (k-1)*ldA + ((side == 'L' ) ? m : n) > len(A))
+ err_buf_len("A");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + m > len(C)) err_buf_len("C");
+ if (len(tau) < k) err_buf_len("tau");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dormqr_(&side, &trans, &m, &n, &k, NULL, &ldA, NULL, NULL,
+ &ldC, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dormqr_(&side, &trans, &m, &n, &k, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(tau), MAT_BUFD(C)+oC, &ldC, (double *) work,
+ &lwork, &info);
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_unmqr[] =
+ "Product with a real or complex orthogonal matrix.\n\n"
+ "ormqr(A, tau, C, side='L', trans='N', m=C.size[0], n=C.size[1],\n"
+ " k=min(A.size), ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),\n"
+ " offsetA=0, offsetC=0)\n\n"
+ "PURPOSE\n"
+ "Computes\n"
+ "C := Q*C if side = 'L' and trans = 'N'.\n"
+ "C := Q^T*C if side = 'L' and trans = 'T'.\n"
+ "C := Q^H*C if side = 'L' and trans = 'C'.\n"
+ "C := C*Q if side = 'R' and trans = 'N'.\n"
+ "C := C*Q^T if side = 'R' and trans = 'T'.\n"
+ "C := C*Q^H if side = 'R' and trans = 'C'.\n"
+ "C is m by n and Q is a square orthogonal/unitary matrix computed\n"
+ "by geqrf. Q is defined as a product of k elementary reflectors,\n"
+ "stored as the first k columns of A and the first k entries of tau."
+ "\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "tau 'd' or 'z' matrix of length at least k. Must have the\n"
+ " same type as A.\n\n"
+ "C 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "side 'L' or 'R'\n\n"
+ "trans 'N', 'T' or 'C'n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "k integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m) if side = 'L'\n"
+ " and ldA >= max(1,n) if side = 'R'. If zero, the\n"
+ " default value is used.\n\n"
+ "ldC nonnegative integer. ldC >= max(1,m). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* unmqr(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *tau, *C;
+ int m=-1, n=-1, k=-1, ldA=0, ldC=0, oA=0, oC=0, info, lwork;
+ void *work;
+ number wl;
+ char side='L', trans='N';
+ char *kwlist[] = {"A", "tau", "C", "side", "trans", "m", "n", "k",
+ "ldA", "ldC", "offsetA", "offsetC", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|cciiiiiii",
+ kwlist, &A, &tau, &C, &side, &trans, &m, &n, &k, &ldA, &ldC,
+ &oA, &oC)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(tau)) err_mtrx("tau");
+ if (!Matrix_Check(C)) err_mtrx("C");
+ if (MAT_ID(A) != MAT_ID(tau) || MAT_ID(A) != MAT_ID(C))
+ err_conflicting_ids;
+ if (side != 'L' && side != 'R') err_char("side", "'L', 'R'");
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+ if (m < 0) m = C->nrows;
+ if (n < 0) n = C->ncols;
+ if (k < 0) k = MIN(A->nrows, A->ncols);
+ if (m == 0 || n == 0 || k == 0) return Py_BuildValue("");
+ if (k > ((side == 'L') ? m : n)) err_ld("k");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < ((side == 'L') ? MAX(1,m) : MAX(1,n))) err_ld("ldA");
+ if (ldC == 0) ldC = MAX(1,C->nrows);
+ if (ldC < MAX(1,m)) err_ld("ldC");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (k-1)*ldA + ((side == 'L' ) ? m : n) > len(A))
+ err_buf_len("A");
+ if (oC < 0) err_nn_int("offsetC");
+ if (oC + (n-1)*ldC + m > len(C)) err_buf_len("C");
+ if (len(tau) < k) err_buf_len("tau");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ if (trans == 'C') trans = 'T';
+ lwork = -1;
+ dormqr_(&side, &trans, &m, &n, &k, NULL, &ldA, NULL, NULL,
+ &ldC, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dormqr_(&side, &trans, &m, &n, &k, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(tau), MAT_BUFD(C)+oC, &ldC, (double *) work,
+ &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ if (trans == 'T') err_char("trans", "'N', 'C'");
+ lwork = -1;
+ zunmqr_(&side, &trans, &m, &n, &k, NULL, &ldA, NULL, NULL,
+ &ldC, &wl.z, &lwork, &info);
+ lwork = (int) creal(wl.z);
+ if (!(work = (void *) calloc(lwork, sizeof(complex))))
+ return PyErr_NoMemory();
+ zunmqr_(&side, &trans, &m, &n, &k, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(tau), MAT_BUFZ(C)+oC, &ldC, (complex *) work,
+ &lwork, &info);
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+static char doc_syev[] =
+ "Eigenvalue decomposition of a real symmetric matrix.\n\n"
+ "syev(A, W, jobz='N', uplo='L', n=A.size[0], "
+ "ldA = max(1,A.size[0]),\n"
+ " offsetA=0, offsetW=0)\n\n"
+ "PURPOSE\n"
+ "Returns eigenvalues/vectors of a real symmetric nxn matrix A.\n"
+ "On exit, W contains the eigenvalues in ascending order. If jobz\n"
+ "is 'V', the (normalized) eigenvectors are also computed and\n"
+ "returned in A. If jobz is 'N', only the eigenvalues are\n"
+ "computed, and the content of A is destroyed.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "W 'd' matrix of length at least n\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* syev(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W;
+ int n=-1, ldA=0, oA=0, oW=0, info, lwork;
+ double *work;
+ number wl;
+ char uplo='L', jobz='N';
+ char *kwlist[] = {"A", "W", "jobz", "uplo", "n", "ldA", "offsetA",
+ "offsetW", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cciiii", kwlist,
+ &A, &W, &jobz, &uplo, &n, &ldA, &oA, &oW)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("i",0);
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork=-1;
+ dsyev_(&jobz, &uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork,
+ &info);
+ lwork = (int) wl.d;
+ if (!(work = calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dsyev_(&jobz, &uplo, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(W)+oW, work, &lwork, &info);
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_heev[] =
+ "Eigenvalue decomposition of a real symmetric or complex Hermitian"
+ "\nmatrix.\n\n"
+ "heev(A, W, jobz='N', uplo='L', n=A.size[0], "
+ "ldA = max(1,A.size[0]),\n"
+ " offsetA=0, offsetW=0)\n\n"
+ "PURPOSE\n"
+ "Returns eigenvalues/vectors of a real symmetric or complex\n"
+ "Hermitian nxn matrix A. On exit, W contains the eigenvalues in\n"
+ "ascending order. If jobz is 'V', the (normalized) eigenvectors\n"
+ "are also computed and returned in A. If jobz is 'N', only the\n"
+ "eigenvalues are computed, and the content of A is destroyed.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "W 'd' matrix of length at least n\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* heev(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W;
+ int n=-1, ldA=0, oA=0, oW=0, info, lwork;
+ double *rwork=NULL;
+ void *work=NULL;
+ number wl;
+ char uplo='L', jobz='N';
+ char *kwlist[] = {"A", "W", "jobz", "uplo", "n", "ldA", "offsetA",
+ "offsetW", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cciiii", kwlist,
+ &A, &W, &jobz, &uplo, &n, &ldA, &oA, &oW)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork=-1;
+ dsyev_(&jobz, &uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork,
+ &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dsyev_(&jobz, &uplo, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(W)+oW, (double *) work, &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork=-1;
+ zheev_(&jobz, &uplo, &n, NULL, &ldA, NULL, &wl.z, &lwork,
+ NULL, &info);
+ lwork = (int) creal(wl.z);
+ work = (void *) calloc(lwork, sizeof(complex));
+ rwork = (double *) calloc(3*n-2, sizeof(double));
+ if (!work || !rwork){
+ free(work); free(rwork);
+ return PyErr_NoMemory();
+ }
+ zheev_(&jobz, &uplo, &n, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFD(W)+oW, (complex *) work, &lwork, rwork,
+ &info);
+ free(work); free(rwork);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_syevx[] =
+ "Computes selected eigenvalues and eigenvectors of a real symmetric"
+ "\nmatrix (expert driver).\n\n"
+ "m = syevx(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, \n"
+ " il=1, iu=1, Z=None, n=A.size[0], ldA=max(1,A.size[0]),\n"
+ " ldZ=None, abstol=0.0, offsetA=0, offsetW=0,\n"
+ " offsetZ=0)\n\n"
+ "PURPOSE\n"
+ "Computes selected eigenvalues/vectors of a real symmetric n by n\n"
+ "matrix A.\n"
+ "If range is 'A', all eigenvalues are computed.\n"
+ "If range is 'V', all eigenvalues in the interval (vl,vu] are\n"
+ "computed.\n"
+ "If range is 'I', all eigenvalues il through iu are computed\n"
+ "(sorted in ascending order with 1 <= il <= iu <= n).\n"
+ "If jobz is 'N', only the eigenvalues are returned in W.\n"
+ "If jobz is 'V', the eigenvectors are also returned in Z.\n"
+ "On exit, the content of A is destroyed.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "W 'd' matrix of length at least n. On exit, contains\n"
+ " the computed eigenvalues in ascending order.\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "range 'A', 'V' or 'I'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "vl,vu doubles. Only required when range is 'V'.\n\n"
+ "il,iu integers. Only required when range is 'I'.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "Z 'd' matrix. Only required when jobz is 'V'. If range\n"
+ " is 'A' or 'V', Z must have at least n columns. If\n"
+ " range is 'I', Z must have at least iu-il+1 columns.\n"
+ " On exit the first m columns of Z contain the computed\n"
+ " (normalized) eigenvectors.\n\n"
+ "abstol double. Absolute error tolerance for eigenvalues.\n"
+ " If nonpositive, the LAPACK default value is used.\n\n"
+ "ldZ nonnegative integer. ldZ >= 1 if jobz is 'N' and\n"
+ " ldZ >= max(1,n) if jobz is 'V'. The default value\n"
+ " is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetW nonnegative integer\n\n"
+ "offsetZ nonnegative integer\n\n"
+ "m the number of eigenvalues computed";
+
+static PyObject* syevx(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W, *Z=NULL;
+ int n=-1, ldA=0, ldZ=0, il=1, iu=1, oA=0, oW=0, oZ=0, info, lwork,
+ *iwork, m, *ifail=NULL;
+ double *work, vl=0.0, vu=0.0, abstol=0.0;
+ double wl;
+ char uplo='L', jobz='N', range='A';
+ char *kwlist[] = {"A", "W", "jobz", "range", "uplo", "vl", "vu",
+ "il", "iu", "Z", "n", "ldA", "ldZ", "abstol", "offsetA",
+ "offsetW", "offsetZ", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cccddiiOiiidiii",
+ kwlist, &A, &W, &jobz, &range, &uplo, &vl, &vu, &il, &iu, &Z,
+ &n, &ldA, &ldZ, &abstol, &oA, &oW, &oZ)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (range != 'A' && range != 'V' && range != 'I')
+ err_char("range", "'A', 'V', 'I'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("i",0);
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (range == 'V' && vl >= vu){
+ PyErr_SetString(PyExc_ValueError, "vl must be less than vu");
+ return NULL;
+ }
+ if (range == 'I' && (il < 1 || il > iu || iu > n)){
+ PyErr_SetString(PyExc_ValueError, "il and iu must satisfy "
+ "1 <= il <= iu <= n");
+ return NULL;
+ }
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+ if (jobz == 'V'){
+ if (!Z || !Matrix_Check(Z) || MAT_ID(Z) != DOUBLE)
+ err_dbl_mtrx("Z");
+ if (ldZ == 0) ldZ = MAX(1,Z->nrows);
+ if (ldZ < MAX(1,n)) err_ld("ldZ");
+ if (oZ < 0) err_nn_int("offsetZ");
+ if (oZ + ((range == 'I') ? iu-il : n-1)*ldZ + n > len(Z))
+ err_buf_len("Z");
+ } else {
+ if (ldZ == 0) ldZ = 1;
+ if (ldZ < 1) err_ld("ldZ");
+ }
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dsyevx_(&jobz, &range, &uplo, &n, NULL, &ldA, &vl, &vu, &il,
+ &iu, &abstol, &m, NULL, NULL, &ldZ, &wl, &lwork, NULL,
+ NULL, &info);
+ lwork = (int) wl;
+ work = (double *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(5*n, sizeof(int));
+ if (jobz == 'V') ifail = (int *) calloc(n, sizeof(int));
+ if (!work || !iwork || (jobz == 'V' && !ifail)){
+ free(work); free(iwork); free(ifail);
+ return PyErr_NoMemory();
+ }
+ dsyevx_(&jobz, &range, &uplo, &n, MAT_BUFD(A)+oA, &ldA, &vl,
+ &vu, &il, &iu, &abstol, &m, MAT_BUFD(W)+oW,
+ (jobz == 'V') ? MAT_BUFD(Z)+oZ : NULL, &ldZ, work,
+ &lwork, iwork, ifail, &info);
+ free(work); free(iwork); free(ifail);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("i", m);
+}
+
+
+static char doc_heevx[] =
+ "Computes selected eigenvalues and eigenvectors of a real symmetric"
+ "\nor complex Hermitian matrix (expert driver).\n\n"
+ "m = syevx(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, \n"
+ " il=1, iu=1, Z=None, n=A.size[0], \n"
+ " ldA = max(1,A.size[0]), ldZ=None, abstol=0.0, \n"
+ " offsetA=0, offsetW=0, offsetZ=0)\n\n"
+ "PURPOSE\n"
+ "Computes selected eigenvalues/vectors of a real symmetric or\n"
+ "complex Hermitian n by n matrix A.\n"
+ "If range is 'A', all eigenvalues are computed.\n"
+ "If range is 'V', all eigenvalues in the interval (vl,vu] are\n"
+ "computed.\n"
+ "If range is 'I', all eigenvalues il through iu are computed\n"
+ "(sorted in ascending order with 1 <= il <= iu <= n).\n"
+ "If jobz is 'N', only the eigenvalues are returned in W.\n"
+ "If jobz is 'V', the eigenvectors are also returned in Z.\n"
+ "On exit, the content of A is destroyed.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "W 'd' matrix of length at least n. On exit, contains\n"
+ " the computed eigenvalues in ascending order.\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "range 'A', 'V' or 'I'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "vl,vu doubles. Only required when range is 'V'.\n\n"
+ "il,iu integers. Only required when range is 'I'.\n\n"
+ "Z 'd' or 'z' matrix. Must have the same type as A.\n"
+ " Z is only required when jobz is 'V'. If range is 'A'\n"
+ " or 'V', Z must have at least n columns. If range is\n"
+ " 'I', Z must have at least iu-il+1 columns. On exit\n"
+ " the first m columns of Z contain the computed\n"
+ " (normalized) eigenvectors.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "ldZ nonnegative integer. ldZ >= 1 if jobz is 'N' and\n"
+ " ldZ >= max(1,n) if jobz is 'V'. The default value\n"
+ " is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.\n"
+ " If zero, the default value is used.\n\n"
+ "abstol double. Absolute error tolerance for eigenvalues.\n"
+ " If nonpositive, the LAPACK default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetW nonnegative integer\n\n"
+ "offsetZ nonnegative integer\n\n"
+ "m the number of eigenvalues computed";
+
+static PyObject* heevx(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W, *Z=NULL;
+ int n=-1, ldA=0, ldZ=0, il=1, iu=1, oA=0, oW=0, oZ=0, info, lwork,
+ *iwork, m, *ifail=NULL;
+ double vl=0.0, vu=0.0, abstol=0.0, *rwork;
+ number wl;
+ void *work;
+ char uplo='L', jobz='N', range='A';
+ char *kwlist[] = {"A", "W", "jobz", "range", "uplo", "vl", "vu",
+ "il", "iu", "Z", "n", "ldA", "ldZ", "abstol", "offsetA",
+ "offsetW", "offsetZ", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cccddiiOiiidiii",
+ kwlist, &A, &W, &jobz, &range, &uplo, &vl, &vu, &il, &iu, &Z,
+ &n, &ldA, &ldZ, &abstol, &oA, &oW, &oZ)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (range != 'A' && range != 'V' && range != 'I')
+ err_char("range", "'A', 'V', 'I'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("i",0);
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (range == 'V' && vl >= vu){
+ PyErr_SetString(PyExc_ValueError, "vl must be less than vu");
+ return NULL;
+ }
+ if (range == 'I' && (il < 1 || il > iu || iu > n)){
+ PyErr_SetString(PyExc_ValueError, "il and iu must satisfy "
+ "1 <= il <= iu <= n");
+ return NULL;
+ }
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+ if (jobz == 'V'){
+ if (!Z || !Matrix_Check(Z)) err_mtrx("Z");
+ if (MAT_ID(Z) != MAT_ID(A)) err_conflicting_ids;
+ if (ldZ == 0) ldZ = MAX(1,Z->nrows);
+ if (ldZ < MAX(1,n)) err_ld("ldZ");
+ if (oZ < 0) err_nn_int("offsetZ");
+ if (oZ + ((range == 'I') ? iu-il : n-1)*ldZ + n > len(Z))
+ err_buf_len("Z");
+ } else {
+ if (ldZ == 0) ldZ = 1;
+ if (ldZ < 1) err_ld("ldZ");
+ }
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dsyevx_(&jobz, &range, &uplo, &n, NULL, &ldA, &vl, &vu, &il,
+ &iu, &abstol, &m, NULL, NULL, &ldZ, &wl.d, &lwork, NULL,
+ NULL, &info);
+ lwork = (int) wl.d;
+ work = (void *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(5*n, sizeof(int));
+ if (jobz == 'V') ifail = (int *) calloc(n, sizeof(int));
+ if (!work || !iwork || (jobz == 'V' && !ifail)){
+ free(work); free(iwork); free(ifail);
+ return PyErr_NoMemory();
+ }
+ dsyevx_(&jobz, &range, &uplo, &n, MAT_BUFD(A)+oA, &ldA, &vl,
+ &vu, &il, &iu, &abstol, &m, MAT_BUFD(W)+oW,
+ (jobz == 'V') ? MAT_BUFD(Z)+oZ : NULL, &ldZ,
+ (double *) work, &lwork, iwork, ifail, &info);
+ free(work); free(iwork); free(ifail);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zheevx_(&jobz, &range, &uplo, &n, NULL, &ldA, &vl, &vu, &il,
+ &iu, &abstol, &m, NULL, NULL, &ldZ, &wl.z, &lwork, NULL,
+ NULL, NULL, &info);
+ lwork = (int) creal(wl.z);
+ work = (void *) calloc(lwork, sizeof(complex));
+ rwork = (double *) calloc(7*n, sizeof(double));
+ iwork = (int *) calloc(5*n, sizeof(int));
+ if (jobz == 'V') ifail = (int *) calloc(n, sizeof(int));
+ if (!work || !rwork || !iwork || (jobz == 'V' && !ifail)){
+ free(work); free(rwork); free(iwork); free(ifail);
+ return PyErr_NoMemory();
+ }
+ zheevx_(&jobz, &range, &uplo, &n, MAT_BUFZ(A)+oA, &ldA, &vl,
+ &vu, &il, &iu, &abstol, &m, MAT_BUFD(W)+oW,
+ (jobz == 'V') ? MAT_BUFZ(Z)+oZ : NULL, &ldZ,
+ (complex *) work, &lwork, rwork, iwork, ifail, &info);
+ free(work); free(rwork); free(iwork); free(ifail);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("i", m);
+}
+
+
+static char doc_syevd[] =
+ "Eigenvalue decomposition of a real symmetric matrix\n"
+ "(divide-and-conquer driver).\n\n"
+ "syevd(A, W, jobz='N', uplo='L', n=A.size[0], "
+ "ldA = max(1,A.size[0]),\n"
+ " offsetA=0, offsetW=0)\n\n"
+ "PURPOSE\n"
+ "Returns eigenvalues/vectors of a real symmetric nxn matrix A.\n"
+ "On exit, W contains the eigenvalues in ascending order.\n"
+ "If jobz is 'V', the (normalized) eigenvectors are also computed\n"
+ "and returned in A. If jobz is 'N', only the eigenvalues are\n"
+ "computed, and the content of A is destroyed.\n"
+ "\n\nARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "W 'd' matrix of length at least n. On exit, contains\n"
+ " the computed eigenvalues in ascending order.\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* syevd(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W;
+ int n=-1, ldA=0, oA=0, oW=0, info, lwork, liwork, *iwork, iwl;
+ double *work=NULL, wl;
+ char uplo='L', jobz='N';
+ char *kwlist[] = {"A", "W", "jobz", "uplo", "n", "ldA", "offsetA",
+ "offsetW", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cciiii", kwlist,
+ &A, &W, &jobz, &uplo, &n, &ldA, &oA, &oW)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || W->id != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ liwork = -1;
+ dsyevd_(&jobz, &uplo, &n, NULL, &ldA, NULL, &wl, &lwork,
+ &iwl, &liwork, &info);
+ lwork = (int) wl;
+ liwork = iwl;
+ work = (double *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(liwork, sizeof(int));
+ if (!work || !iwork){
+ free(work); free(iwork);
+ return PyErr_NoMemory();
+ }
+ dsyevd_(&jobz, &uplo, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(W)+oW, work, &lwork, iwork, &liwork, &info);
+ free(work); free(iwork);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_heevd[] =
+ "Eigenvalue decomposition of a real symmetric or complex Hermitian"
+ "\nmatrix (divide-and-conquer driver).\n\n"
+ "heevd(A, W, jobz='N', uplo='L', n=A.size[0], "
+ "ldA = max(1,A.size[0]),\n"
+ " offsetA=0, offsetW=0)\n\n"
+ "PURPOSE\n"
+ "Returns eigenvalues/vectors of a real symmetric or complex\n"
+ "Hermitian n by n matrix A. On exit, W contains the eigenvalues\n"
+ "in ascending order. If jobz is 'V', the (normalized) eigenvectors"
+ "\nare also computed and returned in A. If jobz is 'N', only the\n"
+ "eigenvalues are computed, and the content of A is destroyed.\n"
+ "\n\nARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "W 'd' matrix of length at least n. On exit, contains\n"
+ " the computed eigenvalues in ascending order.\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* heevd(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W;
+ int n=-1, ldA=0, oA=0, oW=0, info, lwork, liwork, *iwork, iwl,
+ lrwork;
+ double *rwork, rwl;
+ number wl;
+ void *work;
+ char uplo='L', jobz='N';
+ char *kwlist[] = {"A", "W", "jobz", "uplo", "n", "ldA", "offsetA",
+ "offsetW", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cciiii", kwlist,
+ &A, &W, &jobz, &uplo, &n, &ldA, &oA, &oW)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || W->id != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ liwork = -1;
+ dsyevd_(&jobz, &uplo, &n, NULL, &ldA, NULL, &wl.d, &lwork,
+ &iwl, &liwork, &info);
+ lwork = (int) wl.d;
+ liwork = iwl;
+ work = (void *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(liwork, sizeof(int));
+ if (!work || !iwork){
+ free(work); free(iwork);
+ return PyErr_NoMemory();
+ }
+ dsyevd_(&jobz, &uplo, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(W)+oW, (double *) work, &lwork, iwork, &liwork,
+ &info);
+ free(work); free(iwork);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ liwork = -1;
+ lrwork = -1;
+ zheevd_(&jobz, &uplo, &n, NULL, &ldA, NULL, &wl.z, &lwork,
+ &rwl, &lrwork, &iwl, &liwork, &info);
+ lwork = (int) wl.d;
+ lrwork = (int) rwl;
+ liwork = iwl;
+ work = (void *) calloc(lwork, sizeof(complex));
+ rwork = (double *) calloc(lrwork, sizeof(double));
+ iwork = (int *) calloc(liwork, sizeof(int));
+ if (!work || !rwork || !iwork){
+ free(work); free(rwork); free(iwork);
+ return PyErr_NoMemory();
+ }
+ zheevd_(&jobz, &uplo, &n, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFD(W)+oW, (complex *) work, &lwork, rwork,
+ &lrwork, iwork, &liwork, &info);
+ free(work); free(rwork); free(iwork);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_syevr[] =
+ "Computes selected eigenvalues and eigenvectors of a real symmetric"
+ "\n"
+ "matrix (RRR driver).\n\n"
+ "m = syevr(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, \n"
+ " il=1, iu=1, Z=None, n=A.size[0], ldA=max(1,A.size[0]),\n"
+ " ldZ=None, abstol=0.0, offsetA=0, offsetW=0, offsetZ=0)\n"
+ "\n"
+ "PURPOSE\n"
+ "Computes selected eigenvalues/vectors of a real symmetric n by n\n"
+ "matrix A.\n"
+ "If range is 'A', all eigenvalues are computed.\n"
+ "If range is 'V', all eigenvalues in the interval (vl,vu] are\n"
+ "computed.\n"
+ "If range is 'I', all eigenvalues il through iu are computed\n"
+ "(sorted in ascending order with 1 <= il <= iu <= n).\n"
+ "If jobz is 'N', only the eigenvalues are returned in W.\n"
+ "If jobz is 'V', the eigenvectors are also returned in Z.\n"
+ "On exit, the content of A is destroyed.\n"
+ "syevr is usually the fastest of the four eigenvalue routines.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "W 'd' matrix of length at least n. On exit, contains\n"
+ " the computed eigenvalues in ascending order.\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "range 'A', 'V' or 'I'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "vl,vu doubles. Only required when range is 'V'.\n\n"
+ "il,iu integers. Only required when range is 'I'.\n\n"
+ "Z 'd' matrix. Only required when jobz = 'V'.\n"
+ " If range is 'A' or 'V', Z must have at least n columns."
+ "\n"
+ " If range is 'I', Z must have at least iu-il+1 columns.\n"
+ " On exit the first m columns of Z contain the computed\n"
+ " (normalized) eigenvectors.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "ldZ nonnegative integer. ldZ >= 1 if jobz is 'N' and\n"
+ " ldZ >= max(1,n) if jobz is 'V'. The default value\n"
+ " is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.\n"
+ " If zero, the default value is used.\n\n"
+ "abstol double. Absolute error tolerance for eigenvalues.\n"
+ " If nonpositive, the LAPACK default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetW nonnegative integer\n\n"
+ "offsetZ nonnegative integer\n\n"
+ "m the number of eigenvalues computed";
+
+static PyObject* syevr(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W, *Z=NULL;
+ int n=-1, ldA=0, ldZ=0, il=1, iu=1, oA=0, oW=0, oZ=0, info, lwork,
+ *iwork=NULL, liwork, m, *isuppz=NULL, iwl;
+ double *work=NULL, vl=0.0, vu=0.0, abstol=0.0, wl;
+ char uplo='L', jobz='N', range='A';
+ char *kwlist[] = {"A", "W", "jobz", "range", "uplo", "vl", "vu",
+ "il", "iu", "Z", "n", "ldA", "ldZ", "abstol", "offsetA",
+ "offsetW", "offsetZ", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cccddiiOiiidiii",
+ kwlist, &A, &W, &jobz, &range, &uplo, &vl, &vu, &il, &iu, &Z,
+ &n, &ldA, &ldZ, &abstol, &oA, &oW, &oZ)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (range != 'A' && range != 'V' && range != 'I')
+ err_char("range", "'A', 'V', 'I'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("i",0);
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (range == 'V' && vl >= vu){
+ PyErr_SetString(PyExc_ValueError, "vl must be less than vu");
+ return NULL;
+ }
+ if (range == 'I' && (il < 1 || il > iu || iu > n)){
+ PyErr_SetString(PyExc_ValueError, "il and iu must satisfy "
+ "1 <= il <= iu <= n");
+ return NULL;
+ }
+ if (jobz == 'V'){
+ if (!Z || !Matrix_Check(Z) || MAT_ID(Z) != DOUBLE)
+ err_dbl_mtrx("Z");
+ if (ldZ == 0) ldZ = MAX(1,Z->nrows);
+ if (ldZ < MAX(1,n)) err_ld("ldZ");
+ } else {
+ if (ldZ == 0) ldZ = 1;
+ if (ldZ < 1) err_ld("ldZ");
+ }
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+ if (jobz == 'V'){
+ if (oZ < 0) err_nn_int("offsetZ");
+ if (oZ + ((range == 'I') ? iu-il : n-1)*ldZ + n > len(Z))
+ err_buf_len("Z");
+ }
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ liwork = -1;
+ dsyevr_(&jobz, &range, &uplo, &n, NULL, &ldA, &vl, &vu, &il,
+ &iu, &abstol, &m, NULL, NULL, &ldZ, NULL, &wl, &lwork,
+ &iwl, &liwork, &info);
+ lwork = (int) wl;
+ liwork = iwl;
+ work = (void *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(liwork, sizeof(int));
+ if (jobz == 'V')
+ isuppz = (int *) calloc(2*MAX(1, (range == 'I') ?
+ iu-il+1 : n), sizeof(int));
+ if (!work || !iwork || (jobz == 'V' && !isuppz)){
+ free(work); free(iwork); free(isuppz);
+ return PyErr_NoMemory();
+ }
+ dsyevr_(&jobz, &range, &uplo, &n, MAT_BUFD(A)+oA, &ldA, &vl,
+ &vu, &il, &iu, &abstol, &m, MAT_BUFD(W)+oW,
+ (jobz == 'V') ? MAT_BUFD(Z)+oZ : NULL, &ldZ,
+ (jobz == 'V') ? isuppz : NULL, work, &lwork, iwork,
+ &liwork, &info);
+ free(work); free(iwork); free(isuppz);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("i",m);
+}
+
+
+static char doc_heevr[] =
+ "Computes selected eigenvalues and eigenvectors of a real symmetric"
+ "\nor complex Hermitian matrix (RRR driver).\n\n"
+ "m = syevr(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, \n"
+ " il=1, iu=1, Z=None, n=A.size[0], ldA=max(1,A.size[0]),\n"
+ " ldZ=None, abstol=0.0, offsetA=0, offsetW=0, offsetZ=0)\n"
+ "\n"
+ "PURPOSE\n"
+ "Computes selected eigenvalues/vectors of a real symmetric or\n"
+ "complex Hermitian n by n matrix A.\n"
+ "If range is 'A', all eigenvalues are computed.\n"
+ "If range is 'V', all eigenvalues in the interval (vl,vu] are\n"
+ "computed.\n"
+ "If range is 'I', all eigenvalues il through iu are computed\n"
+ "(sorted in ascending order with 1 <= il <= iu <= n).\n"
+ "If jobz is 'N', only the eigenvalues are returned in W.\n"
+ "If jobz is 'V', the eigenvectors are also returned in Z.\n"
+ "On exit, the content of A is destroyed.\n"
+ "syevr is usually the fastest of the four eigenvalue routines.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "W 'd' matrix of length at least n. On exit, contains\n"
+ " the computed eigenvalues in ascending order.\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "range 'A', 'V' or 'I'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "vl,vu doubles. Only required when range is 'V'.\n\n"
+ "il,iu integers. Only required when range is 'I'.\n\n"
+ "Z 'd' or 'z' matrix. Must have the same type as A.\n"
+ " Only required when jobz = 'V'. If range is 'A' or\n"
+ " 'V', Z must have at least n columns. If range is 'I',\n"
+ " Z must have at least iu-il+1 columns. On exit the\n"
+ " first m columns of Z contain the computed (normalized)\n"
+ " eigenvectors.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n).\n"
+ " If zero, the default value is used.\n\n"
+ "ldZ nonnegative integer. ldZ >= 1 if jobz is 'N' and\n"
+ " ldZ >= max(1,n) if jobz is 'V'. The default value\n"
+ " is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.\n"
+ " If zero, the default value is used.\n\n"
+ "abstol double. Absolute error tolerance for eigenvalues.\n"
+ " If nonpositive, the LAPACK default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetW nonnegative integer\n\n"
+ "offsetZ nonnegative integer\n\n"
+ "m the number of eigenvalues computed";
+
+static PyObject* heevr(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *W, *Z=NULL;
+ int n=-1, ldA=0, ldZ=0, il=1, iu=1, oA=0, oW=0, oZ=0, info,
+ lwork, *iwork, liwork, lrwork, m, *isuppz=NULL, iwl;
+ double vl=0.0, vu=0.0, abstol=0.0, *rwork, rwl;
+ void *work;
+ number wl;
+ char uplo='L', jobz='N', range='A';
+ char *kwlist[] = {"A", "W", "jobz", "range", "uplo", "vl", "vu",
+ "il", "iu", "Z", "n", "ldA", "ldZ", "abstol", "offsetA",
+ "offsetW", "offsetZ", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cccddiiOiiidiii",
+ kwlist, &A, &W, &jobz, &range, &uplo, &vl, &vu, &il, &iu, &Z,
+ &n, &ldA, &ldZ, &abstol, &oA, &oW, &oZ)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (range != 'A' && range != 'V' && range != 'I')
+ err_char("range", "'A', 'V', 'I'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("i",0);
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (range == 'V' && vl >= vu){
+ PyErr_SetString(PyExc_ValueError, "vl must be less than vu");
+ return NULL;
+ }
+ if (range == 'I' && (il < 1 || il > iu || iu > n)){
+ PyErr_SetString(PyExc_ValueError, "il and iu must satisfy "
+ "1 <= il <= iu <= n");
+ return NULL;
+ }
+ if (jobz == 'V'){
+ if (!Z || !Matrix_Check(Z)) err_mtrx("Z");
+ if (MAT_ID(Z) != MAT_ID(A)) err_conflicting_ids;
+ if (ldZ == 0) ldZ = MAX(1,Z->nrows);
+ if (ldZ < MAX(1,n)) err_ld("ldZ");
+ } else {
+ if (ldZ == 0) ldZ = 1;
+ if (ldZ < 1) err_ld("ldZ");
+ }
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+ if (jobz == 'V'){
+ if (oZ < 0) err_nn_int("offsetZ");
+ if (oZ + ((range == 'I') ? iu-il : n-1)*ldZ + n > len(Z))
+ err_buf_len("Z");
+ }
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ liwork = -1;
+ dsyevr_(&jobz, &range, &uplo, &n, NULL, &ldA, &vl, &vu, &il,
+ &iu, &abstol, &m, NULL, NULL, &ldZ, NULL, &wl.d, &lwork,
+ &iwl, &liwork, &info);
+ lwork = (int) wl.d;
+ liwork = iwl;
+ work = (void *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(liwork, sizeof(int));
+ if (jobz == 'V')
+ isuppz = (int *) calloc(2*MAX(1, (range == 'I') ?
+ iu-il+1 : n), sizeof(int));
+ if (!work || !iwork || (jobz == 'V' && !isuppz)){
+ free(work); free(iwork); free(isuppz);
+ return PyErr_NoMemory();
+ }
+ dsyevr_(&jobz, &range, &uplo, &n, MAT_BUFD(A)+oA, &ldA, &vl,
+ &vu, &il, &iu, &abstol, &m, MAT_BUFD(W)+oW,
+ (jobz == 'V') ? MAT_BUFD(Z)+oZ : NULL, &ldZ,
+ (jobz == 'V') ? isuppz : NULL, (double *) work, &lwork,
+ iwork, &liwork, &info);
+ free(work); free(iwork); free(isuppz);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ liwork = -1;
+ lrwork = -1;
+ zheevr_(&jobz, &range, &uplo, &n, NULL, &ldA, &vl, &vu, &il,
+ &iu, &abstol, &m, NULL, NULL, &ldZ, NULL, &wl.z, &lwork,
+ &rwl, &lrwork, &iwl, &liwork, &info);
+ lwork = (int) creal(wl.z);
+ lrwork = (int) rwl;
+ liwork = iwl;
+ work = (void *) calloc(lwork, sizeof(complex));
+ rwork = (double *) calloc(lrwork, sizeof(double));
+ iwork = (int *) calloc(liwork, sizeof(int));
+ if (jobz == 'V')
+ isuppz = (int *) calloc(2*MAX(1, (range == 'I') ?
+ iu-il+1 : n), sizeof(int));
+ if (!work || !rwork || !iwork || (jobz == 'V' && !isuppz)){
+ free(work); free(rwork); free(iwork); free(isuppz);
+ return PyErr_NoMemory();
+ }
+ zheevr_(&jobz, &range, &uplo, &n, MAT_BUFZ(A)+oA, &ldA, &vl,
+ &vu, &il, &iu, &abstol, &m, MAT_BUFD(W)+oW,
+ (jobz == 'V') ? MAT_BUFZ(Z)+oZ : NULL, &ldZ,
+ (jobz == 'V') ? isuppz : NULL, (complex *) work, &lwork,
+ rwork, &lrwork, iwork, &liwork, &info);
+ free(work); free(rwork); free(iwork); free(isuppz);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("i",m);
+}
+
+
+static char doc_sygv[] =
+ "Generalized symmetric-definite eigenvalue decomposition with real"
+ "\n"
+ "matrices.\n\n"
+ "sygv(A, B, W, itype=1, jobz='N', uplo='L', n=A.size[0], \n"
+ " ldA = max(1,A.size[0]), ldB = max(1,B.size[0]), offsetA=0, \n"
+ " offsetB=0, offsetW=0)\n\n"
+ "PURPOSE\n"
+ "Returns eigenvalues/vectors of a real generalized \n"
+ "symmetric-definite eigenproblem of order n, with B positive \n"
+ "definite. \n"
+ "1. If itype is 1: A*x = lambda*B*x.\n"
+ "2. If itype is 2: A*Bx = lambda*x.\n"
+ "3. If itype is 3: B*Ax = lambda*x.\n\n"
+ "On exit, W contains the eigenvalues in ascending order. If jobz\n"
+ "is 'V', the matrix of eigenvectors Z is also computed and\n"
+ "returned in A, normalized as follows: \n"
+ "1. If itype is 1: Z^T*A*Z = diag(W), Z^T*B*Z = I\n"
+ "2. If itype is 2: Z^T*A^{-1}*Z = diag(W)^{-1}, Z^T*B*Z = I\n"
+ "3. If itype is 3: Z^T*A*Z = diag(W), Z^T*B^{-1}*Z = I.\n\n"
+ "If jobz is 'N', only the eigenvalues are computed, and the\n"
+ "contents of A is destroyed. On exit, the matrix B is replaced\n"
+ "by its Cholesky factor.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' matrix\n\n"
+ "B 'd' matrix\n\n"
+ "W 'd' matrix of length at least n\n\n"
+ "itype integer 1, 2, or 3\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* sygv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *W;
+ int n=-1, itype=1, ldA=0, ldB=0, oA=0, oB=0, oW=0, info, lwork;
+ double *work;
+ number wl;
+ char uplo='L', jobz='N';
+ char *kwlist[] = {"A", "B", "W", "itype", "jobz", "uplo", "n",
+ "ldA", "ldB", "offsetA", "offsetB", "offsetW", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|icciiiiii",
+ kwlist, &A, &B, &W, &itype, &jobz, &uplo, &n, &ldA, &ldB, &oA,
+ &oB, &oW)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B) || MAT_ID(B) != MAT_ID(A)) err_conflicting_ids;
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (itype != 1 && itype != 2 && itype != 3)
+ err_char("itype", "1, 2, 3");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ if (A->nrows != n || A->ncols != n){
+ PyErr_SetString(PyExc_TypeError, "B must have the same "
+ "dimension as A");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (n-1)*ldB + n > len(B)) err_buf_len("B");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork=-1;
+ dsygv_(&itype, &jobz, &uplo, &n, NULL, &ldA, NULL, &ldB,
+ NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dsygv_(&itype, &jobz, &uplo, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, MAT_BUFD(W)+oW, work, &lwork,
+ &info);
+ free(work);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_hegv[] =
+ "Generalized symmetric-definite eigenvalue decomposition with\n"
+ "real or complex matrices.\n\n"
+ "hegv(A, B, W, itype=1, jobz='N', uplo='L', n=A.size[0], \n"
+ " ldA = max(1,A.size[0]), ldB = max(1,B.size[0]), offsetA=0, \n"
+ " offsetB=0, offsetW=0)\n\n"
+ "PURPOSE\n"
+ "Returns eigenvalues/vectors of a real or complex generalized\n"
+ "symmetric-definite eigenproblem of order n, with B positive\n"
+ "definite. \n"
+ "1. If itype is 1: A*x = lambda*B*x.\n"
+ "2. If itype is 2: A*Bx = lambda*x.\n"
+ "3. If itype is 3: B*Ax = lambda*x.n\n\n"
+ "On exit, W contains the eigenvalues in ascending order. If jobz\n"
+ "is 'V', the matrix of eigenvectors Z is also computed and \n"
+ "returned in A, normalized as follows: \n"
+ "1. If itype is 1: Z^H*A*Z = diag(W), Z^H*B*Z = I\n"
+ "2. If itype is 2: Z^H*A^{-1}*Z = diag(W), Z^H*B*Z = I\n"
+ "3. If itype is 3: Z^H*A*Z = diag(W), Z^H*B^{-1}*Z = I.\n\n"
+ "If jobz is 'N', only the eigenvalues are computed, and the \n"
+ "contents of A is destroyed. On exit, the matrix B is replaced\n"
+ "by its Cholesky factor.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "B 'd' or 'z' matrix. Must have the same type as A.\n\n"
+ "W 'd' matrix of length at least n\n\n"
+ "itype integer 1, 2, or 3\n\n"
+ "jobz 'N' or 'V'\n\n"
+ "uplo 'L' or 'U'\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* hegv(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *B, *W;
+ int n=-1, itype=1, ldA=0, ldB=0, oA=0, oB=0, oW=0, info, lwork;
+ double *rwork=NULL;
+ void *work=NULL;
+ number wl;
+ char uplo='L', jobz='N';
+ char *kwlist[] = {"A", "B", "W", "itype", "jobz", "uplo", "n",
+ "ldA", "offsetA", "offsetB", "offsetW", NULL};
+ int ispec=1, n2=-1, n3=-1, n4=-1;
+ char *name = "zhetrd", *uplol = "L", *uplou = "U";
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|icciiiii",
+ kwlist, &A, &B, &W, &itype, &jobz, &uplo, &n, &ldA, &ldB, &oA,
+ &oB, &oW)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(B) || MAT_ID(B) != MAT_ID(A)) err_conflicting_ids;
+ if (!Matrix_Check(W) || MAT_ID(W) != DOUBLE) err_dbl_mtrx("W");
+ if (itype != 1 && itype != 2 && itype != 3)
+ err_char("itype", "1, 2, 3");
+ if (jobz != 'N' && jobz != 'V') err_char("jobz", "'N', 'V'");
+ if (uplo != 'L' && uplo != 'U') err_char("uplo", "'L', 'U'");
+ if (n < 0){
+ n = A->nrows;
+ if (n != A->ncols){
+ PyErr_SetString(PyExc_TypeError, "A must be square");
+ return NULL;
+ }
+ if (A->nrows != n || A->ncols != n){
+ PyErr_SetString(PyExc_TypeError, "B must have the same "
+ "dimension as A");
+ return NULL;
+ }
+ }
+ if (n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,n)) err_ld("ldA");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + n > len(A)) err_buf_len("A");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (n-1)*ldB + n > len(B)) err_buf_len("B");
+ if (oW < 0) err_nn_int("offsetW");
+ if (oW + n > len(W)) err_buf_len("W");
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork=-1;
+ dsygv_(&itype, &jobz, &uplo, &n, NULL, &ldA, NULL, &ldB,
+ NULL, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = calloc(lwork, sizeof(double))))
+ return PyErr_NoMemory();
+ dsygv_(&itype, &jobz, &uplo, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(B)+oB, &ldB, MAT_BUFD(W)+oW, work, &lwork,
+ &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+#if 0
+ /* zhegv does not handle lwork=-1 correctly */
+ lwork=-1;
+ zhegv_(&itype, &jobz, &uplo, &n, NULL, &n, NULL, &n, NULL,
+ &wl.z, &lwork, NULL, &info);
+ lwork = (int) creal(wl.z);
+#endif
+ /* replaces call to zhegv with lwork=-1 */
+ lwork = n * (1 + ilaenv_(&ispec, &name, (uplo == 'L') ?
+ &uplol : &uplou, &n, &n2, &n3, &n4));
+
+ work = (void *) calloc(lwork, sizeof(complex));
+ rwork = (double *) calloc(3*n-2, sizeof(double));
+ if (!work || !rwork){
+ free(work); free(rwork);
+ return PyErr_NoMemory();
+ }
+ zhegv_(&itype, &jobz, &uplo, &n, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFZ(B)+oB, &ldB, MAT_BUFD(W)+oW, (complex *) work,
+ &lwork, rwork, &info);
+ free(work); free(rwork);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gesvd[] =
+ "Singular value decomposition of a real or complex matrix.\n\n"
+ "gesvd(A, S, jobu='N', jobvt='N', U=None, Vt=None, m=A.size[0],\n"
+ " n=A.size[1], ldA=max(1,A.size[0]), ldU=None, ldVt=None,\n"
+ " offsetA=0, offsetS=0, offsetU=0, offsetVt=0)\n\n"
+ "PURPOSE\n"
+ "Computes singular values and, optionally, singular vectors of a \n"
+ "real or complex m by n matrix A.\n\n"
+ "The argument jobu controls how many left singular vectors are\n"
+ "computed: \n\n"
+ "'N': no left singular vectors are computed.\n"
+ "'A': all left singular vectors are computed and returned as\n"
+ " columns of U.\n"
+ "'S': the first min(m,n) left singular vectors are computed and\n"
+ " returned as columns of U.\n"
+ "'O': the first min(m,n) left singular vectors are computed and\n"
+ " returned as columns of A.\n\n"
+ "The argument jobvt controls how many right singular vectors are\n"
+ "computed:\n\n"
+ "'N': no right singular vectors are computed.\n"
+ "'A': all right singular vectors are computed and returned as\n"
+ " rows of Vt.\n"
+ "'S': the first min(m,n) right singular vectors are computed and\n"
+ " returned as rows of Vt.\n"
+ "'O': the first min(m,n) right singular vectors are computed and\n"
+ " returned as rows of A.\n"
+ "Note that the (conjugate) transposes of the right singular \n"
+ "vectors are returned in Vt or A.\n\n"
+ "On exit (in all cases), the contents of A are destroyed.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "S 'd' matrix of length at least min(m,n). On exit, \n"
+ " contains the computed singular values in descending\n"
+ " order.\n\n"
+ "jobu 'N', 'A', 'S' or 'O'\n\n"
+ "jobvt 'N', 'A', 'S' or 'O'\n\n"
+ "U 'd' or 'z' matrix. Must have the same type as A.\n"
+ " Not referenced if jobu is 'N' or 'O'. If jobu is 'A',\n"
+ " a matrix with at least m columns. If jobu is 'S', a\n"
+ " matrix with at least min(m,n) columns.\n"
+ " On exit (with jobu 'A' or 'S'), the columns of U\n"
+ " contain the computed left singular vectors.\n\n"
+ "Vt 'd' or 'z' matrix. Must have the same type as A.\n"
+ " Not referenced if jobvt is 'N' or 'O'. If jobvt is \n"
+ " 'A' or 'S', a matrix with at least n columns.\n"
+ " On exit (with jobvt 'A' or 'S'), the rows of Vt\n"
+ " contain the computed right singular vectors, or, in\n"
+ " the complex case, their complex conjugates.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "ldU nonnegative integer.\n"
+ " ldU >= 1 if jobu is 'N' or 'O'.\n"
+ " ldU >= max(1,m) if jobu is 'A' or 'S'.\n"
+ " The default value is max(1,U.size[0]) if jobu is 'A' \n"
+ " or 'S', and 1 otherwise.\n"
+ " If zero, the default value is used.\n\n"
+ "ldVt nonnegative integer.\n"
+ " ldVt >= 1 if jobvt is 'N' or 'O'.\n"
+ " ldVt >= max(1,n) if jobvt is 'A'. \n"
+ " ldVt >= max(1,min(m,n)) if ldVt is 'S'.\n"
+ " The default value is max(1,Vt.size[0]) if jobvt is 'A'\n"
+ " or 'S', and 1 otherwise.\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetS nonnegative integer\n\n"
+ "offsetU nonnegative integer\n\n"
+ "offsetVt nonnegative integer";
+
+static PyObject* gesvd(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *S, *U=NULL, *Vt=NULL;
+ int m=-1, n=-1, ldA=0, ldU=0, ldVt=0, oA=0, oS=0, oU=0, oVt=0, info,
+ lwork;
+ double *rwork=NULL;
+ void *work=NULL;
+ number wl;
+ char jobu='N', jobvt='N';
+ char *kwlist[] = {"A", "S", "jobu", "jobvt", "U", "Vt", "m", "n",
+ "ldA", "ldU", "ldVt", "offsetA", "offsetS", "offsetU",
+ "offsetVt", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ccOOiiiiiiiii",
+ kwlist, &A, &S, &jobu, &jobvt, &U, &Vt, &m, &n, &ldA, &ldU,
+ &ldVt, &oA, &oS, &oU, &oVt)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(S) || MAT_ID(S) != DOUBLE) err_dbl_mtrx("S");
+ if (jobu != 'N' && jobu != 'A' && jobu != 'O' && jobu != 'S')
+ err_char("jobu", "'N', 'A', 'S', 'O'");
+ if (jobvt != 'N' && jobvt != 'A' && jobvt != 'O' && jobvt != 'S')
+ err_char("jobvt", "'N', 'A', 'S', 'O'");
+ if (jobu == 'O' && jobvt == 'O') {
+ PyErr_SetString(PyExc_ValueError, "'jobu' and 'jobvt' cannot "
+ "both be 'O'");
+ return NULL;
+ }
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+ if (jobu == 'A' || jobu == 'S'){
+ if (!U || !Matrix_Check(U)) err_mtrx("U");
+ if (MAT_ID(U) != MAT_ID(A)) err_conflicting_ids;
+ if (ldU == 0) ldU = MAX(1,U->nrows);
+ if (ldU < MAX(1,m)) err_ld("ldU");
+ } else {
+ if (ldU == 0) ldU = 1;
+ if (ldU < 1) err_ld("ldU");
+ }
+ if (jobvt == 'A' || jobvt == 'S'){
+ if (!Vt || !Matrix_Check(Vt)) err_mtrx("Vt");
+ if (MAT_ID(Vt) != MAT_ID(A)) err_conflicting_ids;
+ if (ldVt == 0) ldVt = MAX(1,Vt->nrows);
+ if (ldVt < ((jobvt == 'A') ? MAX(1,n) : MAX(1,MIN(m,n))))
+ err_ld("ldVt");
+ } else {
+ if (ldVt == 0) ldVt = 1;
+ if (ldVt < 1) err_ld("ldVt");
+ }
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (oS < 0) err_nn_int("offsetS");
+ if (oS + MIN(m,n) > len(S)) err_buf_len("S");
+ if (jobu == 'A' || jobu == 'S'){
+ if (oU < 0) err_nn_int("offsetU");
+ if (oU + ((jobu == 'A') ? m-1 : MIN(m,n)-1)*ldU + m > len(U))
+ err_buf_len("U");
+ }
+ if (jobvt == 'A' || jobvt == 'S'){
+ if (oVt < 0) err_nn_int("offsetVt");
+ if (oVt + (n-1)*ldVt + ((jobvt == 'A') ? n : MIN(m,n)) >
+ len(Vt)) err_buf_len("Vt");
+ }
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dgesvd_(&jobu, &jobvt, &m, &n, NULL, &ldA, NULL, NULL,
+ &ldU, NULL, &ldVt, &wl.d, &lwork, &info);
+ lwork = (int) wl.d;
+ if (!(work = (void *) calloc(lwork, sizeof(double)))){
+ free(work);
+ return PyErr_NoMemory();
+ }
+ dgesvd_(&jobu, &jobvt, &m, &n, MAT_BUFD(A)+oA, &ldA,
+ MAT_BUFD(S)+oS, (jobu == 'A' || jobu == 'S') ?
+ MAT_BUFD(U)+oU : NULL, &ldU, (jobvt == 'A' ||
+ jobvt == 'S') ? MAT_BUFD(Vt)+oVt : NULL, &ldVt,
+ (double *) work, &lwork, &info);
+ free(work);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zgesvd_(&jobu, &jobvt, &m, &n, NULL, &ldA, NULL, NULL,
+ &ldU, NULL, &ldVt, &wl.z, &lwork, NULL, &info);
+ lwork = (int) creal(wl.z);
+ work = (void *) calloc(lwork, sizeof(complex));
+ rwork = (double *) calloc(5*MIN(m,n), sizeof(double));
+ if (!work || !rwork){
+ free(work); free(rwork);
+ return PyErr_NoMemory();
+ }
+ zgesvd_(&jobu, &jobvt, &m, &n, MAT_BUFZ(A)+oA, &ldA,
+ MAT_BUFD(S)+oS, (jobu == 'A' || jobu == 'S') ?
+ MAT_BUFZ(U)+oU : NULL, &ldU, (jobvt == 'A' ||
+ jobvt == 'S') ? MAT_BUFZ(Vt)+oVt : NULL, &ldVt,
+ (complex *) work, &lwork, rwork, &info);
+ free(work); free(rwork);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static char doc_gesdd[] =
+ "Singular value decomposition of a real or complex matrix\n"
+ "(divide-and-conquer driver).\n\n"
+ "gesdd(A, S, jobz='N', U=None, V=None, m=A.size[0], n=A.size[1], \n"
+ " ldA=max(1,A.size[0]), ldU=None, ldVt=None, offsetA=0, \n"
+ " offsetS=0, offsetU=0, offsetVt=0)\n\n"
+ "PURPOSE\n"
+ "Computes singular values and, optionally, singular vectors of a \n"
+ "real or complex m by n matrix A. The argument jobz controls how\n"
+ "many singular vectors are computed:\n\n"
+ "'N': no singular vectors are computed.\n"
+ "'A': all m left singular vectors are computed and returned as\n"
+ " columns of U; all n right singular vectors are computed \n"
+ " and returned as rows of Vt.\n"
+ "'S': the first min(m,n) left and right singular vectors are\n"
+ " computed and returned as columns of U and rows of Vt.\n"
+ "'O': if m>=n, the first n left singular vectors are returned as\n"
+ " columns of A and the n right singular vectors are returned\n"
+ " as rows of Vt. If m<n, the m left singular vectors are\n"
+ " returned as columns of U and the first m right singular\n"
+ " vectors are returned as rows of A.\n\n"
+ "Note that the (conjugate) transposes of the right singular \n"
+ "vectors are returned in Vt or A.\n\n"
+ "On exit (in all cases), the contents of A are destroyed.\n\n"
+ "ARGUMENTS\n"
+ "A 'd' or 'z' matrix\n\n"
+ "S 'd' matrix of length at least min(m,n). On exit, \n"
+ " contains the computed singular values in descending\n"
+ " order.\n\n"
+ "jobz 'N', 'A', 'S' or 'O'\n\n"
+ "U 'd' or 'z' matrix. Must have the same type as A.\n"
+ " Not referenced if jobz is 'N' or jobz is 'O' and m>=n.\n"
+ " If jobz is 'A' or jobz is 'O' and m<n, a matrix with\n"
+ " at least m columns. If jobz is 'S', a matrix with at\n"
+ " least min(m,n) columns. On exit (except when jobz is\n"
+ " 'N' or jobz is 'O' and m>=n), contains the computed\n"
+ " left singular vectors stored columnwise.\n\n"
+ "Vt 'd' or 'z' matrix. Must have the same type as A.\n"
+ " Not referenced if jobz is 'N' or jobz is 'O' and m<n.\n"
+ " If jobz is 'A' or 'S' or jobz is 'O' and m>=n, a\n"
+ " matrix with at least n columns. On exit (except when\n"
+ " jobz is 'N' or jobz is 'O' and m<n), the rows of Vt\n"
+ " contain the computed right singular vectors, or, in\n"
+ " the complex case, their complex conjugates.\n\n"
+ "m integer. If negative, the default value is used.\n\n"
+ "n integer. If negative, the default value is used.\n\n"
+ "ldA nonnegative integer. ldA >= max(1,m).\n"
+ " If zero, the default value is used.\n\n"
+ "ldU nonnegative integer.\n"
+ " ldU >= 1 if jobz is 'N' or 'O'.\n"
+ " ldU >= max(1,m) if jobz is 'S' or 'A' or jobz is 'O'\n"
+ " and m<n. The default value is max(1,U.size[0]) if\n"
+ " jobz is 'S' or 'A' or jobz is'O' and m<n, and 1\n"
+ " otherwise.\n\n"
+ "ldVt nonnegative integer.\n"
+ " ldVt >= 1 if jobz is 'N'.\n"
+ " ldVt >= max(1,n) if jobz is 'A' or jobz is 'O' and \n"
+ " m>=n. \n"
+ " ldVt >= max(1,min(m,n)) if ldVt is 'S'.\n"
+ " The default value is max(1,Vt.size[0]) if jobvt is 'A'\n"
+ " or 'S' or jobvt is 'O' and m>=n, and 1 otherwise.\n"
+ " If zero, the default value is used.\n\n"
+ "offsetA nonnegative integer\n\n"
+ "offsetS nonnegative integer\n\n"
+ "offsetU nonnegative integer\n\n"
+ "offsetVt nonnegative integer";
+
+static PyObject* gesdd(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *A, *S, *U=NULL, *Vt=NULL;
+ int m=-1, n=-1, ldA=0, ldU=0, ldVt=0, oA=0, oS=0, oU=0, oVt=0, info,
+ *iwork=NULL, lwork;
+ double *rwork=NULL;
+ void *work=NULL;
+ number wl;
+ char jobz='N';
+ char *kwlist[] = {"A", "S", "jobz", "U", "Vt", "m", "n", "ldA",
+ "ldU", "ldVt", "offsetA", "offsetS", "offsetU", "offsetVt",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|cOOiiiiiiiii",
+ kwlist, &A, &S, &jobz, &U, &Vt, &m, &n, &ldA, &ldU, &ldVt, &oA,
+ &oS, &oU, &oVt)) return NULL;
+
+ if (!Matrix_Check(A)) err_mtrx("A");
+ if (!Matrix_Check(S) || MAT_ID(S) != DOUBLE) err_dbl_mtrx("S");
+ if (jobz != 'A' && jobz != 'S' && jobz != 'O' && jobz != 'N')
+ err_char("jobz", "'A', 'S', 'O', 'N'");
+ if (m < 0) m = A->nrows;
+ if (n < 0) n = A->ncols;
+ if (m == 0 || n == 0) return Py_BuildValue("");
+ if (ldA == 0) ldA = MAX(1,A->nrows);
+ if (ldA < MAX(1,m)) err_ld("ldA");
+ if (jobz == 'A' || jobz == 'S' || (jobz == 'O' && m<n)){
+ if (!U || !Matrix_Check(U)) err_mtrx("U");
+ if (MAT_ID(U) != MAT_ID(A)) err_conflicting_ids;
+ if (ldU == 0) ldU = MAX(1,U->nrows);
+ if (ldU < MAX(1,m)) err_ld("ldU");
+ } else {
+ if (ldU == 0) ldU = 1;
+ if (ldU < 1) err_ld("ldU");
+ }
+ if (jobz == 'A' || jobz == 'S' || (jobz == 'O' && m>=n)){
+ if (!Vt || !Matrix_Check(Vt)) err_mtrx("Vt");
+ if (MAT_ID(Vt) != MAT_ID(A)) err_conflicting_ids;
+ if (ldVt == 0) ldVt = MAX(1,Vt->nrows);
+ if (ldVt < ((jobz == 'A' || jobz == 'O') ? MAX(1,n) :
+ MAX(1,MIN(m,n)))) err_ld("ldVt");
+ } else {
+ if (ldVt == 0) ldVt = 1;
+ if (ldVt < 1) err_ld("ldVt");
+ }
+ if (oA < 0) err_nn_int("offsetA");
+ if (oA + (n-1)*ldA + m > len(A)) err_buf_len("A");
+ if (oS < 0) err_nn_int("offsetS");
+ if (oS + MIN(m,n) > len(S)) err_buf_len("S");
+ if (jobz == 'A' || jobz == 'S' || (jobz == 'O' && m<n)){
+ if (oU < 0) err_nn_int("offsetU");
+ if (oU + ((jobz == 'A' || jobz == 'O') ? m-1 : MIN(m,n)-1)*ldU
+ + m > len(U))
+ err_buf_len("U");
+ }
+ if (jobz == 'A' || jobz == 'S' || (jobz == 'O' && m>=n)){
+ if (oVt < 0) err_nn_int("offsetVt");
+ if (oVt + (n-1)*ldVt + ((jobz == 'A' || jobz == 'O') ? n :
+ MIN(m,n)) > len(Vt)) err_buf_len("Vt");
+ }
+
+ switch (MAT_ID(A)){
+ case DOUBLE:
+ lwork = -1;
+ dgesdd_(&jobz, &m, &n, NULL, &ldA, NULL, NULL, &ldU, NULL,
+ &ldVt, &wl.d, &lwork, NULL, &info);
+ lwork = (int) wl.d;
+ work = (void *) calloc(lwork, sizeof(double));
+ iwork = (int *) calloc(8*MIN(m,n), sizeof(int));
+ if (!work || !iwork){
+ free(work); free(iwork);
+ return PyErr_NoMemory();
+ }
+ dgesdd_(&jobz, &m, &n, MAT_BUFD(A)+oA, &ldA, MAT_BUFD(S)+oS,
+ (jobz == 'A' || jobz == 'S' || (jobz == 'O' && m<n)) ?
+ MAT_BUFD(U)+oU : NULL, &ldU, (jobz == 'A' ||
+ jobz == 'S' || (jobz == 'O' && m>=n)) ?
+ MAT_BUFD(Vt)+oVt : NULL, &ldVt, (double *) work, &lwork,
+ iwork, &info);
+ free(work); free(iwork);
+ break;
+
+ case COMPLEX:
+ lwork = -1;
+ zgesdd_(&jobz, &m, &n, NULL, &ldA, NULL, NULL, &ldU, NULL,
+ &ldVt, &wl.z, &lwork, NULL, NULL, &info);
+ lwork = (int) creal(wl.z);
+ work = (void *) calloc(lwork, sizeof(complex));
+ iwork = (int *) calloc(8*MIN(m,n), sizeof(int));
+ rwork = (double *) calloc( (jobz == 'N') ? 7*MIN(m,n) :
+ 5*MIN(m,n)*(MIN(m,n)+1), sizeof(double));
+ if (!work || !iwork || !rwork){
+ free(work); free(iwork); free(rwork);
+ return PyErr_NoMemory();
+ }
+ zgesdd_(&jobz, &m, &n, MAT_BUFZ(A)+oA, &ldA, MAT_BUFD(S)+oS,
+ (jobz == 'A' || jobz == 'S' || (jobz == 'O' && m<n)) ?
+ MAT_BUFZ(U)+oU : NULL, &ldU, (jobz == 'A' ||
+ jobz == 'S' || (jobz == 'O' && m>=n)) ?
+ MAT_BUFZ(Vt)+oVt : NULL, &ldVt, (complex *) work,
+ &lwork, rwork, iwork, &info);
+ free(work); free(iwork); free(rwork);
+ break;
+
+ default:
+ err_invalid_id;
+ }
+
+ if (info) err_lapack
+ else return Py_BuildValue("");
+}
+
+
+static PyMethodDef lapack_functions[] = {
+{"getrf", (PyCFunction) getrf, METH_VARARGS|METH_KEYWORDS, doc_getrf},
+{"getrs", (PyCFunction) getrs, METH_VARARGS|METH_KEYWORDS, doc_getrs},
+{"getri", (PyCFunction) getri, METH_VARARGS|METH_KEYWORDS, doc_getri},
+{"gesv", (PyCFunction) gesv, METH_VARARGS|METH_KEYWORDS, doc_gesv},
+{"gbtrf", (PyCFunction) gbtrf, METH_VARARGS|METH_KEYWORDS, doc_gbtrf},
+{"gbtrs", (PyCFunction) gbtrs, METH_VARARGS|METH_KEYWORDS, doc_gbtrs},
+{"gbsv", (PyCFunction) gbsv, METH_VARARGS|METH_KEYWORDS, doc_gbsv},
+{"gttrf", (PyCFunction) gttrf, METH_VARARGS|METH_KEYWORDS, doc_gttrf},
+{"gttrs", (PyCFunction) gttrs, METH_VARARGS|METH_KEYWORDS, doc_gttrs},
+{"gtsv", (PyCFunction) gtsv, METH_VARARGS|METH_KEYWORDS, doc_gtsv},
+{"potrf", (PyCFunction) potrf, METH_VARARGS|METH_KEYWORDS, doc_potrf},
+{"potrs", (PyCFunction) potrs, METH_VARARGS|METH_KEYWORDS, doc_potrs},
+{"potri", (PyCFunction) potri, METH_VARARGS|METH_KEYWORDS, doc_potri},
+{"posv", (PyCFunction) posv, METH_VARARGS|METH_KEYWORDS, doc_posv},
+{"pbtrf", (PyCFunction) pbtrf, METH_VARARGS|METH_KEYWORDS, doc_pbtrf},
+{"pbtrs", (PyCFunction) pbtrs, METH_VARARGS|METH_KEYWORDS, doc_pbtrs},
+{"pbsv", (PyCFunction) pbsv, METH_VARARGS|METH_KEYWORDS, doc_pbsv},
+{"pttrf", (PyCFunction) pttrf, METH_VARARGS|METH_KEYWORDS, doc_pttrf},
+{"pttrs", (PyCFunction) pttrs, METH_VARARGS|METH_KEYWORDS, doc_pttrs},
+{"ptsv", (PyCFunction) ptsv, METH_VARARGS|METH_KEYWORDS, doc_ptsv},
+{"sytrs", (PyCFunction) sytrs, METH_VARARGS|METH_KEYWORDS, doc_sytrs},
+{"hetrs", (PyCFunction) hetrs, METH_VARARGS|METH_KEYWORDS, doc_hetrs},
+{"sytrf", (PyCFunction) sytrf, METH_VARARGS|METH_KEYWORDS, doc_sytrf},
+{"hetrf", (PyCFunction) hetrf, METH_VARARGS|METH_KEYWORDS, doc_hetrf},
+{"sytri", (PyCFunction) sytri, METH_VARARGS|METH_KEYWORDS, doc_sytri},
+{"sysv", (PyCFunction) sysv, METH_VARARGS|METH_KEYWORDS, doc_sysv},
+{"hetri", (PyCFunction) hetri, METH_VARARGS|METH_KEYWORDS, doc_hetri},
+{"hesv", (PyCFunction) hesv, METH_VARARGS|METH_KEYWORDS, doc_hesv},
+{"trtrs", (PyCFunction) trtrs, METH_VARARGS|METH_KEYWORDS, doc_trtrs},
+{"trtri", (PyCFunction) trtri, METH_VARARGS|METH_KEYWORDS, doc_trtri},
+{"tbtrs", (PyCFunction) tbtrs, METH_VARARGS|METH_KEYWORDS, doc_tbtrs},
+{"gels", (PyCFunction) gels, METH_VARARGS|METH_KEYWORDS, doc_gels},
+{"geqrf", (PyCFunction) geqrf, METH_VARARGS|METH_KEYWORDS, doc_geqrf},
+{"ormqr", (PyCFunction) ormqr, METH_VARARGS|METH_KEYWORDS, doc_ormqr},
+{"unmqr", (PyCFunction) unmqr, METH_VARARGS|METH_KEYWORDS, doc_unmqr},
+{"syev", (PyCFunction) syev, METH_VARARGS|METH_KEYWORDS, doc_syev},
+{"heev", (PyCFunction) heev, METH_VARARGS|METH_KEYWORDS, doc_heev},
+{"syevx", (PyCFunction) syevx, METH_VARARGS|METH_KEYWORDS, doc_syevx},
+{"heevx", (PyCFunction) heevx, METH_VARARGS|METH_KEYWORDS, doc_heevx},
+{"sygv", (PyCFunction) sygv, METH_VARARGS|METH_KEYWORDS, doc_sygv},
+{"hegv", (PyCFunction) hegv, METH_VARARGS|METH_KEYWORDS, doc_hegv},
+{"syevd", (PyCFunction) syevd, METH_VARARGS|METH_KEYWORDS, doc_syevd},
+{"heevd", (PyCFunction) heevd, METH_VARARGS|METH_KEYWORDS, doc_heevd},
+{"syevr", (PyCFunction) syevr, METH_VARARGS|METH_KEYWORDS, doc_syevr},
+{"heevr", (PyCFunction) heevr, METH_VARARGS|METH_KEYWORDS, doc_heevr},
+{"gesvd", (PyCFunction) gesvd, METH_VARARGS|METH_KEYWORDS, doc_gesvd},
+{"gesdd", (PyCFunction) gesdd, METH_VARARGS|METH_KEYWORDS, doc_gesdd},
+{NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC initlapack(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("cvxopt.lapack", lapack_functions, lapack__doc__);
+
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/C/misc.h b/src/C/misc.h
new file mode 100644
index 0000000..fb8a9fb
--- /dev/null
+++ b/src/C/misc.h
@@ -0,0 +1,85 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#ifndef __MISC__
+#define __MISC__
+
+#define PY_NUMBER(O) (PyInt_Check(O) || PyFloat_Check(O) || PyComplex_Check(O))
+
+#ifndef NO_ANSI99_COMPLEX
+typedef union {
+ double d;
+ int_t i;
+ complex z;
+} number;
+#endif
+
+#define MAX(X,Y) ((X) > (Y) ? (X) : (Y))
+#define MIN(X,Y) ((X) < (Y) ? (X) : (Y))
+
+#define PY_ERR(E,str) { PyErr_SetString(E, str); return NULL; }
+#define PY_ERR_INT(E,str) { PyErr_SetString(E, str); return -1; }
+#define PY_ERR_TYPE(str) PY_ERR(PyExc_TypeError, str)
+
+/* Python style cyclic wrap-around for indices*/
+#define CWRAP(i,m) (i >= 0 ? i : m+i)
+#define OUT_RNG(i, dim) (i < -dim || i >= dim)
+
+
+#define VALID_TC_MAT(t) (t=='i' || t=='d' || t=='z')
+#define VALID_TC_SP(t) (t=='d' || t=='z')
+#define TC2ID(c) (c=='i' ? 0 : (c=='d' ? 1 : 2))
+
+#define X_ID(O) (Matrix_Check(O) ? MAT_ID(O) : SP_ID(O))
+#define X_NROWS(O) (Matrix_Check(O) ? MAT_NROWS(O) : SP_NROWS(O))
+#define X_NCOLS(O) (Matrix_Check(O) ? MAT_NCOLS(O) : SP_NCOLS(O))
+
+#define TypeCheck_CObject(O,str,errstr) { \
+ char *descr = PyCObject_GetDesc(O); \
+ if (!descr || strcmp(descr,str)) PY_ERR(PyExc_TypeError,errstr); }
+
+
+#define len(x) (Matrix_Check(x) ? MAT_LGT(x) : SP_LGT(x))
+
+#define err_mtrx(s) PY_ERR_TYPE(s " must be a matrix")
+
+#define err_bool(s) PY_ERR_TYPE(s " must be True or False")
+
+#define err_conflicting_ids { \
+ PY_ERR_TYPE("conflicting types for matrix arguments"); }
+
+#define err_invalid_id {PY_ERR_TYPE( \
+ "matrix arguments must have type 'd' or 'z'") }
+
+#define err_nz_int(s) PY_ERR_TYPE(s " must be a nonzero integer")
+
+#define err_nn_int(s) PY_ERR_TYPE(s " must be a nonnegative integer")
+
+#define err_buf_len(s) PY_ERR_TYPE("length of " s " is too small")
+
+#define err_type(s) PY_ERR_TYPE("incompatible type for " s)
+
+#define err_p_int(s) { \
+ PY_ERR(PyExc_ValueError, s " must be a positive integer") }
+
+#define err_char(s1,s2) { \
+ PY_ERR(PyExc_ValueError, "possible values of " s1 " are: " s2) }
+
+#define err_ld(s) { \
+ PY_ERR(PyExc_ValueError, "illegal value of " s) }
+
+#define err_int_mtrx(s) { \
+ PY_ERR_TYPE(s " must be a matrix with typecode 'i'") }
+
+#define err_dbl_mtrx(s) { \
+ PY_ERR_TYPE(s " must be a matrix with typecode 'd'") }
+
+#define err_CO(s) PY_ERR_TYPE(s " is not a CObject")
+
+
+#define err_msk_noparam "missing options dictionary"
+
+
+#endif
diff --git a/src/C/mosek.c b/src/C/mosek.c
new file mode 100644
index 0000000..6900da3
--- /dev/null
+++ b/src/C/mosek.c
@@ -0,0 +1,778 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+
+#include "cvxopt.h"
+#include "misc.h"
+#include "mosek.h"
+
+PyDoc_STRVAR(mosek__doc__,
+"Interface to the LP and QP solvers in MOSEK.\n\n"
+"The MOSEK control parameters have the default values listed in \n"
+"the MOSEK documentation at\n"
+" http://www.mosek.com/products/3/tools/doc/html/tools/node22.html.\n"
+"They can be modified by making an entry in the dictionary\n"
+"mosek.options. For example, the command\n"
+" mosek.options['MSK_IPAR_LOG']=0\n"
+"turns off the printed output during execution of mosek.solvelp().");
+
+static PyObject *mosek_module;
+
+static void MSKAPI printstr(void *handle, char str[])
+{
+ printf("%s",str);
+} /* printstr */
+
+static char doc_mosek_solvelp[] =
+ "Solves a linear program using MOSEK.\n\n"
+ "(prosta, solsta, x, z, y) = solvelp(c, G, h, A, b)\n"
+ "(prosta, solsta, x, z) = solvelp(c, G, h)\n\n"
+ "PURPOSE\n"
+ "(prosta, solsta, x, z, y) = solvelp(c, G, h, A, b) solves the pair\n"
+ "of primal and dual LPs\n\n"
+ " minimize c'*x maximize -h'*z + b'*y\n"
+ " subject to G*x <= h subject to G'*z + A'*y + c = 0\n"
+ " A*x = b z >= 0.\n\n"
+ "(prosta, solsta, x, z) = solvelp(c, G, h) solves the pair of\n"
+ "primal and dual LPs\n\n"
+ " minimize c'*x maximize -h'*z \n"
+ " subject to G*x <= h subject to G'*z + c = 0\n"
+ " z >= 0.\n\n"
+ "ARGUMENTS\n"
+ "c nx1 'd' matrix with n>=1\n\n"
+ "G mxn 'd' or nonsymmetric sparse matrix with m>=1\n\n"
+ "h mx1 'd' matrix\n\n"
+ "A pxn 'd' or nonsymmetric sparse matrix with p>=0\n\n"
+ "b px1 'd' matrix\n\n"
+ "prosta the problem status string returned by MOSEK\n\n"
+ "solsta the solution status string returned by MOSEK\n\n"
+ "x the primal solution\n\n"
+ "z,y the dual solution.";
+
+static PyObject *
+mosek_solvelp(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *c, *h, *b=NULL, *x=NULL, *z=NULL, *yu=NULL, *yl=NULL;
+ PyObject *G, *A=NULL, *t=NULL;
+ int m, n, p, i, j, k, nnz=0, nnzmax;
+ char *kwlist[] = {"c", "G", "h", "A", "b", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|OO", kwlist, &c,
+ &G, &h, &A, &b)) return NULL;
+
+ if (!((Matrix_Check(G) && MAT_ID(G) == DOUBLE) ||
+ (SpMatrix_Check(G) && SP_ID(G) == DOUBLE))) {
+ PY_ERR(PyExc_ValueError, "G must be a dense or sparse matrix"
+ " with typecode 'd'");
+ return NULL;
+ }
+ if ((m = Matrix_Check(G) ? MAT_NROWS(G) : SP_NROWS(G)) <= 0)
+ err_p_int("m");
+ if ((n = Matrix_Check(G) ? MAT_NCOLS(G) : SP_NCOLS(G)) <= 0)
+ err_p_int("n");
+
+ if (!Matrix_Check(h) || h->id != DOUBLE)
+ err_dbl_mtrx("h");
+ if (h->nrows != m || h->ncols != 1){
+ PyErr_SetString(PyExc_ValueError, "incompatible dimensions");
+ return NULL;
+ }
+
+ if (A){
+ if (!((Matrix_Check(A) && MAT_ID(A) == DOUBLE) ||
+ (SpMatrix_Check(A) && SP_ID(A) == DOUBLE))) {
+ PyErr_SetString(PyExc_ValueError, "A must be a dense "
+ "or sparse matrix with typecode 'd'");
+ return NULL;
+ }
+ if ((p = Matrix_Check(A) ? MAT_NROWS(A) : SP_NROWS(A)) < 0)
+ err_p_int("p");
+ if ((Matrix_Check(A) ? MAT_NCOLS(A) : SP_NCOLS(A)) != n){
+ PyErr_SetString(PyExc_ValueError, "incompatible "
+ "dimensions");
+ return NULL;
+ }
+ }
+ else p = 0;
+ if (b && (!Matrix_Check(b) || b->id != DOUBLE))
+ err_dbl_mtrx("b");
+ if ((b && (b->nrows != p || b->ncols != 1)) || (!b && p !=0 )){
+ PyErr_SetString(PyExc_ValueError, "incompatible dimensions");
+ return NULL;
+ }
+
+
+ /* Setting up MOSEK environment */
+ nnzmax = (SpMatrix_Check(G) ? SP_NNZ(G) : m*n ) +
+ ((A && SpMatrix_Check(A)) ? SP_NNZ(A) : p*n);
+
+ int *bkc, *bkx, *ptrb, *ptre, *sub;
+ bkc = malloc((m+p)*sizeof(int));
+ bkx = malloc(n*sizeof(int));
+ ptrb = malloc(n*sizeof(int));
+ ptre = malloc(n*sizeof(int));
+ sub = malloc(nnzmax*sizeof(int));
+
+ double *blc, *buc, *blx, *bux, *val;
+ blc = malloc((m+p)*sizeof(double));
+ buc = malloc((m+p)*sizeof(double));
+ blx = malloc(n*sizeof(double));
+ bux = malloc(n*sizeof(double));
+ val = malloc(nnzmax*sizeof(double));
+
+ int r;
+ MSKenv_t env;
+ MSKtask_t task;
+
+ /* Make mosek environment. */
+ r = MSK_makeenv(&env,NULL,NULL,NULL,NULL);
+ if (!bkc || !blc || !buc || !bkx || !blx || !buc ||
+ !ptrb || !ptre || !sub || !val || r!=MSK_RES_OK) {
+ free(bkc); free(bkx); free(ptrb); free(ptre); free(sub);
+ free(blc); free(buc); free(blx); free(bux); free(val);
+ return PyErr_NoMemory();
+ }
+
+ /* Directs the env log stream to the user
+ specified procedure 'printstr'. */
+ MSK_linkfunctoenvstream(env,MSK_STREAM_LOG,NULL,printstr);
+
+ /* Initialize the environment. */
+ r = MSK_initenv(env);
+ if (r!=MSK_RES_OK) {
+ free(bkc); free(bkx); free(ptrb); free(ptre); free(sub);
+ free(blc); free(buc); free(blx); free(bux); free(val);
+ return PyErr_NoMemory();
+ }
+
+ /* Make the optimization task. */
+ r = MSK_maketask(env, (m+p), n, &task);
+ if (r!=MSK_RES_OK) {
+ free(bkc); free(bkx); free(ptrb); free(ptre); free(sub);
+ free(blc); free(buc); free(blx); free(bux); free(val);
+ MSK_deleteenv(&env);
+ return PyErr_NoMemory();
+ }
+
+ /* Directs the log task stream to the user
+ specified procedure 'printstr'. */
+ MSK_linkfunctotaskstream(task,MSK_STREAM_LOG,NULL,printstr);
+
+ /* Define bounds for the constraints
+
+ -infty <= G*x <= h
+ b <= A*x <= b
+ */
+
+ for (i=0; i<m; i++) {
+ bkc[i] = MSK_BK_UP;
+ blc[i] = -MSK_INFINITY;
+ buc[i] = MAT_BUFD(h)[i];
+ }
+
+ for (i=0; i<p; i++) {
+ bkc[m+i] = MSK_BK_FX;
+ blc[m+i] = MAT_BUFD(b)[i];
+ buc[m+i] = MAT_BUFD(b)[i];
+ }
+
+ /* bounds on the variables (none) */
+ for (i=0; i<n; i++) {
+ bkx[i] = MSK_BK_FR;
+ blx[i] = -MSK_INFINITY;
+ bux[i] = MSK_INFINITY;
+ }
+
+ /* constraint matrix */
+ for (j=0; j<n; j++) {
+
+ if (SpMatrix_Check(G)) {
+ for (k=SP_COL(G)[j]; k<SP_COL(G)[j+1]; k++) {
+ val[nnz] = SP_VALD(G)[k];
+ sub[nnz++] = SP_ROW(G)[k];
+ }
+ }
+ else {
+ for (k=0; k<m; k++) {
+ if (MAT_BUFD(G)[j*m+k] != 0.0) {
+ val[nnz] = MAT_BUFD(G)[j*m+k];
+ sub[nnz++] = k;
+ }
+ }
+ }
+
+ if (A) {
+ if (SpMatrix_Check(A)) {
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1]; k++) {
+ val[nnz] = SP_VALD(A)[k];
+ sub[nnz++] = m+SP_ROW(A)[k];
+ }
+ }
+ else {
+ for (k=0; k<p; k++) {
+ if (MAT_BUFD(A)[j*p+k] != 0.0) {
+ val[nnz] = MAT_BUFD(A)[j*p+k];
+ sub[nnz++] = m+k;
+ }
+ }
+ }
+ }
+
+ ptrb[j] = (j>0 ? ptre[j-1] : 0);
+ ptre[j] = nnz;
+ }
+
+ r = MSK_inputdata(task,
+ (m+p),n,
+ (m+p),n,
+ MAT_BUFD(c),0.0,
+ ptrb, ptre,
+ sub, val,
+ bkc, blc, buc,
+ bkx, blx, bux);
+
+ free(bkc); free(blc); free(buc);
+ free(bkx); free(blx); free(bux);
+ free(ptrb); free(ptre);
+ free(sub); free(val);
+
+ MSK_putintparam(task,MSK_IPAR_OBJECTIVE_SENSE,MSK_OBJECTIVE_SENSE_MIN);
+
+ PyObject *param;
+ if (!(param = PyObject_GetAttrString(mosek_module, "options")) ||
+ !PyDict_Check(param)) {
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ PY_ERR(PyExc_AttributeError,err_msk_noparam);
+ }
+
+ PyObject *key, *value;
+ int param_id;
+ int_compat pos = 0;
+
+ while (PyDict_Next(param, &pos, &key, &value)) {
+ MSK_isintparname(task, PyString_AS_STRING(key), ¶m_id);
+ if (param_id < MSK_IPAR_SOLUTION_CALLBACK) {
+ if (!PyInt_Check(value))
+ {
+ char err_str[100] = "invalid integer parameter: ";
+ strncat(err_str, PyString_AS_STRING(key), 100);
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ Py_DECREF(param);
+ PY_ERR(PyExc_ValueError,err_str);
+ }
+
+ MSK_putintparam(task, param_id, PyInt_AsLong(value));
+ continue;
+ }
+ MSK_isdouparname(task, PyString_AS_STRING(key), ¶m_id);
+ if (param_id < MSK_DPAR_NONCONVEX_TOL_OPT) {
+ if (!PyInt_Check(value) && !PyFloat_Check(value))
+ {
+ char err_str[100] = "invalid floating point parameter: ";
+ strncat(err_str, PyString_AS_STRING(key), 100);
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ Py_DECREF(param);
+ PY_ERR(PyExc_ValueError,err_str);
+ }
+
+ MSK_putdouparam(task, param_id, PyFloat_AsDouble(value));
+ continue;
+ }
+ }
+ Py_DECREF(param);
+
+ r = MSK_optimize(task);
+ if (r==MSK_RES_OK) {
+
+ if (!(t = PyTuple_New(A ? 5 : 4))) {
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ return PyErr_NoMemory();
+ }
+
+ x = (matrix *) Matrix_New(n,1,DOUBLE);
+ z = (matrix *) Matrix_New(m,1,DOUBLE);
+ if (A) {
+ yu = (matrix *) Matrix_New(p,1,DOUBLE);
+ yl = (matrix *) Matrix_New(p,1,DOUBLE);
+ }
+ if (!x || !z || (A && (!yu || !yl))){
+ Py_XDECREF(x);
+ Py_XDECREF(z);
+ Py_XDECREF(yu);
+ Py_XDECREF(yl);
+ Py_XDECREF(t);
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ return PyErr_NoMemory();
+ }
+
+ char statstr[50];
+ int solsta, prosta;
+ double tmp;
+
+ MSK_getsolutioninf(task, 0, &prosta, &solsta,
+ &tmp, &tmp, &tmp, &tmp, &tmp, &tmp, &tmp, &tmp, &tmp);
+
+ MSK_prostatostr (task, prosta, statstr);
+ PyTuple_SET_ITEM(t, 0, PyString_FromString(statstr));
+
+ MSK_solstatostr (task, solsta, statstr);
+ PyTuple_SET_ITEM(t, 1, PyString_FromString(statstr));
+
+ MSK_getsolutionslice(task, 0, MSK_SOL_ITEM_XX, 0, n, MAT_BUFD(x));
+ PyTuple_SET_ITEM(t, 2, (PyObject *) x);
+
+ MSK_getsolutionslice(task, 0, MSK_SOL_ITEM_SUC, 0, m, MAT_BUFD(z));
+ PyTuple_SET_ITEM(t, 3, (PyObject *) z);
+
+ if (A) {
+ MSK_getsolutionslice(task,0,MSK_SOL_ITEM_SUC,m,m+p,MAT_BUFD(yu));
+ MSK_getsolutionslice(task,0,MSK_SOL_ITEM_SLC,m,m+p,MAT_BUFD(yl));
+
+ for (i=0; i<yu->nrows; i++) MAT_BUFD(yu)[i] -= MAT_BUFD(yl)[i];
+
+ Py_DECREF(yl);
+ PyTuple_SET_ITEM(t, 4, (PyObject *) yu);
+ }
+
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+
+ return (PyObject *) t;
+ }
+
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ t = PyString_FromString("internal mosek error");
+ return (PyObject *) t;
+}
+
+static char doc_mosek_solveqp[] =
+ "Solves a convex quadratic program using MOSEK.\n\n"
+ "(prosta, solsta, x, z, y) = solveqp(P, q, G, h, A, b)\n"
+ "(prosta, solsta, x, z) = solveqp(P, q, G, h)\n\n"
+ "PURPOSE\n"
+ "(prosta, solsta, x, z, y) = solveqp(P, q, G, h, A, b) solves the QP\n\n"
+ " minimize (1/2)*x'*P*x + q'*x\n"
+ " subject to G*x <= h\n"
+ " A*x = b\n\n"
+ "and its dual\n\n"
+ " maximize (1/2)*(q+G'*z+A'*y)'*Pinv*(q+G'*z+A'*y) - h'*z - b'*y\n"
+ " subject to G*x <= h\n"
+ " A*x = b\n"
+ " z >= 0\n"
+ " (I-P*Pinv)*(q+G'*z+A'*y) = 0\n\n"
+ "where Pinv is the Moore-Penrose pseudoinverse of P.\n\n"
+ "(prosta, solsta, x, z) = solveqp(P, q, G, h) solves the LP\n\n"
+ " minimize (1/2)*x'*P*q + q'*x\n"
+ " subject to G*x <= h\n\n"
+ "and its dual\n\n"
+ " maximize (1/2)*(q+G'*z)'*Pinv*(q+G'*z) - h'*z\n"
+ " subject to G*x <= h\n"
+ " z >= 0\n"
+ " (I-P*Pinv)*(q+G'*z) = 0\n\n"
+ "where Pinv is the Moore-Penrose pseudoinverse of P.\n\n"
+ "ARGUMENTS\n"
+ "P nxn 'd' matrix with \n\n"
+ "q nx1 'd' matrix with n>=1\n\n"
+ "G mxn 'd' or nonsymmetric sparse matrix with m>=0\n\n"
+ "h mx1 'd' matrix\n\n"
+ "A pxn 'd' or nonsymmetric sparse matrix with p>=0\n\n"
+ "b px1 'd' matrix\n\n"
+ "prosta the problem status string returned by MOSEK\n\n"
+ "solsta the solution status string returned by MOSEK\n\n"
+ "x the primal solution\n\n"
+ "z,y the dual solution.";
+
+static PyObject *
+mosek_solveqp(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *q, *h=NULL, *b=NULL, *x=NULL, *z=NULL, *yu=NULL, *yl=NULL;
+ PyObject *P, *G=NULL, *A=NULL, *t=NULL;
+ int m, n, p, i, j, k, nnz=0, nnzmax, numqonz;
+ char *kwlist[] = {"P", "q", "G", "h", "A", "b", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|OOOO", kwlist,
+ &P, &q, &G, &h, &A, &b)) return NULL;
+
+ if (!(Matrix_Check(P) && MAT_ID(P) == DOUBLE &&
+ MAT_NCOLS(P) == MAT_NROWS(P)) &&
+ !(SpMatrix_Check(P) && SP_ID(P) == DOUBLE)) {
+ PyErr_SetString(PyExc_ValueError, "P must be a square symmetric"
+ " sparse or dense matrix with typecode 'd'");
+ return NULL;
+ }
+
+ if (G && ((Matrix_Check(G) && MAT_ID(G) != DOUBLE) ||
+ (SpMatrix_Check(G) && SP_ID(G) != DOUBLE))) {
+ PyErr_SetString(PyExc_ValueError, "G must be a sparse or dense"
+ " matrix with typecode 'd'");
+ return NULL;
+ }
+
+ if (!(SpMatrix_Check(P) && ((G && SpMatrix_Check(G)) || !G) &&
+ ((A && SpMatrix_Check(A)) || !A)) &&
+ !(Matrix_Check(P) && ((G && Matrix_Check(G)) || !G) &&
+ ((A && Matrix_Check(A)) || !A)))
+ PY_ERR(PyExc_ValueError, "P, G and A must all be either sparse"
+ " or dense matrices");
+
+ int nP = (Matrix_Check(P) ? MAT_NROWS(P) : SP_NROWS(P));
+ if (!Matrix_Check(q) || MAT_ID(q) != DOUBLE)
+ PY_ERR(PyExc_ValueError, "q must be a 'd' matrix");
+
+ if (G) {
+ if ((m = Matrix_Check(G) ? MAT_NROWS(G) : SP_NROWS(G)) < 0)
+ err_nn_int("m");
+ if ((n = Matrix_Check(G) ? MAT_NCOLS(G) : SP_NCOLS(G)) <= 0)
+ err_p_int("n");
+
+ if (!h || !Matrix_Check(h) || h->id != DOUBLE)
+ err_dbl_mtrx("h");
+ if (h->nrows != m || h->ncols != 1 || nP != n ||
+ q->nrows != n || q->ncols != 1) {
+ PyErr_SetString(PyExc_ValueError, "incompatible dimensions");
+ return NULL;
+ }
+ }
+ else {
+ m = 0; n = nP;
+ }
+
+ if (A) {
+ if ((Matrix_Check(A) && MAT_ID(A) != DOUBLE) ||
+ (SpMatrix_Check(A) && SP_ID(A) != DOUBLE)) {
+ PyErr_SetString(PyExc_ValueError, "A must be a sparse "
+ "or dense matrix with typecode 'd'");
+ return NULL;
+ }
+ if ((p = Matrix_Check(A) ? MAT_NROWS(A) : SP_NROWS(A)) < 0)
+ err_nn_int("p");
+ if ((Matrix_Check(A) ? MAT_NCOLS(A) : SP_NCOLS(A)) != n){
+ PyErr_SetString(PyExc_ValueError, "incompatible "
+ "dimensions");
+ return NULL;
+ }
+ }
+ else p = 0;
+ if (b && (!Matrix_Check(b) || b->id != DOUBLE))
+ err_dbl_mtrx("b");
+ if ((b && (b->nrows != p || b->ncols != 1)) || (!b && p !=0)) {
+ PyErr_SetString(PyExc_ValueError, "incompatible dimensions");
+ return NULL;
+ }
+
+ /* Setting up MOSEK environment */
+ numqonz = (SpMatrix_Check(P) ? SP_NNZ(P) : n*(n+1)/2);
+ nnzmax = ((G && SpMatrix_Check(G)) ? SP_NNZ(G) : m*n ) +
+ ((A && SpMatrix_Check(A)) ? SP_NNZ(A) : p*n);
+
+ int *bkc, *bkx, *ptrb, *ptre, *sub, *qosubi, *qosubj;
+ bkc = malloc((m+p)*sizeof(int));
+ bkx = malloc(n*sizeof(int));
+ ptrb = malloc(n*sizeof(int));
+ ptre = malloc(n*sizeof(int));
+ sub = malloc(nnzmax*sizeof(int));
+ qosubi = malloc(numqonz*sizeof(int));
+ qosubj = malloc(numqonz*sizeof(int));
+
+ double *blc, *buc, *blx, *bux, *val, *qoval;
+ blc = malloc((m+p)*sizeof(double));
+ buc = malloc((m+p)*sizeof(double));
+ blx = malloc(n*sizeof(double));
+ bux = malloc(n*sizeof(double));
+ val = malloc(nnzmax*sizeof(double));
+ qoval = malloc(numqonz*sizeof(double));
+
+ int r;
+ MSKenv_t env;
+ MSKtask_t task;
+
+ /* Make mosek environment. */
+ r = MSK_makeenv(&env,NULL,NULL,NULL,NULL);
+ if (!bkc || !blc || !buc || !bkx || !blx || !buc ||
+ !ptrb || !ptre || !sub || !val ||
+ !qosubi || !qosubj || !qoval || r!=MSK_RES_OK) {
+ free(bkc); free(bkx); free(ptrb); free(ptre); free(sub);
+ free(blc); free(buc); free(blx); free(bux); free(val);
+ free(qosubi); free(qosubj); free(qoval);
+ return PyErr_NoMemory();
+ }
+
+ /* Directs the env log stream to the user
+ specified procedure 'printstr'. */
+ MSK_linkfunctoenvstream(env,MSK_STREAM_LOG,NULL,printstr);
+
+ /* Initialize the environment. */
+ r = MSK_initenv(env);
+ if (r!=MSK_RES_OK) {
+ free(bkc); free(bkx); free(ptrb); free(ptre); free(sub);
+ free(blc); free(buc); free(blx); free(bux); free(val);
+ free(qosubi); free(qosubj); free(qoval);
+ return PyErr_NoMemory();
+ }
+
+ /* Make the optimization task. */
+ r = MSK_maketask(env, (m+p), n, &task);
+ if (r!=MSK_RES_OK) {
+ free(bkc); free(bkx); free(ptrb); free(ptre); free(sub);
+ free(blc); free(buc); free(blx); free(bux); free(val);
+ free(qosubi); free(qosubj); free(qoval);
+ MSK_deleteenv(&env);
+ return PyErr_NoMemory();
+ }
+
+ /* Directs the log task stream to the user
+ specified procedure 'printstr'. */
+ MSK_linkfunctotaskstream(task,MSK_STREAM_LOG,NULL,printstr);
+
+ /* Setup quadratic term of objective */
+ if (Matrix_Check(P)) {
+ for (j=0, k=0; j<n; j++)
+ for (i=j; i<n; i++, k++) {
+ qosubi[k] = i;
+ qosubj[k] = j;
+ qoval[k] = MAT_BUFD(P)[j*n+i];
+ }
+ } else {
+ for (j=0, k=0; j<n; j++) {
+ for (i=SP_COL(P)[j]; i<SP_COL(P)[j+1]; i++, k++) {
+ qosubi[k] = SP_ROW(P)[k];
+ qosubj[k] = j;
+ qoval[k] = SP_VALD(P)[k];
+ }
+ }
+ }
+
+ /* Define bounds for the constraints
+
+ -infty <= G*x <= h
+ b <= A*x <= b
+ */
+
+ for (i=0; i<m; i++) {
+ bkc[i] = MSK_BK_UP;
+ blc[i] = -MSK_INFINITY;
+ buc[i] = MAT_BUFD(h)[i];
+ }
+
+ for (i=0; i<p; i++) {
+ bkc[m+i] = MSK_BK_FX;
+ blc[m+i] = MAT_BUFD(b)[i];
+ buc[m+i] = MAT_BUFD(b)[i];
+ }
+
+ /* bounds on the variables (none) */
+ for (i=0; i<n; i++) {
+ bkx[i] = MSK_BK_FR;
+ blx[i] = -MSK_INFINITY;
+ bux[i] = MSK_INFINITY;
+ }
+
+ /* constraint matrix */
+ for (j=0; j<n; j++) {
+
+ if (G && SpMatrix_Check(G)) {
+ for (k=SP_COL(G)[j]; k<SP_COL(G)[j+1]; k++) {
+ val[nnz] = SP_VALD(G)[k];
+ sub[nnz++] = SP_ROW(G)[k];
+ }
+ }
+ else {
+ for (k=0; k<m; k++) {
+ if (MAT_BUFD(G)[j*m+k] != 0.0) {
+ val[nnz] = MAT_BUFD(G)[j*m+k];
+ sub[nnz++] = k;
+ }
+ }
+ }
+
+ if (A) {
+ if (SpMatrix_Check(A)) {
+ for (k=SP_COL(A)[j]; k<SP_COL(A)[j+1]; k++) {
+ val[nnz] = SP_VALD(A)[k];
+ sub[nnz++] = m+SP_ROW(A)[k];
+ }
+ }
+ else {
+ for (k=0; k<p; k++) {
+ if (MAT_BUFD(A)[j*p+k] != 0.0) {
+ val[nnz] = MAT_BUFD(A)[j*p+k];
+ sub[nnz++] = m+k;
+ }
+ }
+ }
+ }
+
+ ptrb[j] = (j>0 ? ptre[j-1] : 0);
+ ptre[j] = nnz;
+ }
+
+ r = MSK_inputdata(task,
+ (m+p),n,
+ (m+p),n,
+ MAT_BUFD(q),0.0,
+ ptrb, ptre,
+ sub, val,
+ bkc, blc, buc,
+ bkx, blx, bux);
+
+ r = MSK_putqobj (task, numqonz, qosubi, qosubj, qoval);
+
+ free(bkc); free(blc); free(buc);
+ free(bkx); free(blx); free(bux);
+ free(ptrb); free(ptre);
+ free(sub); free(val);
+ free(qosubi); free(qosubj); free(qoval);
+
+ MSK_putintparam(task,MSK_IPAR_OBJECTIVE_SENSE,MSK_OBJECTIVE_SENSE_MIN);
+
+ PyObject *param;
+ if (!(param = PyObject_GetAttrString(mosek_module, "options")) ||
+ !PyDict_Check(param)) {
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ PY_ERR(PyExc_AttributeError,err_msk_noparam);
+ }
+
+ PyObject *key, *value;
+ int param_id;
+ int_compat pos = 0;
+
+ while (PyDict_Next(param, &pos, &key, &value)) {
+ MSK_isintparname(task, PyString_AS_STRING(key), ¶m_id);
+ if (param_id < MSK_IPAR_SOLUTION_CALLBACK) {
+ if (!PyInt_Check(value))
+ {
+ char err_str[100] = "invalid integer parameter: ";
+ strncat(err_str, PyString_AS_STRING(key), 100);
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ Py_DECREF(param);
+ PY_ERR(PyExc_ValueError,err_str);
+ }
+
+ MSK_putintparam(task, param_id, PyInt_AsLong(value));
+ continue;
+ }
+ MSK_isdouparname(task, PyString_AS_STRING(key), ¶m_id);
+ if (param_id < MSK_DPAR_NONCONVEX_TOL_OPT) {
+ if (!PyInt_Check(value) && !PyFloat_Check(value))
+ {
+ char err_str[100] = "invalid floating point parameter: ";
+ strncat(err_str, PyString_AS_STRING(key), 100);
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ Py_DECREF(param);
+ PY_ERR(PyExc_ValueError,err_str);
+ }
+
+ MSK_putdouparam(task, param_id, PyFloat_AsDouble(value));
+ continue;
+ }
+ }
+ Py_DECREF(param);
+
+ r = MSK_optimize(task);
+ if (r==MSK_RES_OK) {
+
+ if (!(t = PyTuple_New(A ? 5 : 4))) {
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ return PyErr_NoMemory();
+ }
+
+ x = (matrix *) Matrix_New(n,1,DOUBLE);
+ z = (matrix *) Matrix_New(m,1,DOUBLE);
+ if (A) {
+ yu = (matrix *) Matrix_New(p,1,DOUBLE);
+ yl = (matrix *) Matrix_New(p,1,DOUBLE);
+ }
+ if (!x || !z || (A && (!yu || !yl))){
+ Py_XDECREF(x);
+ Py_XDECREF(z);
+ Py_XDECREF(yu);
+ Py_XDECREF(yl);
+ Py_XDECREF(t);
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+ return PyErr_NoMemory();
+ }
+
+ char statstr[50];
+ int solsta, prosta;
+ double tmp;
+
+ MSK_getsolutioninf(task, 0, &prosta, &solsta,
+ &tmp, &tmp, &tmp, &tmp, &tmp, &tmp, &tmp, &tmp, &tmp);
+
+ MSK_prostatostr (task, prosta, statstr);
+ PyTuple_SET_ITEM(t, 0, PyString_FromString(statstr));
+
+ MSK_solstatostr (task, solsta, statstr);
+ PyTuple_SET_ITEM(t, 1, PyString_FromString(statstr));
+
+ MSK_getsolutionslice(task, 0, MSK_SOL_ITEM_XX, 0, n, MAT_BUFD(x));
+ PyTuple_SET_ITEM(t, 2, (PyObject *) x);
+
+ MSK_getsolutionslice(task, 0, MSK_SOL_ITEM_SUC, 0, m, MAT_BUFD(z));
+ PyTuple_SET_ITEM(t, 3, (PyObject *) z);
+
+ if (A) {
+ MSK_getsolutionslice(task,0,MSK_SOL_ITEM_SUC,m,m+p,MAT_BUFD(yu));
+ MSK_getsolutionslice(task,0,MSK_SOL_ITEM_SLC,m,m+p,MAT_BUFD(yl));
+
+ for (i=0; i<yu->nrows; i++) MAT_BUFD(yu)[i] -= MAT_BUFD(yl)[i];
+
+ Py_DECREF(yl);
+ PyTuple_SET_ITEM(t, 4, (PyObject *) yu);
+ }
+
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+
+ return (PyObject *) t;
+ }
+
+ MSK_deletetask(&task);
+ MSK_deleteenv(&env);
+
+ char err_str[50];
+
+ switch (r) {
+ case MSK_RES_ERR_INV_PROBLEM:
+ PY_ERR(PyExc_ValueError,"MOSEK error: probably a non-convex "
+ "problem was specified");
+ break;
+ default:
+ sprintf(err_str, "Internal MOSEK error. Error code %i",r);
+ PY_ERR(PyExc_Exception,err_str);
+ }
+
+}
+
+
+static PyMethodDef mosek_functions[] = {
+ {"solvelp", (PyCFunction) mosek_solvelp, METH_VARARGS|METH_KEYWORDS,
+ doc_mosek_solvelp},
+ {"solveqp", (PyCFunction) mosek_solveqp, METH_VARARGS|METH_KEYWORDS,
+ doc_mosek_solveqp},
+ {NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC
+initmosek(void)
+{
+ mosek_module = Py_InitModule3("cvxopt.mosek", mosek_functions, mosek__doc__);
+
+ PyModule_AddObject(mosek_module, "options", PyDict_New());
+
+ if (import_cvxopt() < 0)
+ return;
+}
diff --git a/src/C/random.c b/src/C/random.c
new file mode 100644
index 0000000..49c4bca
--- /dev/null
+++ b/src/C/random.c
@@ -0,0 +1,144 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "cvxopt.h"
+
+#include <complex.h>
+
+#include "misc.h"
+#include "rngs/rngs.h"
+#include "rngs/rvgs.h"
+
+PyDoc_STRVAR(random__doc__,"Random Module.");
+
+static char doc_getseed[] =
+ "Returns the seed value for the random number generator.\n\n"
+ "getseed()";
+static PyObject *
+getseed(PyObject *self)
+{
+ long seed;
+ GetSeed(&seed);
+
+ return Py_BuildValue("l",seed);
+}
+
+static char doc_setseed[] =
+ "Sets the seed value for the random number generator.\n\n"
+ "setseed(value = 0.0)\n\n"
+ "ARGUMENTS\n"
+ "value a nonnegative number that specifies the seed value.\n"
+ " If value is 0, the system clock is used.";
+
+static PyObject *
+setseed(PyObject *self, PyObject *args)
+{
+ long seed = 0;
+
+ if (!PyArg_ParseTuple(args, "|l", &seed))
+ return NULL;
+
+ if (seed < 0) PY_ERR(PyExc_ValueError, "seed value must be non-negative");
+
+ PutSeed( (seed>0 ? seed : -1));
+ return Py_BuildValue("");
+}
+
+static char doc_normal[] =
+ "Randomly generates a matrix with normally distributed entries.\n\n"
+ "normal(nrows, ncols=1, mean=0, std=1)\n\n"
+ "PURPOSE\n"
+ "Returns a matrix with typecode 'd' and size nrows by ncols, with\n"
+ "its entries randomly generated from a normal distribution with mean\n"
+ "m and standard deviation std.\n\n"
+ "ARGUMENTS\n"
+ "nrows number of rows\n\n"
+ "ncols number of columns\n\n"
+ "mean approximate mean of the distribution\n\n"
+ "std standard deviation of the distribution";
+static PyObject *
+normal(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *obj;
+ int i, nrows, ncols = 1;
+ double m = 0, s = 1;
+ char *kwlist[] = {"nrows", "ncols", "mean", "std", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "i|idd", kwlist,
+ &nrows, &ncols, &m, &s)) return NULL;
+
+ if (s < 0.0) PY_ERR(PyExc_ValueError, "std must be non-negative");
+
+ if ((nrows<0) || (ncols<0)) {
+ PyErr_SetString(PyExc_TypeError, "dimensions must be non-negative");
+ return NULL;
+ }
+
+ if (!(obj = Matrix_New(nrows, ncols, DOUBLE)))
+ return PyErr_NoMemory();
+
+ for (i= 0; i < nrows*ncols; i++)
+ MAT_BUFD(obj)[i] = Normal(m,s);
+
+ return (PyObject *)obj;
+}
+
+static char doc_uniform[] =
+ "Randomly generates a matrix with uniformly distributed entries.\n\n"
+ "uniform(nrows, ncols=1, a=0, b=1)\n\n"
+ "PURPOSE\n"
+ "Returns a matrix with typecode 'd' and size nrows by ncols, with\n"
+ "its entries randomly generated from a uniform distribution on the\n"
+ "interval (a,b).\n\n"
+ "ARGUMENTS\n"
+ "nrows number of rows\n\n"
+ "ncols number of columns\n\n"
+ "a lower bound\n\n"
+ "b upper bound";
+
+static PyObject *
+uniform(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ matrix *obj;
+ int i, nrows, ncols = 1;
+ double a = 0, b = 1;
+
+ char *kwlist[] = {"nrows", "ncols", "a", "b", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "i|idd", kwlist,
+ &nrows, &ncols, &a, &b)) return NULL;
+
+ if (a>b) PY_ERR(PyExc_ValueError, "a must be less than b");
+
+ if ((nrows<0) || (ncols<0))
+ PY_ERR_TYPE("dimensions must be non-negative");
+
+ if (!(obj = (matrix *)Matrix_New(nrows, ncols, DOUBLE)))
+ return PyErr_NoMemory();
+
+ for (i= 0; i < nrows*ncols; i++)
+ MAT_BUFD(obj)[i] = Uniform(a,b);
+
+ return (PyObject *)obj;
+}
+
+static PyMethodDef random_functions[] = {
+ {"getseed",(PyCFunction)getseed,METH_NOARGS, doc_getseed},
+ {"setseed",(PyCFunction)setseed,METH_VARARGS, doc_setseed},
+ {"normal", (PyCFunction)normal, METH_VARARGS|METH_KEYWORDS, doc_normal},
+ {"uniform",(PyCFunction)uniform,METH_VARARGS|METH_KEYWORDS, doc_uniform},
+ {NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC
+initrandom(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("cvxopt.random", random_functions, random__doc__);
+
+ if (import_cvxopt() < 0)
+ return;
+}
diff --git a/src/C/rngs/README.cvxopt b/src/C/rngs/README.cvxopt
new file mode 100644
index 0000000..43eab85
--- /dev/null
+++ b/src/C/rngs/README.cvxopt
@@ -0,0 +1,3 @@
+The files in this directory are from the random number generator
+library by Steve Park & Dave Geyer.
+See www.cs.wm.edu/~va/software/park/park.html.
diff --git a/src/C/rngs/rngs.c b/src/C/rngs/rngs.c
new file mode 100644
index 0000000..a55f176
--- /dev/null
+++ b/src/C/rngs/rngs.c
@@ -0,0 +1,179 @@
+/* -------------------------------------------------------------------------
+ * This is an ANSI C library for multi-stream random number generation.
+ * The use of this library is recommended as a replacement for the ANSI C
+ * rand() and srand() functions, particularly in simulation applications
+ * where the statistical 'goodness' of the random number generator is
+ * important. The library supplies 256 streams of random numbers; use
+ * SelectStream(s) to switch between streams indexed s = 0,1,...,255.
+ *
+ * The streams must be initialized. The recommended way to do this is by
+ * using the function PlantSeeds(x) with the value of x used to initialize
+ * the default stream and all other streams initialized automatically with
+ * values dependent on the value of x. The following convention is used
+ * to initialize the default stream:
+ * if x > 0 then x is the state
+ * if x < 0 then the state is obtained from the system clock
+ * if x = 0 then the state is to be supplied interactively.
+ *
+ * The generator used in this library is a so-called 'Lehmer random number
+ * generator' which returns a pseudo-random number uniformly distributed
+ * 0.0 and 1.0. The period is (m - 1) where m = 2,147,483,647 and the
+ * smallest and largest possible values are (1 / m) and 1 - (1 / m)
+ * respectively. For more details see:
+ *
+ * "Random Number Generators: Good Ones Are Hard To Find"
+ * Steve Park and Keith Miller
+ * Communications of the ACM, October 1988
+ *
+ * Name : rngs.c (Random Number Generation - Multiple Streams)
+ * Authors : Steve Park & Dave Geyer
+ * Language : ANSI C
+ * Latest Revision : 09-22-98
+ * -------------------------------------------------------------------------
+ */
+
+#include <stdio.h>
+#include <time.h>
+#include "rngs.h"
+
+#define MODULUS 2147483647 /* DON'T CHANGE THIS VALUE */
+#define MULTIPLIER 48271 /* DON'T CHANGE THIS VALUE */
+#define CHECK 399268537 /* DON'T CHANGE THIS VALUE */
+#define STREAMS 256 /* # of streams, DON'T CHANGE THIS VALUE */
+#define A256 22925 /* jump multiplier, DON'T CHANGE THIS VALUE */
+#define DEFAULT 123456789 /* initial seed, use 0 < DEFAULT < MODULUS */
+
+static long seed[STREAMS] = {DEFAULT}; /* current state of each stream */
+static int stream = 0; /* stream index, 0 is the default */
+static int initialized = 0; /* test for stream initialization */
+
+
+ double Random(void)
+/* ----------------------------------------------------------------
+ * Random returns a pseudo-random real number uniformly distributed
+ * between 0.0 and 1.0.
+ * ----------------------------------------------------------------
+ */
+{
+ const long Q = MODULUS / MULTIPLIER;
+ const long R = MODULUS % MULTIPLIER;
+ long t;
+
+ t = MULTIPLIER * (seed[stream] % Q) - R * (seed[stream] / Q);
+ if (t > 0)
+ seed[stream] = t;
+ else
+ seed[stream] = t + MODULUS;
+ return ((double) seed[stream] / MODULUS);
+}
+
+
+ void PlantSeeds(long x)
+/* ---------------------------------------------------------------------
+ * Use this function to set the state of all the random number generator
+ * streams by "planting" a sequence of states (seeds), one per stream,
+ * with all states dictated by the state of the default stream.
+ * The sequence of planted states is separated one from the next by
+ * 8,367,782 calls to Random().
+ * ---------------------------------------------------------------------
+ */
+{
+ const long Q = MODULUS / A256;
+ const long R = MODULUS % A256;
+ int j;
+ int s;
+
+ initialized = 1;
+ s = stream; /* remember the current stream */
+ SelectStream(0); /* change to stream 0 */
+ PutSeed(x); /* set seed[0] */
+ stream = s; /* reset the current stream */
+ for (j = 1; j < STREAMS; j++) {
+ x = A256 * (seed[j - 1] % Q) - R * (seed[j - 1] / Q);
+ if (x > 0)
+ seed[j] = x;
+ else
+ seed[j] = x + MODULUS;
+ }
+}
+
+
+ void PutSeed(long x)
+/* ---------------------------------------------------------------
+ * Use this function to set the state of the current random number
+ * generator stream according to the following conventions:
+ * if x > 0 then x is the state (unless too large)
+ * if x < 0 then the state is obtained from the system clock
+ * if x = 0 then the state is to be supplied interactively
+ * ---------------------------------------------------------------
+ */
+{
+ char ok = 0;
+
+ if (x > 0)
+ x = x % MODULUS; /* correct if x is too large */
+ if (x < 0)
+ x = ((unsigned long) time((time_t *) NULL)) % MODULUS;
+ if (x == 0)
+ while (!ok) {
+ printf("\nEnter a positive integer seed (9 digits or less) >> ");
+ scanf("%ld", &x);
+ ok = (0 < x) && (x < MODULUS);
+ if (!ok)
+ printf("\nInput out of range ... try again\n");
+ }
+ seed[stream] = x;
+}
+
+
+ void GetSeed(long *x)
+/* ---------------------------------------------------------------
+ * Use this function to get the state of the current random number
+ * generator stream.
+ * ---------------------------------------------------------------
+ */
+{
+ *x = seed[stream];
+}
+
+
+ void SelectStream(int index)
+/* ------------------------------------------------------------------
+ * Use this function to set the current random number generator
+ * stream -- that stream from which the next random number will come.
+ * ------------------------------------------------------------------
+ */
+{
+ stream = ((unsigned int) index) % STREAMS;
+ if ((initialized == 0) && (stream != 0)) /* protect against */
+ PlantSeeds(DEFAULT); /* un-initialized streams */
+}
+
+
+ void TestRandom(void)
+/* ------------------------------------------------------------------
+ * Use this (optional) function to test for a correct implementation.
+ * ------------------------------------------------------------------
+ */
+{
+ long i;
+ long x;
+ double u;
+ char ok = 0;
+
+ SelectStream(0); /* select the default stream */
+ PutSeed(1); /* and set the state to 1 */
+ for(i = 0; i < 10000; i++)
+ u = Random();
+ GetSeed(&x); /* get the new state value */
+ ok = (x == CHECK); /* and check for correctness */
+
+ SelectStream(1); /* select stream 1 */
+ PlantSeeds(1); /* set the state of all streams */
+ GetSeed(&x); /* get the state of stream 1 */
+ ok = ok && (x == A256); /* x should be the jump multiplier */
+ if (ok)
+ printf("\n The implementation of rngs.c is correct.\n\n");
+ else
+ printf("\n\a ERROR -- the implementation of rngs.c is not correct.\n\n");
+}
diff --git a/src/C/rngs/rngs.h b/src/C/rngs/rngs.h
new file mode 100644
index 0000000..4bc7c06
--- /dev/null
+++ b/src/C/rngs/rngs.h
@@ -0,0 +1,19 @@
+/* -----------------------------------------------------------------------
+ * Name : rngs.h (header file for the library file rngs.c)
+ * Author : Steve Park & Dave Geyer
+ * Language : ANSI C
+ * Latest Revision : 09-22-98
+ * -----------------------------------------------------------------------
+ */
+
+#if !defined( _RNGS_ )
+#define _RNGS_
+
+double Random(void);
+void PlantSeeds(long x);
+void GetSeed(long *x);
+void PutSeed(long x);
+void SelectStream(int index);
+void TestRandom(void);
+
+#endif
diff --git a/src/C/rngs/rvgs.c b/src/C/rngs/rvgs.c
new file mode 100644
index 0000000..265ade6
--- /dev/null
+++ b/src/C/rngs/rvgs.c
@@ -0,0 +1,218 @@
+/* --------------------------------------------------------------------------
+ * This is an ANSI C library for generating random variates from six discrete
+ * distributions
+ *
+ * Generator Range (x) Mean Variance
+ *
+ * Bernoulli(p) x = 0,1 p p*(1-p)
+ * Binomial(n, p) x = 0,...,n n*p n*p*(1-p)
+ * Equilikely(a, b) x = a,...,b (a+b)/2 ((b-a+1)*(b-a+1)-1)/12
+ * Geometric(p) x = 0,... p/(1-p) p/((1-p)*(1-p))
+ * Pascal(n, p) x = 0,... n*p/(1-p) n*p/((1-p)*(1-p))
+ * Poisson(m) x = 0,... m m
+ *
+ * and seven continuous distributions
+ *
+ * Uniform(a, b) a < x < b (a + b)/2 (b - a)*(b - a)/12
+ * Exponential(m) x > 0 m m*m
+ * Erlang(n, b) x > 0 n*b n*b*b
+ * Normal(m, s) all x m s*s
+ * Lognormal(a, b) x > 0 see below
+ * Chisquare(n) x > 0 n 2*n
+ * Student(n) all x 0 (n > 1) n/(n - 2) (n > 2)
+ *
+ * For the a Lognormal(a, b) random variable, the mean and variance are
+ *
+ * mean = exp(a + 0.5*b*b)
+ * variance = (exp(b*b) - 1) * exp(2*a + b*b)
+ *
+ * Name : rvgs.c (Random Variate GeneratorS)
+ * Author : Steve Park & Dave Geyer
+ * Language : ANSI C
+ * Latest Revision : 10-28-98
+ * --------------------------------------------------------------------------
+ */
+
+#include <math.h>
+#include "rngs.h"
+#include "rvgs.h"
+
+
+ long Bernoulli(double p)
+/* ========================================================
+ * Returns 1 with probability p or 0 with probability 1 - p.
+ * NOTE: use 0.0 < p < 1.0
+ * ========================================================
+ */
+{
+ return ((Random() < (1.0 - p)) ? 0 : 1);
+}
+
+ long Binomial(long n, double p)
+/* ================================================================
+ * Returns a binomial distributed integer between 0 and n inclusive.
+ * NOTE: use n > 0 and 0.0 < p < 1.0
+ * ================================================================
+ */
+{
+ long i, x = 0;
+
+ for (i = 0; i < n; i++)
+ x += Bernoulli(p);
+ return (x);
+}
+
+ long Equilikely(long a, long b)
+/* ===================================================================
+ * Returns an equilikely distributed integer between a and b inclusive.
+ * NOTE: use a < b
+ * ===================================================================
+ */
+{
+ return (a + (long) ((b - a + 1) * Random()));
+}
+
+ long Geometric(double p)
+/* ====================================================
+ * Returns a geometric distributed non-negative integer.
+ * NOTE: use 0.0 < p < 1.0
+ * ====================================================
+ */
+{
+ return ((long) (log(1.0 - Random()) / log(p)));
+}
+
+ long Pascal(long n, double p)
+/* =================================================
+ * Returns a Pascal distributed non-negative integer.
+ * NOTE: use n > 0 and 0.0 < p < 1.0
+ * =================================================
+ */
+{
+ long i, x = 0;
+
+ for (i = 0; i < n; i++)
+ x += Geometric(p);
+ return (x);
+}
+
+ long Poisson(double m)
+/* ==================================================
+ * Returns a Poisson distributed non-negative integer.
+ * NOTE: use m > 0
+ * ==================================================
+ */
+{
+ double t = 0.0;
+ long x = 0;
+
+ while (t < m) {
+ t += Exponential(1.0);
+ x++;
+ }
+ return (x - 1);
+}
+
+ double Uniform(double a, double b)
+/* ===========================================================
+ * Returns a uniformly distributed real number between a and b.
+ * NOTE: use a < b
+ * ===========================================================
+ */
+{
+ return (a + (b - a) * Random());
+}
+
+ double Exponential(double m)
+/* =========================================================
+ * Returns an exponentially distributed positive real number.
+ * NOTE: use m > 0.0
+ * =========================================================
+ */
+{
+ return (-m * log(1.0 - Random()));
+}
+
+ double Erlang(long n, double b)
+/* ==================================================
+ * Returns an Erlang distributed positive real number.
+ * NOTE: use n > 0 and b > 0.0
+ * ==================================================
+ */
+{
+ long i;
+ double x = 0.0;
+
+ for (i = 0; i < n; i++)
+ x += Exponential(b);
+ return (x);
+}
+
+ double Normal(double m, double s)
+/* ========================================================================
+ * Returns a normal (Gaussian) distributed real number.
+ * NOTE: use s > 0.0
+ *
+ * Uses a very accurate approximation of the normal idf due to Odeh & Evans,
+ * J. Applied Statistics, 1974, vol 23, pp 96-97.
+ * ========================================================================
+ */
+{
+ const double p0 = 0.322232431088; const double q0 = 0.099348462606;
+ const double p1 = 1.0; const double q1 = 0.588581570495;
+ const double p2 = 0.342242088547; const double q2 = 0.531103462366;
+ const double p3 = 0.204231210245e-1; const double q3 = 0.103537752850;
+ const double p4 = 0.453642210148e-4; const double q4 = 0.385607006340e-2;
+ double u, t, p, q, z;
+
+ u = Random();
+ if (u < 0.5)
+ t = sqrt(-2.0 * log(u));
+ else
+ t = sqrt(-2.0 * log(1.0 - u));
+ p = p0 + t * (p1 + t * (p2 + t * (p3 + t * p4)));
+ q = q0 + t * (q1 + t * (q2 + t * (q3 + t * q4)));
+ if (u < 0.5)
+ z = (p / q) - t;
+ else
+ z = t - (p / q);
+ return (m + s * z);
+}
+
+ double Lognormal(double a, double b)
+/* ====================================================
+ * Returns a lognormal distributed positive real number.
+ * NOTE: use b > 0.0
+ * ====================================================
+ */
+{
+ return (exp(a + b * Normal(0.0, 1.0)));
+}
+
+ double Chisquare(long n)
+/* =====================================================
+ * Returns a chi-square distributed positive real number.
+ * NOTE: use n > 0
+ * =====================================================
+ */
+{
+ long i;
+ double z, x = 0.0;
+
+ for (i = 0; i < n; i++) {
+ z = Normal(0.0, 1.0);
+ x += z * z;
+ }
+ return (x);
+}
+
+ double Student(long n)
+/* ===========================================
+ * Returns a student-t distributed real number.
+ * NOTE: use n > 0
+ * ===========================================
+ */
+{
+ return (Normal(0.0, 1.0) / sqrt(Chisquare(n) / n));
+}
+
diff --git a/src/C/rngs/rvgs.h b/src/C/rngs/rvgs.h
new file mode 100644
index 0000000..d3768d6
--- /dev/null
+++ b/src/C/rngs/rvgs.h
@@ -0,0 +1,28 @@
+/* -------------------------------------------------------------
+ * Name : rvgs.h (header file for the library rvgs.c)
+ * Author : Steve Park & Dave Geyer
+ * Language : ANSI C
+ * Latest Revision : 11-03-96
+ * --------------------------------------------------------------
+ */
+
+#if !defined( _RVGS_ )
+#define _RVGS_
+
+long Bernoulli(double p);
+long Binomial(long n, double p);
+long Equilikely(long a, long b);
+long Geometric(double p);
+long Pascal(long n, double p);
+long Poisson(double m);
+
+double Uniform(double a, double b);
+double Exponential(double m);
+double Erlang(long n, double b);
+double Normal(double m, double s);
+double Lognormal(double a, double b);
+double Chisquare(long n);
+double Student(long n);
+
+#endif
+
diff --git a/src/C/sparse.c b/src/C/sparse.c
new file mode 100644
index 0000000..0785ba0
--- /dev/null
+++ b/src/C/sparse.c
@@ -0,0 +1,3992 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#define BASE_MODULE
+
+#include "Python.h"
+#include "cvxopt.h"
+#include "misc.h"
+
+#include <complexobject.h>
+
+#define CONJ(flag, val) (flag == 'C' ? conj(val) : val)
+
+extern PyObject *base_mod;
+
+extern const int E_SIZE[];
+extern const char TC_CHAR[][2];
+extern const char PRINTOPT[][15];
+extern number One[3], MinusOne[3], Zero[3];
+
+extern void (*write_num[])(void *, int, void *, int) ;
+extern int (*convert_num[])(void *, void *, int, int_t) ;
+extern PyObject * (*num2PyObject[])(void *, int) ;
+extern void (*scal[])(int *, number *, void *, int *) ;
+extern void (*axpy[])(int *, void *, void *, int *, void *, int *) ;
+extern void (*gemm[])(char *, char *, int *, int *, int *, void *,
+ void *, int *, void *, int *, void *, void *, int *) ;
+extern int (*div_array[])(void *, number, int) ;
+extern int get_id(void *, int ) ;
+
+extern PyTypeObject matrix_tp ;
+extern matrix * Matrix_NewFromMatrix(matrix *, int) ;
+extern matrix * Matrix_NewFromSequence(PyObject *, int) ;
+extern matrix * Matrix_NewFromArrayStruct(PyObject *, int, int_t *) ;
+extern matrix * Matrix_NewFromNumber(int , int , int , void *, int ) ;
+extern matrix * create_indexlist(int, PyObject *) ;
+extern matrix * Matrix_New(int, int, int) ;
+extern matrix * dense(spmatrix *) ;
+extern PyObject * matrix_add(PyObject *, PyObject *) ;
+extern PyObject * matrix_sub(PyObject *, PyObject *) ;
+extern void * convert_mtx_alloc(matrix *, int) ;
+
+PyTypeObject spmatrix_tp ;
+spmatrix * SpMatrix_New(int, int, int, int ) ;
+
+extern void (*scal[])(int *, number *, void *, int *) ;
+extern void (*gemm[])(char *, char *, int *, int *, int *, void *, void *,
+ int *, void *, int *, void *, void *, int *) ;
+extern void (*syrk[])(char *, char *, int *, int *, void *, void *,
+ int *, void *, void *, int *) ;
+
+static int sp_daxpy(number, void *, void *, int, int, int, void **) ;
+static int sp_zaxpy(number, void *, void *, int, int, int, void **) ;
+int (*sp_axpy[])(number, void *, void *, int, int, int, void **)
+ = { NULL, sp_daxpy, sp_zaxpy };
+
+static int sp_dgemm(char, char, number, void *, void *, number, void *,
+ int, int, int, int, void **, int, int, int) ;
+static int sp_zgemm(char, char, number, void *, void *, number, void *,
+ int, int, int, int, void **, int, int, int) ;
+int (*sp_gemm[])(char, char, number, void *, void *, number, void *,
+ int, int, int, int, void **, int, int, int)
+ = { NULL, sp_dgemm, sp_zgemm };
+
+static int sp_dgemv(char, int, int, number, void *, int,
+ void *, int, number, void *, int) ;
+static int sp_zgemv(char, int, int, number, void *, int,
+ void *, int, number, void *, int) ;
+int (*sp_gemv[])(char, int, int, number, void *, int, void *, int,
+ number, void *, int) = { NULL, sp_dgemv, sp_zgemv } ;
+
+static int sp_dsymv(char, int, number, ccs *, int, void *, int,
+ number, void *, int) ;
+static int sp_zsymv(char, int, number, ccs *, int, void *, int,
+ number, void *, int) ;
+int (*sp_symv[])(char, int, number, ccs *, int, void *, int,
+ number, void *, int) = { NULL, sp_dsymv, sp_zsymv } ;
+
+static int sp_dsyrk(char, char, number, void *, number,
+ void *, int, int, int, int, void **) ;
+int (*sp_syrk[])(char, char, number, void *, number,
+ void *, int, int, int, int, void **) = { NULL, sp_dsyrk, NULL };
+
+typedef struct {
+ int_t key, value;
+} int_list;
+
+static int comp_int(const void *x, const void *y) {
+ if (((int_list *)x)->key == ((int_list *)y)->key)
+ return 0;
+ else
+ return (((int_list *)x)->key > ((int_list *)y)->key ? 1 : -1);
+}
+
+typedef struct {
+ int_t key; double value;
+} double_list;
+
+static int comp_double(const void *x, const void *y) {
+ if (((double_list *)x)->key == ((double_list *)y)->key)
+ return 0;
+ else
+ return (((double_list *)x)->key > ((double_list *)y)->key ? 1 : -1);
+}
+
+typedef struct {
+ int_t key; complex value;
+} complex_list;
+
+static int comp_complex(const void *x, const void *y) {
+ if (((complex_list *)x)->key == ((complex_list *)y)->key)
+ return 0;
+ else
+ return (((complex_list *)x)->key > ((complex_list *)y)->key ? 1 : -1);
+}
+
+#define spmatrix_getitem_i(O,i,v) \
+ spmatrix_getitem_ij(O,i%SP_NROWS(O),i/SP_NROWS(O),v)
+#define spmatrix_setitem_i(O,i,v) \
+ spmatrix_setitem_ij(O,i%SP_NROWS(O),i/SP_NROWS(O),v)
+
+#define free_lists_exit(argI,argJ,I,J,ret) { \
+ if (argI && !Matrix_Check(argI)) { Py_XDECREF(I); } \
+ if (argJ && !Matrix_Check(argJ)) { Py_XDECREF(J); } \
+ return ret; }
+
+#define INCR_SP_ROW_IDX(O, j, k) { \
+ while (((ccs *)O)->colptr[j+1] == k+1) j++; \
+ k++; }
+
+int
+convert_array(void *dest, void *src, int dest_id, int src_id, int n) {
+
+ if (dest_id != MAX(dest_id,src_id))
+ return -1;
+
+ int i;
+ if (dest_id == src_id)
+ memcpy(dest, src, n*E_SIZE[dest_id]);
+ else if (dest_id == DOUBLE) {
+ for (i=0; i<n; i++)
+ ((double *)dest)[i] = ((int *)src)[i];
+ } else {
+ if (src_id == INT) {
+ for (i=0; i<n; i++)
+ ((complex *)dest)[i] = ((int *)src)[i];
+ } else {
+ for (i=0; i<n; i++)
+ ((complex *)dest)[i] = ((double *)src)[i];
+ }
+ }
+ return 0;
+}
+
+ccs * alloc_ccs(int_t nrows, int_t ncols, int nnz, int id)
+{
+ ccs *obj = malloc(sizeof(ccs));
+ if (!obj) return NULL;
+
+ obj->nrows = nrows;
+ obj->ncols = ncols;
+ obj->id = id;
+ obj->nzmax = nnz;
+
+ obj->values = malloc(E_SIZE[id]*nnz);
+ obj->colptr = calloc(ncols+1,sizeof(int_t));
+ obj->rowind = malloc(sizeof(int_t)*nnz);
+
+ if (!obj->values || !obj->colptr || !obj->rowind) {
+ free(obj->values); free(obj->colptr); free(obj->rowind); free(obj);
+ return NULL;
+ }
+
+ return obj;
+}
+
+void free_ccs(ccs *obj) {
+ free(obj->values);
+ free(obj->rowind);
+ free(obj->colptr);
+ free(obj);
+}
+
+static int
+realloc_ccs(ccs *obj, int nzmax) {
+
+ int_t *rowind;
+ void *values;
+
+ if ((rowind = realloc(obj->rowind, nzmax*sizeof(int_t))))
+ obj->rowind = rowind;
+ else
+ return 0;
+
+ if ((values = realloc(obj->values, nzmax*E_SIZE[obj->id])))
+ obj->values = values;
+ else
+ return 0;
+
+ obj->nzmax = nzmax;
+ return 1;
+}
+
+static ccs * convert_ccs(ccs *src, int id) {
+
+ if (src->id == id) return src;
+
+ if (id != MAX(id,src->id)) PY_ERR_TYPE("incompatible matrix types");
+
+ ccs *ret = alloc_ccs(src->nrows,src->ncols,src->nzmax,id);
+ if (!ret) return (ccs *)PyErr_NoMemory();
+
+ convert_array(ret->values, src->values, id, src->id, src->nzmax);
+ memcpy(ret->rowind, src->rowind, src->nzmax*sizeof(int_t));
+ memcpy(ret->colptr, src->colptr, (src->ncols+1)*sizeof(int_t));
+ return ret;
+}
+
+spmatrix *SpMatrix_NewFromMatrix(matrix *src, int id)
+{
+ spmatrix *A;
+ int nnz = 0, i, j;
+
+ if (id < MAT_ID(src)) PY_ERR_TYPE("illegal type conversion");
+
+ for (j=0; j<MAT_NCOLS(src); j++) {
+ for (i=0; i<MAT_NROWS(src); i++) {
+
+ number *a = MAT_BUF(src) + (i+j*MAT_NROWS(src))*E_SIZE[MAT_ID(src)];
+ if (((MAT_ID(src) == INT) && (a->i != Zero[INT].i)) ||
+ ((MAT_ID(src) == DOUBLE) && (a->d != Zero[DOUBLE].d)) ||
+ ((MAT_ID(src) == COMPLEX) && (a->z != Zero[COMPLEX].z)))
+ nnz++;
+ }
+ }
+
+ if (!(A = SpMatrix_New(MAT_NROWS(src), MAT_NCOLS(src), nnz, id)))
+ return (spmatrix *)PyErr_NoMemory();
+
+ int cnt = 0;
+ for (j=0; j<MAT_NCOLS(src); j++) {
+ for (i=0; i<MAT_NROWS(src); i++) {
+
+ number a;
+ convert_num[id](&a, src, 0, i+j*MAT_NROWS(src));
+ if (((id == INT) && (a.i != Zero[INT].i)) ||
+ ((id == DOUBLE) && (a.d != Zero[DOUBLE].d)) ||
+ ((id == COMPLEX) && (a.z != Zero[COMPLEX].z))) {
+ write_num[id](SP_VAL(A), cnt, &a, 0);
+ SP_ROW(A)[cnt++] = i;
+ SP_COL(A)[j+1]++;
+ }
+ }
+ }
+
+ for (i=0; i<SP_NCOLS(A); i++)
+ SP_COL(A)[i+1] += SP_COL(A)[i];
+
+ return A;
+}
+
+spmatrix * sparse_concat(PyObject *L, int id_arg)
+{
+ int m=0, n=0, mk=0, nk=0, i=0, j, id=0, nnz=0;
+ PyObject *col;
+
+ int single_col = (PyList_GET_SIZE(L) > 0 &&
+ !PyList_Check(PyList_GET_ITEM(L, 0)));
+
+ for (j=0; j<(single_col ? 1 : PyList_GET_SIZE(L)); j++) {
+
+ col = (single_col ? L : PyList_GET_ITEM(L, j));
+ if (!PyList_Check(col))
+ PY_ERR_TYPE("L must be a list of lists with matrices");
+
+ mk = 0;
+ for (i=0; i<PyList_GET_SIZE(col); i++) {
+ PyObject *Lij = PyList_GET_ITEM(col, i);
+ if (!Matrix_Check(Lij) && !SpMatrix_Check(Lij) && !PY_NUMBER(Lij))
+ PY_ERR_TYPE("invalid type in list");
+
+ int blk_nrows, blk_ncols;
+ if (Matrix_Check(Lij) || SpMatrix_Check(Lij)) {
+ blk_nrows = X_NROWS(Lij); blk_ncols = X_NCOLS(Lij);
+ id = MAX(id, X_ID(Lij));
+ } else {
+ blk_nrows = 1; blk_ncols = 1;
+ id = MAX(id, get_id(Lij,1));
+ }
+
+ if (Matrix_Check(Lij)) {
+
+ int ik, jk;
+ for (jk=0; jk<MAT_NCOLS(Lij); jk++) {
+ for (ik=0; ik<MAT_NROWS(Lij); ik++) {
+
+ number *a = MAT_BUF(Lij) +
+ (ik+jk*MAT_NROWS(Lij))*E_SIZE[MAT_ID(Lij)];
+
+ if (((MAT_ID(Lij) == INT) && (a->i != Zero[INT].i)) ||
+ ((MAT_ID(Lij) == DOUBLE) && (a->d != Zero[DOUBLE].d)) ||
+ ((MAT_ID(Lij) == COMPLEX) && (a->z != Zero[COMPLEX].z)))
+ nnz++;
+ }
+ }
+ } else if (SpMatrix_Check(Lij)) {
+ int ik, jk;
+ for (jk=0; jk<SP_NCOLS(Lij); jk++) {
+
+ for (ik=SP_COL(Lij)[jk]; ik<SP_COL(Lij)[jk+1]; ik++) {
+ if (((SP_ID(Lij) == DOUBLE) && (SP_VALD(Lij)[ik] != 0.0)) ||
+ ((SP_ID(Lij) == COMPLEX) && (SP_VALZ(Lij)[ik] != 0.0)))
+ nnz++;
+ }
+ }
+ }
+ else nnz += 1;
+
+ if (i==0) {
+ nk = blk_ncols; n += nk;
+ mk = blk_nrows;
+ } else {
+ if (blk_ncols != nk)
+ PY_ERR_TYPE("incompatible dimensions of subblocks");
+ mk += blk_nrows;
+ }
+ }
+ if (j==0)
+ m = mk;
+ else if (m != mk) PY_ERR_TYPE("incompatible dimensions of subblocks");
+ }
+
+ if ((id_arg >= 0) && (id_arg < id))
+ PY_ERR_TYPE("illegal type conversion");
+
+ id = MAX(DOUBLE, MAX(id, id_arg));
+ spmatrix *A = SpMatrix_New(m, n, nnz, id);
+ if (!A) return (spmatrix *)PyErr_NoMemory();
+
+ int ik = 0, jk, cnt = 0;
+ nk = 0;
+ for (j=0; j<(single_col ? 1 : PyList_GET_SIZE(L)); j++) {
+ col = (single_col ? L : PyList_GET_ITEM(L, j));
+
+ if (PyList_GET_SIZE(col) > 0) {
+
+ int tmp = (PY_NUMBER(PyList_GET_ITEM(col, 0)) ? 1 :
+ X_NCOLS(PyList_GET_ITEM(col, 0)));
+
+ for (jk=0; jk<tmp; jk++) {
+
+ mk = 0;
+ int blk_nrows = 0, blk_ncols = 0;
+ for (i=0; i<PyList_GET_SIZE(col); i++) {
+
+ PyObject *Lij = PyList_GET_ITEM(col, i);
+
+ if (Matrix_Check(Lij) || SpMatrix_Check(Lij)) {
+ blk_nrows = X_NROWS(Lij); blk_ncols = X_NCOLS(Lij);
+ } else {
+ blk_nrows = 1; blk_ncols = 1;
+ }
+
+ if (Matrix_Check(Lij)) {
+ for (ik=0; ik<MAT_NROWS(Lij); ik++) {
+
+ number a;
+ convert_num[id](&a, Lij, 0, ik + jk*MAT_NROWS(Lij));
+
+ if (((id == DOUBLE) && (a.d != Zero[DOUBLE].d)) ||
+ ((id == COMPLEX) && (a.z != Zero[COMPLEX].z))) {
+
+ write_num[id](SP_VAL(A), cnt, &a, 0);
+ SP_ROW(A)[cnt++] = mk + ik;
+ SP_COL(A)[nk+1]++;
+ }
+ }
+ } else if SpMatrix_Check(Lij) {
+
+ int ik;
+ for (ik=SP_COL(Lij)[jk]; ik<SP_COL(Lij)[jk+1]; ik++) {
+ if ((SP_ID(Lij) == DOUBLE) && (SP_VALD(Lij)[ik] != 0.0)) {
+ if (id == DOUBLE)
+ SP_VALD(A)[cnt] = SP_VALD(Lij)[ik];
+ else
+ SP_VALZ(A)[cnt] = SP_VALD(Lij)[ik];
+
+ SP_ROW(A)[cnt++] = mk + SP_ROW(Lij)[ik];
+ SP_COL(A)[nk+1]++;
+ nnz++;
+ }
+ else if ((SP_ID(Lij) == COMPLEX) && (SP_VALZ(Lij)[ik] != 0.0)) {
+
+ SP_VALZ(A)[cnt] = SP_VALD(Lij)[ik];
+ SP_ROW(A)[cnt++] = mk + SP_ROW(Lij)[ik];
+ SP_COL(A)[nk+1]++;
+ nnz++;
+ }
+ }
+ } else {
+
+ number a;
+ convert_num[id](&a, Lij, 1, 0);
+
+ if (((id == DOUBLE) && (a.d != Zero[DOUBLE].d)) ||
+ ((id == COMPLEX) && (a.z != Zero[COMPLEX].z))) {
+
+ write_num[id](SP_VAL(A), cnt, &a, 0);
+ SP_ROW(A)[cnt++] = mk;
+ SP_COL(A)[nk+1]++;
+ }
+ }
+ mk += blk_nrows;
+ }
+ nk++;
+ }
+ }
+ }
+
+ for (i=0; i<n; i++)
+ SP_COL(A)[i+1] += SP_COL(A)[i];
+
+ return A;
+}
+
+
+static ccs * transpose(ccs *A, int conjugate) {
+
+ ccs *B = alloc_ccs(A->ncols, A->nrows, A->nzmax, A->id);
+ if (!B) return NULL;
+
+ int_t i, j, *buf = calloc(A->nrows,sizeof(int_t));
+ if (!buf) { free_ccs(B); return NULL; }
+
+ /* Run through matrix and count number of elms in each row */
+ for (i=0; i<A->colptr[A->ncols]; i++) buf[ A->rowind[i] ]++;
+
+ /* generate new colptr */
+ for (i=0; i<B->ncols; i++)
+ B->colptr[i+1] = B->colptr[i] + buf[i];
+
+ /* fill in rowind and values */
+ for (i=0; i<A->nrows; i++) buf[i] = 0;
+ for (i=0; i<A->ncols; i++) {
+ if (A->id == DOUBLE)
+ for (j=A->colptr[i]; j<A->colptr[i+1]; j++) {
+ B->rowind[ B->colptr[A->rowind[j]] + buf[A->rowind[j]] ] = i;
+ ((double *)B->values)[B->colptr[A->rowind[j]] + buf[A->rowind[j]]++] =
+ ((double *)A->values)[j];
+ }
+ else
+ for (j=A->colptr[i]; j<A->colptr[i+1]; j++) {
+ B->rowind[ B->colptr[A->rowind[j]] + buf[A->rowind[j]] ] = i;
+ ((complex *)B->values)[B->colptr[A->rowind[j]]+buf[A->rowind[j]]++] =
+ (conjugate ? conj(((complex *)A->values)[j]) :
+ ((complex *)A->values)[j]);
+ }
+ }
+ free(buf);
+ return B;
+}
+
+static int sort_ccs(ccs *A) {
+
+ ccs *t = transpose(A, 0);
+ if (!t) return -1;
+
+ ccs *t2 = transpose(t, 0);
+ if (!t2) {
+ free_ccs(t); return -1;
+ }
+
+ free(A->colptr); free(A->rowind); free(A->values);
+ A->colptr = t2->colptr; A->rowind = t2->rowind; A->values = t2->values;
+
+ free(t2);
+ free_ccs(t);
+
+ return 0;
+}
+
+/*
+ Sparse accumulator (spa) - dense representation of a sparse vector
+*/
+typedef struct {
+ void *val;
+ char *nz;
+ int *idx;
+ int nnz, n, id;
+} spa;
+
+static spa * alloc_spa(int n, int id) {
+
+ spa *s = malloc(sizeof(spa));
+
+ if (s) {
+ s->val = malloc( E_SIZE[id]*n );
+ s->nz = malloc( n*sizeof(char) );
+ s->idx = malloc( n*sizeof(int) );
+ s->nnz = 0;
+ s->n = n;
+ s->id = id;
+ }
+
+ if (!s || !s->val || !s->nz || !s->idx) {
+ free(s->val); free(s->nz); free(s->idx); free(s);
+ return NULL;
+ }
+
+ int i;
+ for (i=0; i<n; i++) s->nz[i] = 0;
+
+ return s;
+}
+
+static void free_spa(spa *s) {
+ if (s) {
+ free(s->val); free(s->nz); free(s->idx); free(s);
+ }
+}
+
+static void init_spa(spa *s, ccs *X, int col) {
+ int i;
+ for (i=0; i<s->nnz; i++)
+ s->nz[s->idx[i]] = 0;
+
+ s->nnz = 0;
+
+ if (X && X->id == DOUBLE) {
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ s->nz[X->rowind[i]] = 1;
+ ((double *)s->val)[X->rowind[i]] = ((double *)X->values)[i];
+ s->idx[s->nnz++] = X->rowind[i];
+ }
+ } else if (X && X->id == COMPLEX) {
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ s->nz[X->rowind[i]] = 1;
+ ((complex *)s->val)[X->rowind[i]] = ((complex *)X->values)[i];
+ s->idx[s->nnz++] = X->rowind[i];
+ }
+ }
+}
+
+static inline void
+spa_daxpy_partial (double a, ccs *X, int col, spa *y) {
+ int i;
+
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ if (y->nz[X->rowind[i]]) {
+ ((double *)y->val)[X->rowind[i]] += a*((double *)X->values)[i];
+ }
+ }
+}
+
+static inline void
+spa_zaxpy_partial (complex a, ccs *X, int col, spa *y) {
+ int i;
+
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ if (y->nz[X->rowind[i]]) {
+ ((complex *)y->val)[X->rowind[i]] += a*((complex *)X->values)[i];
+ }
+ }
+}
+
+static inline void spa_daxpy (double a, ccs *X, int col, spa *y) {
+ int i;
+
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ if (y->nz[X->rowind[i]]) {
+ ((double *)y->val)[X->rowind[i]] += a*((double *)X->values)[i];
+ }
+ else {
+ ((double *)y->val)[X->rowind[i]] = a*((double *)X->values)[i];
+ y->nz[X->rowind[i]] = 1;
+ y->idx[y->nnz++] = X->rowind[i];
+ }
+ }
+}
+
+static inline void spa_zaxpy (complex a, ccs *X, char conjx, int col, spa *y)
+{
+ int i;
+
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ if (y->nz[X->rowind[i]]) {
+ ((complex *)y->val)[X->rowind[i]] +=
+ a*CONJ(conjx,((complex *)X->values)[i]);
+ }
+ else {
+ ((complex *)y->val)[X->rowind[i]] =
+ a*CONJ(conjx,((complex *)X->values)[i]);
+ y->nz[X->rowind[i]] = 1;
+ y->idx[y->nnz++] = X->rowind[i];
+ }
+ }
+}
+
+static inline void
+spa_daxpy_uplo (double a, ccs *X, int col, spa *y, int j, char uplo) {
+ int i;
+
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ if ((uplo == 'U' && X->rowind[i] <= j) ||
+ (uplo == 'L' && X->rowind[i] >= j)) {
+ if (y->nz[X->rowind[i]]) {
+ ((double *)y->val)[X->rowind[i]] += a*((double *)X->values)[i];
+ }
+ else {
+ ((double *)y->val)[X->rowind[i]] = a*((double *)X->values)[i];
+ y->nz[X->rowind[i]] = 1;
+ y->idx[y->nnz++] = X->rowind[i];
+ }
+ }
+ }
+}
+
+static inline void
+spa_zaxpy_uplo (complex a, ccs *X, int col, spa *y, int j, char uplo) {
+ int i;
+
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++) {
+ if ((uplo == 'U' && X->rowind[i] <= j) ||
+ (uplo == 'L' && X->rowind[i] >= j)) {
+ if (y->nz[X->rowind[i]]) {
+ ((complex *)y->val)[X->rowind[i]] += a*((complex *)X->values)[i];
+ }
+ else {
+ ((complex *)y->val)[X->rowind[i]] = a*((complex *)X->values)[i];
+ y->nz[X->rowind[i]] = 1;
+ y->idx[y->nnz++] = X->rowind[i];
+ }
+ }
+ }
+}
+
+static inline void spa_symb_axpy (ccs *X, int col, spa *y) {
+ int i;
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++)
+ if (!y->nz[X->rowind[i]]) {
+ y->nz[X->rowind[i]] = 1;
+ y->idx[y->nnz++] = X->rowind[i];
+ }
+}
+
+static inline void
+spa_symb_axpy_uplo (ccs *X, int col, spa *y, int j, char uplo) {
+ int i;
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++)
+ if ((uplo == 'U' && X->rowind[i] <= j) ||
+ (uplo == 'L' && X->rowind[i] >= j)) {
+
+ if (!y->nz[X->rowind[i]]) {
+ y->nz[X->rowind[i]] = 1;
+ y->idx[y->nnz++] = X->rowind[i];
+ }
+ }
+}
+
+static inline double spa_ddot (ccs *X, int col, spa *y) {
+ int i;
+ double a = 0;
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++)
+ if (y->nz[X->rowind[i]])
+ a += ((double *)X->values)[i]*((double *)y->val)[X->rowind[i]];
+
+ return a;
+}
+
+static inline
+complex spa_zdot (ccs *X, int col, spa *y, char conjx, char conjy) {
+ int i;
+ complex a = 0;
+ for (i=X->colptr[col]; i<X->colptr[col+1]; i++)
+ if (y->nz[X->rowind[i]])
+ a += CONJ(conjx, ((complex *)X->values)[i])*
+ CONJ(conjy,((complex *)y->val)[X->rowind[i]]);
+
+ return a;
+}
+
+static void spa2compressed(spa *s, ccs *A, int col) {
+ int i, k=0;
+
+ switch (A->id) {
+ case (DOUBLE):
+ for (i=A->colptr[col]; i<A->colptr[col+1]; i++) {
+ A->rowind[i] = s->idx[k];
+ ((double *)A->values)[i] = ((double *)s->val)[s->idx[k++]];
+ }
+ break;
+ case COMPLEX:
+ for (i=A->colptr[col]; i<A->colptr[col+1]; i++) {
+ A->rowind[i] = s->idx[k];
+ ((complex *)A->values)[i] = ((complex *)s->val)[s->idx[k++]];
+ }
+ break;
+ }
+}
+
+static int sp_daxpy(number a, void *x, void *y, int sp_x, int sp_y,
+ int partial, void **z)
+{
+ int j, k;
+ if (sp_x && !sp_y) {
+
+ ccs *X = x;
+ double *Y = y;
+
+ for (j=0; j<X->ncols; j++) {
+ for (k=X->colptr[j]; k<X->colptr[j+1]; k++)
+ Y[X->rowind[k] + j*X->nrows] += a.d*(((double *)X->values)[k]);
+ }
+ }
+ else if (sp_x && sp_y && partial)
+ {
+ ccs *X = x, *Y = y;
+ int kX = 0, jX = 0, nnzX = X->colptr[X->ncols], kY, jY;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++) {
+
+ while ((kX < nnzX) && ((jX<jY) ||
+ (jX==jY && X->rowind[kX] < Y->rowind[kY]))) {
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+
+ if ((jX == jY) && (X->rowind[kX] == Y->rowind[kY]) )
+ ((double *)Y->values)[kY] = a.d*((double *)X->values)[kX] +
+ ((double *)Y->values)[kY];
+ else
+ ((double *)Y->values)[kY] = ((double *)Y->values)[kY];
+ }
+ }
+ }
+ else if (sp_x && sp_y && !partial) {
+
+ ccs *X = x, *Y = y;
+ int kX = 0, jX = 0, nnzX = X->colptr[X->ncols];
+ int kY = 0, jY = 0;
+ int nnzZ = 0;
+
+ while (nnzX && !(X->colptr[jX+1])) jX++;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++) {
+
+ while ((kX < nnzX) && ((jX<jY) ||
+ (jX==jY && X->rowind[kX] < Y->rowind[kY]))) {
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++; nnzZ++;
+ }
+
+ if (jX==jY && X->rowind[kX] == Y->rowind[kY]) {
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+ nnzZ++;
+ }
+ }
+
+ nnzZ += (nnzX - kX);
+
+ ccs *Z;
+ if (!(Z = alloc_ccs(Y->nrows, Y->ncols, nnzZ, Y->id))) return -1;
+
+ kX = 0; jX = 0; kY = 0; jY = 0, nnzZ = 0;
+ while (nnzX && !(X->colptr[jX+1])) jX++;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++) {
+
+ while ((kX < nnzX) && ((jX<jY) ||
+ (jX==jY && X->rowind[kX] < Y->rowind[kY]))) {
+ Z->colptr[jX+1]++;
+ Z->rowind[nnzZ] = X->rowind[kX];
+ ((double *)Z->values)[nnzZ++] = a.d*((double *)X->values)[kX];
+
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+
+ Z->colptr[jY+1]++;
+ Z->rowind[nnzZ] = Y->rowind[kY];
+ if (jX==jY && X->rowind[kX] == Y->rowind[kY]) {
+ ((double *)Z->values)[nnzZ++] = a.d*((double *)X->values)[kX] +
+ ((double *)Y->values)[kY];
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+ else ((double *)Z->values)[nnzZ++] = ((double *)Y->values)[kY];
+ }
+ }
+
+ while (kX < nnzX) {
+ Z->colptr[jX+1]++;
+ Z->rowind[nnzZ] = X->rowind[kX];
+ ((double *)Z->values)[nnzZ++] = a.d*((double *)X->values)[kX];
+
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+
+ int i;
+ for (i=0; i<Z->ncols; i++) Z->colptr[i+1] += Z->colptr[i];
+
+ *z = Z;
+ }
+ else if (!sp_x && sp_y && partial)
+ {
+ double *X = x;
+ ccs *Y = y;
+ int kY, jY;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++)
+ ((double *)Y->values)[kY] += a.d*X[jY*Y->nrows + Y->rowind[kY]];
+ }
+ }
+ else { // if (!p_x && !sp_y) {
+
+ double *X = x;
+ ccs *Y = y;
+
+ int mn = Y->nrows*Y->ncols;
+ ccs *Z = alloc_ccs(Y->nrows, Y->ncols, mn, Y->id);
+ if (!Z) return -1;
+
+ memcpy(Z->values, X, sizeof(double)*mn);
+ scal[Y->id](&mn, &a, Z->values, (int *)&One[INT]);
+
+ int j, k;
+ for (j=0; j<Y->ncols; j++) {
+
+ Z->colptr[j+1] = Z->colptr[j] + Y->nrows;
+
+ for (k=0; k<Y->nrows; k++)
+ Z->rowind[j*Y->nrows+k] = k;
+
+ for (k=Y->colptr[j]; k<Y->colptr[j+1]; k++)
+ ((double *)Z->values)[j*Y->nrows + Y->rowind[k]] +=
+ ((double *)Y->values)[k];
+ }
+ *z = Z;
+ }
+ return 0;
+}
+
+static int sp_zaxpy(number a, void *x, void *y, int sp_x, int sp_y,
+ int partial, void **z)
+{
+ int j, k;
+ if (sp_x && !sp_y) {
+
+ ccs *X = x;
+ complex *Y = y;
+
+ for (j=0; j<X->ncols; j++) {
+ for (k=X->colptr[j]; k<X->colptr[j+1]; k++)
+ Y[X->rowind[k] + j*X->nrows] += a.z*(((complex *)X->values)[k]);
+ }
+ }
+ else if (sp_x && sp_y && partial)
+ {
+ ccs *X = x, *Y = y;
+ int kX = 0, jX = 0, nnzX = X->colptr[X->ncols], kY, jY;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++) {
+
+ while ((kX < nnzX) && ((jX<jY) ||
+ (jX==jY && X->rowind[kX] < Y->rowind[kY]))) {
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+
+ if ((jX == jY) && (X->rowind[kX] == Y->rowind[kY]) )
+ ((complex *)Y->values)[kY] = a.z*((complex *)X->values)[kX] +
+ ((complex *)Y->values)[kY];
+ else
+ ((complex *)Y->values)[kY] = ((complex *)Y->values)[kY];
+ }
+ }
+ }
+ else if (sp_x && sp_y && !partial) {
+
+ ccs *X = x, *Y = y;
+ int kX = 0, jX = 0, nnzX = X->colptr[X->ncols];
+ int kY = 0, jY = 0;
+ int nnzZ = 0;
+
+ while (nnzX && !(X->colptr[jX+1])) jX++;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++) {
+
+ while ((kX < nnzX) && ((jX<jY) ||
+ (jX==jY && X->rowind[kX] < Y->rowind[kY]))) {
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++; nnzZ++;
+ }
+
+ if (jX==jY && X->rowind[kX] == Y->rowind[kY]) {
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+ nnzZ++;
+ }
+ }
+
+ nnzZ += (nnzX - kX);
+
+ ccs *Z;
+ if (!(Z = alloc_ccs(Y->nrows, Y->ncols, nnzZ, Y->id))) return -1;
+
+ kX = 0; jX = 0; kY = 0; jY = 0, nnzZ = 0;
+ while (nnzX && !(X->colptr[jX+1])) jX++;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++) {
+
+ while ((kX < nnzX) && ((jX<jY) ||
+ (jX==jY && X->rowind[kX] < Y->rowind[kY]))) {
+ Z->colptr[jX+1]++;
+ Z->rowind[nnzZ] = X->rowind[kX];
+ ((complex *)Z->values)[nnzZ++] = a.z*((complex *)X->values)[kX];
+
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+
+ Z->colptr[jY+1]++;
+ Z->rowind[nnzZ] = Y->rowind[kY];
+ if (jX==jY && X->rowind[kX] == Y->rowind[kY]) {
+ ((complex *)Z->values)[nnzZ++] = a.z*((complex *)X->values)[kX] +
+ ((complex *)Y->values)[kY];
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+ else ((complex *)Z->values)[nnzZ++] = ((complex *)Y->values)[kY];
+ }
+ }
+
+ while (kX < nnzX) {
+ Z->colptr[jX+1]++;
+ Z->rowind[nnzZ] = X->rowind[kX];
+ ((complex *)Z->values)[nnzZ++] = a.z*((complex *)X->values)[kX];
+
+ while (X->colptr[jX+1] == kX+1) jX++;
+ kX++;
+ }
+
+ int i;
+ for (i=0; i<Z->ncols; i++) Z->colptr[i+1] += Z->colptr[i];
+
+ *z = Z;
+ }
+ else if (!sp_x && sp_y && partial)
+ {
+ complex *X = x;
+ ccs *Y = y;
+ int kY, jY;
+
+ for (jY=0; jY<Y->ncols; jY++) {
+ for (kY=Y->colptr[jY]; kY<Y->colptr[jY+1]; kY++)
+ ((complex *)Y->values)[kY] += a.z*X[jY*Y->nrows + Y->rowind[kY]];
+ }
+ }
+ else { // if (!p_x && !sp_y) {
+
+ complex *X = x;
+ ccs *Y = y;
+
+ int mn = Y->nrows*Y->ncols;
+ ccs *Z = alloc_ccs(Y->nrows, Y->ncols, mn, Y->id);
+ if (!Z) return -1;
+
+ memcpy(Z->values, X, sizeof(complex)*mn);
+ scal[Y->id](&mn, &a, Z->values, (int *)&One[INT]);
+
+ int j, k;
+ for (j=0; j<Y->ncols; j++) {
+
+ Z->colptr[j+1] = Z->colptr[j] + Y->nrows;
+
+ for (k=0; k<Y->nrows; k++)
+ Z->rowind[j*Y->nrows+k] = k;
+
+ for (k=Y->colptr[j]; k<Y->colptr[j+1]; k++)
+ ((complex *)Z->values)[j*Y->nrows + Y->rowind[k]] +=
+ ((complex *)Y->values)[k];
+ }
+ *z = Z;
+ }
+ return 0;
+}
+
+static int sp_dgemv(char tA, int m, int n, number alpha, void *a, int oA,
+ void *x, int ix, number beta, void *y, int iy)
+{
+ ccs *A = a;
+ double *X = x, *Y = y;
+
+ scal[A->id]((tA == 'N' ? &m : &n), &beta, Y, &iy);
+
+ if (!m) return 0;
+ int i, j, k, oi = oA % A->nrows, oj = oA / A->nrows;
+
+ if (tA == 'N') {
+ for (j=oj; j<n+oj; j++) {
+ for (k=A->colptr[j]; k<A->colptr[j+1]; k++)
+ if ((A->rowind[k] >= oi) && (A->rowind[k] < oi+m))
+ Y[iy*(A->rowind[k]-oi + (iy > 0 ? 0 : 1 - m))] +=
+ alpha.d*((double *)A->values)[k]*
+ X[ix*(j-oj + (ix > 0 ? 0 : 1 - n))];
+
+ }
+ } else {
+ for (i=oj; i<oj+n; i++) {
+ for (k=A->colptr[i]; k<A->colptr[i+1]; k++) {
+ if ((A->rowind[k] >= oi) && (A->rowind[k] < oi+m))
+ Y[iy*(i-oj + (iy > 0 ? 0 : 1 - n))] += alpha.d*
+ ((double *)A->values)[k]*
+ X[ix*(A->rowind[k]-oi + (ix > 0 ? 0 : 1 - m))];
+ }
+ }
+ }
+ return 0;
+}
+
+static int sp_zgemv(char tA, int m, int n, number alpha, void *a, int oA,
+ void *x, int ix, number beta, void *y, int iy)
+{
+ ccs *A = a;
+ complex *X = x, *Y = y;
+
+ scal[A->id]((tA == 'N' ? &m : &n), &beta, Y, &iy);
+
+ if (!m) return 0;
+ int i, j, k, oi = oA % A->nrows, oj = oA / A->nrows;
+
+ if (tA == 'N') {
+ for (j=oj; j<n+oj; j++) {
+ for (k=A->colptr[j]; k<A->colptr[j+1]; k++)
+ if ((A->rowind[k] >= oi) && (A->rowind[k] < oi+m))
+ Y[iy*(A->rowind[k]-oi + (iy > 0 ? 0 : 1 - m))] +=
+ alpha.z*((complex *)A->values)[k]*
+ X[ix*(j-oj + (ix > 0 ? 0 : 1 - n))];
+ }
+ } else {
+ for (i=oj; i<oj+n; i++) {
+ for (k=A->colptr[i]; k<A->colptr[i+1]; k++) {
+ if ((A->rowind[k] >= oi) && (A->rowind[k] < oi+m))
+ Y[iy*(i-oj + (iy > 0 ? 0 : 1 - n))] += alpha.z*
+ CONJ(tA, ((complex *)A->values)[k])*
+ X[ix*(A->rowind[k]-oi + (ix > 0 ? 0 : 1 - m))];
+ }
+ }
+ }
+ return 0;
+}
+
+
+int sp_dsymv(char uplo, int n, number alpha, ccs *A, int oA, void *x, int ix,
+ number beta, void *y, int iy)
+{
+ double *X = x, *Y = y;
+ scal[A->id](&n, &beta, y, &iy);
+
+ if (!n) return 0;
+ int i, j, k, oi = oA % A->nrows, oj = oA / A->nrows;
+ for (j=0; j<n; j++) {
+
+ for (k = A->colptr[j+oj]; k < A->colptr[j+oj+1]; k++) {
+ i = A->rowind[k] - oi;
+
+ if ((i >= 0) && (i < n)) {
+ if ((uplo == 'U') && (i > j))
+ break;
+ if ((uplo == 'U') && (i <= j)) {
+ Y[iy*(i + (iy > 0 ? 0 : 1 - n))] += alpha.d*((double *)A->values)[k]*
+ X[ix*(j + (ix > 0 ? 0 : 1-n))];
+ if (i != j)
+ Y[iy*(j + (iy > 0 ? 0 : 1-n))] += alpha.d*((double *)A->values)[k]*
+ X[ix*(i + (ix > 0 ? 0 : 1-n))];
+ }
+ else if ((uplo == 'L') && (i >= j)) {
+ Y[iy*(i + (iy > 0 ? 0 : 1-n))] += alpha.d*((double *)A->values)[k]*
+ X[ix*(j + (ix > 0 ? 0 : 1-n))];
+ if (i != j)
+ Y[iy*(j + (iy > 0 ? 0 : 1-n))] += alpha.d*((double *)A->values)[k]*
+ X[ix*(i + (ix > 0 ? 0 : 1-n))];
+ }
+ }
+ }
+ }
+ return 0;
+}
+
+int sp_zsymv(char uplo, int n, number alpha, ccs *A, int oA, void *x, int ix,
+ number beta, void *y, int iy)
+{
+ complex *X = x, *Y = y;
+ scal[A->id](&n, &beta, y, &iy);
+
+ if (!n) return 0;
+ int i, j, k, oi = oA % A->nrows, oj = oA / A->nrows;
+ for (j=0; j<n; j++) {
+
+ for (k = A->colptr[j+oj]; k < A->colptr[j+oj+1]; k++) {
+ i = A->rowind[k] - oi;
+
+ if ((i >= 0) && (i < n)) {
+ if ((uplo == 'U') && (i > j))
+ break;
+ if ((uplo == 'U') && (i <= j)) {
+ Y[iy*(i + (iy > 0 ? 0 : 1-n))] += alpha.z*((complex *)A->values)[k]*
+ X[ix*(j + (ix > 0 ? 0 : 1-n))];
+ if (i != j)
+ Y[iy*(j+(iy>0 ? 0 : 1-n))] += alpha.z*((complex *)A->values)[k]*
+ X[ix*(i + (ix > 0 ? 0 : 1-n))];
+ }
+ else if ((uplo == 'L') && (i >= j)) {
+ Y[iy*(i + (iy > 0 ? 0 : 1-n))] += alpha.z*((complex *)A->values)[k]*
+ X[ix*(j + (ix > 0 ? 0 : 1-n))];
+ if (i != j)
+ Y[iy*(j+(iy > 0 ? 0 : 1-n))] += alpha.z*((complex *)A->values)[k]*
+ X[ix*(i + (ix > 0 ? 0 : 1-n))];
+ }
+ }
+ }
+ }
+ return 0;
+}
+
+static int sp_dgemm(char tA, char tB, number alpha, void *a, void *b,
+ number beta, void *c, int sp_a, int sp_b, int sp_c, int partial, void **z,
+ int m, int n, int k)
+{
+
+ if (sp_a && sp_b && sp_c && partial) {
+
+ ccs *A = (tA == 'T' ? a : transpose(a, 0));
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+ ccs *C = c;
+ int j, l;
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s) {
+ if (A != a) free_ccs(A);
+ return -1;
+ }
+
+ for (j=0; j<n; j++) {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ init_spa(s, A, C->rowind[l]);
+ ((double *)C->values)[l] = alpha.d*spa_ddot (B, j, s) +
+ beta.d*((double *)C->values)[l];
+ }
+ }
+ free_spa(s);
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ }
+
+ else if (sp_a && sp_b && sp_c && !partial) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a, 0));
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+ ccs *C = c;
+ int_t *colptr_new = calloc(C->ncols+1,sizeof(int_t));
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s || !colptr_new) {
+ free(colptr_new);
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ return -1;
+ }
+
+ int j, l;
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+ if (beta.d != 0.0)
+ spa_symb_axpy (C, j, s);
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++)
+ spa_symb_axpy (A, B->rowind[l], s);
+
+ colptr_new[j+1] = colptr_new[j] + s->nnz;
+ }
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(m, n, MAX(nnz,C->nzmax), C->id);
+ if (!Z) {
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ free(colptr_new); free_spa(s);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+ if (beta.d != 0.0)
+ spa_daxpy (beta.d, C, j, s);
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++)
+ spa_daxpy (((double *)B->values)[l], A, B->rowind[l], s);
+
+ spa2compressed(s, Z, j);
+ }
+
+ free_spa(s);
+
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+
+ if (sort_ccs(Z)) {
+ free_ccs(Z); return -1;
+ }
+ *z = Z;
+ }
+ else if (sp_a && sp_b && !sp_c) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a, 0));
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+ double *C = c;
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s) {
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ return -1;
+ }
+
+ int mn = m*n;
+ scal[A->id](&mn, &beta, C, (int *)&One[DOUBLE]);
+
+ int j, l;
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++)
+ spa_daxpy (((double *)B->values)[l], A, B->rowind[l], s);
+
+ for (l=0; l<s->nnz; l++)
+ C[j*A->nrows + s->idx[l]] += alpha.d*((double *)s->val)[s->idx[l]];
+ }
+ free_spa(s);
+
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ }
+
+ else if (!sp_a && sp_b && !sp_c) {
+
+ double *A = a, *C = c;
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+
+ int j, l, mn_ = m*n;
+ scal[DOUBLE](&mn_, &beta, C, (int *)&One[DOUBLE]);
+
+ for (j=0; j<n; j++) {
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++) {
+ double a_ = alpha.d*((double *)B->values)[l];
+ axpy[DOUBLE](&m, &a_, A + (tA=='N' ? B->rowind[l]*m : B->rowind[l]),
+ (tA=='N' ? (int *)&One[INT] : &k), C + j*m, (int *)&One[INT]);
+ }
+ }
+ if (B != b) free_ccs(B);
+ }
+
+ else if (sp_a && !sp_b && !sp_c) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a, 0));
+ double *B = b, *C = c;
+
+ int j, l, mn_ = m*n, ib = (tB == 'N' ? k : 1);
+ scal[DOUBLE](&mn_, &beta, C, (int *)&One[INT]);
+
+ for (j=0; j<A->ncols; j++) {
+ for (l=A->colptr[j]; l<A->colptr[j+1]; l++) {
+
+ double a_ = alpha.d*((double *)A->values)[l];
+ axpy[DOUBLE](&n, &a_, B + (tB == 'N' ? j : j*n), &ib,
+ C + A->rowind[l], &m);
+ }
+ }
+ if (A != a) free_ccs(A);
+ }
+
+ else if (!sp_a && sp_b && sp_c && partial) {
+
+ double *A = a, val;
+ ccs *B = (tB == 'N' ? b : transpose(b, 0)), *C = c;
+ int j, l, o;
+
+ for (j=0; j<n; j++) {
+ for (o=C->colptr[j]; o<C->colptr[j+1]; o++) {
+
+ val = 0;
+ for (l=B->colptr[j]; l < B->colptr[j+1]; l++)
+ val += A[tA == 'N' ? C->rowind[o] + B->rowind[l]*m :
+ B->rowind[l] + C->rowind[o]*B->nrows]*
+ ((double *)B->values)[l];
+
+ ((double *)C->values)[o] = alpha.d*val +
+ beta.d*((double *)C->values)[o];
+ }
+ }
+ if (B != b) free_ccs(B);
+ }
+ else if (!sp_a && sp_b && sp_c && !partial) {
+
+ double *A = a;
+ ccs *B = (tB == 'N' ? b : transpose(b,0)), *C = c;
+ int_t *colptr_new = calloc(C->ncols+1,sizeof(int_t));
+
+ if (!colptr_new) {
+ if (B != b) free_ccs(B);
+ free(colptr_new);
+ return -1;
+ }
+
+ int j, l;
+ for (j=0; j<n; j++)
+ colptr_new[j+1] = colptr_new[j] +
+ MAX(((B->colptr[j+1]-B->colptr[j])>0)*m, C->colptr[j+1]-C->colptr[j]);
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(m, n, nnz, C->id);
+ if (!Z) {
+ if (B != b) free_ccs(B);
+ free(colptr_new);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+ for (l=0; l<nnz; l++) ((double *)Z->values)[l] = 0;
+
+ for (j=0; j<C->ncols; j++) {
+
+ if (B->colptr[j+1]-B->colptr[j])
+ for (l=0; l<m; l++)
+ Z->rowind[Z->colptr[j]+l] = l;
+
+ for (k=B->colptr[j]; k<B->colptr[j+1]; k++) {
+
+ double a_ = alpha.d*((double *)B->values)[k];
+ axpy[DOUBLE](&m, &a_, A +
+ (tA=='N' ? B->rowind[k]*m : B->rowind[k]),
+ (tA=='N' ? (int *)&One[INT] : &k),
+ (double *)Z->values + Z->colptr[j], (int *)&One[INT]);
+ }
+
+ if (beta.d != 0.0) {
+ if (Z->colptr[j+1]-Z->colptr[j] == m) {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ ((double *)Z->values)[Z->colptr[j]+C->rowind[l]] +=
+ beta.d*((double *)C->values)[l];
+ }
+ }
+ else {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ ((double *)Z->values)[Z->colptr[j]+l-C->colptr[j]] =
+ beta.d*((double *)C->values)[l];
+ Z->rowind[Z->colptr[j]+l-C->colptr[j]] = C->rowind[l];
+ }
+ }
+ }
+ }
+ if (B != b) free_ccs(B);
+ *z = Z;
+ }
+ else if (sp_a && !sp_b && sp_c && partial) {
+
+ ccs *A = (tA == 'N' ? transpose(a,0) : a), *C = c;
+ double *B = b, val;
+
+ int j, l, o;
+ for (j=0; j<n; j++) {
+ for (o=C->colptr[j]; o<C->colptr[j+1]; o++) {
+
+ val = 0;
+ for (l=A->colptr[C->rowind[o]]; l < A->colptr[C->rowind[o]+1]; l++)
+ val += ((double *)A->values)[l]*
+ B[tB == 'N' ? j*A->nrows + A->rowind[l] :
+ A->rowind[l]*C->ncols + j];
+
+ ((double *)C->values)[o] = alpha.d*val +
+ beta.d*((double *)C->values)[o];
+ }
+ }
+ if (A != a) free_ccs(A);
+ }
+ else if (sp_a && !sp_b && sp_c && !partial) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a,0)), *C = c;
+ double *B = b;
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ int_t *colptr_new = calloc(n+1,sizeof(int_t));
+ if (!s || !colptr_new) {
+ free(s); free(colptr_new);
+ if (A != a) free_ccs(A);
+ return -1;
+ }
+
+ int j, l;
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+
+ for (l=0; l<A->ncols; l++)
+ spa_symb_axpy(A, l, s);
+
+ if (beta.d != 0.0) spa_symb_axpy(C, j, s);
+ colptr_new[j+1] = colptr_new[j] + s->nnz;
+ }
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(m, n, nnz, C->id);
+ if (!Z) {
+ if (A != a) free_ccs(A);
+ free_spa(s); free(colptr_new);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+
+ for (l=0; l<k; l++) {
+ spa_daxpy(alpha.d*B[tB == 'N' ? l + j*k : j + l*n], A, l, s);
+ }
+
+ if (beta.d != 0.0) spa_daxpy(beta.d, C, j, s);
+ spa2compressed(s, Z, j);
+ }
+ free_spa(s);
+ if (A != a) free_ccs(A);
+ if (sort_ccs(Z)) {
+ free_ccs(Z); return -1;
+ }
+ *z = Z;
+ }
+ else if (!sp_a && !sp_b && sp_c && partial) {
+ ccs *C = c;
+ double *A = a, *B = b, val;
+
+ int j, l, o;
+ for (j=0; j<C->ncols; j++) {
+ for (o=C->colptr[j]; o<C->colptr[j+1]; o++) {
+
+ val = 0;
+ for (l=0; l<k; l++)
+ val += A[tA == 'N' ? m*l + C->rowind[o] : l + C->rowind[o]*k]*
+ B[tB == 'N' ? j*k + l : l*n + j];
+
+ ((double *)C->values)[o] = alpha.d*val +
+ beta.d*((double *)C->values)[o];
+ }
+ }
+ }
+ else if (!sp_a && !sp_b && sp_c && !partial) {
+
+ double *A = a, *B = b;
+ ccs *C = c;
+
+ ccs *Z = alloc_ccs(m, n, m*n, C->id);
+ if (!Z) return -1;
+
+ int j, l;
+ for (j=0; j<m*n; j++) ((double *)Z->values)[j] = 0.0;
+
+ int ldA = MAX(1, (tA == 'N' ? m : k));
+ int ldB = MAX(1, (tB == 'N' ? k : n));
+ int ldC = MAX(1, m);
+
+ gemm[DOUBLE](&tA, &tB, &m, &n, &k, &alpha, A, &ldA,
+ B, &ldB, &Zero[DOUBLE], Z->values, &ldC);
+
+ for (j=0; j<n; j++) {
+ for (l=0; l<m; l++)
+ Z->rowind[j*m + l] = l;
+
+ Z->colptr[j+1] = Z->colptr[j] + m;
+ }
+
+ if (beta.d != 0.0) {
+ for (j=0; j<n; j++) {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ ((double *)Z->values)[j*m + C->rowind[l]] +=
+ beta.d*((double *)C->values)[l];
+ }
+ }
+ }
+ *z = Z;
+ }
+ return 0;
+}
+
+static int sp_zgemm(char tA, char tB, number alpha, void *a, void *b,
+ number beta, void *c, int sp_a, int sp_b, int sp_c, int partial, void **z,
+ int m, int n, int k)
+{
+
+ if (sp_a && sp_b && sp_c && partial) {
+
+ ccs *A = (tA == 'N' ? transpose(a, 0) : a);
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+ ccs *C = c;
+ int j, l;
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s) {
+ if (A != a) free_ccs(A);
+ return -1;
+ }
+
+ for (j=0; j<n; j++) {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ init_spa(s, A, C->rowind[l]);
+ ((complex *)C->values)[l] = alpha.z*spa_zdot(B, j, s, tB, tA) +
+ beta.z*((complex *)C->values)[l];
+ }
+ }
+ free_spa(s);
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ }
+
+ else if (sp_a && sp_b && sp_c && !partial) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a, 0));
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+ ccs *C = c;
+ int_t *colptr_new = calloc(C->ncols+1,sizeof(int_t));
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s || !colptr_new) {
+ free(colptr_new);
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ return -1;
+ }
+
+ int j, l;
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+ if (beta.z != 0.0)
+ spa_symb_axpy (C, j, s);
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++)
+ spa_symb_axpy (A, B->rowind[l], s);
+
+ colptr_new[j+1] = colptr_new[j] + s->nnz;
+ }
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(m, n, nnz, A->id);
+ if (!Z) {
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ free(colptr_new); free_spa(s);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+ if (beta.z != 0.0)
+ spa_zaxpy (beta.z, C, 'N', j, s);
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++)
+ spa_zaxpy(CONJ(tB, ((complex *)B->values)[l]), A, tA, B->rowind[l], s);
+
+ spa2compressed(s, Z, j);
+ }
+
+ free_spa(s);
+
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+
+ if (sort_ccs(Z)) {
+ free_ccs(Z); return -1;
+ }
+ *z = Z;
+ }
+ else if (sp_a && sp_b && !sp_c) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a, 0));
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+ complex *C = c;
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s) {
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ return -1;
+ }
+
+ int mn = m*n;
+ scal[A->id](&mn, &beta, C, (int *)&One[COMPLEX]);
+
+ int j, l;
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++)
+ spa_zaxpy (CONJ(tB,((complex *)B->values)[l]), A, tA, B->rowind[l], s);
+
+ for (l=0; l<s->nnz; l++)
+ C[j*A->nrows + s->idx[l]] += alpha.z*((complex *)s->val)[s->idx[l]];
+ }
+ free_spa(s);
+
+ if (A != a) free_ccs(A);
+ if (B != b) free_ccs(B);
+ }
+
+ else if (!sp_a && sp_b && !sp_c) {
+
+ complex *A = a, *C = c;
+ ccs *B = (tB == 'N' ? b : transpose(b, 0));
+
+ int i, j, l, mn_ = m*n;
+ scal[COMPLEX](&mn_, &beta, C, (int *)&One[COMPLEX]);
+
+ for (j=0; j<n; j++) {
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++) {
+
+ for (i=0; i<m; i++)
+ C[i+j*m] += alpha.z*CONJ(tA,A[tA=='N' ? i+B->rowind[l]*m :
+ B->rowind[l]+i*k])*
+ CONJ(tB,((complex *)B->values)[l]);
+ }
+ }
+ if (B != b) free_ccs(B);
+ }
+
+ else if (sp_a && !sp_b && !sp_c) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a, 0));
+ complex *B = b, *C = c;
+
+ int i, j, l, mn_ = m*n;
+ scal[COMPLEX](&mn_, &beta, C, (int *)&One[INT]);
+
+ for (j=0; j<A->ncols; j++) {
+ for (l=A->colptr[j]; l<A->colptr[j+1]; l++) {
+
+ for (i=0; i<n; i++)
+ C[A->rowind[l]+i*m] += alpha.z*CONJ(tA,((complex *)A->values)[l])*
+ CONJ(tB,B[tB=='N' ? j+i*k : i+j*n]);
+ }
+ }
+ if (A != a) free_ccs(A);
+ }
+
+ else if (!sp_a && sp_b && sp_c && partial) {
+
+ complex *A = a, val;
+ ccs *B = (tB == 'N' ? b : transpose(b, 0)), *C = c;
+ int j, l, o;
+
+ for (j=0; j<n; j++) {
+ for (o=C->colptr[j]; o<C->colptr[j+1]; o++) {
+
+ val = 0;
+ for (l=B->colptr[j]; l < B->colptr[j+1]; l++)
+ val += CONJ(tA,A[tA == 'N' ? C->rowind[o] + B->rowind[l]*m :
+ B->rowind[l] + C->rowind[o]*B->nrows])*
+ CONJ(tB,((complex *)B->values)[l]);
+
+ ((complex *)C->values)[o] = alpha.z*val +
+ beta.z*((complex *)C->values)[o];
+ }
+ }
+ if (B != b) free_ccs(B);
+ }
+ else if (!sp_a && sp_b && sp_c && !partial) {
+
+ complex *A = a;
+ ccs *B = (tB == 'N' ? b : transpose(b,0)), *C = c;
+ int_t *colptr_new = calloc(C->ncols+1,sizeof(int_t));
+
+ if (!colptr_new) {
+ if (B != b) free_ccs(B);
+ free(colptr_new);
+ return -1;
+ }
+
+ int i, j, l;
+ for (j=0; j<n; j++)
+ colptr_new[j+1] = colptr_new[j] +
+ MAX(((B->colptr[j+1]-B->colptr[j])>0)*m, C->colptr[j+1]-C->colptr[j]);
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(m, n, nnz, C->id);
+ if (!Z) {
+ if (B != b) free_ccs(B);
+ free(colptr_new);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+ for (l=0; l<nnz; l++) ((complex *)Z->values)[l] = 0;
+
+ for (j=0; j<C->ncols; j++) {
+
+ if (B->colptr[j+1]-B->colptr[j])
+ for (l=0; l<m; l++)
+ Z->rowind[Z->colptr[j]+l] = l;
+
+ for (l=B->colptr[j]; l<B->colptr[j+1]; l++) {
+
+ for (i=0; i<m; i++) {
+ ((complex*)Z->values)[Z->colptr[j]+i] += alpha.z*
+ CONJ(tA,A[tA=='N' ? B->rowind[l]*m+i : B->rowind[l]+i*k])*
+ CONJ(tB,((complex *)B->values)[l]);
+
+ }
+ }
+
+ if (beta.z != 0.0) {
+ if (Z->colptr[j+1]-Z->colptr[j] == m) {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ ((complex *)Z->values)[Z->colptr[j]+C->rowind[l]] +=
+ beta.z*((complex *)C->values)[l];
+ }
+ }
+ else {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ ((complex *)Z->values)[Z->colptr[j]+l-C->colptr[j]] =
+ beta.z*((complex *)C->values)[l];
+ Z->rowind[Z->colptr[j]+l-C->colptr[j]] = C->rowind[l];
+ }
+ }
+ }
+ }
+ if (B != b) free_ccs(B);
+ *z = Z;
+ }
+ else if (sp_a && !sp_b && sp_c && partial) {
+
+ ccs *A = (tA == 'N' ? transpose(a,0) : a), *C = c;
+ complex *B = b, val;
+
+ int j, l, o;
+ for (j=0; j<n; j++) {
+ for (o=C->colptr[j]; o<C->colptr[j+1]; o++) {
+
+ val = 0;
+ for (l=A->colptr[C->rowind[o]]; l < A->colptr[C->rowind[o]+1]; l++)
+ val += CONJ(tA, ((complex *)A->values)[l])*
+ CONJ(tB, B[tB == 'N' ? j*A->nrows + A->rowind[l] :
+ A->rowind[l]*C->ncols + j]);
+
+ ((complex *)C->values)[o] = alpha.z*val +
+ beta.z*((complex *)C->values)[o];
+ }
+ }
+ if (A != a) free_ccs(A);
+ }
+ else if (sp_a && !sp_b && sp_c && !partial) {
+
+ ccs *A = (tA == 'N' ? a : transpose(a,0)), *C = c;
+ complex *B = b;
+
+ spa *s = alloc_spa(A->nrows, A->id);
+ int_t *colptr_new = calloc(n+1,sizeof(int_t));
+ if (!s || !colptr_new) {
+ free(s); free(colptr_new);
+ if (A != a) free_ccs(A);
+ return -1;
+ }
+
+ int j, l;
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+
+ for (l=0; l<A->ncols; l++)
+ spa_symb_axpy(A, l, s);
+
+ if (beta.z != 0.0) spa_symb_axpy(C, j, s);
+ colptr_new[j+1] = colptr_new[j] + s->nnz;
+ }
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(m, n, nnz, C->id);
+ if (!Z) {
+ if (A != a) free_ccs(A);
+ free_spa(s); free(colptr_new);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+
+ for (j=0; j<n; j++) {
+ init_spa(s, NULL, 0);
+
+ for (l=0; l<k; l++) {
+ spa_zaxpy(alpha.z*CONJ(tB, B[tB == 'N' ? l + j*k : j + l*n]),
+ A, tA, l, s);
+ }
+
+ if (beta.z != 0.0) spa_zaxpy(beta.z, C, 'N', j, s);
+ spa2compressed(s, Z, j);
+ }
+ free_spa(s);
+ if (A != a) free_ccs(A);
+ if (sort_ccs(Z)) {
+ free_ccs(Z); return -1;
+ }
+ *z = Z;
+ }
+ else if (!sp_a && !sp_b && sp_c && partial) {
+ ccs *C = c;
+ complex *A = a, *B = b, val;
+
+ int j, l, o;
+ for (j=0; j<C->ncols; j++) {
+ for (o=C->colptr[j]; o<C->colptr[j+1]; o++) {
+
+ val = 0;
+ for (l=0; l<k; l++)
+ val += CONJ(tA, A[tA=='N' ? m*l+C->rowind[o] : l+C->rowind[o]*k])*
+ CONJ(tB, B[tB == 'N' ? j*k + l : l*n + j]);
+
+ ((complex *)C->values)[o] = alpha.z*val +
+ beta.z*((complex *)C->values)[o];
+ }
+ }
+ }
+ else if (!sp_a && !sp_b && sp_c && !partial) {
+
+ complex *A = a, *B = b;
+ ccs *C = c;
+
+ ccs *Z = alloc_ccs(m, n, m*n, C->id);
+ if (!Z) return -1;
+
+ int j, l;
+ for (j=0; j<m*n; j++) ((complex *)Z->values)[j] = 0.0;
+
+ int ldA = MAX(1, (tA == 'N' ? m : k));
+ int ldB = MAX(1, (tB == 'N' ? k : n));
+ int ldC = MAX(1, m);
+
+ gemm[COMPLEX](&tA, &tB, &m, &n, &k, &alpha, A, &ldA,
+ B, &ldB, &Zero[COMPLEX], Z->values, &ldC);
+
+ for (j=0; j<n; j++) {
+ for (l=0; l<m; l++)
+ Z->rowind[j*m + l] = l;
+
+ Z->colptr[j+1] = Z->colptr[j] + m;
+ }
+
+ if (beta.z != 0.0) {
+ for (j=0; j<n; j++) {
+ for (l=C->colptr[j]; l<C->colptr[j+1]; l++) {
+ ((complex *)Z->values)[j*m + C->rowind[l]] +=
+ beta.z*((complex *)C->values)[l];
+ }
+ }
+ }
+ *z = Z;
+ }
+ return 0;
+}
+
+static int sp_dsyrk(char uplo, char trans, number alpha, void *a,
+ number beta, void *c, int sp_a, int sp_c, int partial, int k, void **z)
+{
+ if (sp_a && sp_c && partial) {
+
+ ccs *A = (trans == 'N' ? transpose(a, 0) : a), *C = c;
+ spa *s = alloc_spa(A->nrows, C->id);
+ if (!A || !s) {
+ if (A != a) free_ccs(A);
+ free_spa(s);
+ return -1;
+ }
+ int j, k;
+ for (j=0; j<C->ncols; j++) {
+ for (k=C->colptr[j]; k<C->colptr[j+1]; k++) {
+ if ((uplo == 'L' && C->rowind[k] >= j) ||
+ (uplo == 'U' && C->rowind[k] <= j)) {
+ init_spa(s, A, C->rowind[k]);
+ ((double *)C->values)[k] = alpha.d*spa_ddot(A, j, s) +
+ beta.d*((double *)C->values)[k];
+ }
+ }
+ }
+ free_spa(s);
+ if (A != a) free_ccs(A);
+ }
+ else if (sp_a && sp_c && !partial) {
+
+ ccs *A = (trans == 'N' ? a : transpose(a, 0));
+ ccs *B = (trans == 'N' ? transpose(a, 0) : a);
+ ccs *C = c;
+ spa *s = alloc_spa(C->nrows, C->id);
+ int_t *colptr_new = calloc(C->ncols+1,sizeof(int_t));
+
+ if (!A || !B || !s || !colptr_new) {
+ if (A != a) free_ccs(A);
+ if (B != a) free_ccs(B);
+ free_spa(s); free(colptr_new);
+ return -1;
+ }
+
+ int j, k;
+ for (j=0; j<B->ncols; j++) {
+ init_spa(s, NULL, 0);
+ if (beta.d != 0.0)
+ spa_symb_axpy_uplo(C, j, s, j, uplo);
+
+ for (k=B->colptr[j]; k<B->colptr[j+1]; k++)
+ spa_symb_axpy_uplo(A, B->rowind[k], s, j, uplo);
+
+ colptr_new[j+1] = colptr_new[j] + s->nnz;
+ }
+
+ int nnz = colptr_new[C->ncols];
+ ccs *Z = alloc_ccs(C->nrows, C->ncols, nnz, C->id);
+ if (!Z) {
+ if (A != a) free_ccs(A);
+ if (B != a) free_ccs(B);
+ free_spa(s); free(colptr_new);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+
+ for (j=0; j<B->ncols; j++) {
+ init_spa(s, NULL, 0);
+ if (beta.d != 0.0)
+ spa_daxpy_uplo(beta.d, C, j, s, j, uplo);
+
+ for (k=B->colptr[j]; k<B->colptr[j+1]; k++) {
+ spa_daxpy_uplo(alpha.d*((double *)B->values)[k], A, B->rowind[k],
+ s, j, uplo);
+ }
+ spa2compressed(s, Z, j);
+ }
+
+ if (A != a) free_ccs(A);
+ if (B != a) free_ccs(B);
+ free_spa(s);
+
+ if (sort_ccs(Z)) {
+ free_ccs(Z); return -1;
+ }
+ *z = Z;
+ }
+ else if (sp_a && !sp_c) {
+
+ int n = (trans == 'N' ? ((ccs *)a)->nrows : ((ccs *)a)->ncols);
+ ccs *A = (trans == 'N' ? a : transpose(a, 0));
+ ccs *B = (trans == 'N' ? transpose(a, 0) : a);
+ double *C = c;
+
+ spa *s = alloc_spa(n, A->id);
+ if (!A || !B || !s) {
+ if (A != a) free_ccs(A);
+ if (B != a) free_ccs(B);
+ free_spa(s);
+ return -1;
+ }
+
+ int j, k;
+ for (j=0; j<B->ncols; j++) {
+ init_spa(s, NULL, 0);
+
+ for (k=B->colptr[j]; k<B->colptr[j+1]; k++) {
+ spa_daxpy_uplo(alpha.d*((double *)B->values)[k], A, B->rowind[k],
+ s, j, uplo);
+ }
+
+ if (uplo == 'U') {
+ int m = j+1;
+ scal[DOUBLE](&m, &beta, C + j*n, (int *)&One[INT]);
+
+ for (k=0; k<s->nnz; k++) {
+ if (s->idx[k] <= j)
+ C[j*n + s->idx[k]] += alpha.d*((double *)s->val)[s->idx[k]];
+ }
+ } else {
+ int m = n-j;
+ scal[DOUBLE](&m, &beta, C + j*(n+1), (int *)&One[INT]);
+
+ for (k=0; k<s->nnz; k++) {
+ if (s->idx[k] >= j)
+ C[j*n + s->idx[k]] += alpha.d*((double *)s->val)[s->idx[k]];
+ }
+ }
+ }
+ if (A != a) free_ccs(A);
+ if (B != a) free_ccs(B);
+ free_spa(s);
+ }
+ else if (!sp_a && sp_c && partial) {
+
+ ccs *C = c;
+ double *A = a;
+
+ int j, i, l, n=C->nrows;
+ for (j=0; j<n; j++) {
+ for (i=C->colptr[j]; i<C->colptr[j+1]; i++) {
+ if ((uplo == 'L' && C->rowind[i] >= j) ||
+ (uplo == 'U' && C->rowind[i] <= j)) {
+
+ ((double *)C->values)[i] *= beta.d;
+
+ for (l=0; l<k; l++)
+ ((double *)C->values)[i] +=
+ alpha.d*A[trans == 'N' ? C->rowind[i]+l*n : l+C->rowind[i]*k]*
+ A[trans == 'N' ? j+l*n : l+j*k];
+ }
+ }
+ }
+ }
+ else if (!sp_a && sp_c) {
+
+ ccs *C = c;
+ double *A = a, *C_ = malloc( C->nrows*C->nrows*sizeof(double) );
+ int_t *colptr_new = calloc(C->ncols+1,sizeof(int_t));
+
+ if (!C_ || !colptr_new) {
+ free(C_); free(colptr_new); return -1;
+ }
+ int j, i, n=C->nrows;
+ for (j=0; j<n; j++)
+ colptr_new[j+1] = colptr_new[j] + (uplo == 'U' ? j+1 : n-j);
+
+ int nnz = colptr_new[n];
+ ccs *Z = alloc_ccs(n, n, nnz, C->id);
+ if (!Z) {
+ free(C_); free(colptr_new);
+ return -1;
+ }
+ free(Z->colptr); Z->colptr = colptr_new;
+
+ syrk[DOUBLE](&uplo, &trans, &n, &k, &alpha, A,
+ (trans == 'N' ? &n : &k), &Zero[DOUBLE], C_, &n);
+
+ for (j=0; j<n; j++) {
+ for (i=Z->colptr[j]; i<Z->colptr[j+1]; i++) {
+ if (uplo == 'U') {
+ ((double *)Z->values)[i] = C_[j*n + i-Z->colptr[j]];
+ Z->rowind[i] = i-Z->colptr[j];
+ } else {
+ ((double *)Z->values)[i] = C_[j*(n+1) + i-Z->colptr[j]];
+ Z->rowind[i] = j+i-Z->colptr[j];
+ }
+ }
+
+ for (i=C->colptr[j]; i<C->colptr[j+1]; i++) {
+ if (uplo == 'U' && C->rowind[i] <= j)
+ ((double *)Z->values)[Z->colptr[j]+C->rowind[i]] +=
+ beta.d*((double *)C->values)[i];
+ else if (uplo == 'L' && C->rowind[i] >= j)
+ ((double *)Z->values)[Z->colptr[j]+C->rowind[i]-j] +=
+ beta.d*((double *)C->values)[i];
+ }
+ }
+ free(C_);
+ *z = Z;
+ }
+
+ return 0;
+}
+
+/* No error checking: Il and Jl must be valid indexlist,
+ and Il,Jl,V must be of same length (V can also be NULL) */
+static spmatrix *
+triplet2dccs(matrix *Il, matrix *Jl, matrix *V,
+ int_t nrows, int_t ncols, int nzmax)
+{
+ spmatrix *ret = SpMatrix_New(nrows,ncols, MAX(MAT_LGT(Il),nzmax), DOUBLE);
+ double_list *dlist = malloc(MAT_LGT(Jl)*sizeof(double_list));
+ int_t *colcnt = calloc(ncols,sizeof(int_t));
+
+ if (!ret || !dlist || !colcnt) {
+ Py_XDECREF(ret); free(dlist); free(colcnt);
+ return (spmatrix *)PyErr_NoMemory();
+ }
+
+ /* build colptr */
+ int_t i,j,k,l;
+ for (j=0; j<ncols+1; j++) SP_COL(ret)[j] = 0;
+ for (j=0; j<MAT_LGT(Jl); j++) {
+ SP_COL(ret)[1+MAT_BUFI(Jl)[j]]++;
+ dlist[j].key = -1;
+ }
+
+ for (j=0; j<ncols; j++) SP_COL(ret)[j+1] += SP_COL(ret)[j];
+
+ /* build rowind and values */
+ for (k=0; k<MAT_LGT(Il); k++) {
+ i = MAT_BUFI(Il)[k], j = MAT_BUFI(Jl)[k];
+
+ for (l=SP_COL(ret)[j]; l<SP_COL(ret)[j+1]; l++)
+ if (dlist[l].key == i) {
+
+ number n;
+ if (V) {
+ convert_num[DOUBLE](&n, V, 0, k);
+ dlist[l].value += n.d;
+ }
+
+ goto skip;
+ }
+
+ if (V)
+ convert_num[DOUBLE](&dlist[SP_COL(ret)[j]+colcnt[j]].value, V, 0, k);
+
+ dlist[SP_COL(ret)[j] + colcnt[j]++].key = i;
+
+ skip:
+ ;
+ }
+
+ for (j=0; j<ncols; j++)
+ qsort(&dlist[SP_COL(ret)[j]],colcnt[j],sizeof(double_list),&comp_double);
+
+ int_t cnt = 0;
+ for (j=0; j<ncols; j++) {
+ for (i=0; i<colcnt[j]; i++) {
+
+ SP_ROW(ret)[cnt] = dlist[i + SP_COL(ret)[j]].key;
+ SP_VALD(ret)[cnt++] = dlist[i + SP_COL(ret)[j]].value;
+
+ }
+ }
+
+ for (j=0; j<ncols; j++)
+ SP_COL(ret)[j+1] = colcnt[j] + SP_COL(ret)[j];
+
+ free(dlist); free(colcnt);
+ return ret;
+}
+
+static spmatrix *
+triplet2zccs(matrix *Il, matrix *Jl, matrix *V,
+ int_t nrows, int_t ncols, int nzmax)
+{
+ spmatrix *ret = SpMatrix_New(nrows,ncols, MAX(MAT_LGT(Il),nzmax), COMPLEX);
+ complex_list *zlist = malloc(MAT_LGT(Jl)*sizeof(complex_list));
+ int_t *colcnt = calloc(ncols,sizeof(int_t));
+
+ if (!ret || !zlist || !colcnt) {
+ Py_XDECREF(ret); free(zlist); free(colcnt);
+ return (spmatrix *)PyErr_NoMemory();
+ }
+
+ /* build colptr */
+ int_t i,j,k,l;
+ for (j=0; j<ncols+1; j++) SP_COL(ret)[j] = 0;
+ for (j=0; j<MAT_LGT(Jl); j++) {
+ SP_COL(ret)[1+MAT_BUFI(Jl)[j]]++;
+ zlist[j].key = -1;
+ }
+
+ for (j=0; j<ncols; j++) SP_COL(ret)[j+1] += SP_COL(ret)[j];
+
+ /* build rowind and values */
+ for (k=0; k<MAT_LGT(Il); k++) {
+ i = MAT_BUFI(Il)[k], j = MAT_BUFI(Jl)[k];
+
+ for (l=SP_COL(ret)[j]; l<SP_COL(ret)[j+1]; l++)
+ if (zlist[l].key == i) {
+
+ number n;
+ if (V) {
+ convert_num[COMPLEX](&n, V, 0, k);
+ zlist[l].value += n.z;
+ }
+
+ goto skip;
+ }
+
+ if (V)
+ convert_num[COMPLEX](&zlist[SP_COL(ret)[j]+colcnt[j]].value, V, 0, k);
+
+ zlist[SP_COL(ret)[j] + colcnt[j]++].key = i;
+
+ skip:
+ ;
+ }
+
+ for (j=0; j<ncols; j++)
+ qsort(&zlist[SP_COL(ret)[j]],colcnt[j],sizeof(complex_list),&comp_complex);
+
+ int_t cnt = 0;
+ for (j=0; j<ncols; j++) {
+ for (i=0; i<colcnt[j]; i++) {
+
+ SP_ROW(ret)[cnt] = zlist[i + SP_COL(ret)[j]].key;
+ SP_VALZ(ret)[cnt++] = zlist[i + SP_COL(ret)[j]].value;
+
+ }
+ }
+
+ for (j=0; j<ncols; j++)
+ SP_COL(ret)[j+1] = colcnt[j] + SP_COL(ret)[j];
+
+ free(zlist); free(colcnt);
+ return ret;
+}
+
+/*
+ SpMatrix_New. In API.
+
+ Returns an uninitialized spmatrix object.
+
+ Arguments:
+ mrows,nrows : Dimension of spmatrix.
+ nzmax : Number of nonzero elements.
+ id : DOUBLE/COMPLEX
+*/
+spmatrix *
+SpMatrix_New(int nrows, int ncols, int nzmax, int id)
+{
+ spmatrix *ret;
+ if (!(ret = (spmatrix *)spmatrix_tp.tp_alloc(&spmatrix_tp, 0)))
+ return (spmatrix *)PyErr_NoMemory();
+
+ ret->obj = alloc_ccs(nrows, ncols, nzmax, id);
+ if (!ret->obj) { Py_DECREF(ret); return (spmatrix *)PyErr_NoMemory(); }
+
+ return ret;
+ }
+
+static spmatrix * SpMatrix_NewFromCCS(ccs *x)
+{
+ spmatrix *ret;
+ if (!(ret = (spmatrix *)spmatrix_tp.tp_alloc(&spmatrix_tp, 0)))
+ return (spmatrix *)PyErr_NoMemory();
+
+ ret->obj = x;
+ return ret;
+}
+
+/*
+ SpMatrix_NewFromSpMatrix. In API.
+
+ Returns a copy of an spmatrix object.
+
+ Arguments:
+ A : spmatrix object
+ nzmax : Number of nonzero elements. If nzmax is smaller than
+ the actual size, it is ignored.
+ id : DOUBLE/COMPLEX
+*/
+spmatrix * SpMatrix_NewFromSpMatrix(spmatrix *A, int nzmax, int id)
+{
+ if ((id == DOUBLE) && (SP_ID(A) == COMPLEX))
+ PY_ERR_TYPE("cannot convert complex to double");
+
+ spmatrix *ret = SpMatrix_New
+ (SP_NROWS(A), SP_NCOLS(A), MAX(SP_NNZ(A),nzmax), id);
+
+ if (!ret) return (spmatrix *)PyErr_NoMemory();
+
+ convert_array(SP_VAL(ret), SP_VAL(A), id, SP_ID(A), SP_NNZ(A));
+ memcpy(SP_COL(ret), SP_COL(A), (SP_NCOLS(A)+1)*sizeof(int_t));
+ memcpy(SP_ROW(ret), SP_ROW(A), SP_NNZ(A)*sizeof(int_t));
+
+ return ret;
+}
+
+/*
+ SpMatrix_NewFromIJV.
+
+ Returns a spmatrix object from a triplet description.
+
+ Arguments:
+ Il,Jl,V : (INT,INT,DOUBLE/COMPLEX) triplet description
+ m,n : Dimension of spmatrix. If either m==0 or n==0, then
+ the dimension is taken as MAX(I) x MAX(Jl).
+ nzmax : Number of nonzero elements. If nzmax is less than the nnz of
+ the resulting matrix then nzmax is ignored.
+ id : DOUBLE, COMPLEX
+*/
+spmatrix * SpMatrix_NewFromIJV(matrix *Il, matrix *Jl, matrix *V,
+ int_t m, int_t n, int nzmax, int id)
+{
+
+ if (MAT_ID(Il) != INT || MAT_ID(Jl) != INT)
+ PY_ERR_TYPE("index sets I and J must be integer");
+
+ if (MAT_LGT(Il) != MAT_LGT(Jl))
+ PY_ERR_TYPE("index sets I and J must be of same length");
+
+ if (V && !Matrix_Check(V)) PY_ERR_TYPE("invalid V argument");
+
+ if (V && Matrix_Check(V) && (MAX(id,MAT_ID(V)) != id))
+ PY_ERR_TYPE("matrix V has invalid type");
+
+ if (V && (MAT_LGT(V) != MAT_LGT(Il)))
+ PY_ERR_TYPE("I, J and V must have same length");
+
+ if (!Il || !Jl) return SpMatrix_New(0,0,nzmax,id);
+
+ int_t k, Imax=-1, Jmax=-1;
+ for (k=0; k<MAT_LGT(Il); k++) {
+ if (MAT_BUFI(Il)[k]>Imax) Imax = MAT_BUFI(Il)[k];
+ if (MAT_BUFI(Jl)[k]>Jmax) Jmax = MAT_BUFI(Jl)[k];
+ }
+
+ if ((m<0) || (n<0)) { m = MAX(Imax+1,m); n = MAX(Jmax+1,n);}
+
+ if (m < Imax+1 || n < Jmax+1) PY_ERR_TYPE("dimension too small");
+
+ for (k=0; k<MAT_LGT(Il); k++)
+ if ((MAT_BUFI(Il)[k] < 0) || (MAT_BUFI(Il)[k] >= m) ||
+ (MAT_BUFI(Jl)[k] < 0) || (MAT_BUFI(Jl)[k] >= n) )
+ PY_ERR_TYPE("index out of range");
+
+ return (id == DOUBLE ? triplet2dccs(Il,Jl,V,m,n,nzmax) :
+ triplet2zccs(Il,Jl,V,m,n,nzmax));
+}
+
+static void spmatrix_dealloc(spmatrix* self)
+{
+ free(SP_VAL(self));
+ free(SP_ROW(self));
+ free(SP_COL(self));
+ self->ob_type->tp_free((PyObject*)self);
+}
+
+static PyObject *
+spmatrix_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+ PyObject *size = NULL;
+ matrix *Il=NULL, *Jl=NULL, *V=NULL;
+ int_t nrows = -1, ncols = -1, nzmax = 0;
+ char tc = 0;
+
+ static char *kwlist[] = { "V", "I", "J", "size","tc","nzmax", NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwds, "OOO|Ocl:spmatrix", kwlist,
+ &V, &Il, &Jl, &size, &tc, &nzmax))
+ return NULL;
+
+ if (!(PySequence_Check((PyObject *)V) || Matrix_Check(V) || PY_NUMBER(V))) {
+ PY_ERR_TYPE("V must be either a sequence type, a matrix, or a number");
+ }
+
+ if (size && !PyArg_ParseTuple(size, "ll", &nrows, &ncols))
+ PY_ERR_TYPE("invalid dimension tuple");
+
+ if (size && (nrows < 0 || ncols < 0))
+ PY_ERR_TYPE("dimensions must be non-negative");
+
+ if (tc && !(VALID_TC_SP(tc))) PY_ERR_TYPE("tc must be 'd' or 'z'");
+ int id = (tc ? TC2ID(tc) : -1);
+
+ if (nzmax < 0) PY_ERR_TYPE("nzmax must be non-negative");
+
+ int_t ndim = 0;
+ /* convert lists to matrices */
+ if (Matrix_Check(Il))
+ Py_INCREF(Il);
+ else if (PyObject_HasAttrString((PyObject *)Il,"__array_struct__")) {
+ if (!(Il = Matrix_NewFromArrayStruct((PyObject *)Il, INT, &ndim)))
+ return NULL;
+ }
+ else if (PySequence_Check((PyObject *)Il))
+ Il = Matrix_NewFromSequence((PyObject *)Il, INT);
+
+
+ if (Matrix_Check(Jl))
+ Py_INCREF(Jl);
+ else if (PyObject_HasAttrString((PyObject *)Jl,"__array_struct__")) {
+ if (!(Jl = Matrix_NewFromArrayStruct((PyObject *)Jl, INT, &ndim)))
+ return NULL;
+ }
+ else if (PySequence_Check((PyObject *)Jl))
+ Jl = Matrix_NewFromSequence((PyObject *)Jl, INT);
+
+
+ if (Matrix_Check(V))
+ Py_INCREF(V);
+ else if (PyObject_HasAttrString((PyObject *)V,"__array_struct__")) {
+ int_t ndim = 0;
+ if (!(V = Matrix_NewFromArrayStruct((PyObject *)V, id, &ndim)))
+ return NULL;
+ }
+ else if (PySequence_Check((PyObject *)V))
+ {
+ if (!(V = Matrix_NewFromSequence((PyObject *)V, id)))
+ return NULL;
+ }
+ else if (PY_NUMBER(V))
+ {
+ if (!(V = Matrix_NewFromNumber(MAT_LGT(Il), 1, get_id(V, 1), V, 1)))
+ return PyErr_NoMemory();
+ }
+
+ id = (id == -1 ? MAX(get_id(V, !Matrix_Check(V)), DOUBLE) : id);
+
+ spmatrix *ret = SpMatrix_NewFromIJV(Il, Jl, V, nrows, ncols, nzmax,
+ id == -1 ? MAX(MAT_ID(V),DOUBLE) : id);
+
+ if (Matrix_Check(Il)) { Py_DECREF(Il); }
+ if (Matrix_Check(Jl)) { Py_DECREF(Jl); }
+ if (Matrix_Check(V)) { Py_DECREF(V); }
+
+ return (PyObject *)ret;
+}
+
+static PyObject *
+spmatrix_str(spmatrix *self)
+{
+ char s[50] = "(%li, %li) %- ";
+
+ /* these PyObject variables will all be borrowed references */
+ PyObject *printopt, *opt;
+
+ if (!(printopt = PyObject_GetAttrString(base_mod, "print_options")) ||
+ !PyDict_Check(printopt)) {
+ PY_ERR(PyExc_AttributeError, "cannot access 'print_options' dictionary");
+ }
+
+ if (!(opt = PyDict_GetItemString(printopt, PRINTOPT[SP_ID(self)]))) {
+ Py_DECREF(printopt);
+ PY_ERR(PyExc_KeyError, "missing print format key in 'base_options'");
+ }
+
+ char tmp[50], format_im[20] = "%";
+ if (SP_ID(self)==COMPLEX)
+ strncat(format_im, PyString_AsString(opt), 18);
+
+ strncat(s, PyString_AsString(opt), 37);
+
+ PyObject *ret = PyString_FromFormat("SIZE: (%ld,%ld)\n",
+ (long)SP_NROWS(self),(long)SP_NCOLS(self));
+
+ int_t j, k;
+ for (k=0; k<SP_NCOLS(self); k++)
+ for (j=SP_COL(self)[k]; j<SP_COL(self)[k+1]; j++) {
+
+ char t[100];
+ switch (SP_ID(self)) {
+ case DOUBLE:
+ if (snprintf(t,100,s,SP_ROW(self)[j],k,SP_VALD(self)[j])<0)
+ goto fail;
+ break;
+ case COMPLEX:
+
+ if (snprintf(t,100,s,SP_ROW(self)[j],k,creal(SP_VALZ(self)[j]))<0)
+ goto fail;
+
+ if (strncat(t,(cimag(SP_VALZ(self)[j])>0 ? "+j" : "-j"),100)<0)
+ goto fail;
+
+ if (snprintf(tmp,100,format_im,fabs(cimag(SP_VALZ(self)[j])))<0)
+ goto fail;
+
+ if (strncat(t,tmp,100)<0)
+ goto fail;
+
+ break;
+ }
+
+ PyString_ConcatAndDel(&ret, PyString_FromFormat("%s\n",t));
+ }
+
+ Py_DECREF(printopt);
+ return ret;
+
+ fail:
+ Py_DECREF(printopt);
+ Py_DECREF(ret); return PyErr_NoMemory();
+
+}
+
+static PyObject *
+spmatrix_repr(spmatrix *self) {
+
+ PyObject *s = PyString_FromFormat("<%ldx%ld spmatrix, tc='%s', nnz=%ld>",
+ (long)SP_NROWS(self), (long)SP_NCOLS(self),
+ TC_CHAR[SP_ID(self)], (long)SP_NNZ(self));
+
+ return s;
+}
+
+
+static PyObject * spmatrix_get_size(spmatrix *self, void *closure)
+{
+ PyObject *t = PyTuple_New(2);
+
+ PyTuple_SET_ITEM(t, 0, PyInt_FromLong(SP_NROWS(self)));
+ PyTuple_SET_ITEM(t, 1, PyInt_FromLong(SP_NCOLS(self)));
+
+ return t;
+}
+
+static int spmatrix_set_size(spmatrix *self, PyObject *value, void *closure)
+{
+ if (!value) PY_ERR_INT(PyExc_TypeError,"size attribute cannot be deleted");
+
+ PY_ERR_INT(PyExc_TypeError, "sparse reshape not implemented");
+ return -1;
+}
+
+static PyObject * spmatrix_get_typecode(matrix *self, void *closure)
+{
+ return PyString_FromStringAndSize(TC_CHAR[SP_ID(self)], 1);
+}
+
+static PyObject *
+spmatrix_get_V(spmatrix *self, void *closure)
+{
+ matrix *ret = Matrix_New(SP_NNZ(self), 1, SP_ID(self));
+ if (!ret) return PyErr_NoMemory();
+
+ memcpy(MAT_BUF(ret), SP_VAL(self), SP_NNZ(self)*E_SIZE[SP_ID(self)]);
+ return (PyObject *)ret;
+}
+
+static int
+spmatrix_set_V(spmatrix *self, PyObject *value, void *closure)
+{
+ if (!value) PY_ERR_INT(PyExc_AttributeError, "attribute cannot be deleted");
+
+ if (PY_NUMBER(value)) {
+ number val;
+ if (convert_num[SP_ID(self)](&val, value, 1, 0))
+ PY_ERR_INT(PyExc_TypeError, "invalid type in assignment");
+
+ int i;
+ for (i=0; i<SP_NNZ(self); i++)
+ write_num[SP_ID(self)](SP_VAL(self),i,&val,0);
+
+ return 0;
+ }
+ else if (Matrix_Check(value) && MAT_ID(value) == SP_ID(self) &&
+ MAT_LGT(value) == SP_NNZ(self) && MAT_NCOLS(value) == 1) {
+
+ memcpy(SP_VAL(self), MAT_BUF(value), MAT_LGT(value)*E_SIZE[SP_ID(self)]);
+ return 0;
+ } else PY_ERR_INT(PyExc_TypeError, "invalid assignment for V attribute");
+}
+
+static PyObject *spmatrix_get_I(spmatrix *self, void *closure)
+{
+ matrix *A = Matrix_New( SP_NNZ(self), 1, INT);
+ if (!A) return PyErr_NoMemory();
+
+ memcpy(MAT_BUF(A), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
+ return (PyObject *)A;
+}
+
+static PyObject * spmatrix_get_J(spmatrix *self, void *closure)
+{
+ matrix *A = Matrix_New( SP_NNZ(self), 1, INT);
+ if (!A) return PyErr_NoMemory();
+
+ int_t k, j;
+ for (k=0; k<SP_NCOLS(self); k++)
+ for (j=SP_COL(self)[k]; j<SP_COL(self)[k+1]; j++)
+ MAT_BUFI(A)[j] = k;
+
+ return (PyObject *)A;
+}
+
+static spmatrix * spmatrix_get_T(spmatrix *self, void *closure)
+{
+ return SpMatrix_NewFromCCS(transpose(((spmatrix *)self)->obj,0));
+}
+
+static spmatrix * spmatrix_get_H(spmatrix *self, void *closure)
+{
+ return SpMatrix_NewFromCCS(transpose(((spmatrix *)self)->obj,1));
+}
+
+
+static PyGetSetDef spmatrix_getsets[] = {
+ {"size", (getter) spmatrix_get_size, (setter) spmatrix_set_size,
+ "matrix dimensions"},
+ {"typecode", (getter) spmatrix_get_typecode, NULL, "type character"},
+ {"V", (getter) spmatrix_get_V, (setter) spmatrix_set_V,
+ "the value list of the matrix in triplet form"},
+ {"I", (getter) spmatrix_get_I, NULL,
+ "the I (row) list of the matrix in triplet form"},
+ {"J", (getter) spmatrix_get_J, NULL,
+ "the J (column) list of the matrix in triplet form"},
+ {"T", (getter) spmatrix_get_T, NULL, "transpose"},
+ {"H", (getter) spmatrix_get_H, NULL, "conjugate transpose"},
+ {NULL} /* Sentinel */
+};
+
+static PyObject *
+spmatrix_getstate(spmatrix *self)
+{
+ PyObject *Il = spmatrix_get_I(self, NULL);
+ PyObject *Jl = spmatrix_get_J(self, NULL);
+ PyObject *V = spmatrix_get_V(self, NULL);
+ PyObject *size = PyTuple_New(2);
+ if (!Il || !Jl || !V || !size) {
+ Py_XDECREF(Il); Py_XDECREF(Jl); Py_XDECREF(V); Py_XDECREF(size);
+ return NULL;
+ }
+
+ PyTuple_SET_ITEM(size, 0, PyInt_FromLong(SP_NROWS(self)));
+ PyTuple_SET_ITEM(size, 1, PyInt_FromLong(SP_NCOLS(self)));
+
+ return Py_BuildValue("NNNNs", V, Il, Jl, size, TC_CHAR[SP_ID(self)]);
+
+ return NULL;
+}
+
+static PyObject * spmatrix_trans(spmatrix *self) {
+
+ return (PyObject *)SpMatrix_NewFromCCS(transpose(((spmatrix *)self)->obj,0));
+
+}
+
+static PyObject * spmatrix_ctrans(spmatrix *self) {
+
+ return (PyObject *)SpMatrix_NewFromCCS(transpose(((spmatrix *)self)->obj,1));
+
+}
+
+static PyObject * spmatrix_real(spmatrix *self) {
+
+ if (SP_ID(self) != COMPLEX)
+ return (PyObject *)SpMatrix_NewFromSpMatrix(self, 0, SP_ID(self));
+
+ spmatrix *ret = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self),
+ SP_NNZ(self), DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i < SP_NNZ(self); i++)
+ SP_VALD(ret)[i] = creal(SP_VALZ(self)[i]);
+
+ memcpy(SP_COL(ret), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t));
+ memcpy(SP_ROW(ret), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
+ return (PyObject *)ret;
+}
+
+static PyObject * spmatrix_imag(spmatrix *self) {
+
+ if (SP_ID(self) != COMPLEX)
+ return (PyObject *)SpMatrix_NewFromSpMatrix(self, 0, SP_ID(self));
+
+ spmatrix *ret = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self),
+ SP_NNZ(self), DOUBLE);
+ if (!ret) return PyErr_NoMemory();
+
+ int i;
+ for (i=0; i < SP_NNZ(self); i++)
+ SP_VALD(ret)[i] = cimag(SP_VALZ(self)[i]);
+
+ memcpy(SP_COL(ret), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t));
+ memcpy(SP_ROW(ret), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
+ return (PyObject *)ret;
+}
+
+static PyObject *
+spmatrix_reduce(spmatrix* self)
+{
+ return Py_BuildValue("ON", self->ob_type, spmatrix_getstate(self));
+}
+
+static PyMethodDef spmatrix_methods[] = {
+ {"real", (PyCFunction)spmatrix_real, METH_NOARGS,
+ "Returns real part of sparse matrix"},
+ {"imag", (PyCFunction)spmatrix_imag, METH_NOARGS,
+ "Returns imaginary part of sparse matrix"},
+ {"trans", (PyCFunction)spmatrix_trans, METH_NOARGS,
+ "Returns the matrix transpose"},
+ {"ctrans", (PyCFunction)spmatrix_ctrans, METH_NOARGS,
+ "Returns the matrix conjugate transpose"},
+ {"__reduce__", (PyCFunction)spmatrix_reduce, METH_NOARGS,
+ "__reduce__() -> (cls, state)"},
+ {NULL} /* Sentinel */
+};
+
+
+static int
+bsearch_int(int_t *lower, int_t *upper, int_t key, int_t *k) {
+
+ if (lower>upper) { *k = 0; return 0; }
+
+ int_t *mid, *start = lower;
+
+ while (upper - lower > 1) {
+ mid = lower+((upper-lower)>>1);
+ if (*mid > key)
+ upper = mid;
+ else if (*mid < key)
+ lower = mid;
+ else {
+ *k = mid - start;
+ return 1;
+ }
+ }
+
+ if (*upper == key) {
+ *k = upper - start; return 1;
+ }
+ else if (*lower == key) {
+ *k = lower - start; return 1;
+ }
+ else {
+ if (*lower > key)
+ *k = lower - start;
+ else if (*upper < key)
+ *k = upper - start + 1;
+ else
+ *k = upper - start;
+ return 0;
+ }
+}
+
+int spmatrix_getitem_ij(spmatrix *A, int_t i, int_t j, number *value)
+{
+ int_t k;
+
+ if (SP_NNZ(A) && bsearch_int(&(SP_ROW(A)[SP_COL(A)[j]]),&
+ (SP_ROW(A)[SP_COL(A)[j+1]-1]), i, &k)) {
+
+ write_num[SP_ID(A)](value, 0, SP_VAL(A), SP_COL(A)[j]+k);
+ return 1;
+
+ } else {
+
+ write_num[SP_ID(A)](value, 0, &Zero, 0);
+ return 0;
+ }
+}
+
+static void
+spmatrix_setitem_ij(spmatrix *A, int_t i, int_t j, number *value) {
+
+ int_t k,l;
+
+ if (bsearch_int(&(SP_ROW(A)[SP_COL(A)[j]]),
+ &(SP_ROW(A)[SP_COL(A)[j+1]-1]),i, &k)) {
+
+ write_num[SP_ID(A)](SP_VAL(A), SP_COL(A)[j] + k, value, 0);
+ return;
+ }
+ k += SP_COL(A)[j];
+
+ for (l=j+1; l<SP_NCOLS(A)+1; l++) SP_COL(A)[l]++;
+
+ /* split rowind and value lists at position 'k' and insert element */
+ for (l=SP_NNZ(A)-1; l>k; l--) {
+ SP_ROW(A)[l] = SP_ROW(A)[l-1];
+ write_num[SP_ID(A)](SP_VAL(A),l,SP_VAL(A),l-1);
+ }
+
+ SP_ROW(A)[k] = i;
+ write_num[SP_ID(A)](SP_VAL(A), k, value, 0);
+}
+
+static int
+spmatrix_length(spmatrix *self)
+{
+ return SP_NNZ(self);
+}
+
+static PyObject*
+spmatrix_subscr(spmatrix* self, PyObject* args)
+{
+ int_t i = 0, j = 0;
+ number val;
+ matrix *Il = NULL, *Jl = NULL;
+
+ /* single integer */
+ if (PyInt_Check(args)) {
+ i = PyInt_AS_LONG(args);
+ if ( i<-SP_LGT(self) || i >= SP_LGT(self) )
+ PY_ERR(PyExc_IndexError, "index out of range");
+
+ spmatrix_getitem_i(self, CWRAP(i,SP_LGT(self)), &val);
+
+ return num2PyObject[SP_ID(self)](&val, 0);
+ }
+
+ else if (PyList_Check(args) || Matrix_Check(args) || PySlice_Check(args)) {
+
+ if (!(Il = create_indexlist(SP_LGT(self), args))) return NULL;
+
+ int_t i, idx, lgt = MAT_LGT(Il), nnz = 0, k = 0;
+ /* count # elements in index list */
+ for (i=0; i<lgt; i++) {
+ idx = MAT_BUFI(Il)[i];
+ if (idx < -SP_LGT(self) || idx >= SP_LGT(self)) {
+ Py_DECREF(Il);
+ PY_ERR(PyExc_IndexError, "index out of range");
+ }
+ nnz += spmatrix_getitem_i(self, CWRAP(idx,SP_LGT(self)), &val);
+ }
+
+ spmatrix *B = SpMatrix_New(lgt,1,nnz,SP_ID(self));
+ if (!B) { Py_DECREF(Il); return PyErr_NoMemory(); }
+
+ SP_COL(B)[1] = nnz;
+ /* fill up rowind and values */
+ for (i=0; i<lgt; i++) {
+ idx = MAT_BUFI(Il)[i];
+ if (spmatrix_getitem_i(self, CWRAP(idx,SP_LGT(self)), &val)) {
+ SP_ROW(B)[k] = i;
+ write_num[SP_ID(B)](SP_VAL(B), k++, &val, 0);
+ }
+ }
+ free_lists_exit(args,(PyObject *)NULL,Il,(PyObject *)NULL,(PyObject *)B);
+ }
+
+ /* remainding cases are different two argument indexing */
+ PyObject *argI = NULL, *argJ = NULL;
+ if (!PyArg_ParseTuple(args, "OO", &argI, &argJ))
+ PY_ERR(PyExc_TypeError, "invalid index sets I or J");
+
+ /* two integers, subscript form, handle separately */
+ if (PyInt_Check(argI) && PyInt_Check(argJ)) {
+ i = PyInt_AS_LONG(argI); j = PyInt_AS_LONG(argJ);
+ if ( OUT_RNG(i, SP_NROWS(self)) || OUT_RNG(j, SP_NCOLS(self)) )
+ PY_ERR(PyExc_IndexError, "index out of range");
+
+ spmatrix_getitem_ij(self,CWRAP(i,SP_NROWS(self)),
+ CWRAP(j,SP_NCOLS(self)), &val);
+
+ return num2PyObject[SP_ID(self)](&val,0);
+ }
+
+ if (!(Il = create_indexlist(SP_NROWS(self), argI)) ||
+ !(Jl = create_indexlist(SP_NCOLS(self), argJ))) {
+ PyErr_SetNone(PyExc_MemoryError);
+ free_lists_exit(argI, argJ, Il, Jl, NULL);
+ }
+
+ int lgt_row = MAT_LGT(Il), lgt_col = MAT_LGT(Jl), k, nnz = 0;
+ ccs *A = self->obj;
+ spa *s = alloc_spa(A->nrows, A->id);
+ if (!s) {
+ PyErr_SetString(PyExc_MemoryError, "insufficient memory");
+ free_lists_exit(argI, argJ, Il, Jl, NULL);
+ }
+
+ for (j=0; j<lgt_col; j++) {
+ init_spa(s, A, CWRAP(MAT_BUFI(Jl)[j], SP_NCOLS(self)));
+
+ for (k=0; k<lgt_row; k++)
+ nnz += s->nz[CWRAP(MAT_BUFI(Il)[k], SP_NROWS(self))];
+ }
+ spmatrix *B = SpMatrix_New(lgt_row, lgt_col,nnz,A->id);
+ if (!B) {
+ free_spa(s);
+ PyErr_SetNone(PyExc_MemoryError);
+ free_lists_exit(argI, argJ, Il, Jl, NULL);
+ }
+
+ nnz = 0;
+ for (j=0; j<lgt_col; j++) {
+ init_spa(s, A, CWRAP(MAT_BUFI(Jl)[j],SP_NCOLS(self)));
+
+ for (k=0; k<lgt_row; k++) {
+ if (s->nz[ CWRAP(MAT_BUFI(Il)[k], SP_NROWS(self))]) {
+ if (A->id == DOUBLE)
+ SP_VALD(B)[nnz] = ((double *)s->val)
+ [CWRAP(MAT_BUFI(Il)[k],SP_NROWS(self))];
+ else
+ SP_VALZ(B)[nnz] = ((complex *)s->val)
+ [CWRAP(MAT_BUFI(Il)[k],SP_NROWS(self))];
+ SP_ROW(B) [nnz++] = k;
+ SP_COL(B)[j+1]++;
+ }
+ }
+ SP_COL(B)[j+1] += SP_COL(B)[j];
+ }
+ free_spa(s);
+ free_lists_exit(argI, argJ, Il, Jl, (PyObject *)B);
+}
+
+
+static int
+spmatrix_ass_subscr(spmatrix* self, PyObject* args, PyObject* value)
+{
+ int_t i = 0, j = 0, id = SP_ID(self), decref_val = 0, arraystruct_nd = 0;
+ char itype;
+ number val, tempval;
+ matrix *Il = NULL, *Jl = NULL;
+
+ if (!value) PY_ERR_INT(PyExc_NotImplementedError,
+ "cannot delete matrix entries");
+
+ if (!(PY_NUMBER(value) || Matrix_Check(value) || SpMatrix_Check(value))) {
+ if (PyObject_HasAttrString(value,"__array_struct__"))
+ value = (PyObject *)Matrix_NewFromArrayStruct(value, -1,
+ &arraystruct_nd);
+ else
+ value = (PyObject *)Matrix_NewFromSequence(value, SP_ID(self));
+
+ if (!value)
+ PY_ERR_INT(PyExc_NotImplementedError, "invalid type in assignment");
+
+ decref_val = 1;
+ }
+
+ int val_id = get_id(value, (PY_NUMBER(value) ? 1 : 0));
+ if (val_id > id)
+ PY_ERR_INT(PyExc_TypeError, "invalid type in assignment");
+
+ /* assigment value is matrix or number ? */
+ if (PY_NUMBER(value)) {
+ if (convert_num[id](&val, value, 1, 0))
+ PY_ERR_INT(PyExc_TypeError, "invalid argument type");
+ itype = 'n';
+ }
+ else if (Matrix_Check(value) && MAT_LGT(value)==1) {
+ convert_num[id](&val, value, 0, 0);
+ itype = 'n';
+ }
+ else if (Matrix_Check(value))
+ itype = 'd';
+ else
+ itype = 's';
+
+ /* single integer */
+ if (PyInt_Check(args)) {
+ if (itype != 'n')
+ PY_ERR_INT(PyExc_IndexError, "incompatible sizes in assigment");
+
+ i = PyInt_AsLong(args);
+ if ( i<-SP_LGT(self) || i >= SP_LGT(self) )
+ PY_ERR_INT(PyExc_IndexError, "index out of range");
+
+ i = CWRAP(i,SP_LGT(self));
+
+ if (spmatrix_getitem_i(self, i, &tempval))
+ spmatrix_setitem_i(self, i, &val);
+ else {
+ if (SP_NNZ(self) == SP_NZMAX(self))
+ if (!realloc_ccs(self->obj, SP_NZMAX(self)+1))
+ PY_ERR_INT(PyExc_MemoryError, "Cannot reallocate sparse matrix");
+ spmatrix_setitem_i(self, i, &val);
+ }
+ return 0;
+ }
+
+ /* integer matrix list */
+ if (PyList_Check(args) || Matrix_Check(args) || PySlice_Check(args)) {
+
+ if (!(Il = create_indexlist(SP_LGT(self), args))) {
+ if (decref_val) { Py_DECREF(value); }
+ return -1;
+ }
+
+ int_t i, lgtI = MAT_LGT(Il);
+ int_t nnz = MAX(SP_NNZ(self)+MAT_LGT(Il),SP_NZMAX(self));
+
+ if (((itype == 'd') &&
+ ((lgtI != MAT_LGT(value) || MAT_NCOLS(value) != 1))) ||
+ (((itype == 's') &&
+ ((lgtI != SP_LGT(value)) || SP_NROWS(value) != 1)))) {
+ if (!Matrix_Check(args)) { Py_DECREF(Il); }
+ if (decref_val) { Py_DECREF(value); }
+ PY_ERR_INT(PyExc_TypeError, "incompatible sizes in assigment");
+ }
+
+ /* ass. argument is dense matrix or number */
+ if (itype == 'd' || itype == 'n') {
+
+ int_t *col_merge = calloc(SP_NCOLS(self)+1,sizeof(int_t));
+ int_t *row_merge = malloc(nnz*sizeof(int_t));
+ void *val_merge = malloc(nnz*E_SIZE[id]);
+ int_list *ilist = malloc(lgtI*sizeof(int_list));
+ if (!col_merge || !row_merge || !val_merge || !ilist) {
+ if (!Matrix_Check(args)) { Py_DECREF(Il); }
+ free(col_merge); free(row_merge); free(val_merge); free(ilist);
+ if (decref_val) { Py_DECREF(value); }
+ PY_ERR_INT(PyExc_MemoryError, "insufficient memory");
+ }
+
+ for (i=0; i<lgtI; i++) {
+ ilist[i].key = CWRAP(MAT_BUFI(Il)[i],SP_NROWS(self)*SP_NCOLS(self));
+ ilist[i].value = i;
+ }
+ qsort(ilist, lgtI, sizeof(int_list), comp_int);
+
+ /* merge lists */
+ int_t rhs_cnt = 0, tot_cnt = 0;
+ int_t rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ int_t rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ for (j=0; j<SP_NCOLS(self); j++) {
+ for (i=SP_COL(self)[j]; i<SP_COL(self)[j+1]; i++) {
+ while (rhs_cnt<lgtI && rhs_j == j && rhs_i < SP_ROW(self)[i]) {
+ if (rhs_cnt == 0 || (rhs_cnt>0 &&
+ ilist[rhs_cnt].key != ilist[rhs_cnt-1].key)) {
+ row_merge[tot_cnt] = rhs_i;
+ if (itype == 'n')
+ write_num[id](val_merge, tot_cnt++, &val, 0);
+ else
+ convert_num[id](val_merge + E_SIZE[id]*tot_cnt++,
+ value, 0, ilist[rhs_cnt].value);
+
+ col_merge[j+1]++;
+ }
+ if (rhs_cnt++ < lgtI-1) {
+ rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ }
+ }
+ if (rhs_cnt<lgtI && rhs_i == SP_ROW(self)[i] && rhs_j == j) {
+ if (rhs_cnt == 0 ||
+ (rhs_cnt>0 && ilist[rhs_cnt].key != ilist[rhs_cnt-1].key)) {
+ row_merge[tot_cnt] = rhs_i;
+ if (itype == 'n')
+ write_num[id](val_merge, tot_cnt++, &val, 0);
+ else
+ convert_num[id](val_merge + E_SIZE[id]*tot_cnt++,
+ value, 0, ilist[rhs_cnt].value);
+ col_merge[j+1]++;
+ }
+ if (rhs_cnt++ < lgtI-1) {
+ rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ }
+ }
+ else {
+ row_merge[tot_cnt] = SP_ROW(self)[i];
+ write_num[id](val_merge, tot_cnt++, SP_VAL(self), i);
+ col_merge[j+1]++;
+ }
+ }
+ while (rhs_cnt<lgtI && rhs_j == j) {
+ if (rhs_cnt == 0 ||
+ (rhs_cnt>0 && ilist[rhs_cnt].key != ilist[rhs_cnt-1].key)) {
+ row_merge[tot_cnt] = rhs_i;
+ if (itype == 'n')
+ write_num[id](val_merge, tot_cnt++, &val, 0);
+ else
+ convert_num[id](val_merge + E_SIZE[id]*tot_cnt++,
+ value, 0, ilist[rhs_cnt].value);
+ col_merge[j+1]++;
+ }
+ if (rhs_cnt++ < lgtI-1) {
+ rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ }
+ }
+ }
+
+ for (i=0; i<SP_NCOLS(self); i++)
+ col_merge[i+1] += col_merge[i];
+
+ free(SP_COL(self)); SP_COL(self) = col_merge;
+ free(SP_ROW(self)); SP_ROW(self) = row_merge;
+ free(SP_VAL(self)); SP_VAL(self) = val_merge;
+ free(ilist);
+
+ int_t nzmax = MAX(SP_NNZ(self),SP_NZMAX(self));
+ if (nnz > nzmax) realloc_ccs(self->obj, nzmax);
+ }
+ /* ass. argument is a sparse matrix */
+ else
+ {
+ int_list *ilist = malloc(lgtI*sizeof(int_list));
+ int_t *col_merge = calloc(SP_NCOLS(self)+1,sizeof(int_t));
+ int_t *row_merge = malloc(nnz*sizeof(int_t));
+ void *val_merge = malloc(nnz*E_SIZE[id]);
+ if (!ilist || !col_merge || !row_merge || !val_merge) {
+ free(ilist); free(col_merge); free(row_merge); free(val_merge);
+ if (!Matrix_Check(args)) { Py_DECREF(Il); }
+ if (decref_val) { Py_DECREF(value); }
+ PY_ERR_INT(PyExc_MemoryError, "insufficient memory");
+ }
+
+ for (i=0; i<lgtI; i++) {
+ ilist[i].key = CWRAP(MAT_BUFI(Il)[i],SP_NROWS(self)*SP_NCOLS(self));
+ ilist[i].value = -1;
+ }
+
+ for (i=0; i<SP_NNZ(value); i++)
+ ilist[SP_ROW(value)[i]].value = i;
+
+ qsort(ilist, lgtI, sizeof(int_list), comp_int);
+
+ /* merge lists */
+ int_t rhs_cnt = 0, tot_cnt = 0;
+ int_t rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ int_t rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ for (j=0; j<SP_NCOLS(self); j++) {
+ for (i=SP_COL(self)[j]; i<SP_COL(self)[j+1]; i++) {
+
+ while (rhs_cnt<lgtI && rhs_j == j && rhs_i < SP_ROW(self)[i]) {
+ if (ilist[rhs_cnt].value >= 0 &&
+ (rhs_cnt==0 || (rhs_cnt>0 && ilist[rhs_cnt].key !=
+ ilist[rhs_cnt-1].key))) {
+ row_merge[tot_cnt] = rhs_i;
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(value) + E_SIZE[val_id]*ilist[rhs_cnt].value,
+ id, val_id, 1);
+ col_merge[j+1]++;
+ }
+ if (rhs_cnt++ < lgtI-1) {
+ rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ }
+ }
+
+ if (rhs_cnt<lgtI && rhs_i == SP_ROW(self)[i] && rhs_j == j) {
+ if (ilist[rhs_cnt].value >= 0 && (rhs_cnt==0 ||
+ (rhs_cnt>0 && ilist[rhs_cnt].key !=
+ ilist[rhs_cnt-1].key))) {
+ row_merge[tot_cnt] = rhs_i;
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(value) + E_SIZE[val_id]*ilist[rhs_cnt].value,
+ id, val_id, 1);
+ col_merge[j+1]++;
+ }
+ if (rhs_cnt++ < lgtI-1) {
+ rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ }
+ }
+ else {
+ row_merge[tot_cnt] = SP_ROW(self)[i];
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(self) + E_SIZE[id]*i, id, id, 1);
+ col_merge[j+1]++;
+ }
+ }
+ while (rhs_cnt<lgtI && rhs_j == j) {
+ if (ilist[rhs_cnt].value >= 0 && (rhs_cnt==0 || (rhs_cnt>0 &&
+ ilist[rhs_cnt].key != ilist[rhs_cnt-1].key))) {
+ row_merge[tot_cnt] = rhs_i;
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(value) + E_SIZE[val_id]*ilist[rhs_cnt].value,
+ id, val_id, 1);
+ col_merge[j+1]++;
+ }
+ if (rhs_cnt++ < lgtI-1) {
+ rhs_j = ilist[rhs_cnt].key / SP_NROWS(self);
+ rhs_i = ilist[rhs_cnt].key % SP_NROWS(self);
+ }
+ }
+ }
+
+ for (i=0; i<SP_NCOLS(self); i++)
+ col_merge[i+1] += col_merge[i];
+
+ free(SP_COL(self)); SP_COL(self) = col_merge;
+ free(SP_ROW(self)); SP_ROW(self) = row_merge;
+ free(SP_VAL(self)); SP_VAL(self) = val_merge;
+ free(ilist);
+
+ int_t nzmax = MAX(SP_NNZ(self),SP_NZMAX(self));
+ if (nnz > nzmax) realloc_ccs(self->obj, nzmax);
+ }
+
+ if (!Matrix_Check(args)) { Py_DECREF(Il); }
+ if (decref_val) { Py_DECREF(value); }
+
+ SP_NZMAX(self) = MAX(SP_NNZ(self),SP_NZMAX(self));
+ return 0;
+ }
+
+ /* remainding cases are different two argument indexing */
+ PyObject *argI = NULL, *argJ = NULL;
+ if (!PyArg_ParseTuple(args, "OO", &argI, &argJ))
+ PY_ERR_INT(PyExc_TypeError, "invalid index arguments");
+
+ /* two integers, subscript form, handle separately */
+ if (PyInt_Check(argI) && PyInt_Check(argJ)) {
+
+ if (itype != 'n')
+ PY_ERR_INT(PyExc_TypeError, "argument has wrong size");
+
+ i = PyInt_AS_LONG(argI); j = PyInt_AS_LONG(argJ);
+ if ( OUT_RNG(i, SP_NROWS(self)) || OUT_RNG(j, SP_NCOLS(self)) )
+ PY_ERR_INT(PyExc_IndexError, "index out of range");
+
+ i = CWRAP(i,SP_NROWS(self)); j = CWRAP(j,SP_NCOLS(self));
+ if (spmatrix_getitem_ij(self, i, j, &tempval))
+ spmatrix_setitem_ij(self, i, j, &val);
+ else {
+ if (SP_NNZ(self) == SP_NZMAX(self))
+ if (!realloc_ccs(self->obj, SP_NZMAX(self)+1))
+ PY_ERR_INT(PyExc_MemoryError, "insufficient memory");
+
+ spmatrix_setitem_ij(self, i, j, &val);
+ }
+ return 0;
+ }
+
+ if (!(Il = create_indexlist(SP_NROWS(self), argI)) ||
+ !(Jl = create_indexlist(SP_NCOLS(self), argJ))) {
+ PyErr_SetNone(PyExc_MemoryError);
+ free_lists_exit(argI,argJ,Il,Jl,-1);
+ }
+
+ if (decref_val && arraystruct_nd < 2 &&
+ MAT_LGT(value) == MAT_LGT(Il)*MAT_LGT(Jl)) {
+ MAT_NROWS(value) = MAT_LGT(Il); MAT_NCOLS(value) = MAT_LGT(Jl);
+ }
+
+ int_t lgtI = MAT_LGT(Il), lgtJ = MAT_LGT(Jl);
+
+ if ((itype == 'd' && (lgtI != MAT_NROWS(value) ||
+ lgtJ != MAT_NCOLS(value))) ||
+ (itype == 's' && (lgtI != SP_NROWS(value) ||
+ lgtJ != SP_NCOLS(value)))) {
+ if (!Matrix_Check(argI)) { Py_DECREF(Il); }
+ if (!Matrix_Check(argJ)) { Py_DECREF(Jl); }
+ if (decref_val) { Py_DECREF(value); }
+ PY_ERR_INT(PyExc_TypeError, "incompatible size of assigment");
+ }
+
+ /* ass. argument is dense matrix or number */
+ if ((itype == 'd' || itype == 'n') && lgtI*lgtJ> 0) {
+
+ int_t nnz = MAX(SP_NNZ(self)+lgtI*lgtJ,SP_NZMAX(self));
+
+ int_t *col_merge = calloc(SP_NCOLS(self)+1,sizeof(int_t));
+ int_t *row_merge = malloc(nnz*sizeof(int_t));
+ void *val_merge = malloc(nnz*E_SIZE[id]);
+ int_list *Is = malloc(lgtI*sizeof(int_list));
+ int_list *Js = malloc(lgtJ*sizeof(int_list));
+ if (!Is || !Js || !col_merge || !row_merge || !val_merge) {
+ if (!Matrix_Check(argI)) { Py_DECREF(Il); }
+ if (!Matrix_Check(argJ)) { Py_DECREF(Jl); }
+ free(Is); free(Js);
+ free(col_merge); free(row_merge); free(val_merge);
+ if (decref_val) { Py_DECREF(value); }
+ PY_ERR_INT(PyExc_MemoryError, "insufficient memory");
+ }
+
+ for (i=0; i<lgtI; i++) {
+ Is[i].key = CWRAP(MAT_BUFI(Il)[i],SP_NROWS(self));
+ Is[i].value = i;
+ }
+ qsort(Is, lgtI, sizeof(int_list), comp_int);
+
+ for (i=0; i<lgtJ; i++) {
+ Js[i].key = CWRAP(MAT_BUFI(Jl)[i],SP_NCOLS(self));
+ Js[i].value = i;
+ }
+ qsort(Js, lgtJ, sizeof(int_list), comp_int);
+
+ int_t rhs_cnti, rhs_cntj = 0, tot_cnt = 0;
+ int_t rhs_i, rhs_j = Js[0].key;
+ for (j=0; j<SP_NCOLS(self); j++) {
+
+ if (rhs_j < j && rhs_cntj++ < lgtJ-1) {
+ rhs_j = Js[rhs_cntj].key;
+ }
+
+ rhs_cnti = 0; rhs_i = Is[0].key;
+ for (i=SP_COL(self)[j]; i<SP_COL(self)[j+1]; i++) {
+
+ while (rhs_cnti<lgtI && rhs_j == j && rhs_i < SP_ROW(self)[i]) {
+ if (rhs_cnti == 0 || (rhs_cnti>0 &&
+ Is[rhs_cnti].key != Is[rhs_cnti-1].key)) {
+ row_merge[tot_cnt] = rhs_i;
+
+ if (itype == 'n')
+ write_num[id](val_merge, tot_cnt++, &val, 0);
+ else
+ convert_num[id](val_merge + E_SIZE[id]*tot_cnt++,
+ value, 0, Is[rhs_cnti].value + lgtI*Js[rhs_cntj].value);
+ col_merge[j+1]++;
+ }
+ if (rhs_cnti++ < lgtI-1)
+ rhs_i = Is[rhs_cnti].key;
+ }
+
+ if (rhs_cnti<lgtI && rhs_i == SP_ROW(self)[i] && rhs_j == j) {
+ if (rhs_cnti == 0 || (rhs_cnti>0 &&
+ Is[rhs_cnti].key != Is[rhs_cnti-1].key)) {
+ row_merge[tot_cnt] = rhs_i;
+
+ if (itype == 'n')
+ write_num[id](val_merge, tot_cnt++, &val, 0);
+ else
+ convert_num[id](val_merge + E_SIZE[id]*tot_cnt++,
+ value, 0, Is[rhs_cnti].value + lgtI*Js[rhs_cntj].value);
+
+ col_merge[j+1]++;
+ }
+ if (rhs_cnti++ < lgtI-1)
+ rhs_i = Is[rhs_cnti].key;
+ }
+ else {
+ row_merge[tot_cnt] = SP_ROW(self)[i];
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(self) + E_SIZE[id]*i, id, id, 1);
+ col_merge[j+1]++;
+ }
+ }
+ while (rhs_cnti<lgtI && rhs_j == j) {
+ if (rhs_cnti == 0 || (rhs_cnti>0 &&
+ Is[rhs_cnti].key != Is[rhs_cnti-1].key)) {
+
+ row_merge[tot_cnt] = rhs_i;
+
+ if (itype == 'n')
+ write_num[id](val_merge, tot_cnt++, &val, 0);
+ else
+ convert_num[id](val_merge + E_SIZE[id]*tot_cnt++,
+ value, 0, Is[rhs_cnti].value + lgtI*Js[rhs_cntj].value);
+
+ col_merge[j+1]++;
+ }
+ if (rhs_cnti++ < lgtI-1)
+ rhs_i = Is[rhs_cnti].key;
+ }
+ }
+
+ for (i=0; i<SP_NCOLS(self); i++)
+ col_merge[i+1] += col_merge[i];
+
+ free(SP_COL(self)); SP_COL(self) = col_merge;
+ free(SP_ROW(self)); SP_ROW(self) = row_merge;
+ free(SP_VAL(self)); SP_VAL(self) = val_merge;
+ free(Is); free(Js);
+
+ int nzmax = MAX(SP_NNZ(self),SP_NZMAX(self));
+ if (nnz > nzmax) realloc_ccs(self->obj, nzmax);
+
+ }
+ /* ass. argument is a sparse matrix */
+ else if (itype == 's' && lgtI*lgtJ > 0) {
+
+ int_t nnz = MAX(SP_NNZ(self)+SP_NNZ(value),SP_NZMAX(self));
+
+ int_t *col_merge = calloc((SP_NCOLS(self)+1),sizeof(int_t));
+ int_t *row_merge = malloc(nnz*sizeof(int_t));
+ void *val_merge = malloc(nnz*E_SIZE[id]);
+ int_list *Is = malloc(lgtI*sizeof(int_list));
+ int_list *Js = malloc(lgtJ*sizeof(int_list));
+ if (!Is || !Js || !col_merge || !row_merge || !val_merge) {
+ if (!Matrix_Check(argI)) { Py_DECREF(Il); }
+ if (!Matrix_Check(argJ)) { Py_DECREF(Jl); }
+ free(Is); free(Js);
+ free(col_merge); free(row_merge); free(val_merge);
+ if (decref_val) { Py_DECREF(value); }
+ PY_ERR_INT(PyExc_MemoryError,"insufficient memory");
+ }
+
+ for (i=0; i<lgtJ; i++) {
+ Js[i].key = CWRAP(MAT_BUFI(Jl)[i],SP_NCOLS(self));
+ Js[i].value = i;
+ }
+ qsort(Js, lgtJ, sizeof(int_list), comp_int);
+
+ int_t rhs_cnti, rhs_cntj = -1, tot_cnt = 0, rhs_offs_rptr = 0;
+ int_t rhs_i, rhs_j = -1;
+ for (j=0; j<SP_NCOLS(self); j++) {
+ if (rhs_j < j && rhs_cntj++ < lgtJ-1) {
+ rhs_j = Js[rhs_cntj].key;
+ rhs_offs_rptr = SP_COL(value)[Js[rhs_cntj].value];
+
+ for (i=0; i<lgtI; i++) {
+ Is[i].key = CWRAP(MAT_BUFI(Il)[i],SP_NROWS(self));
+ Is[i].value = -1;
+ }
+
+ for (i=rhs_offs_rptr; i<SP_COL(value)[Js[rhs_cntj].value+1]; i++)
+ Is[SP_ROW(value)[i]].value = i-rhs_offs_rptr;
+
+ qsort(Is, lgtI, sizeof(int_list), comp_int);
+
+ }
+
+ rhs_cnti = 0; rhs_i = Is[0].key;
+ for (i=SP_COL(self)[j]; i<SP_COL(self)[j+1]; i++) {
+
+ while (rhs_cnti<lgtI && rhs_j == j && rhs_i < SP_ROW(self)[i]) {
+ if (Is[rhs_cnti].value >= 0 && (rhs_cnti==0 ||
+ (rhs_cnti>0 && Is[rhs_cnti].key != Is[rhs_cnti-1].key))) {
+ row_merge[tot_cnt] = rhs_i;
+
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(value) + E_SIZE[val_id]*
+ (Is[rhs_cnti].value+rhs_offs_rptr), id, val_id, 1);
+
+ col_merge[j+1]++;
+ }
+ if (rhs_cnti++ < lgtI-1)
+ rhs_i = Is[rhs_cnti].key;
+ }
+ if (rhs_cnti<lgtI && rhs_i == SP_ROW(self)[i] && rhs_j == j) {
+ if (Is[rhs_cnti].value >= 0 && (rhs_cnti==0 ||
+ (rhs_cnti>0 && Is[rhs_cnti].key != Is[rhs_cnti-1].key))) {
+ row_merge[tot_cnt] = rhs_i;
+
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(value) + E_SIZE[val_id]*
+ (Is[rhs_cnti].value+rhs_offs_rptr), id, val_id, 1);
+
+ col_merge[j+1]++;
+ }
+ if (rhs_cnti++ < lgtI-1)
+ rhs_i = Is[rhs_cnti].key;
+ }
+ else {
+ row_merge[tot_cnt] = SP_ROW(self)[i];
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(self) + E_SIZE[id]*i, id, id, 1);
+ col_merge[j+1]++;
+ }
+ }
+ while (rhs_cnti<lgtI && rhs_j == j) {
+ if (Is[rhs_cnti].value >= 0 && (rhs_cnti == 0 || (rhs_cnti>0 &&
+ Is[rhs_cnti].key != Is[rhs_cnti-1].key))) {
+
+ row_merge[tot_cnt] = rhs_i;
+
+ convert_array(val_merge + E_SIZE[id]*tot_cnt++,
+ SP_VAL(value) + E_SIZE[val_id]*
+ (Is[rhs_cnti].value+rhs_offs_rptr), id, val_id, 1);
+
+ col_merge[j+1]++;
+ }
+ if (rhs_cnti++ < lgtI-1)
+ rhs_i = Is[rhs_cnti].key;
+ }
+ }
+
+ for (i=0; i<SP_NCOLS(self); i++)
+ col_merge[i+1] += col_merge[i];
+
+ free(SP_COL(self)); SP_COL(self) = col_merge;
+ free(SP_ROW(self)); SP_ROW(self) = row_merge;
+ free(SP_VAL(self)); SP_VAL(self) = val_merge;
+ free(Is); free(Js);
+
+ int_t nzmax = MAX(SP_NNZ(self),SP_NZMAX(self));
+ if (nnz > nzmax) realloc_ccs(self->obj, nzmax);
+
+ }
+ if (!Matrix_Check(argI)) { Py_DECREF(Il); }
+ if (!Matrix_Check(argJ)) { Py_DECREF(Jl); }
+ if (decref_val) { Py_DECREF(value); }
+
+ SP_NZMAX(self) = MAX(SP_NNZ(self),SP_NZMAX(self));
+ return 0;
+
+}
+
+static PyMappingMethods spmatrix_as_mapping = {
+ (lenfunc)spmatrix_length,
+ (binaryfunc)spmatrix_subscr,
+ (objobjargproc)spmatrix_ass_subscr
+};
+
+
+static PyObject * spmatrix_neg(spmatrix *self)
+{
+ spmatrix *x = SpMatrix_NewFromSpMatrix(self,0,SP_ID(self));
+ if (!x) return PyErr_NoMemory();
+
+ int n=SP_NNZ(x);
+ scal[SP_ID(self)](&n, &MinusOne[SP_ID(self)], SP_VAL(x), (int *)&One[INT]);
+
+ return (PyObject *)x;
+}
+
+static PyObject * spmatrix_pos(spmatrix *self)
+{
+ spmatrix *x = SpMatrix_NewFromSpMatrix(self,0,SP_ID(self));
+ if (!x) return PyErr_NoMemory();
+
+ return (PyObject *)x;
+}
+
+static PyObject * spmatrix_abs(spmatrix *self)
+{
+ spmatrix *x = SpMatrix_New(SP_NROWS(self), SP_NCOLS(self),
+ SP_NNZ(self), DOUBLE);
+ if (!x) return PyErr_NoMemory();
+
+ int_t i;
+
+ if (SP_ID(self) == DOUBLE)
+ for (i=0; i<SP_NNZ(self); i++) SP_VALD(x)[i] = fabs(SP_VALD(self)[i]);
+ else
+ for (i=0; i<SP_NNZ(self); i++) SP_VALD(x)[i] = cabs(SP_VALZ(self)[i]);
+
+ memcpy(SP_ROW(x), SP_ROW(self), SP_NNZ(self)*sizeof(int_t));
+ memcpy(SP_COL(x), SP_COL(self), (SP_NCOLS(self)+1)*sizeof(int_t));
+
+ return (PyObject *)x;
+}
+
+static PyObject *
+spmatrix_add_helper(PyObject *self, PyObject *other, int add)
+{
+ if (!SpMatrix_Check(self) ||
+ !(Matrix_Check(other) || SpMatrix_Check(other)))
+ {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ if ((X_NROWS(self) != X_NROWS(other)) || (X_NCOLS(self) != X_NCOLS(other)))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ int id = MAX(SP_ID(self),X_ID(other));
+
+ ccs *x, *z = NULL;
+ void *y;
+
+ if (!(x = convert_ccs(((spmatrix *)self)->obj, id)))
+ return NULL;
+
+ if (!(y = (Matrix_Check(other) ?
+ (void *)Matrix_NewFromMatrix((matrix *)other, id) :
+ (void *)convert_ccs(((spmatrix *)other)->obj, id)))) {
+ if (x->id != id) free_ccs(x);
+ return NULL;
+ }
+
+ if (sp_axpy[id]((add ? One[id] : MinusOne[id]), x,
+ (Matrix_Check(other) ? MAT_BUF(y) : y),
+ 1, SpMatrix_Check(other), 0, (void *)&z))
+ {
+ if (x->id != id) free_ccs(x);
+ if (Matrix_Check(other))
+ Py_DECREF((PyObject *)y);
+ else
+ if (((ccs *)y)->id != id) free_ccs(y);
+
+ return PyErr_NoMemory();
+ }
+
+ if (x->id != id) free_ccs(x);
+ if (SpMatrix_Check(other)) {
+ if (((ccs *)y)->id != id) free_ccs(y);
+ spmatrix *ret = SpMatrix_New(SP_NROWS(other), SP_NCOLS(other), 0, id);
+ if (!ret) return PyErr_NoMemory();
+ ret->obj = z;
+ return (PyObject *)ret;
+ }
+ else return (PyObject *)y;
+}
+
+static PyObject *
+spmatrix_add(PyObject *self, PyObject *other)
+{
+ if (!SpMatrix_Check(self) && SpMatrix_Check(other)) {
+ void *ptr = other; other = self; self = ptr;
+ }
+
+ PyObject *ret, *tmp;
+ if (PY_NUMBER(other) || (Matrix_Check(other) && MAT_LGT(other)==1))
+ if ((tmp = (PyObject *)dense((spmatrix *)self))) {
+ ret = matrix_add(tmp, other);
+ Py_DECREF(tmp);
+ return ret;
+ }
+ else return NULL;
+
+ else return spmatrix_add_helper(self, other, 1);
+}
+
+
+static PyObject *
+spmatrix_iadd(PyObject *self, PyObject *other)
+{
+ if (!SpMatrix_Check(other))
+ PY_ERR_TYPE("invalid inplace operation");
+
+ int id = SP_ID(self);
+ if (SP_ID(other) > id)
+ PY_ERR_TYPE("incompatible types for inplace operation");
+
+ if ((SP_NROWS(self) != SP_NROWS(other)) ||
+ (SP_NCOLS(self) != SP_NCOLS(other)))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ ccs *x = ((spmatrix *)self)->obj, *y;
+ void *z;
+
+ if (!(y = convert_ccs(((spmatrix *)other)->obj, id)))
+ return NULL;
+
+ if (sp_axpy[id](One[id], x, y, 1, 1, 0, &z))
+ {
+ if (y->id != id) free_ccs(y);
+ return PyErr_NoMemory();
+ }
+
+ free_ccs(x); ((spmatrix *)self)->obj = z;
+ if (y->id != id) free_ccs(y);
+
+ Py_INCREF(self);
+ return self;
+}
+
+
+static PyObject *
+spmatrix_sub(PyObject *self, PyObject *other)
+{
+ PyObject *ret, *tmp;
+ if (PY_NUMBER(self) || (Matrix_Check(self) && MAT_LGT(self)==1)) {
+ if ((tmp = (PyObject *)dense((spmatrix *)other))) {
+ ret = matrix_sub(self, tmp);
+ Py_DECREF(tmp);
+ return ret;
+ }
+ else return NULL;
+ }
+ else if (PY_NUMBER(other) || (Matrix_Check(other) && MAT_LGT(other)==1)) {
+ if ((tmp = (PyObject *)dense((spmatrix *)self))) {
+ ret = matrix_sub(tmp, other);
+ Py_DECREF(tmp);
+ return ret;
+ }
+ else return NULL;
+ }
+ else if (!SpMatrix_Check(self) && SpMatrix_Check(other))
+ {
+ return spmatrix_add_helper(other, self, 0);
+ }
+ else if (SpMatrix_Check(self) && !SpMatrix_Check(other)) {
+ if ((ret = spmatrix_add_helper(self, other, 0))) {
+ int n = MAT_LGT(other), id = MAT_ID(ret);
+ scal[id](&n, &MinusOne[id], MAT_BUF(ret), (int *)&One[INT]);
+ return ret;
+ }
+ else return NULL;
+ }
+ else return spmatrix_add_helper(other, self, 0);
+}
+
+static PyObject *
+spmatrix_isub(PyObject *self, PyObject *other)
+{
+ if (!SpMatrix_Check(other))
+ PY_ERR_TYPE("invalid inplace operation");
+
+ int id = SP_ID(self);
+
+ if (SP_ID(other) > id)
+ PY_ERR_TYPE("incompatible types for inplace operation");
+
+ if ((SP_NROWS(self) != SP_NROWS(other)) ||
+ (SP_NCOLS(self) != SP_NCOLS(other)))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ ccs *x = ((spmatrix *)self)->obj, *y;
+ void *z;
+
+ if (!(y = convert_ccs(((spmatrix *)other)->obj, id)))
+ return NULL;
+
+ if (sp_axpy[id](MinusOne[id], y, x, 1, 1, 0, &z))
+ {
+ if (y->id != id) free_ccs(y);
+ return PyErr_NoMemory();
+ }
+
+ free_ccs(x); ((spmatrix *)self)->obj = z;
+ if (y->id != id) free_ccs(y);
+
+ Py_INCREF(self);
+ return self;
+}
+
+static PyObject *
+spmatrix_mul(PyObject *self, PyObject *other)
+{
+ if (!(SpMatrix_Check(self) || Matrix_Check(self) || PY_NUMBER(self)) ||
+ !(SpMatrix_Check(other) || Matrix_Check(other) || PY_NUMBER(other)))
+ {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ int id = MAX(get_id(self, PY_NUMBER(self)),get_id(other, PY_NUMBER(other)));
+ if (PY_NUMBER(self) || (Matrix_Check(self) && MAT_LGT(self) == 1) ||
+ PY_NUMBER(other) || (Matrix_Check(other) && MAT_LGT(other) == 1)) {
+
+ spmatrix *ret = SpMatrix_NewFromSpMatrix((spmatrix *)
+ (SpMatrix_Check(self) ? self : other), 0, id);
+
+ number val;
+ convert_num[id](&val, !SpMatrix_Check(self) ? self : other,
+ PY_NUMBER(other) || PY_NUMBER(self), 0);
+
+ scal[id]((int *)&SP_NNZ(ret), &val, SP_VAL(ret), (void *)&One[INT]);
+ return (PyObject *)ret;
+ }
+
+ else {
+ if (X_NCOLS(self) != X_NROWS(other))
+ PY_ERR_TYPE("incompatible dimensions");
+
+ void *x, *y, *z = NULL;
+ int sp_c = SpMatrix_Check(self) && SpMatrix_Check(other);
+ PyObject *C = (sp_c ?
+ (PyObject *)SpMatrix_New(SP_NROWS(self), SP_NCOLS(other), 0, id) :
+ (PyObject *)Matrix_New(X_NROWS(self), X_NCOLS(other), id));
+
+ if (SpMatrix_Check(self))
+ x = convert_ccs(((spmatrix *)self)->obj, id);
+ else
+ x = convert_mtx_alloc((matrix *)self, id);
+
+ if (SpMatrix_Check(other))
+ y = convert_ccs(((spmatrix *)other)->obj, id);
+ else
+ y = convert_mtx_alloc((matrix *)other, id);
+
+ if (!C || !x || !y) {
+ PyErr_SetNone(PyExc_MemoryError);
+ Py_XDECREF(C);
+ C = NULL;
+ goto cleanup;
+ }
+ if (sp_gemm[id]('N', 'N', One[id], x, y, Zero[id],
+ sp_c ? ((spmatrix *)C)->obj : MAT_BUF(C),
+ SpMatrix_Check(self), SpMatrix_Check(other), sp_c, 0, &z,
+ X_NROWS(self), X_NCOLS(other), X_NROWS(other)))
+ {
+ Py_DECREF(C); C = NULL;
+ }
+
+ if (z) {
+ free_ccs( ((spmatrix *)C)->obj );
+ ((spmatrix *)C)->obj = z;
+ }
+
+ cleanup:
+ if (SpMatrix_Check(self)) {
+ if (((ccs *)x)->id != id) free_ccs(x);
+ }
+ else if (MAT_ID(self) != id) free(x);
+
+ if (SpMatrix_Check(other)) {
+ if (((ccs *)y)->id != id) free_ccs(y);
+ }
+ else if (MAT_ID(other) != id) free(y);
+
+ return (PyObject *)C;
+ }
+}
+
+static PyObject *
+spmatrix_imul(PyObject *self, PyObject *other)
+{
+ if (!(PY_NUMBER(other) || (Matrix_Check(other) && MAT_LGT(other) == 1)))
+ PY_ERR_TYPE("invalid operands for sparse multiplication");
+
+ if (SP_ID(self) < get_id(other, PY_NUMBER(other)))
+ PY_ERR_TYPE("invalid operands for inplace sparse multiplication");
+
+ number val;
+ convert_num[SP_ID(self)](&val, other, !Matrix_Check(other), 0);
+ scal[SP_ID(self)]((int *)&SP_NNZ(self), &val, SP_VAL(self),
+ (void *)&One[INT]);
+
+ Py_INCREF(self);
+ return self;
+}
+
+static PyObject *
+spmatrix_div_generic(spmatrix *A, PyObject *B, int inplace)
+{
+ if (!SpMatrix_Check(A) || !(PY_NUMBER(B) ||
+ (Matrix_Check(B) && MAT_LGT(B)) == 1))
+ PY_ERR_TYPE("invalid operands for sparse division");
+
+ int idA = get_id(A, 0);
+ int idB = get_id(B, (Matrix_Check(B) ? 0 : 1));
+ int id = MAX(idA,idB);
+
+ number n;
+ convert_num[id](&n, B, (Matrix_Check(B) ? 0 : 1), 0);
+
+ if (!inplace) {
+ PyObject *ret = (PyObject *)SpMatrix_NewFromSpMatrix((spmatrix *)A, 0, id);
+ if (!ret) return NULL;
+
+ if (div_array[id](SP_VAL(ret), n, SP_NNZ(ret))) {
+ Py_DECREF(ret); return NULL;
+ }
+ return ret;
+ } else {
+ if (id != idA) PY_ERR_TYPE("invalid inplace operation");
+
+ if (div_array[id](SP_VAL(A), n, SP_NNZ(A)))
+ return NULL;
+
+ Py_INCREF(A);
+ return (PyObject *)A;
+ }
+}
+
+static PyObject * spmatrix_div(PyObject *self,PyObject *other) {
+ return spmatrix_div_generic((spmatrix *)self, other, 0);
+}
+
+static PyObject * spmatrix_idiv(PyObject *self,PyObject *other) {
+ return spmatrix_div_generic((spmatrix *)self, other, 1);
+}
+
+
+static PyNumberMethods spmatrix_as_number = {
+ (binaryfunc)spmatrix_add, /*nb_add*/
+ (binaryfunc)spmatrix_sub, /*nb_subtract*/
+ (binaryfunc)spmatrix_mul, /*nb_multiply*/
+ (binaryfunc)spmatrix_div, /*nb_divide*/
+ 0, /*nb_remainder*/
+ 0, /*nb_divmod*/
+ 0, /*nb_power*/
+ (unaryfunc)spmatrix_neg,/*nb_negative*/
+ (unaryfunc)spmatrix_pos,/*nb_positive*/
+ (unaryfunc)spmatrix_abs,/*nb_absolute*/
+ 0, /*nb_nonzero*/
+ 0, /*nb_invert*/
+ 0, /*nb_lshift*/
+ 0, /*nb_rshift*/
+ 0, /*nb_and*/
+ 0, /*nb_xor*/
+ 0, /*nb_or*/
+ 0, /*nb_coerce*/
+ 0, /*nb_int*/
+ 0, /*nb_long*/
+ 0, /*nb_float*/
+ 0, /*nb_oct*/
+ 0, /*nb_hex*/
+ (binaryfunc)spmatrix_iadd,/*nb_inplace_add*/
+ (binaryfunc)spmatrix_isub,/*nb_inplace_subtract*/
+ (binaryfunc)spmatrix_imul,/*nb_inplace_multiply*/
+ (binaryfunc)spmatrix_idiv,/*nb_inplace_divide*/
+ 0, /*nb_inplace_remainder*/
+ 0, /*nb_inplace_power*/
+ 0, /*nb_inplace_lshift*/
+ 0, /*nb_inplace_rshift*/
+ 0, /*nb_inplace_and*/
+ 0, /*nb_inplace_xor*/
+ 0, /*nb_inplace_or*/
+ 0, /* nb_floor_divide */
+ 0, /* nb_true_divide */
+ 0, /* nb_inplace_floor_divide */
+ 0, /* nb_inplace_true_divide */
+};
+
+
+/*********************** Iterator **************************/
+
+typedef struct {
+ PyObject_HEAD
+ long index;
+ spmatrix *mObj; /* Set to NULL when iterator is exhausted */
+} spmatrixiter;
+
+static PyTypeObject spmatrixiter_tp;
+
+#define SpMatrixIter_Check(O) PyObject_TypeCheck(O, &spmatrixiter_tp)
+
+static PyObject *
+spmatrix_iter(spmatrix *obj)
+{
+ spmatrixiter *it;
+
+ if (!SpMatrix_Check(obj)) {
+ PyErr_BadInternalCall();
+ return NULL;
+ }
+
+ spmatrixiter_tp.tp_iter = PyObject_SelfIter;
+ spmatrixiter_tp.tp_getattro = PyObject_GenericGetAttr;
+
+ it = PyObject_GC_New(spmatrixiter, &spmatrixiter_tp);
+ if (it == NULL)
+ return NULL;
+
+ Py_INCREF(obj);
+ it->index = 0;
+ it->mObj = obj;
+ PyObject_GC_Track(it);
+
+ return (PyObject *)it;
+}
+
+static void
+spmatrixiter_dealloc(spmatrixiter *it)
+{
+ PyObject_GC_UnTrack(it);
+ Py_XDECREF(it->mObj);
+ PyObject_GC_Del(it);
+}
+
+static int
+spmatrixiter_traverse(spmatrixiter *it, visitproc visit, void *arg)
+{
+ if (it->mObj == NULL)
+ return 0;
+
+ return visit((PyObject *)(it->mObj), arg);
+}
+
+static PyObject *
+spmatrixiter_next(spmatrixiter *it)
+{
+ assert(SpMatrixIter_Check(it));
+ if (it->index >= SP_NNZ(it->mObj))
+ return NULL;
+
+ return num2PyObject[SP_ID(it->mObj)](SP_VAL(it->mObj), it->index++);
+}
+
+static PyTypeObject spmatrixiter_tp = {
+ PyObject_HEAD_INIT(NULL)
+ 0, /* ob_size */
+ "spmatrixiter", /* tp_name */
+ sizeof(spmatrixiter), /* tp_basicsize */
+ 0, /* tp_itemsize */
+ (destructor)spmatrixiter_dealloc, /* tp_dealloc */
+ 0, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ 0, /* tp_compare */
+ 0, /* tp_repr */
+ 0, /* tp_as_number */
+ 0, /* tp_as_sequence */
+ 0, /* tp_as_mapping */
+ 0, /* tp_hash */
+ 0, /* tp_call */
+ 0, /* tp_str */
+ 0, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,/* tp_flags */
+ 0, /* tp_doc */
+ (traverseproc)spmatrixiter_traverse, /* tp_traverse */
+ 0, /* tp_clear */
+ 0, /* tp_richcompare */
+ 0, /* tp_weaklistoffset */
+ 0, /* tp_iter */
+ (iternextfunc)spmatrixiter_next, /* tp_iternext */
+ 0, /* tp_methods */
+};
+
+
+PyTypeObject spmatrix_tp = {
+ PyObject_HEAD_INIT(NULL)
+ 0,
+ "cvxopt.base.spmatrix",
+ sizeof(spmatrix),
+ 0,
+ (destructor)spmatrix_dealloc, /* tp_dealloc */
+ 0, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ 0, /* tp_compare */
+ (reprfunc)spmatrix_repr, /* tp_repr */
+ &spmatrix_as_number, /* tp_as_number */
+ 0, /* tp_as_sequence */
+ &spmatrix_as_mapping, /* tp_as_mapping */
+ 0, /* tp_hash */
+ 0, /* tp_call */
+ (reprfunc)spmatrix_str, /* tp_str */
+ 0, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE |
+ Py_TPFLAGS_CHECKTYPES, /* tp_flags */
+ 0, /* tp_doc */
+ 0, /* tp_traverse */
+ 0, /* tp_clear */
+ 0, /* tp_richcompare */
+ 0, /* tp_weaklistoffset */
+ (getiterfunc)spmatrix_iter, /* tp_iter */
+ 0, /* tp_iternext */
+ spmatrix_methods, /* tp_methods */
+ 0, /* tp_members */
+ spmatrix_getsets, /* tp_getset */
+ 0, /* tp_base */
+ 0, /* tp_dict */
+ 0, /* tp_descr_get */
+ 0, /* tp_descr_set */
+ 0, /* tp_dictoffset */
+ 0, /* tp_init */
+ 0, /* tp_alloc */
+ spmatrix_new, /* tp_new */
+};
diff --git a/src/C/umfpack.c b/src/C/umfpack.c
new file mode 100644
index 0000000..e79468c
--- /dev/null
+++ b/src/C/umfpack.c
@@ -0,0 +1,448 @@
+/*
+ * This file is part of CVXOPT version 0.8.2.
+ * Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+ */
+
+#include "cvxopt.h"
+#include "umfpack.h"
+#include "misc.h"
+
+#if (SIZEOF_INT < SIZEOF_LONG)
+#define UMFD(name) umfpack_dl_ ## name
+#define UMFZ(name) umfpack_zl_ ## name
+#else
+#define UMFD(name) umfpack_di_ ## name
+#define UMFZ(name) umfpack_zi_ ## name
+#endif
+
+const int E_SIZE[] = {sizeof(int_t), sizeof(double), sizeof(complex)};
+
+static char umfpack_error[20];
+
+PyDoc_STRVAR(umfpack__doc__,"Interface to the UMFPACK library.\n\n"
+ "Routines for symbolic and numeric LU factorization of sparse\n"
+ "matrices and for solving sparse sets of linear equations.\n"
+ "The default control settings of UMPFACK are used.\n\n"
+ "See also http://www.cise.ufl.edu/research/sparse/umfpack.");
+
+static void free_umfpack_d_symbolic(void *F, void *descr)
+{
+ UMFD(free_symbolic)(&F);
+}
+
+static void free_umfpack_z_symbolic(void *F, void *descr)
+{
+ UMFZ(free_symbolic)(&F);
+}
+
+static void free_umfpack_d_numeric(void *F, void *descr)
+{
+ UMFD(free_numeric)(&F);
+}
+
+static void free_umfpack_z_numeric(void *F, void *descr)
+{
+ UMFZ(free_numeric)(&F);
+}
+
+static char doc_linsolve[] =
+ "Solves a sparse set of linear equations.\n\n"
+ "linsolve(A, B, trans='N', nrhs=B.size[1], ldB=max(1,B.size[0]),\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X = B.\n"
+ "If trans is 'T', solves A^T*X = B.\n"
+ "If trans is 'C', solves A^H*X = B.\n"
+ "A is a sparse n by n matrix, and B is n by nrhs.\n"
+ "On exit B is replaced by the solution. A is not modified.\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix\n\n"
+ "B dense matrix of the same type as A, stored following \n"
+ " the BLAS conventions\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "nrhs integer. If negative, the default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* linsolve(PyObject *self, PyObject *args,
+ PyObject *kwrds)
+{
+ spmatrix *A;
+ matrix *B;
+ char trans='N';
+ double info[UMFPACK_INFO];
+ int oB=0, n, nrhs=-1, ldB=0, k;
+ void *symbolic, *numeric, *x;
+ char *kwlist[] = {"A", "B", "trans", "nrhs", "ldB", "offsetB",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OO|ciii", kwlist,
+ &A, &B, &trans, &nrhs, &ldB, &oB)) return NULL;
+
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A))
+ PY_ERR_TYPE("A must be a square sparse matrix");
+ n = SP_NROWS(A);
+ if (!Matrix_Check(B) || MAT_ID(B) != SP_ID(A))
+ PY_ERR_TYPE("B must a dense matrix of the same numeric type "
+ "as A");
+
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("i", 0);
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > MAT_LGT(B)) err_buf_len("B");
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+
+ if (SP_ID(A) == DOUBLE)
+ UMFD(symbolic)(n, n, SP_COL(A), SP_ROW(A), SP_VAL(A), &symbolic,
+ NULL, info);
+ else
+ UMFZ(symbolic)(n, n, SP_COL(A), SP_ROW(A), SP_VAL(A), NULL,
+ &symbolic, NULL, info);
+
+ if (info[UMFPACK_STATUS] != UMFPACK_OK){
+ if (SP_ID(A) == DOUBLE)
+ UMFD(free_symbolic)(&symbolic);
+ else
+ UMFZ(free_symbolic)(&symbolic);
+ if (info[UMFPACK_STATUS] == UMFPACK_ERROR_out_of_memory)
+ return PyErr_NoMemory();
+ else {
+ snprintf(umfpack_error,20,"%s %i","UMFPACK ERROR",
+ (int) info[UMFPACK_STATUS]);
+ PyErr_SetString(PyExc_ValueError, umfpack_error);
+ return NULL;
+ }
+ }
+
+ if (SP_ID(A) == DOUBLE) {
+ UMFD(numeric)(SP_COL(A), SP_ROW(A), SP_VAL(A), symbolic,
+ &numeric, NULL, info);
+ UMFD(free_symbolic)(&symbolic);
+ } else {
+ UMFZ(numeric)(SP_COL(A), SP_ROW(A), SP_VAL(A), NULL, symbolic,
+ &numeric, NULL, info);
+ UMFZ(free_symbolic)(&symbolic);
+ }
+ if (info[UMFPACK_STATUS] != UMFPACK_OK){
+ if (SP_ID(A) == DOUBLE)
+ UMFD(free_numeric)(&numeric);
+ else
+ UMFZ(free_numeric)(&numeric);
+ if (info[UMFPACK_STATUS] == UMFPACK_ERROR_out_of_memory)
+ return PyErr_NoMemory();
+ else {
+ if (info[UMFPACK_STATUS] == UMFPACK_WARNING_singular_matrix)
+ PyErr_SetString(PyExc_ArithmeticError, "singular "
+ "matrix");
+ else {
+ snprintf(umfpack_error,20,"%s %i","UMFPACK ERROR",
+ (int) info[UMFPACK_STATUS]);
+ PyErr_SetString(PyExc_ValueError, umfpack_error);
+ }
+ return NULL;
+ }
+ }
+
+ if (!(x = malloc(n*E_SIZE[SP_ID(A)]))) {
+ if (SP_ID(A) == DOUBLE)
+ UMFD(free_numeric)(&numeric);
+ else
+ UMFZ(free_numeric)(&numeric);
+ return PyErr_NoMemory();
+ }
+ for (k=0; k<nrhs; k++){
+ if (SP_ID(A) == DOUBLE)
+ UMFD(solve)(trans == 'N' ? UMFPACK_A: UMFPACK_Aat,
+ SP_COL(A), SP_ROW(A), SP_VAL(A), x,
+ MAT_BUFD(B) + k*ldB + oB, numeric, NULL, info);
+ else
+ UMFZ(solve)(trans == 'N' ? UMFPACK_A: trans == 'C' ?
+ UMFPACK_At : UMFPACK_Aat, SP_COL(A), SP_ROW(A),
+ SP_VAL(A), NULL, x, NULL,
+ (double *)(MAT_BUFZ(B) + k*ldB + oB), NULL, numeric,
+ NULL, info);
+ if (info[UMFPACK_STATUS] == UMFPACK_OK)
+ memcpy(B->buffer + (k*ldB + oB)*E_SIZE[SP_ID(A)], x,
+ n*E_SIZE[SP_ID(A)]);
+ else
+ break;
+ }
+ free(x);
+ if (SP_ID(A) == DOUBLE)
+ UMFD(free_numeric)(&numeric);
+ else
+ UMFZ(free_numeric)(&numeric);
+
+ if (info[UMFPACK_STATUS] != UMFPACK_OK){
+ if (info[UMFPACK_STATUS] == UMFPACK_ERROR_out_of_memory)
+ return PyErr_NoMemory();
+ else {
+ if (info[UMFPACK_STATUS] == UMFPACK_WARNING_singular_matrix)
+ PyErr_SetString(PyExc_ArithmeticError, "singular "
+ "matrix");
+ else {
+ snprintf(umfpack_error,20,"%s %i","UMFPACK ERROR",
+ (int) info[UMFPACK_STATUS]);
+ PyErr_SetString(PyExc_ValueError, umfpack_error);
+ }
+ return NULL;
+ }
+ }
+ return Py_BuildValue("");
+}
+
+
+static char doc_symbolic[] =
+ "Symbolic LU factorization of a sparse matrix.\n\n"
+ "F = symbolic(A)\n\n"
+ "ARGUMENTS\n"
+ "A sparse matrix with at least one row and at least one\n"
+ " column. A may be rectangular.\n\n"
+ "F the symbolic factorization as an opaque C object";
+
+static PyObject* symbolic(PyObject *self, PyObject *args)
+{
+ spmatrix *A;
+ double info[UMFPACK_INFO];
+ void *symbolic;
+
+ if (!PyArg_ParseTuple(args, "O", &A)) return NULL;
+
+ if (!SpMatrix_Check(A)) PY_ERR_TYPE("A must be a sparse matrix");
+ if (SP_NCOLS(A) == 0 || SP_NROWS(A) == 0) {
+ PyErr_SetString(PyExc_ValueError, "A must have at least one "
+ "row and column");
+ return NULL;
+ }
+
+ switch (SP_ID(A)){
+ case DOUBLE:
+ UMFD(symbolic)(SP_NROWS(A), SP_NCOLS(A), SP_COL(A),
+ SP_ROW(A), SP_VAL(A), &symbolic, NULL, info);
+ if (info[UMFPACK_STATUS] == UMFPACK_OK)
+ return (PyObject *) PyCObject_FromVoidPtrAndDesc(
+ (void *) symbolic, "UMFPACK SYM D FACTOR",
+ free_umfpack_d_symbolic);
+ else
+ UMFD(free_symbolic)(&symbolic);
+ break;
+
+ case COMPLEX:
+ UMFZ(symbolic)(SP_NROWS(A), SP_NCOLS(A), SP_COL(A),
+ SP_ROW(A), SP_VAL(A), NULL, &symbolic, NULL, info);
+ if (info[UMFPACK_STATUS] == UMFPACK_OK)
+ return (PyObject *) PyCObject_FromVoidPtrAndDesc(
+ (void *) symbolic, "UMFPACK SYM Z FACTOR",
+ free_umfpack_z_symbolic);
+ else
+ UMFZ(free_symbolic)(&symbolic);
+ break;
+ }
+
+ if (info[UMFPACK_STATUS] == UMFPACK_ERROR_out_of_memory)
+ return PyErr_NoMemory();
+ else {
+ snprintf(umfpack_error,20,"%s %i","UMFPACK ERROR",
+ (int) info[UMFPACK_STATUS]);
+ PyErr_SetString(PyExc_ValueError, umfpack_error);
+ return NULL;
+ }
+}
+
+
+static char doc_numeric[] =
+ "Numeric LU factorization of a sparse matrix, given a symbolic\n"
+ "factorization computed by umfpack.symbolic. Raises an\n"
+ "ArithmeticError if A is singular.\n\n"
+ "Fn = numeric(A, Fs)\n\n"
+ "ARGUMENTS\n"
+ "A sparse matrix; may be rectangular\n\n"
+ "Fs symbolic factorization of A, or a matrix with the same\n"
+ " sparsity pattern, dimensions, and typecode as A, \n"
+ " created by umfpack.symbolic\n\n"
+ "Fn the numeric factorization, as an opaque C object";
+
+static PyObject* numeric(PyObject *self, PyObject *args)
+{
+ spmatrix *A;
+ PyObject *Fs;
+ double info[UMFPACK_INFO];
+ void *numeric;
+
+ if (!PyArg_ParseTuple(args, "OO", &A, &Fs)) return NULL;
+
+ if (!SpMatrix_Check(A)) PY_ERR_TYPE("A must be a sparse matrix");
+ if (!PyCObject_Check(Fs)) err_CO("Fs");
+
+ switch (SP_ID(A)) {
+ case DOUBLE:
+ TypeCheck_CObject(Fs, "UMFPACK SYM D FACTOR", "Fs is not "
+ "the UMFPACK symbolic factor of a 'd' matrix");
+ UMFD(numeric)(SP_COL(A), SP_ROW(A), SP_VAL(A),
+ (void *) PyCObject_AsVoidPtr(Fs), &numeric, NULL, info);
+ if (info[UMFPACK_STATUS] == UMFPACK_OK)
+ return (PyObject *) PyCObject_FromVoidPtrAndDesc(
+ (void *) numeric, "UMFPACK NUM D FACTOR",
+ free_umfpack_d_numeric);
+ else
+ UMFD(free_numeric)(&numeric);
+ break;
+
+ case COMPLEX:
+ TypeCheck_CObject(Fs, "UMFPACK SYM Z FACTOR", "Fs is not "
+ "the UMFPACK symbolic factor of a 'z' matrix");
+ UMFZ(numeric)(SP_COL(A), SP_ROW(A), SP_VAL(A), NULL,
+ (void *) PyCObject_AsVoidPtr(Fs), &numeric, NULL,
+ info);
+ if (info[UMFPACK_STATUS] == UMFPACK_OK)
+ return (PyObject *) PyCObject_FromVoidPtrAndDesc(
+ (void *) numeric, "UMFPACK NUM Z FACTOR",
+ free_umfpack_z_numeric);
+ else
+ UMFZ(free_numeric)(&numeric);
+ break;
+ }
+
+ if (info[UMFPACK_STATUS] == UMFPACK_ERROR_out_of_memory)
+ return PyErr_NoMemory();
+ else {
+ if (info[UMFPACK_STATUS] == UMFPACK_WARNING_singular_matrix)
+ PyErr_SetString(PyExc_ArithmeticError, "singular matrix");
+ else {
+ snprintf(umfpack_error,20,"%s %i","UMFPACK ERROR",
+ (int) info[UMFPACK_STATUS]);
+ PyErr_SetString(PyExc_ValueError, umfpack_error);
+ }
+ return NULL;
+ }
+}
+
+
+static char doc_solve[] =
+ "Solves a factored set of linear equations.\n\n"
+ "solve(A, F, B, trans='N', nrhs=B.size[1], ldB=max(1,B.size[0]),\n"
+ " offsetB=0)\n\n"
+ "PURPOSE\n"
+ "If trans is 'N', solves A*X = B.\n"
+ "If trans is 'T', solves A^T*X = B.\n"
+ "If trans is 'C', solves A^H*X = B.\n"
+ "A is a sparse n by n matrix, and B is n by nrhs. F is the\n"
+ "numeric factorization of A, computed by umfpack.numeric.\n"
+ "On exit B is replaced by the solution. A is not modified.\n\n"
+ "ARGUMENTS\n"
+ "A square sparse matrix\n\n"
+ "F numeric factorization, as returned by umfpack.numeric\n"
+ "\n"
+ "B dense matrix of the same type as A, stored following \n"
+ " the BLAS conventions\n\n"
+ "trans 'N', 'T' or 'C'\n\n"
+ "nrhs integer. If negative, the default value is used.\n\n"
+ "ldB nonnegative integer. ldB >= max(1,n). If zero, the\n"
+ " default value is used.\n\n"
+ "offsetB nonnegative integer";
+
+static PyObject* solve(PyObject *self, PyObject *args, PyObject *kwrds)
+{
+ spmatrix *A;
+ PyObject *F;
+ matrix *B;
+ char trans='N';
+ double *x, info[UMFPACK_INFO];
+ int oB=0, n, ldB=0, nrhs=-1, k;
+ char *kwlist[] = {"A", "F", "B", "trans", "nrhs", "ldB", "offsetB",
+ NULL};
+
+ if (!PyArg_ParseTupleAndKeywords(args, kwrds, "OOO|ciii", kwlist,
+ &A, &F, &B, &trans, &nrhs, &ldB, &oB)) return NULL;
+
+ if (!SpMatrix_Check(A) || SP_NROWS(A) != SP_NCOLS(A))
+ PY_ERR_TYPE("A must a square sparse matrix");
+ n = SP_NROWS(A);
+
+ if (!PyCObject_Check(F)) err_CO("F");
+ if (SP_ID(A) == DOUBLE) {
+ TypeCheck_CObject(F, "UMFPACK NUM D FACTOR", "F is not the "
+ "UMFPACK numeric factor of a 'd' matrix");
+ }
+ else {
+ TypeCheck_CObject(F, "UMFPACK NUM Z FACTOR", "F is not the "
+ "UMFPACK numeric factor of a 'z' matrix");
+ }
+
+ if (!Matrix_Check(B) || MAT_ID(B) != SP_ID(A))
+ PY_ERR_TYPE("B must a dense matrix of the same numeric type "
+ "as A");
+ if (nrhs < 0) nrhs = B->ncols;
+ if (n == 0 || nrhs == 0) return Py_BuildValue("");
+ if (ldB == 0) ldB = MAX(1,B->nrows);
+ if (ldB < MAX(1,n)) err_ld("ldB");
+ if (oB < 0) err_nn_int("offsetB");
+ if (oB + (nrhs-1)*ldB + n > MAT_LGT(B)) err_buf_len("B");
+
+ if (trans != 'N' && trans != 'T' && trans != 'C')
+ err_char("trans", "'N', 'T', 'C'");
+
+ if (!(x = malloc(n*E_SIZE[SP_ID(A)]))) return PyErr_NoMemory();
+
+ for (k=0; k<nrhs; k++) {
+ if (SP_ID(A) == DOUBLE)
+ UMFD(solve)(trans == 'N' ? UMFPACK_A : UMFPACK_Aat,
+ SP_COL(A), SP_ROW(A), SP_VAL(A), x,
+ MAT_BUFD(B) + k*ldB + oB,
+ (void *) PyCObject_AsVoidPtr(F), NULL, info);
+ else
+ UMFZ(solve)(trans == 'N' ? UMFPACK_A : trans == 'C' ?
+ UMFPACK_At : UMFPACK_Aat, SP_COL(A), SP_ROW(A),
+ SP_VAL(A), NULL, x, NULL,
+ (double *)(MAT_BUFZ(B) + k*ldB + oB), NULL,
+ (void *) PyCObject_AsVoidPtr(F), NULL, info);
+ if (info[UMFPACK_STATUS] == UMFPACK_OK)
+ memcpy(B->buffer + (k*ldB + oB)*E_SIZE[SP_ID(A)], x,
+ n*E_SIZE[SP_ID(A)]);
+ else
+ break;
+ }
+ free(x);
+
+ if (info[UMFPACK_STATUS] != UMFPACK_OK){
+ if (info[UMFPACK_STATUS] == UMFPACK_ERROR_out_of_memory)
+ return PyErr_NoMemory();
+ else {
+ if (info[UMFPACK_STATUS] == UMFPACK_WARNING_singular_matrix)
+ PyErr_SetString(PyExc_ArithmeticError,
+ "singular matrix");
+ else {
+ snprintf(umfpack_error,20,"%s %i","UMFPACK ERROR",
+ (int) info[UMFPACK_STATUS]);
+ PyErr_SetString(PyExc_ValueError, umfpack_error);
+ }
+ return NULL;
+ }
+ }
+
+ return Py_BuildValue("");
+}
+
+static PyMethodDef umfpack_functions[] = {
+{"linsolve", (PyCFunction) linsolve, METH_VARARGS|METH_KEYWORDS,
+ doc_linsolve},
+{"symbolic", (PyCFunction) symbolic, METH_VARARGS, doc_symbolic},
+{"numeric", (PyCFunction) numeric, METH_VARARGS, doc_numeric},
+{"solve", (PyCFunction) solve, METH_VARARGS|METH_KEYWORDS, doc_solve},
+{NULL} /* Sentinel */
+};
+
+PyMODINIT_FUNC initumfpack(void)
+{
+ PyObject *m;
+
+ m = Py_InitModule3("cvxopt.umfpack", umfpack_functions,
+ umfpack__doc__);
+
+ if (import_cvxopt() < 0) return;
+}
diff --git a/src/python/__init__.py b/src/python/__init__.py
new file mode 100644
index 0000000..896a33c
--- /dev/null
+++ b/src/python/__init__.py
@@ -0,0 +1,2 @@
+__all__ = ['base', 'random', 'blas', 'lapack', 'amd', 'umfpack',
+ 'cholmod', 'solvers', 'modeling', 'info']
diff --git a/src/python/coneprog.py b/src/python/coneprog.py
new file mode 100644
index 0000000..50b0ce2
--- /dev/null
+++ b/src/python/coneprog.py
@@ -0,0 +1,2151 @@
+"""
+Linear and semidefinite programming solver.
+"""
+
+# This file is part of CVXOPT version 0.8.2.
+# Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+
+import math
+from cvxopt import base, blas, lapack, cholmod, misc
+from cvxopt.base import matrix, spmatrix
+cholmod.options['supernodal'] = 2
+
+__all__ = []
+options = {}
+
+def conelp(c, kktsolver, Gl=None, hl=None, Gs=None, hs=None, A=None,
+ b=None, primalstart=None, dualstart=None, xnewcopy=matrix,
+ xdot=blas.dot, xaxpy=blas.axpy, xscal=blas.scal, ynewcopy=matrix,
+ ydot=blas.dot, yaxpy=blas.axpy, yscal=blas.scal):
+ """
+
+ Solves a pair of primal and dual cone programs
+
+ minimize <c,x>
+ subject to Gl(x) + sl = hl
+ Gs(x) + ss = hs
+ A(x) = b
+ sl >= 0, ss >= 0
+
+ maximize -<hl,zl> - <hs,zs> - <b,y>
+ subject to Gl'(zl) + Gs'(zs) + A'(y) + c = 0
+ zl >= 0, zs >= 0
+
+ Gl: V -> reals^ml, Gs: V -> S^m1 x ... x S^mN, and A: V -> W are
+ linear mappings, where V and W are real vector spaces.
+
+ Input arguments:
+
+ c is a matrix, list of matrices, dictionary of matrices, ...
+ representing a vector in the vector space V.
+
+ Gl is a function Gl(x, y, alpha=1.0, beta=0.0, trans='N'):
+
+ y := alpha*Gl(x) + beta*y if trans is 'N'
+ y := alpha*Gl'(x) + beta*y if trans is 'T'.
+
+ If trans is 'N', x is in V and y is in R^ml.
+ If trans is 'T', x is in R^ml and y is in V.
+
+ hl is a dense 'd' matrix of size (ml,1).
+
+ Gs is a function Gs(x, y, alpha=1.0, beta=0.0, trans='N'):
+
+ y := alpha*Gs(x) + beta*y if trans is 'N'
+ y := alpha*Gs'(x) + beta*y if trans is 'T'.
+
+ If trans is 'N', x is in V and y is in S^m1 x ... x S^mN.
+ If trans is 'T', x is in S^m1 x ... x S^mN and y is in V.
+
+ hs is a list of N square dense 'd' matrices, representing a
+ symmetric block diagonal matrix in 'L' storage.
+
+ A is a function A(x, y, alpha, beta, trans='N'):
+
+ y := alpha*A(x) + beta*y if trans is 'N'
+ y := alpha*A'(x) + beta*y if trans is 'T'.
+
+ If trans is 'N', x is in V and y is in W
+ If trans is 'T', x is in S^m1 x ... x S^mN and y is in V.
+
+ b is a matrix, list of matrices, dictionary of matrices, ...
+ representing a vector in the vector space W.
+
+ kktsolver is a function that returns a function for solving
+ KKT systems
+
+ [ 0 A' Gl' Gs' ] [ x ] [ bx ]
+ [ A 0 0 0 ] [ y ] = [ by ].
+ [ Gl 0 -diag(d)^2 0 ] [ zl ] [ bzl ]
+ [ Gs 0 0 -r*r'*()*r*r' ] [ zs ] [ bzs ]
+
+ Called as f = kktsolver(di, rti) with di = 1.0./d (a dense 'd'
+ matrix of size (ml,1)) and rti = (r')^{-1} (a list of square
+ dense 'd' matrices of size (mk,mk)).
+ The KKT system is solved by f(x,y,zl,zs). On entry, x, y, zl,
+ zs contain the righthand side. On exit, they contain the
+ solution, with zl, zs scaled: d.*zl and r'*zs*r are returned
+ instead of zl and zs.
+
+ xnewcopy, xdot, xscal, xaxpy, ynewcopy, ydot, yscal, yaxpy are
+ Python functions.
+ xnewcopy(x), ynewcopy(x) create new copies of vectors in V and
+ W, respectively.
+ xdot(x,y), ydot(x,y) return the inner product of vectors in V
+ and W, respectively.
+ xscal(alpha, x), yscal(alpha,x) compute x := alpha*x for x in V
+ and W, respectively.
+ xaxpy(x, y, alpha=1, beta=0), yaxpy(x, y, alpha=1, beta=0)
+ compute y := alpha*x + y for vectors in V and W, respectively.
+
+ conelp() returns a dictionary with keys 'status', 'x', 'sl',
+ 'ss', 'y', 'zl', 'zs'.
+
+ The control parameters can be modified by adding an entry to the
+ dictionary options.
+
+ options['show_progress'] True/False (default: True)
+ options['maxiters'] positive integer (default: 100)
+ options['abstol'] scalar (default: 1e-7)
+ options['reltol'] scalar (default: 1e-7)
+ options['feastol'] scalar (default: 1e-7)
+ options['refinement'] True/False (default: True)
+ """
+
+ EXPON = 3
+ STEP = 0.99
+
+ try: DEBUG = options['debug']
+ except KeyError: DEBUG = False
+
+ try: MAXITERS = options['maxiters']
+ except KeyError: MAXITERS = 100
+ else:
+ if type(MAXITERS) is not int or MAXITERS < 1:
+ raise ValueError, "options['maxiters'] must be a positive "\
+ "integer"
+
+ try: ABSTOL = options['abstol']
+ except KeyError: ABSTOL = 1e-7
+ else:
+ if type(ABSTOL) is not float and type(ABSTOL) is not int:
+ raise ValueError, "options['abstol'] must be a scalar"
+
+ try: RELTOL = options['reltol']
+ except KeyError: RELTOL = 1e-7
+ else:
+ if type(RELTOL) is not float and type(RELTOL) is not int:
+ raise ValueError, "options['reltol'] must be a scalar"
+
+ try: FEASTOL = options['feastol']
+ except KeyError: FEASTOL = 1e-7
+ else:
+ if type(FEASTOL) is not float and type(FEASTOL) is not int:
+ raise ValueError, "options['feastol'] must be a scalar"
+
+ try: show_progress = options['show_progress']
+ except KeyError: show_progress = True
+
+ try: refinement = options['refinement']
+ except KeyError: refinement = True
+
+ def f0(x, y, alpha=1.0, beta=0.0, trans='N'):
+ # y := alpha*F(x) + beta*y (trans = 'N')
+ # y := alpha*F'(x) + beta*y (trans = 'T')
+ # when F : R^n -> a 0-dimensional space
+ if trans == 'N': pass
+ else: xscal(beta, y)
+ if Gl is None: Gl = f0
+ if Gs is None: Gs = f0
+ if A is None: A = f0
+ if hl is None: hl = matrix(0.0, (0,1))
+ if hs is None: hs = []
+ if b is None: b = matrix(0.0, (0,1))
+ ml, ms, p = hl.size[0], [ h_k.size[0] for h_k in hs ], b.size[0]
+ maxm = max( [0] + ms )
+ m = ml + sum(ms)
+
+ def xcopy(x, y): xscal(0, y); xaxpy(x, y)
+ def ycopy(x, y): yscal(0, y); yaxpy(x, y)
+
+ x = xnewcopy(c); xscal(0,x)
+ sl = matrix(1.0, (ml,1))
+ ss = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ for sk in ss: sk[::sk.size[0]+1] = 1.0
+ y = ynewcopy(b); yscal(0,y)
+ zl = matrix(1.0, (ml,1))
+ zs = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ for zk in zs: zk[::zk.size[0]+1] = 1.0
+
+ resx, hresx = xnewcopy(c), xnewcopy(c)
+ reszl, hreszl = matrix(0.0, (ml,1)), matrix(0.0, (ml,1))
+ reszs = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ hreszs = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ resy, hresy = ynewcopy(b), ynewcopy(b)
+ dx = xnewcopy(c)
+ dsl = matrix(0.0, (ml,1))
+ dss = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ dy = ynewcopy(b)
+ dzl = matrix(0.0, (ml,1))
+ dzs = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ dkappa, dtau = matrix(0.0, (1,1)), matrix(0.0, (1,1))
+ dx1 = xnewcopy(c)
+ dy1 = ynewcopy(b)
+ dsl1 = matrix(0.0, (ml,1))
+ dss1 = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ dzl1 = matrix(0.0, (ml,1))
+ dzs1 = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ if refinement:
+ dx2 = xnewcopy(c)
+ dy2 = ynewcopy(b)
+ dsl2 = matrix(0.0, (ml,1))
+ dss2 = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ dzl2 = matrix(0.0, (ml,1))
+ dzs2 = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ dkappa2, dtau2 = matrix(0.0, (1,1)), matrix(0.0, (1,1))
+ r = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ rti = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ lmbda = matrix(0.0, (m+1,1))
+ gamma = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ thl = matrix(0.0, (ml,1))
+ ths = [ matrix(0.0, (m_k, m_k)) for m_k in ms ]
+ sigs, sigz = matrix(0.0, (m+1,1)), matrix(0.0, (m+1,1))
+ ones = matrix(1.0, (max(maxm,ml),1))
+ work, work2 = matrix(0.0, (maxm,maxm)), matrix(0.0, (maxm,maxm))
+
+
+ # Initial points more or less as in Mehrotra's paper.
+
+ if primalstart is None or dualstart is None:
+
+ # Factor
+ #
+ # [ 0 A' Gl' Gs' ]
+ # [ A 0 0 0 ]
+ # [ Gl 0 -I 0 ]
+ # [ Gs 0 0 -I ]
+
+ dli = matrix(1.0, (ml,1))
+ for e in rti:
+ blas.scal(0.0, e)
+ e[::e.size[0]+1] = 1.0
+ try:
+ f = kktsolver(dli, rti)
+ except ArithmeticError:
+ raise ValueError, "Rank(A) < p or Rank([Gl; Gs; A]) < n"
+
+ if primalstart is None:
+
+ # minimize || Gl(x) - hl ||^2
+ # subject to A(x) = b
+ #
+ # by solving
+ #
+ # [ 0 A' Gl' Gs' ] [x ] [0 ]
+ # [ A 0 0 0 ] [dy ] = [b ]
+ # [ Gl 0 -I 0 ] [dzl] [hl]
+ # [ Gs 0 0 -I ] [dzs] [hs]
+ #
+ # (sl, ss) = (hl-Gl*x, hs-Gs(x)) and add a multiple of the
+ # identity to make (sl,ss) >= 0.
+
+ xscal(0.0, x)
+ ycopy(b, dy)
+ blas.copy(hl, dzl)
+ misc.scopy(hs, dzs)
+ f(x, dy, dzl, dzs)
+ blas.scal(0.0, sl); blas.axpy(dzl, sl, alpha=-1)
+ misc.sscal(0.0, ss); misc.saxpy(dzs, ss, alpha=-1)
+ blas.copy(sl, lmbda)
+ if sl: ap = min(sl)
+ else: ap = 0.0
+ for e in ss:
+ if e.size[0]:
+ lapack.syevr(+e, lmbda, range='I', il=1, iu=1)
+ ap = min(ap, lmbda[0])
+ if ap < 0.0:
+ sl += -1.5*ap
+ for e in ss: e[::e.size[0]+1] -= 1.5*ap
+
+ else:
+ xcopy(primalstart['x'], x)
+ if ml: blas.copy(primalstart['sl'], sl)
+ if ms: misc.scopy(primalstart['ss'], ss)
+
+
+ if dualstart is None:
+
+ # minimize || zl ||^2
+ # subject to Gl'(zl) + A'(y) + c = 0
+ #
+ # by solving
+ #
+ # [ 0 A' Gl' Gs' ] [dx] [-c]
+ # [ A 0 0 0 ] [y ] = [ 0]
+ # [ Gl 0 -I 0 ] [zl] [ 0]
+ # [ Gs 0 0 -I ] [zs] [ 0]
+
+ xcopy(c, dx); xscal(-1.0, dx)
+ yscal(0.0, y)
+ blas.scal(0.0, zl)
+ misc.sscal(0.0, zs)
+ f(dx, y, zl, zs)
+ blas.copy(zl, lmbda)
+ if zl: ad = min(zl)
+ else: ad = 0.0
+ for e in zs:
+ if e.size[0]:
+ lapack.syevr(+e, lmbda, range='I', il=1, iu=1)
+ ad = min(ad, lmbda[0])
+ if ad <= 0.0:
+ zl += -1.5*ad
+ for e in zs: e[::e.size[0]+1] -= 1.5*ad
+
+ else:
+ if p: ycopy(dualstart['y'], y)
+ if ml: blas.copy(dualstart['zl'], zl)
+ if ms: misc.scopy(dualstart['zs'], zs)
+
+ gap = blas.dot(sl,zl) + misc.sdot(ss, zs)
+
+ if primalstart is None and dualstart is None and gap < 1e-10:
+ # If gap is zero, z, s must have zero components, and this means
+ # that ad and ap were zero. Therefore the initial point
+ # happens to be feasible and optimal. So it does not matter
+ # if (sl,ss) or (zl,zs) are not strictly positive and we can
+ # skip to the computation of the residuals.
+ pass
+
+ else:
+ if primalstart is None:
+ # (sl, ss) >= could be non-strictly positive so we need to
+ # make it positive definite. Note that sum(zl) + tr(zs)
+ # cannot be zero, because (zl,zs)=0 means dualstart is None
+ # and gap = 0, and that was handled above.
+ trz = blas.asum(zl) + sum([ blas.asum(e, inc=e.size[0]+1)
+ for e in zs ])
+ a = max(gap, 1e-8) / trz
+ sl += a
+ for e in ss: e[::e.size[0]+1] += a
+
+ if dualstart is None:
+ # Idem for (zl, zs).
+ trs = blas.asum(sl) + sum([ blas.asum(e, inc=e.size[0]+1)
+ for e in ss ])
+ a = max(gap, 1e-8) / trs
+ zl += a
+ for e in zs: e[::e.size[0]+1] += a
+
+ tau, kappa = 1.0, 1.0
+ gap = blas.dot(sl, zl) + misc.sdot(ss, zs)
+
+ for iters in xrange(MAXITERS):
+
+ # hresx = -A'(y) - Gl'(zl) - Gs'(zs)
+ A(y, hresx, alpha=-1.0, trans='T')
+ Gl(zl, hresx, alpha=-1.0, beta=1.0, trans='T')
+ Gs(zs, hresx, alpha=-1.0, beta=1.0, trans='T')
+
+ # resx = hresx - c*tau = -A'(y) - Gl'(zl) - Gs'(zs) - c*tau
+ xcopy(hresx, resx)
+ xaxpy(c, resx, alpha=-tau)
+
+ # hresy = A(x)
+ A(x, hresy)
+
+ # resy = hresy - b*tau = A(x) - b*tau
+ ycopy(hresy, resy)
+ yaxpy(b, resy, alpha=-tau)
+
+ # hreszl = sl + Gl(x)
+ Gl(x, hreszl)
+ blas.axpy(sl, hreszl)
+
+ # reszl = hreszl - hl*tau = sl + Gl(x) - hl*tau
+ blas.scal(0, reszl)
+ blas.axpy(hreszl, reszl)
+ blas.axpy(hl, reszl, alpha=-tau)
+
+ # hreszs = ss + Gs(x)
+ Gs(x, hreszs)
+ misc.saxpy(ss, hreszs)
+
+ # reszs = hreszs - hs*tau = ss + Gs(x) - hs*tau
+ misc.sscal(0, reszs)
+ misc.saxpy(hreszs, reszs)
+ misc.saxpy(hs, reszs, alpha=-tau)
+
+ # rest = kappa + <c,x> + <b,y> + <hl,zl> + <hs,zs>
+ cx, by = xdot(c,x), ydot(b,y)
+ hlzl, hszs = blas.dot(hl,zl), misc.sdot(hs,zs)
+ rest = kappa + cx + by + hlzl + hszs
+
+ # stopping criteria
+ pcost, dcost = cx/tau, -(by + hlzl + hszs) / tau
+ nrmhresx = math.sqrt(xdot(hresx, hresx))
+ nrmresx = math.sqrt(xdot(resx, resx)) / tau
+ nrmhresy = math.sqrt(ydot(hresy, hresy))
+ nrmresy = math.sqrt(ydot(resy, resy)) / tau
+ nrmhreszl = blas.nrm2(hreszl)
+ nrmreszl = blas.nrm2(reszl) / tau
+ nrmhreszs = misc.snrm2(hreszs)
+ nrmreszs = misc.snrm2(reszs) / tau
+ if pcost < 0.0:
+ relgap = gap / -pcost
+ elif dcost > 0.0:
+ relgap = gap / dcost
+ else:
+ relgap = None
+
+ if iters == 0:
+ nrmresx0 = max(1.0, math.sqrt(xdot(c,c)))
+ nrmresy0 = max(1.0, math.sqrt(ydot(b,b)))
+ nrmreszl0 = max(1.0, blas.nrm2(hl))
+ nrmreszs0 = max(1.0, misc.snrm2(hs))
+
+ if show_progress:
+ if iters==0:
+ print "% 10s% 12s% 10s% 8s% 7s % 5s" %("pcost", "dcost",
+ "gap", "pres", "dres", "k/t")
+ print "%2d: % 8.4e % 8.4e % 4.0e% 7.0e% 7.0e% 7.0e" \
+ %(iters, pcost, dcost, gap, max(nrmreszl/nrmreszl0,
+ nrmreszs/nrmreszs0, nrmresy/nrmresy0), nrmresx/nrmresx0,
+ kappa/tau)
+
+ if max(nrmreszl/nrmreszl0, nrmreszs/nrmreszs0,
+ nrmresy/nrmresy0) <= FEASTOL and \
+ nrmresx/nrmresx0 <= FEASTOL and (gap <= ABSTOL or
+ (relgap is not None and relgap <= RELTOL)):
+ xscal(1.0/tau, x)
+ yscal(1.0/tau, y)
+ blas.scal(1.0/tau, sl)
+ misc.sscal(1.0/tau, ss)
+ blas.scal(1.0/tau, zl)
+ misc.sscal(1.0/tau, zs)
+ return {'status': 'optimal', 'x': x, 'y': y, 'sl': sl,
+ 'ss': ss, 'zl': zl, 'zs': zs}
+
+ elif hlzl + hszs + by < 0.0 and nrmhresx / (-hlzl - hszs - by) \
+ <= FEASTOL:
+ yscal(1.0/(-hlzl - hszs - by), y)
+ blas.scal(1.0/(-hlzl - hszs - by), zl)
+ misc.sscal(1.0/(-hlzl - hszs - by), zs)
+ return {'status': 'primal infeasible', 'x': None,
+ 'sl': None, 'ss': None, 'y': y, 'zl': zl, 'zs': zs}
+
+ elif cx < 0.0 and max(nrmhresy, nrmhreszl, nrmhreszs) / (-cx) \
+ <= FEASTOL:
+ xscal(1.0/(-cx), x)
+ blas.scal(1.0/(-cx), sl)
+ misc.sscal(1.0/(-cx), ss)
+ return {'status': 'dual infeasible', 'x': x, 'sl': sl,
+ 'ss': ss, 'y': None, 'zl': None, 'zs': None}
+
+
+ if iters == 0:
+
+ # Compute initial scaling.
+ #
+ # For the linear inequalities:
+ #
+ # dl = sqrt(sl./zl), dli = sqrt(zl./sl)
+ # lmbdl = sqrt(sl.*zl).
+ #
+ # Store lmbdl in lmbda[:ml].
+ #
+ # Matrix inequalities: lists of square matrices r, rti with
+ #
+ # r[k]'*ss[k]^{-1}*r[k] = diag(lmbds[k])^{-1}
+ # r[k]'*zs[k]*r[k] = diag(lmbds[k])
+ #
+ # rti[k] is the inverse of r[k]', so that
+ #
+ # rti[k]'*ss[k]*rti[k] = diag(lmbds[k])^{-1}
+ # rti[k]'*zs[k]^{-1}*rti[k] = diag(lmbds[k]).
+ #
+ # Store (lmbds[0], ..., lmbds[N-1]) in lmbda[ml:ml+sum(ms)].
+ #
+ # Also compute gamma: gamma[k] has entries
+ #
+ # gamma[k][i,j] = 0.5*(lmbds[k][i]+lmbds[k][j])
+ #
+ # For kappa, tau:
+ #
+ # dg = sqrt(kappa/tau), dgi = sqrt(tau/kappa)
+ # lmbdg = sqrt(tau*kappa)
+ #
+ # Store lmbdg in lmbda[-1].
+
+ dli = base.sqrt(misc.ihad(zl, sl))
+ lmbda[:ml] = base.sqrt(misc.had(sl,zl))
+
+ dgi = math.sqrt(tau/kappa)
+ lmbda[-1] = math.sqrt(tau*kappa)
+
+ ind = ml
+ for k in xrange(len(ms)):
+
+ # Factor ss = L1*L1', zs = L2*L2'. Store L1 and L2 in
+ # dss and dzs.
+ blas.copy(ss[k], dss[k]); lapack.potrf(dss[k])
+ blas.copy(zs[k], dzs[k]); lapack.potrf(dzs[k])
+
+ # SVD of L2'*L1 = U*diag(lambda)*V'. Keep U in work.
+ for i in xrange(ms[k]): dss[k][i,i+1:] = 0
+ blas.copy(dss[k], work)
+ blas.trmm(dzs[k], work, transA='T', ldB=ms[k], n=ms[k],
+ m=ms[k])
+ lapack.gesvd(work, lmbda, jobu='O', ldA=ms[k], m=ms[k],
+ n=ms[k], offsetS=ind)
+
+ # r = L2^{-T}*U*diag(sqrt(lambda))
+ # = L1*V*diag(1./sqrt(lambda))
+ # rti = L2*U*diag(1./sqrt(lambda))
+ # = L1^{-T}*V*diag(sqrt(lambda))
+ blas.copy(work, r[k], n=ms[k]*ms[k])
+ blas.trsm(dzs[k], r[k], transA='T')
+ blas.copy(work, rti[k], n=ms[k]*ms[k])
+ blas.trmm(dzs[k], rti[k])
+ for i in xrange(ms[k]):
+ a = math.sqrt(lmbda[ind+i])
+ blas.scal(a, r[k], offset=ms[k]*i, n=ms[k])
+ blas.scal(1/a, rti[k], offset=ms[k]*i, n=ms[k])
+
+ # gamma[k][i,j] = .5 * (lambda_i + lambda_j)
+ # Use blas.ger to make sure there are no zeros or nan's
+ # in upper triangular part.
+ blas.scal(0.0, gamma[k])
+ blas.ger(lmbda, ones, gamma[k], alpha=.5, offsetx=ind)
+ blas.ger(ones, lmbda, gamma[k], alpha=.5, offsety=ind)
+
+ ind += ms[k]
+
+
+ # Define a function
+ #
+ # solve_newton(dx, dy, dzl, dzs, dtau, dsl, dss, dkappa)
+ #
+ # for solving
+ #
+ # [0 ] [ 0 A' Gl' Gs' 0 ] [dx ] [rhsx ]
+ # [0 ] [-A 0 0 0 b ] [dy ] [rhsy ]
+ # [dsl ] - [-Gl 0 0 0 hl] [dzl ] = -[rhszl ]
+ # [dsk ] [-Gs 0 0 0 hs] [dzs ] [rhszs ]
+ # [dkappa] [-c' -b' -hl' -hs' 0 ] [dtau] [rhstau]
+ #
+ # sl.*dzl + zl.*dsl = -rhssl
+ # Hc(dzs*ss + zs*dss) = -rhsss
+ # kappa*dtau + tau*dkappa = -rhskappa.
+ #
+ # where Hc(x) = 0.5 * (r'*x*(r')^{-1} + r^{-1}*x'*r).
+
+ try: f = kktsolver(dli, rti)
+ except ArithmeticError:
+ if iters == 0 and primalstart and dualstart:
+ raise ValueError, "Rank(A) < p or Rank([Gl; Gs; A]) < n"
+ else:
+ raise ArithmeticError, "singular KKT matrix"
+
+ # thl := dli .* hl; ths := rti'*hs*rti
+ blas.copy(hl, thl)
+ misc.had2(thl, dli)
+ misc.cngrnc(rti, hs, ths, trans='T')
+
+ # Solve
+ #
+ # [ 0 A' Gl' Gs' ] [dx1 ] [c ]
+ # [-A 0 0 0 ] [dy1 ] = -dgi * [b ]
+ # [-Gl 0 diag(dl)^2 0 ] [dzl1] [hl]
+ # [-Gs 0 0 r*r'*()*r*r'] [dzs1] [hs]
+
+ xcopy(c, dx1); xscal(-1, dx1)
+ ycopy(b, dy1)
+ blas.copy(hl, dzl1)
+ misc.scopy(hs, dzs1)
+ f(dx1, dy1, dzl1, dzs1)
+ xscal(dgi, dx1)
+ yscal(dgi, dy1)
+ blas.scal(dgi, dzl1)
+ misc.sscal(dgi, dzs1)
+
+ if DEBUG:
+ print "first 4x4 system"
+
+ # unscaled variables
+ duzl1 = misc.had(dzl1, dli)
+ duzs1 = [ +z_k for z_k in dzs1 ]
+ misc.cngrnc(rti, duzs1, duzs1)
+
+ rxdb = xnewcopy(c)
+ A(dy1, rxdb, alpha=1, beta=dgi, trans='T')
+ Gl(duzl1, rxdb, alpha=1, beta=1, trans='T')
+ Gs(duzs1, rxdb, alpha=1, beta=1, trans='T')
+ print " norm(rxdb) = %e" %math.sqrt(xdot(rxdb,rxdb))
+
+ rydb = ynewcopy(b)
+ A(dx1, rydb, alpha=-1.0, beta=dgi)
+ print " norm(rydb) = %e" %math.sqrt(ydot(rydb,rydb))
+
+ rzldb = +hl
+ Gl(dx1, rzldb, alpha=-1.0, beta=dgi)
+ rzldb += misc.ihad(duzl1, misc.had(dli,dli))
+ print " norm(rzldb) = %e" %blas.nrm2(rzldb)
+
+ rzsdb = [ +hs_k for hs_k in hs ]
+ Gs(dx1, rzsdb, alpha=-1.0, beta=dgi)
+ misc.cngrnc(r, duzs1, duzs1, trans='T')
+ misc.cngrnc(r, duzs1, rzsdb, alpha=1.0, beta=1.0)
+ print " norm(rzsdb) = %e\n" %misc.snrm2(rzsdb)
+
+
+ def solve_newton1(dx, dy, dzl, dzs, dtau, dsl, dss, dkappa):
+
+ # Solve without refinement
+ #
+ # [0 ] [ 0 A' Gl' Gs' 0 ] [dx ] [rhsx ]
+ # [0 ] [-A 0 0 0 b ] [dy ] [rhsy ]
+ # [dsl ] - [-Gl 0 0 0 hl] [dzl ] = -[rhszl ]
+ # [dsk ] [-Gs 0 0 0 hs] [dzs ] [rhszs ]
+ # [dkappa] [-c' -b' -hl' -hs' 0 ] [dtau] [rhstau]
+ #
+ # sl.*dzl + zl.*dsl = -rhssl
+ # Hc(dzs*ss + zs*dss) = -rhsss
+ # kappa*dtau + tau*dkappa = -rhskappa
+ #
+ # Last three equations in scaled variables:
+ #
+ # lmbdl .* (dzl + dsl) = -rhssl
+ # gamma .* (dzs + dss) = -rhsss
+ # lmbdg * (dtau + dkappa) = -rhskappa.
+ #
+ # On entry, the righthand sides are stored in dx, dy, dzl,
+ # dzs, dtau, dssl, dsss, dkappa.
+ # On exit, scaled quantities are returned for dsl, dzl,
+ # dss, dzs.
+
+ if DEBUG:
+ rxdb = xnewcopy(dx)
+ rydb = ynewcopy(dy)
+ rzldb = +dzl
+ rzsdb = [ +dzs_k for dzs_k in dzs ]
+ rtdb = dtau[0]
+ rsldb = +dsl
+ rssdb = [ +dss_k for dss_k in dss ]
+ rkdb = dkappa[0]
+
+ # dy := -dy = -rhsy
+ yscal(-1.0, dy)
+
+ # dsl := -dsl ./ lmbdl (replace with btmv)
+ misc.ihad2(dsl, lmbda, n=ml); blas.scal(-1,dsl)
+
+ # dzl := -(dzl + dsl ./ dli) = -(rhszl - rhssl./zl)
+ blas.axpy(misc.ihad(dsl,dli), dzl); blas.scal(-1, dzl)
+
+ # dss := -dss ./ gamma
+ for num, den in zip(dss, gamma): misc.ihad2(num, den)
+ misc.sscal(-1.0, dss)
+
+ # dzs := -(dzs + r*dss*r') = -(rhszs - r*(rhss./gamma)*r')
+ misc.cngrnc(r, dss, dzs, alpha=-1.0, beta=-1.0)
+
+ # dkappa[0] := -dkappa[0]/lmbd[-1]
+ # = -rhskappa / sqrt(kappa*tau)
+ dkappa[0] = -dkappa[0] / lmbda[-1]
+
+ # dtau[0] = dtau[0] + dkappa[0] / dgi
+ # = rhstau[0] - rhskappa / tau
+ dtau[0] += dkappa[0] / dgi
+
+
+ # Solve
+ #
+ # [ 0 A' Gl' Gs' 0 ][dx ] [rhsx ]
+ # [-A 0 0 0 b ][dy ] [rhsy ]
+ # [-Gl 0 Dl 0 hl ][dzl ] = [rhszl-rhssl./zl ]
+ # [-Gs 0 0 Ds hs ][dzs ] [rhszs-r*(rhszs./ga)*r']
+ # [-c' -b' -hl' -hs' k/t][dtau] [rhst-rhsk/tau ]
+ #
+ # Dl = diag(dl)^2, Ds = r*r'*()*r*r'.
+
+ if DEBUG:
+ rxdb2 = xnewcopy(dx)
+ rydb2 = ynewcopy(dy); xscal(-1, rydb2)
+ rzldb2 = -dzl
+ rzsdb2 = [-dzs_k for dzs_k in dzs]
+
+ rxdb3 = xnewcopy(dx)
+ rydb3 = ynewcopy(dy); xscal(-1, rydb3)
+ rzldb3 = -dzl
+ rzsdb3 = [-dzs_k for dzs_k in dzs]
+
+ f(dx, dy, dzl, dzs)
+
+ if DEBUG:
+ print "second 4x4 system"
+
+ # unscaled variables
+ duzl = misc.had(dzl, dli)
+ duzs = [ +z_k for z_k in dzs ]
+ misc.cngrnc(rti, duzs, duzs)
+
+ A(dy, rxdb2, alpha=-1.0, beta=1.0, trans='T')
+ Gl(duzl, rxdb2, alpha=-1.0, beta=1.0, trans='T')
+ Gs(duzs, rxdb2, alpha=-1.0, beta=1.0, trans='T')
+ print " norm(rxdb2) = %e" \
+ %math.sqrt(xdot(rxdb2,rxdb2))
+
+ A(dx, rydb2, alpha=1.0, beta=1.0)
+ print " norm(rydb2) = %e" \
+ %math.sqrt(ydot(rydb2,rydb2))
+
+ Gl(dx, rzldb2, alpha=1.0, beta=1.0)
+ rzldb2 -= misc.ihad(duzl, misc.had(dli,dli))
+ print " norm(rzldb2) = %e" %blas.nrm2(rzldb2)
+
+ Gs(dx, rzsdb2, alpha=1.0, beta=1.0)
+ misc.cngrnc(r, duzs, duzs, trans='T')
+ misc.cngrnc(r, duzs, rzsdb2, alpha=-1.0, beta=1.0)
+ print " norm(rzsdb2) = %e\n" %misc.snrm2(rzsdb2)
+
+ dtau[0] = dgi * ( dtau[0] + xdot(c,dx) + ydot(b,dy) +
+ blas.dot(thl, dzl) + misc.sdot(ths, dzs) ) / \
+ ( 1.0 + blas.dot(dzl1, dzl1) + misc.sdot(dzs1, dzs1) )
+ xaxpy(dx1, dx, alpha=dtau[0])
+ yaxpy(dy1, dy, alpha=dtau[0])
+ blas.axpy(dzl1, dzl, alpha=dtau[0])
+ misc.saxpy(dzs1, dzs, alpha=dtau[0])
+
+ # dsl := dsl - dzl = -rhsl ./ lmbdl - dtzl
+ blas.axpy(dzl, dsl, alpha=-1)
+
+ # dss := dss - dzs = -rhss ./ Gamma - dzs
+ misc.saxpy(dzs, dss, alpha=-1)
+
+ dkappa[0] -= dtau[0]
+
+ if DEBUG:
+ print "solvenewton errors"
+
+ # unscaled variables
+ duzl = misc.had(dzl, dli)
+ dusl = misc.ihad(dsl, dli)
+ duzs = [ +z_k for z_k in dzs ]
+ misc.cngrnc(rti, duzs, duzs)
+ duss = [ +s_k for s_k in dss ]
+ misc.cngrnc(r, duss, duss)
+ dutau = dtau[0] * dgi
+ dukappa = dkappa[0] / dgi
+
+ print " norm(rsldb) = %e" %blas.nrm2(rsldb +
+ misc.had(lmbda[:ml], dzl+dsl))
+
+ for k in xrange(len(ms)):
+ for j in xrange(ms[k]):
+ rssdb[k][j,j+1:] = rssdb[k][j+1:,j].trans()
+ rssdb[k] += misc.had(dzs[k] + dss[k], gamma[k])
+ print " norm(rssdb) = %e" %misc.snrm2(rssdb)
+
+ print " abs(rtdb) = %e" %abs(rtdb + dukappa +
+ xdot(c,dx) + ydot(b,dy) + blas.dot(hl,duzl) +
+ misc.sdot(hs,duzs))
+
+ A(dy, rxdb, alpha=-1.0, beta=1.0, trans='T')
+ Gl(duzl, rxdb, alpha=-1.0, beta=1.0, trans='T')
+ Gs(duzs, rxdb, alpha=-1.0, beta=1.0, trans='T')
+ xaxpy(c, rxdb, alpha=-dutau)
+ print " norm(rxdb) = %e" %math.sqrt(xdot(rxdb,rxdb))
+
+ A(dx, rydb, alpha=1.0, beta=1.0)
+ yaxpy(b, rydb, alpha=-dutau)
+ print " norm(rydb) = %e" %math.sqrt(ydot(rydb,rydb))
+
+ rzldb += dusl - hl*dutau
+ Gl(dx, rzldb, alpha=1.0, beta=1.0)
+ print " norm(rzldb) = %e" %blas.nrm2(rzldb)
+
+ misc.saxpy(duss, rzsdb)
+ misc.saxpy(hs, rzsdb, alpha=-dutau)
+ Gs(dx, rzsdb, alpha=1.0, beta=1.0)
+ print " norm(rzsdb) = %e\n" %misc.snrm2(rzsdb)
+
+ if refinement:
+ def solve_newton(dx, dy, dzl, dzs, dtau, dsl, dss, dkappa):
+
+ if DEBUG:
+ rxdb2 = xnewcopy(dx)
+ rydb2 = ynewcopy(dy)
+ rzldb2 = +dzl
+ rzsdb2 = [+dzs_k for dzs_k in dzs]
+ rtdb2 = dtau[0]
+ rsldb2 = +dsl
+ rssdb2 = [+dss_k for dss_k in dss]
+ rkdb2 = dkappa[0]
+
+ # copy righthand sides to dx2 etc
+ xcopy(dx, dx2)
+ ycopy(dy, dy2)
+ blas.copy(dzl, dzl2)
+ misc.scopy(dzs, dzs2)
+ dtau2[0] = dtau[0]
+ blas.copy(dsl, dsl2)
+ misc.scopy(dss, dss2)
+ dkappa2[0] = dkappa[0]
+
+ solve_newton1(dx, dy, dzl, dzs, dtau, dsl, dss, dkappa)
+
+ # store residuals in dx2, dy2, etc
+ #
+ # [0 ] [ 0 A' Gl' Gs' c ] [dx ] [rhsx ]
+ # [0 ] [-A 0 0 0 b ] [dy ] [rhsy ]
+ # [dsl ] - [-Gl 0 0 0 hl] [dzl ] + [rhszl ]
+ # [dss ] [-Gs 0 0 0 hs] [dzs ] [rhszs ]
+ # [dkappa] [-c' -b' -hl' -hs' 0 ] [dtau] [rhstau]
+ #
+ # sl.*dzl + zl.*dsl + rhssl
+ # Hc(dzs*ss + zs*dss) + rhsss
+ # kappa*dtau + tau*dkappa + rhskappa
+ #
+ # Last 3 equations with scaled variables:
+ #
+ # lmbdl .* (dzl + dsl) + rhssl
+ # 0.5 * (diag(lmbds)*dzs + dzs*diag(lmbds) +
+ # diag(lmbds)*dss + dss*diag(lmbds)) + rhsss
+ # lmbdg * (dtau + dkappa) + rhskappa.
+
+ # Store unscaled steps in sl, zl, ss, zs.
+ blas.copy(dzl, zl)
+ misc.had2(zl, dli)
+ blas.copy(dsl, sl)
+ misc.ihad2(sl, dli)
+ misc.scopy(dzs, zs)
+ misc.cngrnc(rti, zs, zs)
+ misc.scopy(dss, ss)
+ misc.cngrnc(r, ss, ss)
+ dutau = dtau[0] * dgi
+ dukappa = dkappa[0] / dgi
+
+ A(dy, dx2, alpha=-1.0, beta=1.0, trans='T')
+ Gl(zl, dx2, alpha=-1.0, beta=1.0, trans='T')
+ Gs(zs, dx2, alpha=-1.0, beta=1.0, trans='T')
+ xaxpy(c, dx2, alpha=-dutau)
+
+ A(dx, dy2, alpha=1.0, beta=1.0)
+ yaxpy(b, dy2, alpha=-dutau)
+
+ Gl(dx, dzl2, alpha=1.0, beta=1.0)
+ blas.axpy(hl, dzl2, alpha=-dutau)
+ blas.axpy(sl, dzl2)
+
+ Gs(dx, dzs2, alpha=1.0, beta=1.0)
+ misc.saxpy(hs, dzs2, alpha=-dutau)
+ misc.saxpy(ss, dzs2)
+
+ dtau2[0] += dukappa + xdot(c,dx) + ydot(b,dy) + \
+ blas.dot(hl, zl) + misc.sdot(hs, zs)
+
+ dsl2[:] += misc.had(dzl+dsl, lmbda[:ml])
+
+ for k in xrange(len(ms)):
+ dss2[k] += misc.had(dzs[k]+dss[k], gamma[k])
+
+ dkappa2[0] += lmbda[-1] * (dtau[0] + dkappa[0])
+
+ solve_newton1(dx2, dy2, dzl2, dzs2, dtau2, dsl2, dss2,
+ dkappa2)
+
+ xaxpy(dx2, dx)
+ yaxpy(dy2, dy)
+ blas.axpy(dzl2, dzl)
+ misc.saxpy(dzs2, dzs)
+ dtau[0] += dtau2[0]
+ blas.axpy(dsl2, dsl)
+ misc.saxpy(dss2, dss)
+ dkappa[0] += dkappa2[0]
+
+ if DEBUG:
+ print "solvenewton2 errors"
+
+ # unscaled variables
+ duzl = misc.had(dzl, dli)
+ dusl = misc.ihad(dsl, dli)
+ duzs = [ +z_k for z_k in dzs ]
+ misc.cngrnc(rti, duzs, duzs)
+ duss = [ +s_k for s_k in dss ]
+ misc.cngrnc(r, duss, duss)
+ dutau = dtau[0]*dgi
+ dukappa = dkappa[0]/dgi
+
+ print " norm(rsldb2) = %e" %blas.nrm2(rsldb2 +
+ misc.had(lmbda[:ml],dzl+dsl))
+
+ for k in xrange(len(ms)):
+ for j in xrange(ms[k]): rssdb2[k][j,j+1:] = \
+ rssdb2[k][j+1:,j].trans()
+ rssdb2[k] += misc.had(dzs[k] + dss[k], gamma[k])
+ print " norm(rssdb2) = %e" %misc.snrm2(rssdb2)
+
+ print " abs(rtdb2) = %e" %abs(rtdb2 + dukappa
+ + xdot(c,dx) + ydot(b,dy) + blas.dot(hl,duzl)
+ + misc.sdot(hs,duzs))
+
+ A(dy, rxdb2, alpha=-1.0, beta=1.0, trans='T')
+ Gl(duzl, rxdb2, alpha=-1.0, beta=1.0, trans='T')
+ Gs(duzs, rxdb2, alpha=-1.0, beta=1.0, trans='T')
+ xaxpy(c, rxdb2, alpha=-dutau)
+ print " norm(rxdb2) = %e" \
+ %math.sqrt(xdot(rxdb2,rxdb2))
+
+ A(dx, rydb2, alpha=1.0, beta=1.0)
+ yaxpy(b, rydb2, alpha=-dutau)
+ print " norm(rydb2) = %e" \
+ %math.sqrt(ydot(rydb2,rydb2))
+ rzldb2 += dusl - hl*dutau
+ Gl(dx, rzldb2, alpha=1.0, beta=1.0)
+ print " norm(rzldb2) = %e" %blas.nrm2(rzldb2)
+
+ misc.saxpy(duss, rzsdb2)
+ misc.saxpy(hs, rzsdb2, alpha=-dutau)
+ Gs(dx, rzsdb2, alpha=1.0, beta=1.0)
+ print " norm(rzsdb2) = %e\n" %misc.snrm2(rzsdb2)
+
+ else:
+ solve_newton = solve_newton1
+
+ mu = blas.dot(lmbda,lmbda) / (m+1)
+
+ # Affine scaling step
+ blas.copy(lmbda, dsl, n=ml)
+ misc.had2(dsl,lmbda, n=ml)
+ misc.sscal(0.0, dss)
+ ind = ml
+ for e, mk in zip(dss, ms):
+ blas.copy(lmbda, e, n=mk, offsetx=ind, incy=mk+1)
+ blas.tbmv(lmbda, e, n=mk, k=0, ldA=1, offsetA=ind,
+ incx=mk+1)
+ ind += mk
+ dkappa[0] = kappa*tau
+ xcopy(resx, dx)
+ ycopy(resy, dy)
+ blas.copy(reszl, dzl)
+ misc.scopy(reszs, dzs)
+ dtau[0] = rest
+ solve_newton(dx, dy, dzl, dzs, dtau, dsl, dss, dkappa)
+
+ # Maximum step to boundary
+ blas.copy(dzl, sigz)
+ misc.ihad2(sigz, lmbda, n=ml)
+ blas.copy(dsl, sigs)
+ misc.ihad2(sigs, lmbda, n=ml)
+ misc.scopy(dss, ss)
+ misc.scopy(dzs, zs)
+ ind = ml
+ for k in xrange(len(ms)):
+ for i in xrange(ms[k]):
+ a = 1.0 / math.sqrt(lmbda[ind+i])
+ blas.scal(a, ss[k], offset=i, n=i+1, inc=ms[k])
+ blas.scal(a, ss[k], offset=i*ms[k]+i, n=ms[k]-i)
+ blas.scal(a, zs[k], offset=i, n=i+1, inc=ms[k])
+ blas.scal(a, zs[k], offset=i*ms[k]+i, n=ms[k]-i)
+ lapack.syevd(ss[k], sigs, offsetW=ind, jobz='V')
+ lapack.syevd(zs[k], sigz, offsetW=ind, jobz='V')
+ ind += ms[k]
+ sigz[-1], sigs[-1] = dtau[0]/lmbda[-1], dkappa[0]/lmbda[-1]
+ step = min(1.0, STEP / max(-min(sigz), -min(sigs)))
+
+ newmu = ( (1-step) * blas.dot(lmbda,lmbda) + step**2 *
+ (blas.dot(dsl, dzl) + misc.sdot(dss, dzs) +
+ dkappa[0]*dtau[0]) ) / ( m+1)
+ sigma = min(1.0, (newmu/mu)**EXPON)
+
+ # Centering-corrector step
+ misc.had2(dsl, dzl)
+ blas.axpy(misc.had(lmbda[:ml], lmbda[:ml]), dsl)
+ blas.axpy(ones, dsl, alpha=-sigma*mu, n=ml)
+ ind = ml
+ for k in xrange(len(ms)):
+ # work := dss[k] with upper triangular part
+ for i in xrange(ms[k]-1):
+ dss[k][i,i+1:] = dss[k][i+1:,i].trans()
+ dzs[k][i,i+1:] = dzs[k][i+1:,i].trans()
+ blas.copy(dss[k], work)
+
+ # dss[k] := 0.5 * (work*dzs[k] + dzs[k]*work)
+ # = 0.5 * (dss[k]*dzs[k] + dzs[k]*dss[k])
+ blas.syr2k(work, dzs[k], dss[k], n=ms[k], k=ms[k],
+ ldA=ms[k], alpha=0.5)
+
+ # dss[k] := dss[k] + diag(lambda)^2 - sigma*mu*I
+ blas.copy(lmbda, work, n=ms[k], offsetx=ind)
+ blas.tbmv(lmbda, work, n=ms[k], k=0, ldA=1, offsetA=ind)
+ blas.axpy(work, dss[k], incy=ms[k]+1, n=ms[k])
+ blas.axpy(ones, dss[k], alpha=-sigma*mu, incy=ms[k]+1,
+ n=ms[k])
+
+ ind += ms[k]
+
+ dkappa[0] = lmbda[-1]**2 + dkappa[0]*dtau[0] - sigma*mu
+ xcopy(resx, dx); xscal(1.0-sigma, dx)
+ ycopy(resy,dy); yscal(1.0-sigma, dy)
+ blas.copy(reszl, dzl); blas.scal(1.0-sigma, dzl)
+ misc.scopy(reszs, dzs); misc.sscal(1.0-sigma, dzs)
+ dtau[0] = (1.0-sigma)*rest
+ solve_newton(dx, dy, dzl, dzs, dtau, dsl, dss, dkappa)
+
+ # Maximum step to boundary
+ blas.copy(dzl, sigz)
+ misc.ihad2(sigz, lmbda, n=ml)
+ blas.copy(dsl, sigs)
+ misc.ihad2(sigs, lmbda, n=ml)
+ ind = ml
+ for k in xrange(len(ms)):
+ for i in xrange(ms[k]):
+ a = 1.0 / math.sqrt(lmbda[ind+i])
+ blas.scal(a, dss[k], offset=i, n=i+1, inc=ms[k])
+ blas.scal(a, dss[k], offset=i*(ms[k]+1), n=ms[k]-i)
+ blas.scal(a, dzs[k], offset=i, n=i+1, inc=ms[k])
+ blas.scal(a, dzs[k], offset=i*(ms[k]+1), n=ms[k]-i)
+ lapack.syevd(dss[k], sigs, offsetW=ind, jobz='V')
+ lapack.syevd(dzs[k], sigz, offsetW=ind, jobz='V')
+ ind += ms[k]
+ sigz[-1], sigs[-1] = dtau[0]/lmbda[-1], dkappa[0]/lmbda[-1]
+ step = min(1.0, STEP / max(-min(sigz), -min(sigs)))
+
+ # Update lmbdl, dli
+ dli = misc.ihad(dli, base.sqrt(misc.ihad(lmbda[:ml] + step*dsl,
+ lmbda[:ml] + step*dzl)))
+ lmbda[:ml] = base.sqrt(misc.had(lmbda[:ml]+step*dsl,
+ lmbda[:ml]+step*dzl))
+
+ dgi = dgi * math.sqrt( (lmbda[-1] + step*dtau[0]) /
+ (lmbda[-1] + step*dkappa[0]) )
+ lmbda[-1] = math.sqrt( (lmbda[-1] + step*dtau[0]) *
+ (lmbda[-1] + step*dkappa[0]) )
+
+ # Update scaling matrices, lmbdas, gamma.
+ ind = ml
+ for k in xrange(len(ms)):
+ for i in xrange(ms[k]):
+ # dss[k] := L1
+ # = lmbdas[k]^{1/2} * dss[k] * (1+step*sigs)^{1/2}
+ # dzs[k] := L2
+ # = lmbdas[k]^{1/2} * dzs[k] * (1+step*sigz)^{1/2}
+ a = math.sqrt(lmbda[ind+i])
+ blas.scal(a, dss[k], offset=i, inc=ms[k], n=ms[k])
+ blas.scal(a, dzs[k], offset=i, inc=ms[k], n=ms[k])
+ blas.scal(math.sqrt(1+step*sigs[ind+i]), dss[k],
+ offset=ms[k]*i, n=ms[k])
+ blas.scal(math.sqrt(1+step*sigz[ind+i]), dzs[k],
+ offset=ms[k]*i, n=ms[k])
+
+ # r[k] := r[k]*dss[k] = r[k]*L1[k]
+ # rti[k] := rti[k]*dzs[k] = rti[k]*L2[k]
+ blas.gemm(r[k], dss[k], work, ldC=ms[k])
+ blas.copy(work, r[k], n=ms[k]**2)
+ blas.gemm(rti[k], dzs[k], work, ldC=ms[k])
+ blas.copy(work, rti[k], n=ms[k]**2)
+
+ # SVD of L2'*L1 = U*lmbds^+*V', store U in dss[k] and V' in
+ # dzs[k]
+ blas.gemm(dzs[k], dss[k], work, transA='T', ldC=ms[k])
+ lapack.gesvd(work, lmbda, jobu='A', jobvt='A', m=ms[k],
+ n=ms[k], ldA=ms[k], U=dss[k], Vt=dzs[k], offsetS=ind)
+
+ # r[k] := r[k]*V, rti[k] := rti[k]*U
+ blas.gemm(r[k], dzs[k], work, transB='T', ldC=ms[k])
+ blas.copy(work, r[k], n=ms[k]**2)
+ blas.gemm(rti[k], dss[k], work, ldC=ms[k])
+ blas.copy(work, rti[k], n=ms[k]**2)
+
+ # r[k] := r[k]*lambda^{-1/2}; rti[k] := rti[k]*lambda^{-1/2}
+ for i in xrange(ms[k]):
+ a = 1.0 / math.sqrt(lmbda[ind+i])
+ blas.scal(a, r[k], offset=ms[k]*i, n=ms[k])
+ blas.scal(a, rti[k], offset=ms[k]*i, n=ms[k])
+
+ # gamma[k][i,j] = .5 * (lambda_i + lambda_j)
+ # Use blas.ger to make sure there are no zeros or nan's in
+ # upper triangular part.
+
+ blas.scal(0.0, gamma[k])
+ blas.ger(lmbda, ones, gamma[k], alpha=.5, offsetx=ind)
+ blas.ger(ones, lmbda, gamma[k], alpha=.5, offsety=ind)
+
+ ind += ms[k]
+
+
+ # Compute new sl, zl, ss, zs, tau, kappa (used to evaluate the
+ # residuals).
+
+ # sl := lmbdl ./ dli
+ blas.copy(lmbda, sl, n=ml)
+ misc.ihad2(sl, dli)
+
+ # zl = lmbdl .* dli
+ blas.copy(lmbda, zl, n=ml)
+ misc.had2(zl, dli)
+
+ kappa, tau = lmbda[-1]/dgi, lmbda[-1]*dgi
+
+ # ss = r*lambda*r', zs = rti*lambda*rti'
+ ind = ml
+ for k in xrange(len(ms)):
+ blas.copy(r[k], work)
+ blas.copy(rti[k], work2)
+ for i in xrange(ms[k]):
+ a = math.sqrt(lmbda[ind+i])
+ blas.scal(a, work, offset=ms[k]*i, n=ms[k])
+ blas.scal(a, work2, offset=ms[k]*i, n=ms[k])
+ blas.syrk(work, ss[k], ldA=ms[k], n=ms[k], k=ms[k])
+ blas.syrk(work2, zs[k], ldA=ms[k], n=ms[k], k=ms[k])
+ ind += ms[k]
+
+ xaxpy(dx, x, alpha=step)
+ yaxpy(dy, y, alpha=step)
+
+ gap = blas.dot(lmbda, lmbda, n=m-1) / tau**2
+
+
+ return {'status': 'unknown', 'x': None, 'y': None, 'sl': None,
+ 'ss': None, 'zl': None, 'zs': None}
+
+
+
+def lp(c, G, h, A=None, b=None, solver=None, primalstart=None,
+ dualstart=None):
+ """
+
+ Solves a pair of primal and dual LPs
+
+ minimize c'*x maximize -h'*z - b'*y
+ subject to G*x + s = h subject to G'*z + A'*y + c = 0
+ A*x = b z >= 0
+ s >= 0
+
+ Input arguments:
+
+ G is mxn, h is mx1, A is pxn, b is px1. G and A must be dense
+ or sparse 'd' matrices. h and b are dense 'd' matrices with
+ one column. The default values for A and b are empty matrices
+ with zero rows.
+
+ solver is None, 'glpk' or 'mosek'. The default solver (None)
+ uses an LP solver implemented in Python. The 'glpk' solver is
+ the simplex LP solver from GLPK. The 'mosek' solver is the LP
+ solver from MOSEK.
+
+ The arguments primalstart and dualstart are ignored when solver
+ is 'glpk' or 'mosek' and are optional when solver is None.
+ The argument primalstart is a dictionary with keys 'x' and 's'
+ and specifies a primal starting point. primalstart['x'] must
+ be a dense 'd' matrix of length n; primalstart['s'] must be a
+ positive dense 'd' matrix of length m.
+ The argument dualstart is a dictionary with keys 'z' and 'y'
+ and specifies a dual starting point. dualstart['y'] must
+ be a dense 'd' matrix of length p; dualstart['z'] must be a
+ positive dense 'd' matrix of length m.
+
+ When solver is None, we require n >= 1, Rank(A) = p and
+ Rank([G; A]) = n
+
+
+ Returns a dictionary with keys 'status', 'x', 's', 'y', 'z'.
+
+ If solver is None or 'mosek':
+
+ If status is 'optimal', x, s, y, z are the primal and dual
+ optimal solutions.
+
+ If status is 'primal infeasible', x = s = None, and z, y
+ are a proof of infeasibility:
+
+ h'*z + b'*y = -1, G'*z + A'*y = 0, z >= 0.
+
+ If status is 'dual infeasible', z = y = None, and x, s are
+ a proof of dual infeasibility:
+
+ c'*x = -1, G*x + s = 0, A*x = 0, s >= 0.
+
+ If status is 'unknown', x, y, s, z are None.
+
+
+ If solver is 'glpk':
+
+ If status is 'optimal', x, s, y, z are the primal and dual
+ optimal solutions.
+
+ If status is 'primal infeasible', 'dual infeasible',
+ or 'unknown', then x = s = z = y = None.
+
+
+ The control parameters for the different solvers can be modified by
+ adding an entry to the dictionary cvxopt.solvers.options. The
+ following parameters control the execution of the default solver.
+
+ options['show_progress'] True/False (default: True)
+ options['maxiters'] positive integer (default: 100)
+ options['abstol'] scalar (default: 1e-7)
+ options['reltol'] scalar (default: 1e-7)
+ options['feastol'] scalar (default: 1e-7)
+ options['refinement'] True/False (default: True)
+
+ The control parameter names for GLPK and MOSEK can be found in the
+ GLPK and MOSEK documentation. Options that are not recognized are
+ replaced by their default values.
+ """
+
+ if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
+ raise TypeError, "'c' must be a dense column matrix"
+ n = c.size[0]
+ if n < 1: raise ValueError, "number of variables must be at least 1"
+
+ if (type(G) is not matrix and type(G) is not spmatrix) or \
+ G.typecode != 'd' or G.size[1] != n:
+ raise TypeError, "'G' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ m = G.size[0]
+ if type(h) is not matrix or h.typecode != 'd' or h.size != (m,1):
+ raise TypeError, "'h' must be a 'd' matrix of size (%d,1)" %m
+
+ if A is None: A = spmatrix([], [], [], (0,n), 'd')
+ if (type(A) is not matrix and type(A) is not spmatrix) or \
+ A.typecode != 'd' or A.size[1] != n:
+ raise TypeError, "'A' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ p = A.size[0]
+ if b is None: b = matrix(0.0, (0,1))
+ if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
+ raise TypeError, "'b' must be a dense matrix of size (%d,1)" %p
+
+ if solver == 'glpk':
+ try: from cvxopt import glpk
+ except ImportError: raise ValueError, "invalid option "\
+ "(solver='glpk'): cvxopt.glpk is not installed"
+ glpk.options = options
+ status, x, z, y = glpk.solvelp(c,G,h,A,b)
+ if status == 'optimal':
+ s = matrix(h)
+ base.gemv(G, x, s, alpha=-1.0, beta=1.0)
+ else:
+ s = None
+ return {'status': status, 'x': x, 's': s, 'y': y, 'z': z}
+
+ if solver == 'mosek':
+ try: from cvxopt import mosek
+ except ImportError: raise ValueError, "invalid option "\
+ "(solver='mosek'): cvxopt.mosek is not installed"
+ mosek.options = options
+ prosta, solsta, x, z, y = mosek.solvelp(c,G,h,A,b)
+ if solsta == 'OPTIMAL':
+ s = matrix(h)
+ base.gemv(G, x, s, alpha=-1.0, beta=1.0)
+ status = 'optimal'
+ elif solsta == 'PRIMAL_INFEASIBLE_CER':
+ status = 'primal infeasible'
+ ducost = -blas.dot(h,z) - blas.dot(b,y)
+ blas.scal(1.0/ducost, y)
+ blas.scal(1.0/ducost, z)
+ x, s = None, None
+ elif solsta == 'DUAL_INFEASIBLE_CER':
+ status = 'dual infeasible'
+ pcost = blas.dot(c,x)
+ blas.scal(-1.0/pcost, x)
+ s = matrix(0.0, (m,1))
+ base.gemv(G, x, s, alpha=-1.0)
+ z, y = None, None
+ else:
+ status = 'unknown'
+ x, s, y, z = None, None, None, None
+ return {'status': status, 'x': x, 's': s, 'y': y, 'z': z}
+
+ if p > n or n-p > m:
+ raise ValueError, "Rank(A) < p or Rank([G; A]) < n"
+
+ def Fi(x, y, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(G, x, y, alpha=alpha, beta=beta, trans=trans)
+
+ def Fe(x, y, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(A, x, y, alpha=alpha, beta=beta, trans=trans)
+
+ def Fs(x, y, alpha=1.0, beta=0.0, trans='N'):
+ pass
+
+
+ # kktsolver(di, rti) returns a function for solving
+ #
+ # [ 0 A' G' ] [x] [bx]
+ # [ A 0 0 ] [y] = [by].
+ # [ G 0 -diag(di)^{-2} ] [z] [bz]
+ #
+ # di is a positive mx1 'd' matrix; the argument rti is ignored.
+ #
+ # We return the scaled z: z./di instead of z.
+
+ global kktmethod
+ try: kktmethod = options['kktmethod']
+ except KeyError: kktmethod = 3
+ else:
+ if type(kktmethod) is not int or kktmethod not in [1,2,3]:
+ raise ValueError, "options['kktmethod'] must be 1, 2, or 3"
+
+ if kktmethod == 1:
+
+ # The entire matrix is factored using a dense LDL factorization.
+
+ K = matrix(0.0, (n+p+m,n+p+m))
+ ipiv = matrix(0, (n+p+m,1))
+ u = matrix(0.0, (n+p+m,1))
+ def kktsolver(di, rti):
+ blas.scal(0, K)
+ K[n:n+p,:n], K[n+p:,:n] = A, G
+ K[(m+p+n+1)*(p+n)::n+m+p+1] = -misc.ihad(1.0,
+ misc.had(di, di))
+ lapack.sytrf(K, ipiv)
+ def solve_kkt(x, y, z, zs):
+ blas.copy(x, u)
+ blas.copy(y, u, offsety=n)
+ blas.copy(z, u, offsety=n+p)
+ lapack.sytrs(K, ipiv, u)
+ blas.copy(u, x, n=n)
+ blas.copy(u, y, offsetx=n, n=p)
+ blas.copy(u, z, offsetx=n+p, n=m)
+ misc.ihad2(z, di)
+ return solve_kkt
+
+ else:
+ if type(G) is matrix:
+ Gsc = matrix(0.0, (m,n))
+ else:
+ Gsc = spmatrix(0.0, G.I, G.J, (m,n))
+
+ def GDG(Gsc, S, di, pattern_S_is_correct=True):
+
+ # Compute
+ #
+ # Gsc := diag(di)*G and
+ # S[:n,:n] := G' * diag(di)^2 * G.
+ #
+ # If G is dense, Gsc and S must be dense. If G is sparse,
+ # Gsc is sparse and S may be dense or sparse.
+
+ base.gemm(spmatrix(di, range(m), range(m), tc='d'), G,
+ Gsc, partial=True)
+ base.syrk(Gsc, S, trans='T', partial=pattern_S_is_correct)
+
+ if kktmethod == 2:
+
+ # We compute x, y, z by solving
+ #
+ # [G'*diag(di)^2*G A'] [x] [bx + G'*(di.^2).*bz)]
+ # [ ]*[ ] = [ ]
+ # [A 0 ] [y] [by ]
+ #
+ # z = (di.^2) .* (G*x - bz).
+ #
+ # We return the scaled z: z = di .* (G*x - bz).
+ #
+ # The coefficient matrix is factored using a dense LDL
+ # (if p>0) or dense Cholesky factorization (if p=0).
+
+ K = matrix(0.0, (n+p,n+p))
+ if p: ipiv = matrix(0, (n+p,1))
+ u = matrix(0.0, (n+p,1))
+ def kktsolver(di, rti):
+ blas.scal(0.0, K)
+ K[n:,:n] = A
+ GDG(Gsc, K, di)
+ if p: lapack.sytrf(K, ipiv)
+ else: lapack.potrf(K)
+ def solve_kkt(x, y, z, zs):
+ blas.copy(x, u)
+ blas.copy(y, u, offsety=n)
+ misc.had2(z, di)
+ base.gemv(Gsc, z, u, trans='T', beta=1.0)
+ if p: lapack.sytrs(K, ipiv, u)
+ else: lapack.potrs(K, u)
+ blas.copy(u, x, n=n)
+ blas.copy(u, y, n=p, offsetx=n)
+ base.gemv(Gsc, x, z, beta=-1.0)
+ return solve_kkt
+
+ else:
+
+ # Solve
+ #
+ # K*y = A * S^{-1} * (bx + G'*((di.^2).*bz)) - by
+ # S*x = bx + G'*((di.^2).*bz) - A'*y
+ # z = (di.^2) .* (G*x - bz).
+ #
+ # where K = A*S^{-1}*A', S = G'*diag(di)^2*G.
+ #
+ # If in the first call to kktsolver, S is singular, switch
+ # to kktmethod 4, i.e., solve
+ #
+ # K*y = A * S^{-1} * (bx + G'*((di.^2).*bz) + A'*by) - by
+ # S*x = bx + G'*((di.^2).*bz) + A'*by - A'*y
+ # z = (di.^2) .* (G*x - bz).
+ #
+ # where K = A'*S^{-1}*A, S = G'*diag(di)^2*G + A'*A
+ #
+ # The matrices K and S are factored using dense or sparse
+ # Cholesky factorizations.
+ #
+ # We return the scaled z: z = di .* (G*x - bz).
+
+ global S, Sf, firstcall
+ firstcall = True
+
+ if type(G) is matrix:
+ S = matrix(0.0, (n,n))
+ K = matrix(0.0, (p,p))
+ else:
+ S = spmatrix([], [], [], (n,n), 'd')
+ if type(A) is matrix: K = matrix(0.0, (p,p))
+ else: K = spmatrix([], [], [], (p,p), tc='d')
+
+ def factorS(di,S):
+
+ # Factor S = G'*diag(di)^2*G if kktmethod = 3.
+ # Factor S = G'*diag(di)^2*G + A'*A if kktmethod = 4.
+ # If S is sparse, store factorization in Sf.
+
+ global Sf
+ GDG(Gsc, S, di, not firstcall)
+ if kktmethod == 4:
+ base.syrk(A, S, trans='T', beta=1.0, partial=not
+ firstcall)
+ if type(S) is matrix:
+ lapack.potrf(S)
+ else:
+ if firstcall: Sf = cholmod.symbolic(S)
+ cholmod.numeric(S, Sf)
+
+ def kktsolver(di, rti):
+ global firstcall, kktmethod, S
+ if kktmethod == 3:
+ try: factorS(di,S)
+ except ArithmeticError:
+ if firstcall:
+ kktmethod = 4
+ if type(S) is spmatrix and type(A) is \
+ matrix: S = matrix(0.0, (n,n))
+ factorS(di,S)
+ else: raise ArithmeticError
+ else:
+ factorS(di,S)
+ firstcall = False
+
+ if type(S) is matrix:
+ # Asct := L^{-1}*A', factor K = Asct'*Asct
+ if type(A) is matrix:
+ Asct = A.trans()
+ else:
+ Asct = matrix(A.trans())
+ blas.trsm(S, Asct)
+ blas.syrk(Asct, K, trans='T')
+ lapack.potrf(K)
+
+ else:
+ # Asct := L^{-1}*P*A' and factor K = Asct'*Asct.
+ if type(A) is matrix:
+ Asct = A.trans()
+ cholmod.solve(Sf, Asct, sys=7)
+ cholmod.solve(Sf, Asct, sys=4)
+ blas.syrk(Asct, K, trans='T')
+ lapack.potrf(K)
+ else:
+ Asct = cholmod.spsolve(Sf, A.trans(), sys=7)
+ Asct = cholmod.spsolve(Sf, Asct, sys=4)
+ base.syrk(Asct, K, trans='T')
+ Kf = cholmod.symbolic(K)
+ cholmod.numeric(K, Kf)
+
+ def solve_kkt(x, y, z, zs):
+
+ # If kktmethod is 3:
+ # x := L^{-1}*P * (x + G'*((di.^2).*z))
+ # = L^{-1}*P * (bx + G'*((di.^2).*bz))
+ #
+ # If kktmethod is 4:
+ # x := L^{-1}*P * (x + G'*((di.^2).*z) + A'*y)
+ # = L^{-1}*P * (bx + G'*((di.^2).*bz) + A'*by)
+ misc.had2(z, di)
+ base.gemv(Gsc, z, x, trans='T', beta=1.0)
+ if kktmethod == 4:
+ base.gemv(A, y, x, trans='T', beta=1.0)
+ if type(S) is matrix:
+ blas.trsv(S, x)
+ else:
+ cholmod.solve(Sf, x, sys=7)
+ cholmod.solve(Sf, x, sys=4)
+
+ # y := K^{-1} * (Asc*x - y)
+ # = K^{-1} * (A*S^{-1}* (bx + G'*((di.^2).*bz))
+ # - by) (kktmethod = 3)
+ # = K^{-1} * (A*S^{-1}* (bx + G'*((di.^2).*bz))
+ # + A'*by) - by) (kktmethod = 4)
+ base.gemv(Asct, x, y, trans='T', beta=-1.0)
+ if type(K) is matrix:
+ lapack.potrs(K, y)
+ else:
+ cholmod.solve(Kf, y)
+
+ # x := P' * L^{-T} * (x - Asc'*y)
+ # = S^{-1}* (bx + G'*((di.^2).*bz) - A'*y)
+ # (kktmethod = 3)
+ # = S^{-1}*(bx + G'*((di.^2).*bz) + A'*by -
+ # A'*y) (kktmethod = 4)
+ base.gemv(Asct, y, x, alpha=-1.0, beta=1.0)
+ if type(S) is matrix:
+ blas.trsv(S, x, trans='T')
+ else:
+ cholmod.solve(Sf, x, sys=5)
+ cholmod.solve(Sf, x, sys=8)
+
+ # z := Gsc*x - z = di .* (G*x - bz)
+ base.gemv(Gsc, x, z, beta=-1.0)
+
+ return solve_kkt
+
+ if primalstart:
+ pst = {'x': primalstart['x'], 'sl': primalstart['s'], 'ss': []}
+ else:
+ pst = None
+ if dualstart:
+ dst = {'y': dualstart['y'], 'zl': dualstart['z'], 'zs': []}
+ else:
+ dst = None
+ sol = conelp(c, kktsolver, Gl=Fi, hl=h, A=Fe, b=b, primalstart=pst,
+ dualstart=dst)
+ return {'status': sol['status'], 'x': sol['x'], 'y': sol['y'],
+ 'z': sol['zl'], 's': sol['sl']}
+
+
+
+def sdp(c, Gl=None, hl=None, Gs=None, hs=None, A=None, b=None,
+ solver=None, primalstart=None, dualstart=None):
+ """
+
+ Solves a pair of primal and dual SDPs
+
+ minimize c'*x
+ subject to Gl*x + sl = hl
+ Gs(x) + ss = hs
+ A*x = b
+ sl >= 0, ss >= 0
+
+ maximize -hl'*z - tr(hs,zs) - b'*y
+ subject to Gl'*zl + Gs'(zs) + A'*y + c = 0
+ zl >= 0, zs >= 0
+
+ Input arguments:
+
+ Gl is an mlxn dense or sparse 'd' matrix.
+ hl is an mlx1 dense 'd' matrix. The default values of Gl and
+ hl are matrices with zero rows.
+
+ The argument Gs is a list of N dense or sparse 'd' matrices of
+ size (ms[k]**2, n), k=1,...,N.
+ The matrix-vector products Gs[k]*x, k=1,...,N, represent a
+ block-diagonal symmetric matrix with N diagonal blocks of size
+ (ms[k],ms[k]), stored columnwise as vectors.
+ hs is a list of dense 'd' matrices of size (ms[k],ms[k]).
+ Only the lower-triangular part of hs[k] is accessed.
+
+ A is a pxn dense or sparse 'd' matrix.
+ b is a px1 dense 'd' matrix. The default values of A and b are
+ matrices with zero rows.
+
+ solver is None or 'dsdp'. The default solver (None) uses an
+ SDP solver implemented in Python. The 'dsdp' solver uses an
+ interface to DSDP5. It does not accept problems with equality
+ constraints (A and b must have zero rows, or be absent).
+
+ The argument primalstart is a dictionary with keys 'x', 'sl',
+ 'ss', and specifies a primal starting point. primalstart['x']
+ must be a dense 'd' matrix of length n; primalstart['sl'] must
+ be a positive dense 'd' matrix of length ml; primalstart['ss']
+ must be a list of positive definite matrices of size
+ ms[k]xms[k].
+ The argument dualstart is a dictionary with keys 'zl', 'zs',
+ 'y' and specifies a dual starting point. primalstart['y']
+ must be a dense 'd' matrix of length p; primalstart['zl']
+ must be a positive dense 'd' matrix of length ml;
+ primalstart['zs'] must be a list of positive definite matrices
+ of size (ms[k],ms[k]).
+ The arguments primalstart and dualstart are ignored when solver
+ is 'dsdp'.
+
+ Returns a dictionary with keys 'status', 'x', 'sl', 'ss', 'y', 'zl',
+ 'zs'.
+
+ If status is 'optimal', x, sl, ss, y, zl, zs are the primal and
+ dual optimal solutions.
+
+ If status is 'primal infeasible', x = sl = ss = None, and zl,
+ zs, y are a proof of infeasibility:
+
+ hl'*zl + tr(hs,zs) + b'*y = -1,
+ Gl'*zl + Gs'(zs) + A'*y = 0,
+ zl >= 0, zs >= 0.
+
+ If status is 'dual infeasible', zl = zs = y = None, and x, sl,
+ ss are a proof of dual infeasibility:
+
+ c'*x = -1, Gl*x + sl = 0, Gs(x) + ss = 0, A*x = 0,
+ sl >= 0, ss >= 0.
+
+ If status is 'unknown', x, y, sl, ss, zl, zs are None.
+
+ The following parameters control the execution of the default
+ solver.
+
+ options['show_progress'] True/False (default: True)
+ options['maxiters'] positive integer (default: 100)
+ options['abstol'] scalar (default: 1e-7)
+ options['reltol'] scalar (default: 1e-7)
+ options['feastol'] scalar (default: 1e-7)
+ options['refinement'] True/False (default: True).
+
+ The execution of the 'dsdp' solver is controlled by:
+
+ options['show_progress'] integer (default: 0)
+ options['maxiters'] positive integer
+ options['rgaptol'] scalar (default: 1e-5).
+ """
+
+ if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
+ raise TypeError, "'c' must be a dense column matrix"
+ n = c.size[0]
+ if n < 1: raise ValueError, "number of variables must be at least 1"
+
+ if Gl is None: Gl = spmatrix([], [], [], (0,n), tc='d')
+ if (type(Gl) is not matrix and type(Gl) is not spmatrix) or \
+ Gl.typecode != 'd' or Gl.size[1] != n:
+ raise TypeError, "'Gl' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ ml = Gl.size[0]
+ if hl is None: hl = matrix(0.0, (0,1))
+ if type(hl) is not matrix or hl.typecode != 'd' or \
+ hl.size != (ml,1):
+ raise TypeError, "'hl' must be a 'd' matrix of size (%d,1)" %ml
+
+ if Gs is None: Gs = []
+ if type(Gs) is not list or [ Gs_k for Gs_k in Gs if (type(Gs_k) is
+ not matrix and type(Gs_k) is not spmatrix) or
+ Gs_k.typecode != 'd' or Gs_k.size[1] != n ]:
+ raise TypeError, "'Gs' must be a list of sparse or dense 'd' "\
+ "matrices with %d columns" %n
+ ms = [ int(math.sqrt(Gs_k.size[0])) for Gs_k in Gs ]
+ maxm, N = max([0] + ms), len(ms)
+ a = [ k for k in xrange(len(Gs)) if ms[k]**2 != Gs[k].size[0] ]
+ if a: raise TypeError, "the squareroot of the number of rows in "\
+ "'Gs[%d]' is not an integer" %k
+ if hs is None: hs = []
+ if type(hs) is not list or len(hs) != N or [ k for k in xrange(N)
+ if type(hs[k]) not in (matrix, spmatrix) or
+ hs[k].typecode != 'd' or hs[k].size != (ms[k],ms[k]) ]:
+ raise TypeError, "'hs' must be a list of %d dense or sparse "\
+ "'d' matrices of size (%d,%d)" %(N,ms[k],ms[k])
+
+ if A is None: A = spmatrix([], [], [], (0,n), 'd')
+ if (type(A) is not matrix and type(A) is not spmatrix) or \
+ A.typecode != 'd' or A.size[1] != n:
+ raise TypeError, "'A' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ p = A.size[0]
+ if b is None: b = matrix(0.0, (0,1))
+ if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
+ raise TypeError, "'b' must be a dense matrix of size (%d,1)" %p
+
+ if p > n or n-p > ml+ sum([mk*(mk+1)/2 for mk in ms]):
+ raise ValueError, "Rank(A) < p or Rank([Gl; Gs; A]) < n"
+
+ if not sum(ms): # call lp()
+ if primalstart is not None:
+ ps = primalstart.copy()
+ if ps.has_key('sl'): ps['s'] = ps['sl']
+ else:
+ ps = None
+ if dualstart is not None:
+ ds = dualstart.copy()
+ if ds.has_key('zl'): ds['z'] = ds['zl']
+ else:
+ ds = None
+ sol = lp(c, Gl, hl, A, b, solver=solver, primalstart=ps,
+ dualstart=ds)
+ sol['sl'] = sol['s']; del sol['s']
+ sol['ss'] = [ matrix(0.0, (0,0)) for k in xrange(N)]
+ sol['zl'] = sol['z']; del sol['z']
+ sol['zs'] = [ matrix(0.0, (0,0)) for k in xrange(N)];
+ return sol
+
+ if solver == 'dsdp':
+ try: from cvxopt import dsdp
+ except ImportError: raise ValueError, "invalid option "\
+ "(solver = 'dsdp'): cvxopt.dsdp is not installed"
+ dsdp.options = options
+ if p: raise ValueError, "sdp() with the 'solver=dsdp' option "\
+ "does not handle problems with equality constraints"
+ dsdpstatus, x, r, zl, zs = dsdp.sdp(c, Gl, hl, Gs, hs)
+ sl = hl - Gl*x
+ ss = [ hs[k] - matrix(Gs[k]*x, hs[k].size) for k in
+ xrange(len(hs)) ]
+ if dsdpstatus == 'DSDP_PDFEASIBLE':
+ y = matrix(0.0, (0,1))
+ status = 'optimal'
+ elif dsdpstatus == 'DSDP_UNBOUNDED':
+ pcost = blas.dot(c,x)
+ x /= -pcost
+ sl /= -pcost
+ ss = [sk / -pcost for sk in ss]
+ zl, zs = None, None
+ status = 'dual infeasible'
+ elif dsdpstatus == 'DSDP_INFEASIBLE':
+ dcost = -blas.dot(hl,zl) - misc.sdot(hs, zs)
+ zl /= -dcost
+ zs = [zs / -docst for zk in zs]
+ y = matrix(0.0, (0,1))
+ x, sl, ss = None, None, None
+ status = 'primal infeasible'
+ else:
+ status = 'unknown'
+ x, sl, ss, y, zl, zs, = None, None, None, None, None, None
+
+ return {'status': status, 'x': x, 'y': y, 'sl': sl, 'ss': ss,
+ 'zl': zl, 'zs': zs}
+
+
+ def Fi(x, y, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(Gl, x, y, alpha=alpha, beta=beta, trans=trans)
+
+ def Fs(x, y, alpha=1.0, beta=0.0, trans='N'):
+ if trans == 'N':
+ for k in xrange(N):
+ # y[k] := alpha*mat(Gs[k]*x) + beta*y[k]
+ base.gemv(Gs[k], x, y[k], alpha=alpha, beta=beta)
+
+ else:
+ # y[i] := alpha*sum_k tr(mat(Gs[k][:,i])*x[k]) + beta*y[i]
+ # for i=0,...,n-1.
+
+ for k in xrange(N):
+ # Scale diagonal of x[k] by 1/2 and set the upper
+ # triangular part to zero, so that the matrix product
+ # of Gs[k]' and vec(x[k]) is equal to the inner
+ # product of mat(Gs[k][:j]) with x[k]. Then make the
+ # matrix-vector product.
+ blas.scal(0.5, x[k], inc=ms[k]+1)
+ for j in xrange(ms[k]):
+ blas.scal(0.0, x[k], offset=j+ms[k]*(j+1),
+ inc=ms[k])
+ if k == 0:
+ base.gemv(Gs[k], x[k], y, alpha=2*alpha, beta=beta,
+ trans='T')
+ else:
+ base.gemv(Gs[k], x[k], y, alpha=2*alpha, beta=1.0,
+ trans='T')
+ blas.scal(2.0, x[k], inc=ms[k]+1)
+
+ def Fe(x, y, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(A, x, y, alpha=alpha, beta=beta, trans=trans)
+
+
+ # kktsolver(di, rti) returns a function for solving
+ #
+ # [ 0 A' Gl' Gs()' ] [x ] [bx ]
+ # [ A 0 0 0 ] [y ] = [by ].
+ # [ Gl 0 -diag(d)^2 0 ] [zl] [bzl]
+ # [ Gs 0 0 -r*r'*()*r*r' ] [zs] [bzs]
+ #
+ # di = 1./d is a positive mx1 'd' matrix;
+ # rti = inv(r') is a list of square matrices.
+ #
+ # The scaled zl and zs are returned: d.*zl instead of zl, r'*zs*r
+ # instead of zs.
+
+ global kktmethod
+ try: kktmethod = options['kktmethod']
+ except KeyError: kktmethod = 5
+ else:
+ if type(kktmethod) is not int or kktmethod not in [1,4,5]:
+ raise ValueError, "options['kktmethod'] must be 1, 4, or 5"
+
+ if kktmethod == 1:
+
+ # The matrix
+ #
+ # [ 0 A' Glsc' Gssc()' ]
+ # [ A 0 0 0 ]
+ # [ Glsc 0 -I 0 ]
+ # [ Gssc 0 0 -(1/2)*I ]
+ #
+ # is factored as LDL, with:
+ #
+ # Glsc = diag(d)^{-1}*G = diag(di)*G
+ # Gssc() = rti'*Gs()*rti in packed storage with diagonal
+ # elements scaled by 1/sqrt(2).
+
+ pms = [ mk*(mk+1)/2 for mk in ms ]
+ K = matrix(0.0, (n+p+ml+sum(pms), n+p+ml+sum(pms)))
+ ipiv = matrix(0, (K.size[0],1))
+ Gssc = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ u = matrix(0.0, (K.size[0],1))
+
+ def kktsolver(di, rti):
+ blas.scal(0.0, K)
+
+ # 3,3-block of K is -I.
+ K[ (K.size[0]+1)*(p+n) : (K.size[0]+1)*(p+n+ml):
+ K.size[0]+1 ] = -1.0
+
+ # 4,4-block of K is -I/2.
+ K[ (K.size[0]+1)*(p+n+ml) :: K.size[0]+1 ] = -0.5
+
+ # 2,1-block of K is A.
+ K[n:n+p,:n] = A
+
+ # 3,1-block of K is diag(di)*Gl.
+ K[n+p:n+p+ml, :n] = Gl
+ for k in xrange(ml):
+ blas.scal(di[k], K, n=n, offset=n+p+k, inc=K.size[0])
+
+ # 4,1-block of K is rti'*G()*rti in packed storage with
+ # diagonal elements scaled by 1/sqrt(2).
+ for j in xrange(n):
+ # Gssc = rti' * mat(Gs[:,j]) * rti.
+ for k in xrange(N): Gssc[k][:] = Gs[k][:,j]
+ misc.cngrnc(rti, Gssc, Gssc, trans='T')
+
+ # copy Gssc in packed storage to column j of K
+ ind = n+p+ml + j*K.size[0]
+ for k in xrange(N):
+ blas.scal(1.0/math.sqrt(2), Gssc[k], inc=ms[k]+1)
+ for i in xrange(ms[k]):
+ blas.copy(Gssc[k], K, n=ms[k]-i,
+ offsetx=(ms[k]+1)*i, offsety=ind)
+ ind += ms[k]-i
+
+ lapack.sytrf(K, ipiv)
+
+ def solve_kkt(x, y, zl, zs):
+
+ # Solve
+ #
+ # [0 A' Glsc' Gssc()'] [x ] [bx ]
+ # [A 0 0 0 ] [y ] = [by ]
+ # [Glsc 0 -I 0 ] [d.*zl ] [di.*zl ]
+ # [Gssc 0 0 -(1/2)*I] [2*r'*zs*r] [rti'*zs*rti]
+ #
+ # and return x, y, d.*zl, r'*zs*r.
+
+ blas.copy(x, u)
+ blas.copy(y, u, offsety=n)
+ misc.had2(zl, di)
+ blas.copy(zl, u, offsety=n+p)
+ misc.cngrnc(rti, zs, zs, trans='T')
+ ind = n+p+ml
+ for k in xrange(N):
+ blas.scal(1.0/math.sqrt(2), zs[k], inc=ms[k]+1)
+ for i in xrange(ms[k]):
+ blas.copy(zs[k], u, n=ms[k]-i,
+ offsetx=(ms[k]+1)*i, offsety=ind)
+ ind += ms[k]-i
+ lapack.sytrs(K, ipiv, u)
+ blas.copy(u, x, n=n)
+ blas.copy(u, y, offsetx=n, n=p)
+ blas.copy(u, zl, offsetx=n+p, n=ml)
+ ind = n+p+ml
+ for k in xrange(N):
+ for i in xrange(ms[k]):
+ blas.copy(u, zs[k], offsetx=ind,
+ offsety=i*(ms[k]+1), n=ms[k]-i)
+ zs[k][i,i] *= math.sqrt(2)
+ ind += ms[k]-i
+ misc.sscal(0.5, zs)
+
+ return solve_kkt
+
+ elif kktmethod == 2:
+
+ pass # not implemented
+
+ elif kktmethod == 3:
+
+ pass # not implemented
+
+ elif kktmethod == 4:
+
+ # Factor the matrices
+ #
+ # S = Gl'*diag(di)^2*Gl + Gs'(rti*rti'*Gs(x)*rti*rti')
+ # + A'*A
+ # K = A*S^{-1}*A'.
+ #
+ # Solve for y, x:
+ #
+ # K*y = A * S^{-1} * (bx + Gl'*diag(di)^2*bzl
+ # + Gs'(rti*rti'*bzs*rti*rti') + A'*by) - by
+ # S*x = bx + Gl'*diag(di)^2*bzl + Gs'(rti*rti'*bzs*rti*rti')
+ # + A'*by - A'*y.
+ #
+ # Compute scaled zl, zs:
+ #
+ # zl = di .* (Gl*x - bzl)
+ # zs = rti' * (Gs(x) - bzs) * rti.
+
+ S, K = matrix(0.0, (n,n)), matrix(0.0, (p,p))
+ if type(Gl) is matrix:
+ Glsc = matrix(0.0, (ml,n))
+ else:
+ Glsc = spmatrix(0.0, Gl.I, Gl.J, (ml,n))
+ T = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ Gssc = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ zsc = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+
+ def kktsolver(di, rti):
+
+ # S = Gl'*diag(di)^2*Gl
+ base.gemm(spmatrix(di, range(ml), range(ml), tc='d'), Gl,
+ Glsc, partial=True)
+ base.syrk(Glsc, S, trans='T')
+
+ # T = rti*rti' as a nonsymmetric matrix
+ for k in xrange(N):
+ blas.gemm(rti[k], rti[k], T[k], transB='T')
+
+ for j in xrange(n):
+ # Gssc[k] = T[k] * mat(Gs[k][:,j]) * T[k]
+ for k in xrange(N): Gssc[k][:] = Gs[k][:,j]
+ misc.cngrnc(T, Gssc, Gssc, trans='T')
+
+ # N matrix vector products to get lower triangular part
+ # of column j of S.
+ for k in xrange(N):
+ blas.scal(0.5, Gssc[k], inc=ms[k]+1)
+ for i in xrange(ms[k]):
+ blas.scal(0.0, Gssc[k], offset=i+ms[k]*(i+1),
+ inc=ms[k])
+ base.gemv(Gs[k], Gssc[k], S, trans='T', n=n-j,
+ alpha=2.0, beta=1.0, offsetA=j*(ms[k]**2),
+ offsety=j*(n+1))
+
+ # S += A'*A
+ base.syrk(A, S, trans='T', beta=1.0)
+
+ # factor S = L*L'
+ lapack.potrf(S)
+
+ # Asct := L^{-1}*A', factor K = Asct'*Asct
+ if type(A) is matrix:
+ Asct = A.trans()
+ else:
+ Asct = matrix(A.trans())
+ blas.trsm(S, Asct)
+ blas.syrk(Asct, K, trans='T')
+ lapack.potrf(K)
+
+ def solve_kkt(x, y, zl, zs):
+
+ # zl := di.*zl = di.*bzl
+ # zsc := T*zs*T = T*bzs*T
+ misc.had2(zl, di)
+ misc.cngrnc(T, zs, zsc, trans='T')
+
+ # x := x + Glsc'*zl + Gs'(zsc) + A'*y
+ # = bx + Gl'*diag(di)^2*bzl) + Gs'(T*bzs*T) + A'*by
+ base.gemv(Glsc, zl, x, trans='T', beta=1.0)
+ Fs(zsc, x, alpha=1.0, beta=1.0, trans='T')
+ base.gemv(A, y, x, trans='T', beta=1.0)
+
+ # x := L^{-1}*x
+ # = L^{-1} * (bx + Gl'*diag(di)^2*bzl + Gs'(T*bzs*T)
+ # + A'*by)
+ blas.trsv(S, x)
+
+ # y := Asc*x - y
+ # = A*S^{-1}* (bx + Gl'*diag(di)^2.*bzl +
+ # Gs'(T*mat(bzs)*T) + A'*by) - by
+ base.gemv(Asct, x, y, trans='T', beta=-1.0)
+
+ # y := K^{-1} * y
+ # = K^{-1} * (A*S^{-1}* (bx + Gl'*diag(di)^2*bzl +
+ # Gs'(T*mat(bzs)*T) + A'*by) - by)
+ lapack.potrs(K, y)
+
+ # x := x - Asc'*y
+ base.gemv(Asct, y, x, alpha=-1.0, beta=1.0)
+
+ # x := L^{-T} * x
+ # = S^{-1} * (bx + Gl'*diag(di)^2*bzl +
+ # Gs'*(T*bzs*T) + A'*by - A'*y)
+ blas.trsv(S, x, trans='T')
+
+ # zl := Glsc*x - zl
+ # = di .* (Gl*x - bzl)
+ base.gemv(Glsc, x, zl, beta=-1.0)
+
+ # zs = rti' * (Gs(x) - bzs) * rti
+ Fs(x, zs, alpha=1.0, beta=-1.0)
+ misc.cngrnc(rti, zs, zs, trans='T')
+
+ return solve_kkt
+
+ elif kktmethod == 5:
+
+ # Solve by eliminating the equality constraints and using
+ # QR factorizations
+ #
+ # A' = Q1*R1, G*Q1 = Q3*R3
+ #
+ # where G = [Glsc; Gssc], Glsc = diag(di)*G, and
+ # Gssc = rti'*Gs()*rti (in packed storage with off-diagonal
+ # elements scaled by sqrt(2)).
+
+ # A' = [Q1, Q2] * [R1; 0]
+ if type(A) is matrix:
+ QA = +A.trans()
+ else:
+ QA = matrix(A.trans())
+ tauA, tauG = matrix(0.0, (p,1)), matrix(0.0, (n-p,1))
+ lapack.geqrf(QA, tauA)
+
+ pms = [ mk*(mk+1)/2 for mk in ms ]
+ Gssc = [ matrix(0.0, (m_k,m_k)) for m_k in ms ]
+ G = matrix(0.0, (ml+sum(pms), n))
+ z = matrix(0.0, (ml+sum(pms),1))
+ w = matrix(0.0, (ml+sum(pms),1))
+ v = matrix(0.0, (n,1))
+ def kktsolver(di, rti):
+
+ # G = [Glsc; Gssc] where , Glsc = diag(di)*G, and
+ # Gssc = rti'*Gs()*rti (in packed storage with off-diagonal
+ # elements scaled by sqrt(2)).
+
+ G[:ml,:] = Gl
+ for k in xrange(ml):
+ blas.scal(di[k], G, n=n, offset=k, inc=G.size[0])
+
+ for j in xrange(n):
+ # Gssc = sqrt(2) * rti' * mat(Gs[:,j]) * rti.
+ for k in xrange(N): Gssc[k][:] = Gs[k][:,j]
+ misc.cngrnc(rti, Gssc, Gssc, trans='T',
+ alpha=math.sqrt(2))
+ # copy Gssc in packed storage to column j of G and
+ # scale diagonal elements by 1/sqrt(2).
+ ind = ml + j*G.size[0]
+ for k in xrange(N):
+ blas.scal(1.0/math.sqrt(2), Gssc[k], inc=ms[k]+1)
+ for i in xrange(ms[k]):
+ blas.copy(Gssc[k], G, n=ms[k]-i,
+ offsetx=(ms[k]+1)*i, offsety=ind)
+ ind += ms[k]-i
+
+ # G = [G1, G2] := G * [Q1, Q2]
+ lapack.ormqr(QA, tauA, G, side='R')
+
+ # QR factorization G2 := [Q3, Q4] * [R3; 0].
+ lapack.geqrf(G, tauG, n=n-p, offsetA=G.size[0]*p)
+
+ def solve_kkt(x, y, zl, zs):
+
+ # Solve
+ #
+ # [0 A' G'] [x ] [bx]
+ # [A 0 0 ] [y ] = [by]
+ # [G 0 -I ] [z ] [bz]
+ #
+ # where
+ # z = [d.*zl; r'*zs*r] (with r'*zs*r in packed
+ # storage with off-diagonal elements scaled by
+ # sqrt(2))
+ # bz = [di.*bzl; rti'*bzs*rti] (with rti'*bzs*rti in
+ # packed storage with off-diagonal elements
+ # scaled by sqrt(2))
+ #
+ # If we eliminate x = [Q1 Q2] * [ R1^{-T}*by; v ] the
+ # equations reduce to
+ #
+ # G2'*z = Q2'*bx
+ # G2*v - z = bz - G1*R1^{-T}*by
+ # R1*y = Q1'*bx - G1'*z.
+ #
+ # This can be solved in 5 steps:
+ #
+ # w := bz - G1*R1^{-T}*by
+ # u := Q3'*w + R3^{-T}*Q2'*bx
+ # z := Q3*u - w
+ # x := [Q1, Q2] * [ R1^{-T}*by; R3^{-1}*u]
+ # y := R1^{-1} * (Q1'*bx - G1'*z).
+
+ # w := bz = [bzlc; bzsc]
+ misc.had2(zl, di)
+ blas.copy(zl, w)
+ misc.cngrnc(rti, zs, zs, trans='T', alpha=math.sqrt(2))
+ ind = ml
+ for k in xrange(N):
+ blas.scal(1.0/math.sqrt(2), zs[k], inc=ms[k]+1)
+ for i in xrange(ms[k]):
+ blas.copy(zs[k], w, n=ms[k]-i,
+ offsetx=(ms[k]+1)*i, offsety=ind)
+ ind += ms[k]-i
+
+ # v := [Q1'*bx; R3^{-T}*Q2'*bx]
+ blas.copy(x, v)
+ lapack.ormqr(QA, tauA, v, trans='T')
+ lapack.trtrs(G, v, uplo='U', trans='T', n=n-p,
+ offsetA=G.size[0]*p, offsetB=p)
+
+ # x[:p] := R1^{-T}*by
+ blas.copy(y, x)
+ lapack.trtrs(QA, x, uplo='U', trans='T', n=p)
+
+ # w := w - G1*x[:p]
+ # = bz - G1*R1^{-T}*by
+ blas.gemv(G, x, w, alpha=-1.0, beta=1.0, n=p)
+
+ # z := [Q3'*w + v[p:]; 0]
+ # = [Q3'*w + R3^{-T}*Q2'*bx; 0]
+ blas.copy(w, z)
+ lapack.ormqr(G, tauG, z, trans='T', k=n-p,
+ offsetA=G.size[0]*p)
+ blas.axpy(v, z, offsetx=p, n=n-p)
+ blas.scal(0.0, z, offset=n-p)
+
+ # x[p:] := R3^{-1}*z[:n-p]
+ blas.copy(z, x, offsety=p, n=n-p)
+ lapack.trtrs(G, x, uplo='U', n=n-p, offsetA=G.size[0]*p,
+ offsetB=p)
+
+ # x is now [ R1^{-T}*by; Q3'*w + R3^{-T}*Q2'*bx ]
+ # x := [Q1 Q2]*x
+ lapack.ormqr(QA, tauA, x)
+
+ # z := [Q3, Q4] * z - w
+ lapack.ormqr(G, tauG, z, k=n-p, offsetA=G.size[0]*p)
+ blas.axpy(w, z, alpha=-1.0)
+
+ # y := R1^{-1} * ( v[:p] - G1'*z )
+ # = R1^{-1} * ( Q1'*bx - G1'*z )
+ blas.copy(v, y, n=p)
+ blas.gemv(G, z, y, n=p, trans='T', alpha=-1.0, beta=1.0)
+ lapack.trtrs(QA, y, uplo='U', n=p)
+
+ # zl = z[:ml]
+ blas.copy(z, zl, n=ml)
+
+ # zs = z[ml:] unpacked and with offdiagonal elts
+ # scaled by 1/sqrt(2)
+ ind = ml
+ for k in xrange(N):
+ for i in xrange(ms[k]):
+ blas.copy(z, zs[k], offsetx=ind,
+ offsety=i*(ms[k]+1), n=ms[k]-i)
+ ind += ms[k]-i
+ blas.scal(math.sqrt(2.0), zs[k], inc=ms[k]+1)
+ misc.sscal(1.0/math.sqrt(2.0), zs)
+
+ return solve_kkt
+
+ return conelp(c, kktsolver, Gl=Fi, hl=hl, Gs=Fs, hs=hs, A=Fe, b=b,
+ primalstart=primalstart, dualstart=dualstart)
diff --git a/src/python/cvxprog.py b/src/python/cvxprog.py
new file mode 100644
index 0000000..59658d3
--- /dev/null
+++ b/src/python/cvxprog.py
@@ -0,0 +1,1074 @@
+"""
+Convex programming solver.
+
+A primal-dual interior-point solver written in Python and interfaces
+for quadratic and geometric programming. Also includes an interface
+to the quadratic programming solver from MOSEK.
+"""
+
+# This file is part of CVXOPT version 0.8.2.
+# Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+
+import math
+from cvxopt import base, blas, lapack, misc
+from cvxopt.base import matrix, spmatrix, sqrt, exp, mul, div
+
+__all__ = []
+options = {}
+
+def nlclp(c, kktsolver, F=None, G=None, h=None, A=None, b=None,
+ xnewcopy=matrix, xdot=blas.dot, xaxpy=blas.axpy, xscal=blas.scal,
+ ynewcopy=matrix, ydot=blas.dot, yaxpy=blas.axpy, yscal=blas.scal):
+
+ """
+ Solves a nonlinearly constrained convex optimization problem with a
+ linear objective
+
+ minimize c'*x
+ subject to f(x) <= 0
+ G(x) <= h
+ A(x) = b.
+
+ f: V -> R^mnl is convex and twice differentiable, G: V -> R^ml and
+ A: V -> W are linear mappings, where V and W are real vector spaces.
+ The default choices for V and W are Euclidean vector spaces V=R^n
+ and W=R^p, with elements represented as 'd' matrices of size (n,1)
+ and (p,1).
+
+
+ Input arguments
+
+ c is an element in V (stored as a matrix, list, dictionary,...).
+
+ kktsolver is a function for the factorization of a KKT system
+
+ [ H * * * ] [ ux ] [ bx ]
+ [ A 0 * * ] [ uy ] = [ by ]
+ [ Df 0 -Dnl * ] [ uznl ] [ bznl ]
+ [ G 0 0 -Dl ] [ uzl ] [ bzl ]
+
+ where H = sum_k z[k]*Hk, Hk is the Hessian of fk, Df is the
+ derivative matrix of f, and Dnl and Dl are positive diagonal
+ matrices.
+ Called as g = kktsolver(x, z, dnl, dl), it returns a function g
+ that can be used to solve the system with Df and H evaluated
+ at x and z, Dnl = diag(dnl)^-2, and Dl = diag(dl)^-2. It can
+ be assumed that x is in the domain of f and that z is positive.
+ The function call g(bx, by, bznl, bzl) replaces its arguments
+ with the solution ux, uy, uznl, uzl.
+
+
+ F is a function that handles the following arguments.
+
+ F() returns a tuple (mnl, x0). mnl is the number of
+ nonlinear inequality constraints. x0 is a point in the
+ domain of f.
+
+ F(x), with x an element in V, returns a tuple (f, Df).
+
+ f is a dense 'd' matrix of size (mnl,1) with the
+ function values f(x).
+
+ Df is a function or a dense or sparse 'd' matrix.
+ When Df is a function, Df(u, v) where u is a 'd' matrix
+ of size (mnl,1) and v an element in V, updates v as
+
+ v := sum_k u[k] * grad fk(x) + v.
+
+ When V=R^n, Df can also be passed as 'd' matrix of
+ size (mnl,n) that contains the derivative matrix of f
+ at x, i.e., Df[k,:] is the transpose of the gradient of
+ fk at x.
+
+ If x is not in dom f, F(x) should return (None, None)
+ or None.
+
+ If F is None, it is assumed that mnl = 0.
+
+
+ G is None, a function, or a sparse or dense 'd' matrix.
+
+ If G is None, it is assumed that ml = 0.
+
+ If G is a function, then
+
+ G(u, v, alpha=1.0, beta=0.0, trans='N')
+
+ evaluates
+
+ v := alpha*G(u) + beta*v if trans is 'N'
+ v := alpha*G'(u) + beta*v if trans is 'T'.
+
+
+ h is None, or a dense 'd' matrix with one column. If h is None,
+ it is interpreted as a 0x1 matrix.
+
+
+ A is None, a function, or a dense or sparse 'd' matrix.
+
+ If A is None, it is assumed that dim W = 0.
+
+ If A is a function then
+
+ A(u, v, alpha=1.0, beta=0.0, trans='N')
+
+ evaluates
+
+ v := alpha*A(u) + beta*v if trans is 'N'
+ v := alpha*A'(u) + beta*v if trans is 'T'.
+
+
+ b is None, or an element in W. If b is None, it is assumed
+ that dim W = 0.
+
+
+ Returns a dictionary with keys 'status', 'x', 'snl', 'sl', 'y',
+ 'znl', 'zl'.
+
+ status is 'optimal' or 'unknown'.
+
+ x, s, snl, sl, y, znl, zl are None if status is 'unknown'.
+ Otherwise x is the optimal solution; snl, sl are the optimal
+ slacks for the nonlinear and linear inequalities; y is the
+ optimal dual variable associated with the equality constraints;
+ znl, zl are the optimal dual variables associated with the
+ nonlinear and linear inequalities.
+ """
+
+ STEP = 0.99
+ BETA = 0.5
+ ALPHA = 0.01
+ GAMMA1 = 1e5
+ GAMMA2 = 1e-5
+ GAMMA3 = 0.5
+ GAMMA4 = 1.0
+
+ try: MAXITERS = options['maxiters']
+ except KeyError: MAXITERS = 100
+ else:
+ if type(MAXITERS) is not int or MAXITERS < 1:
+ raise ValueError, "options['maxiters'] must be a positive "\
+ "integer"
+
+ try: ABSTOL = options['abstol']
+ except KeyError: ABSTOL = 1e-7
+ else:
+ if type(ABSTOL) is not float and type(ABSTOL) is not int:
+ raise ValueError, "options['abstol'] must be a scalar"
+
+ try: RELTOL = options['reltol']
+ except KeyError: RELTOL = 1e-7
+ else:
+ if type(RELTOL) is not float and type(RELTOL) is not int:
+ raise ValueError, "options['reltol'] must be a scalar"
+
+ try: FEASTOL = options['feastol']
+ except KeyError: FEASTOL = 1e-7
+ else:
+ if type(FEASTOL) is not float and type(FEASTOL) is not int:
+ raise ValueError, "options['feastol'] must be a scalar"
+
+ try: show_progress = options['show_progress']
+ except KeyError: show_progress = True
+
+ if F is None: # There are no nonlinear inequality constraints.
+ def F(x=None, z=None):
+ if x is None:
+ x0 = xnewcopy(c)
+ xscal(0.0, x0)
+ return 0, x0
+ def Df(u, v): pass
+ return matrix(0.0, (0,1)), Df
+
+ mnl, x0 = F()
+
+ def fzero(x, y, alpha=1.0, beta=0.0, trans='N'):
+ if trans == 'T': xscal(beta, y)
+
+ if G is None: G = fzero
+ if h is None: h = matrix(0.0, (0,1))
+ ml = h.size[0]
+ if type(G) in (matrix, spmatrix):
+ if G.typecode != 'd' or G.size[0] != ml:
+ raise TypeError, "'G' must be a 'd' matrix with %d rows" %ml
+ def fG(u, v, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(G, u, v, alpha=alpha, beta=beta, trans=trans)
+ else:
+ fG = G
+
+ if (mnl+ml == 0):
+ raise ValueError, "problem must have at least one inequality "\
+ "constraint"
+
+ if A is None: A = fzero
+ if b is None: b = matrix(0.0, (0,1))
+ if type(A) in (matrix,spmatrix):
+ if A.typecode != 'd' or A.size[0] != b.size[0]:
+ raise TypeError, "'A' must be a 'd' matrix with %d rows" \
+ %b.size[0]
+ def fA(u, v, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(A, u, v, alpha=alpha, beta=beta, trans=trans)
+ else:
+ fA = A
+
+ def xcopy(x, y): xscal(0.0, y); xaxpy(x, y)
+ def ycopy(x, y): yscal(0.0, y); yaxpy(x, y)
+
+ x = xnewcopy(x0)
+ y = ynewcopy(b); yscal(0.0, y)
+ znl, zl = matrix(1.0, (mnl,1)), matrix(1.0, (ml,1))
+ snl, sl = matrix(1.0, (mnl,1)), matrix(1.0, (ml,1))
+ rx, rx2 = xnewcopy(x0), xnewcopy(x0)
+ ry = ynewcopy(b)
+ rznl, rznl2 = matrix(0.0, (mnl,1)), matrix(0.0, (mnl,1))
+ rzl = matrix(0.0, (ml,1))
+ dx, dy = xnewcopy(x), ynewcopy(y)
+ newx, newy = xnewcopy(x), ynewcopy(y)
+
+ if show_progress:
+ print "% 10s% 12s% 10s% 8s% 7s" %("pcost", "dcost", "gap",
+ "pres", "dres")
+
+ for iters in xrange(MAXITERS):
+
+ f, Df = F(x)
+ f = matrix(f, tc='d')
+ if f.typecode != 'd' or f.size != (mnl,1):
+ raise TypeError, "first output argument of F() must be a "\
+ "'d' matrix of size (%d,%d)" %(mnl,1)
+ if type(Df) in (matrix, spmatrix):
+ if Df.typecode != 'd' or Df.size[0] != mnl:
+ raise TypeError, "second output argument of F() must "\
+ "be a 'd' matrix with %d rows" %mnl
+ def fDf(u, v):
+ base.gemv(Df, u, v, beta=1.0, trans='T')
+ else:
+ fDf = Df
+
+ gap = blas.dot(snl, znl) + blas.dot(sl, zl)
+ mu = gap / (mnl + ml)
+
+ # rx = c + A'*y + Df'*znl + G'*zl
+ xcopy(c, rx)
+ fA(y, rx, beta=1.0, trans='T')
+ fDf(znl, rx)
+ fG(zl, rx, beta=1.0, trans='T')
+ resx = math.sqrt(xdot(rx, rx))
+
+ # ry = A*x - b
+ ycopy(b, ry)
+ fA(x, ry, alpha=1.0, beta=-1.0)
+ resy = math.sqrt(ydot(ry, ry))
+
+ # rznl = snl + f
+ blas.copy(snl, rznl)
+ blas.axpy(f, rznl)
+ resznl = blas.nrm2(rznl)
+
+ # rzl = sl + G*x - h
+ blas.copy(sl, rzl)
+ blas.axpy(h, rzl, alpha=-1.0)
+ fG(x, rzl, beta=1.0)
+ reszl = blas.nrm2(rzl)
+
+ # pcost = c'*x
+ # dcost = c'*x + y'*(Ax-b) + znl'*f(x) + zl'*(G*x-h)
+ # = c'*x + y'*(Ax-b) + znl'*(f(x)+snl) + zl'*(G*x-h+sl)
+ # - znl'*snl - zl'*sl
+ pcost = xdot(c,x)
+ dcost = pcost + ydot(y, ry) + blas.dot(znl, rznl) + \
+ blas.dot(zl, rzl) - gap
+
+ pres = math.sqrt( resy**2 + resznl**2 + reszl**2 )
+ dres = resx
+ if iters == 0:
+ pres0 = max(1.0, pres)
+ pres0_nl = max(1.0, resznl)
+ dres0 = max(1.0, dres)
+
+ if show_progress:
+ print "%2d: % 8.4e % 8.4e % 4.0e% 7.0e% 7.0e" \
+ %(iters, pcost, dcost, gap, pres/pres0, dres/dres0)
+
+ # Stopping criteria.
+ if pres/pres0 <= FEASTOL and dres/dres0 <= FEASTOL and \
+ (gap <= ABSTOL or (dcost > 0 and gap/dcost <= RELTOL) or
+ (pcost < 0 and gap/(-pcost) <= RELTOL)):
+ return {'status': 'optimal', 'x': x, 'y': y, 'znl': znl,
+ 'zl': zl, 'snl': snl, 'sl': sl}
+
+ dnl, dl = sqrt(div(znl, snl)), sqrt(div(zl, sl)),
+ g = kktsolver(x, znl, dnl, dl)
+
+ sigma = 0.0
+ for i in [0,1]:
+
+ # Solve
+ #
+ # [0 ] [ hessian A^T [Df;G]' ] [dx]
+ # [0 ] + [ A 0 0 ] * [dy] = -r
+ # [ds] [ [Df;G] 0 0 ] [dz]
+ #
+ # s.*dz + z.*ds = -s.*z + sigma*mu
+ #
+ # by solving
+ #
+ # [ hessian A^T [Df;G]^T ] [dx]
+ # [ A 0 0 ] * [dy] = rhs
+ # [ [Df;G] 0 -diag(s./z) ] [dz]
+ #
+ # with rhs = -r + (0,0,0, (s*z - sigma*mu)./z).
+ # Take ds = -(s.*z - sigma*mu + s.*dz) ./ z.
+
+ rcpnl = mul(snl, znl) - sigma*mu
+ rcpl = mul(sl, zl) - sigma*mu
+ xscal(0.0, dx); xaxpy(rx, dx, alpha=-1.0)
+ yscal(0.0, dy); yaxpy(ry, dy, alpha=-1.0)
+ dznl = -rznl + div(rcpnl, znl)
+ dzl = -rzl + div(rcpl, zl)
+ g(dx, dy, dznl, dzl)
+ dsnl = -div( rcpnl + mul(snl,dznl), znl )
+ dsl = -div( rcpl + mul(sl,dzl), zl )
+
+ # line search
+ step = min( 1.0, STEP / max( list(-div(dsnl,snl)) +
+ list(-div(dsl, sl)) + list(-div(dznl,znl))
+ + list(-div(dzl,zl))) )
+ rescpnl, rescpl = blas.nrm2(rcpnl), blas.nrm2(rcpl)
+ aa, bb = max(rescpnl, rescpl), min(rescpnl, rescpl)
+ if aa: rescp = aa * math.sqrt( 1.0 + (bb/aa)**2 )
+ else: rescp = 0.0
+ phi = resx + resznl + rescp
+
+ for lsiters in xrange(50):
+
+ xcopy(x, newx); xaxpy(dx, newx, alpha=step)
+ ycopy(y, newy); yaxpy(dy, newy, alpha=step)
+ newznl, newzl = znl + step*dznl, zl+step*dzl
+ newsnl, newsl = snl + step*dsnl, sl+step*dsl
+ newgap = blas.dot(newsnl, newznl) + \
+ blas.dot(newsl, newzl)
+ t = F(newx)
+ if t is None: newf = None
+ else: newf, newDf = t[0], t[1]
+
+ if newf is not None:
+ newf = matrix(newf, tc='d')
+ if type(newDf) in (matrix, spmatrix):
+ def fDf(u, v):
+ base.gemv(newDf, u, v, beta=1.0, trans='T')
+ else:
+ fDf = newDf
+
+ # rx2 = c + A'*newy + newDf'*newznl + G'*newzl
+ xcopy(c, rx2)
+ fA(newy, rx2, beta=1.0, trans='T')
+ fDf(newznl, rx2)
+ fG(newzl, rx2, beta=1.0, trans='T')
+ resx2 = math.sqrt(xdot(rx2, rx2))
+
+ # rznl2 = newsnl + newf
+ blas.copy(newsnl, rznl2)
+ blas.axpy(newf, rznl2)
+ resznl2 = blas.nrm2(rznl2)
+
+ # rcpnl = newsnl .* newznl
+ # rcpl = newsl .* newzl
+ rcpnl = mul(newsnl, newznl)
+ rcpl = mul(newsl, newzl)
+ rescpnl = blas.nrm2(rcpnl - sigma*mu)
+ rescpl = blas.nrm2(rcpl - sigma*mu)
+ aa, bb = max(rescpnl, rescpl), min(rescpnl, rescpl)
+ if aa: rescp = aa * math.sqrt( 1.0 + (bb/aa)**2 )
+ else: rescp = 0.0
+
+ newphi = resx2 + resznl2 + rescp
+ newmu = newgap / (mnl+ml)
+
+ if resx2 <= GAMMA1 * dres0 * newgap and \
+ resznl2 <= GAMMA1 * pres0_nl * newgap and \
+ (not rcpnl or min(rcpnl) >= GAMMA2*newmu) \
+ and (not rcpl or min(rcpl) >= GAMMA2*newmu) \
+ and newphi <= (1.0 - ALPHA*step) * phi:
+ break
+
+ step *= BETA
+
+ else: raise StandardError, "line search did not terminate"
+
+ if i == 0: sigma = min(GAMMA3*newmu/mu, (newmu/mu)**GAMMA4)
+
+ xaxpy(dx, x, alpha=step)
+ yaxpy(dy, y, alpha=step)
+ blas.axpy(dznl, znl, alpha=step)
+ blas.axpy(dzl, zl, alpha=step)
+ blas.axpy(dsnl, snl, alpha=step)
+ blas.axpy(dsl, sl, alpha=step)
+
+ return {'status': 'unknown', 'x': None, 'y': None, 'znl': None,
+ 'zl': None, 'snl': None, 'sl': None}
+
+
+
+def nlcp(kktsolver, F, G=None, h=None, A=None, b=None,
+ xnewcopy=matrix, xdot=blas.dot, xaxpy=blas.axpy, xscal=blas.scal,
+ ynewcopy=matrix, ydot=blas.dot, yaxpy=blas.axpy, yscal=blas.scal):
+
+ """
+ Solves a convex optimization problem
+
+ minimize f0(x)
+ subject to fk(x) <= 0, k=1,...,mnl
+ G(x) <= h
+ A(x) = b.
+
+ fk: V -> R is convex and twice differentiable.
+ G: V -> R^ml and A: V -> W are linear mappings, where V and W are
+ real vector spaces. The default choices for V and W are Euclidean
+ vector spaces V=R^n and W=R^p, with elements stored as 'd' matrices
+ of size (n,1) and (p,1).
+
+ Input arguments
+
+ kktsolver is a function for the factorization of a KKT system
+
+ [ H * * * ] [ ux ] [ bx ]
+ [ A 0 * * ] [ uy ] = [ by ]
+ [ Df[1:] 0 -Dnl * ] [ uznl ] [ bznl ]
+ [ G 0 0 -Dl ] [ uzl ] [ bzl ]
+
+ where H = sum_{k=0}^mnl z[k]*Hk and H[k] is the Hessian
+ of fk, Df is the derivative of f and Dnl and Dl are positive
+ diagonal matrices.
+ g = kktsolver(x, z, dnl, dl) returns a function g that can be
+ used to solve the system with H and Df evaluated at x and z,
+ Dnl = diag(dnl)^-2, Dl = diag(dl)^-2.
+ It can be assumed that x is in the domain of f0 and f.
+ The function calll g(bx, by, bznl, bzl) replaces the
+ arguments with the solution ux, uy, uznl, uzl.
+
+ F: a function that handles the following arguments.
+
+ F() returns a tuple (mnl, x0).
+
+ mnl is the number of nonlinear inequality constraints.
+ x0 is a point in dom f.
+
+ F(x), with x a point in V, returns (f, Df).
+
+ f is a dense 'd' matrix of size (mnl+1,1) with the
+ function values f0(x), ...., fmnl(x).
+ Df is a function or a sparse or dense 'd' matrix.
+ If Df is a function, Df(u, v) evaluates
+
+ v := sum_k=0^mnl u[k]*gradfk + v.
+
+ If V = Rn, Df can also be a 'd' matrix or sparse matrix
+ of size (mnl, n). In this case Df[k,:] contains the
+ transpose of gradfk.
+
+ If x is not in dom f, F(x) returns None or (None, None).
+
+
+ G is None, a function, or a sparse or dense 'd' matrix.
+
+ If G is a function then
+
+ G(u, v, alpha=1.0, beta=0.0, trans='N')
+
+ evaluates
+
+ v := alpha * G(u) + beta * v if trans is 'N'
+ v := alpha * G'(u) + beta * v if trans is 'T'.
+
+ If G is None, it is assumed that ml = 0.
+
+
+ h is None, or a dense 'd' matrix with one column. If h is None,
+ it is interpreted as a 0x1 matrix.
+
+
+ A is None, a function, or a dense or sparse 'd' matrix.
+
+ If A is a function then
+
+ A(u, v, alpha=1.0, beta=0.0, trans='N')
+
+ evaluates
+
+ v := alpha * A(u) + beta * v if trans is 'N'
+ v := alpha * A'(u) + beta * v if trans is 'T'.
+
+ If A is None, it is assumed that dim W = 0.
+
+
+ b is None, or an element in W. If b is None, it is assumed
+ that dim W = 0.
+
+
+ Returns a dictionary with keys 'status', 'x', 'snl', 'sl', 'y',
+ 'znl', 'zl'.
+
+ status is 'optimal' or 'unknown'.
+
+ x, s, snl, sl, y, znl, zl are None if status is 'unknown'.
+ Otherwise x is the optimal solution; snl, sl are the optimal
+ slacks for the nonlinear and linear inequalities; y is the
+ optimal dual variable associated with the equality constraints;
+ znl, zl are the optimal dual variables associated with the
+ nonlinear and linear inequalities.
+ """
+
+ mnl, x0 = F()
+ if type(mnl) is not int or mnl < 0:
+ raise TypeError, "invalid return value for 'mnl, x = F()'"
+
+ def fzero(x, y, alpha=1.0, beta=0.0, trans='N'):
+ if trans == 'T': xscal(beta, y)
+
+ if G is None: G = fzero
+ if h is None: h = matrix(0.0, (0,1))
+ ml = h.size[0]
+ if type(G) in (matrix, spmatrix):
+ if G.typecode != 'd' or G.size[0] != ml:
+ raise TypeError, "'G' must be a 'd' matrix with %d rows" %ml
+ def fG(u, v, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(G, u, v, alpha=alpha, beta=beta, trans=trans)
+ else:
+ fG = G
+
+ if A is None: A = fzero
+ if b is None: b = matrix(0.0, (0,1))
+ if type(A) in (matrix,spmatrix):
+ if A.typecode != 'd' or A.size[0] != b.size[0]:
+ raise TypeError, "'A' must be a 'd' matrix with %d rows" \
+ %b.size[0]
+ def fA(u, v, alpha=1.0, beta=0.0, trans='N'):
+ base.gemv(A, u, v, alpha=alpha, beta=beta, trans=trans)
+ else:
+ fA = A
+
+ def xcopy(x, y): xscal(0.0, y); xaxpy(x, y)
+ def ycopy(x, y): yscal(0.0, y); yaxpy(x, y)
+
+
+ # Apply nlclp() to problem in epigraph form:
+ #
+ # minimize t
+ # subject to f0(x) - t <= 0
+ # fk(x) <= 0, k=1,...,mnl
+ # G(x) <= h
+ # A(x) = b.
+ #
+ # Store the variable as a list [ x, t ].
+
+ # c = [0, 1.0]
+ c = [ xnewcopy(x0), 1.0 ]
+ xscal(0.0, c[0])
+
+ ux, uznl = xnewcopy(x0), matrix(0.0, (mnl,1))
+
+ def kktsolver_epi(x, z, dnl, dl):
+
+ # g(x, y, znl, zl) is a solver for the smaller KKT system
+ #
+ # [ H * * * ] [ x ] [ bx ]
+ # [ A 0 * * ] [ y ] = [ by ]
+ # [ Df[1:,:] 0 -Dnl * ] [ znl ] [ bznl ]
+ # [ G 0 0 -Dl ] [ zl ] [ bzl ]
+ #
+ # where H = sum_k=0^mnl zk*Hk, Df is the derivative matrix of
+ # (f0, ..., fmnl), Dnl = diag(dnl[1:])^-2, and Dl = diag(dl)^-2.
+ # The variables are x (in V), y (in W), znl (in R^mnl),
+ # zl (in R^ml).
+
+ g = kktsolver(x[0], z, dnl[1:], dl)
+
+ f, Df = F(x[0])
+ if type(Df) in (matrix, spmatrix):
+ gradf0 = Df[0,:].T
+ else:
+ gradf0 = xnewcopy(x[0])
+ xscal(0.0, gradf0)
+ e0 = matrix(0.0, (mnl+1,1))
+ e0[0] = 1.0
+ Df(e0, gradf0)
+
+ def g_epi(x, y, znl, zl):
+
+ # g_epi(x, y, znl, zl) solves the augmented KKT system
+ #
+ # [ [H, 0; ] [ x ] [ bx ]
+ # [ 0, 0] * * * ] [ ] [ ]
+ # [ [A, 0] 0 * * ] [ y ] = [ by ]
+ # [ [Df, -e0] 0 -Dnl * ] [ znl ] [ bznl ]
+ # [ [G, 0] 0 0 -Dl ] [ zl ] [ bzl ]
+ #
+ # The variables are x (a tuple (x[0], x[1]) with x[0] in
+ # V and x[1] in R), y (in W), znl (in R^(mnl+1)) and
+ # zl (in R^ml).
+ #
+ # The system is solved as follows:
+ #
+ # x[0], y, znl[1:], zl solve the smaller KKT system
+ # with rhs (bx[0] + bx[1]*Df[0,:]', by, bnl[1:], bl).
+ #
+ # Take znl[0] = -bx[1] and
+ # x[1] = Df[0,:]*x[0] + bx[1]/dnl[0]**2 - bnl[0].
+
+ a = znl[0]
+ xcopy(x[0], ux)
+ xaxpy(gradf0, ux, alpha=x[1])
+ uznl[:] = znl[1:]
+ g(ux, y, uznl, zl)
+ znl[1:] = uznl
+ znl[0] = -x[1]
+ xcopy(ux , x[0])
+ x[1] = xdot(gradf0, x[0]) - znl[0] / dnl[0]**2 - a
+
+ return g_epi
+
+
+ # fA_epi evaluates [A, 0] * [x[0]; x[1]] and its adjoint.
+ #
+ # v := alpha * A(u[0]) + beta*v if trans is 'N'
+ # v := alpha * ( A'(u), 0 ) + beta*v if trans is 'N'
+
+ def fA_epi(u, v, alpha=1.0, beta=0.0, trans='N'):
+ if trans == 'N':
+ fA(u[0], v, alpha=alpha, beta=beta)
+ else:
+ fA(u, v[0], alpha=alpha, beta=beta, trans='T')
+ v[1] *= beta
+
+
+ # fG_epi evaluates [G, 0] * [x[0]; x[1]] and its adjoint
+ #
+ # v := alpha * G(u[0]) + beta*v if trans is 'N'
+ # v := alpha * ( G'(u), 0 ) + beta*v if trans is 'T'.
+
+ def fG_epi(u, v, alpha=1.0, beta=0.0, trans='N'):
+ if trans == 'N':
+ fG(u[0], v, alpha=alpha, beta=beta)
+ else:
+ fG(u, v[0], alpha=alpha, beta=beta, trans='T')
+ v[1] *= beta
+
+
+ # F_epi evaluates nonlinear constraint functions and derivatives.
+
+ def F_epi(x=None, z=None):
+ if x is None:
+ x0_epi = (x0, 0.0)
+ return mnl+1, x0_epi
+ else:
+ t = F(x[0])
+ if t is None or t[0] is None: return None, None
+ f_epi, Df = matrix(t[0]), t[1]
+ f_epi[0] -= x[1]
+ def Df_epi(u, v):
+ # Evaluates v := [Df, -e0]' * u + v
+ if type(Df) in (matrix, spmatrix):
+ base.gemv(Df, u, v[0], beta=1.0, trans='T')
+ else:
+ Df(u, v[0])
+ v[1] -= u[0]
+ return f_epi, Df_epi
+
+ def xnewcopy_epi(x):
+ return [ xnewcopy(x[0]), 0.0 ]
+
+ def xdot_epi(x, y):
+ return xdot(x[0], y[0]) + x[1]*y[1]
+
+ def xaxpy_epi(x, y, alpha=1.0):
+ xaxpy(x[0], y[0], alpha=alpha)
+ y[1] += alpha*x[1]
+
+ def xscal_epi(alpha, x):
+ xscal(alpha, x[0])
+ x[1] *= alpha
+
+ sol = nlclp(c, kktsolver_epi, F_epi, fG_epi, h, fA_epi, b,
+ xnewcopy_epi, xdot_epi, xaxpy_epi, xscal_epi, ynewcopy, ydot,
+ yaxpy, yscal)
+ if sol['status'] == 'optimal':
+ sol['x'] = sol['x'][0]
+ sol['znl'], sol['snl'] = sol['znl'][1:], sol['snl'][1:]
+ else:
+ sol['x'] = None
+ sol['znl'], sol['snl'] = None, None
+ return sol
+
+
+def cp(F, G=None, h=None, A=None, b=None):
+
+ """
+ Solves a convex optimization problem
+
+ minimize f0(x)
+ subject to fk(x) <= 0, k=1,...,m
+ G*x <= h
+ A*x = b.
+
+ f: R^n -> R^(m+1) is convex and twice differentiable.
+
+ Input arguments
+
+ F is a function that handles the following arguments.
+
+ F() returns a tuple (m, x0).
+
+ m is the number of nonlinear inequality constraints.
+ x0 is an nx1 dense 'd' matrix specifying a point in
+ dom f.
+
+ F(x), with x a 'd' matrix of size (n,1), returns (f, Df).
+
+ f is a dense 'd' matrix of size (m+1,1) with the
+ function values f(x).
+
+ Df is a dense or sparse 'd' matrix of size (m+1,n).
+ Its kth row contains the transpose of the gradient
+ of fk at x.
+
+ If x is not in dom f, F(x) returns None or (None, None).
+
+ F(x, z), with x a 'd' matrix of size (n,1) and z a positive
+ 'd' matrix of size (m+1,1), returns (f, Df, H).
+
+ f and Df are defined as above.
+
+ H is a dense or sparse 'd' matrix of size (n,n). The
+ lower triangular part of H contains the lower triangular
+ part of sum_{k=0}^m z[k]*Hk where Hk is the Hessian of
+ fk at x.
+
+ If F is called with two arguments, it can be assumed
+ that x is dom f.
+
+ G is None or a sparse or dense 'd' matrix. If G is None, it
+ is interpreted as a 0xn matrix.
+
+ h is None or a dense 'd' matrix with one column. If h is None,
+ it is interpreted as a 0x1 matrix.
+
+ A is None, or a dense or sparse 'd' matrix. If A is None, it
+ is interpreted as a 0xn matrix.
+
+ b is a dense 'd' matrix with one column or None. If b is None,
+ it is interpreted as a 0x1 matrix.
+
+ Returns a dictionary with keys 'status', 'x', 'snl', 'sl', 'y',
+ 'znl', 'zl'.
+
+ status is 'optimal' or 'unknown'.
+
+ x, s, snl, sl, y, znl, zl are None if status is 'unknown'.
+ Otherwise x is the optimal solution; snl, sl are the optimal
+ slacks for the nonlinear and linear inequalities; y is the
+ optimal dual variable associated with the equality constraints;
+ znl, zl are the optimal dual variables associated with the
+ nonlinear and linear inequalities.
+ """
+
+ try: kktmethod = options['kktmethod']
+ except KeyError: kktmethod = 3
+ else:
+ if type(kktmethod) is not int or kktmethod not in [1,2,3]:
+ raise ValueError, "options['kktmethod'] must be 1, 2 or 3"
+
+ mnl, x0 = F()
+ if type(mnl) is not int or mnl < 0 or type(x0) is not matrix or \
+ x0.typecode != 'd' or x0.size[1] != 1:
+ raise TypeError, "invalid return values for '(m, x) = F()'"
+ n = x0.size[0]
+
+ if G is None: G = spmatrix([], [], [], (0,n))
+ if h is None: h = matrix(0.0, (0,1))
+ if type(G) not in (matrix, spmatrix) or G.typecode != 'd' or \
+ G.size[1] != n:
+ raise TypeError, "'G' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ ml = G.size[0]
+ if type(h) is not matrix or h.typecode != 'd' or h.size != (ml,1):
+ raise TypeError, "'h' must be a dense 'd' matrix of size "\
+ "(%d,1)" %ml
+
+ if A is None: A = spmatrix([], [], [], (0,n))
+ if b is None: b = matrix(0.0, (0,1))
+ if type(A) not in (matrix, spmatrix) or A.typecode != 'd' or \
+ A.size[1] != n:
+ raise TypeError, "'A' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ p = A.size[0]
+ if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
+ raise TypeError, "'b' must be a dense 'd' matrix of "\
+ "size (%d,1)" %p
+
+ status = {'kkt_num': None} # 'pointer' to numeric factorization
+ def kkt(x, z, dnl, dl):
+ f, Df, H = F(x, z)
+ if mnl==0:
+ Df2 = spmatrix([],[],[],(0,n))
+ else:
+ Df2 = Df[1:,:]
+ if status['kkt_num'] is None:
+ status['kkt_num'] = misc.kkt(H, A, Df2, G, kktmethod)
+ return status['kkt_num'](H, Df2, dnl, dl)
+
+ return nlcp(kkt, F, G, h, A, b)
+
+
+def qp(P, q, G=None, h=None, A=None, b=None, solver=None):
+
+ """
+ Solves a quadratic program
+
+ minimize (1/2)*x'*P*x + q'*x
+ subject to G*x <= h
+ A*x = b.
+
+
+ Input arguments
+
+ P is a nxn dense or sparse 'd' matrix with the lower triangular
+ part of P stored in the lower triangle. Must be positive
+ semidefinite.
+
+ q is an nx1 dense 'd' matrix.
+
+ G is an mxn dense or sparse 'd' matrix.
+
+ h is an mx1 dense 'd' matrix.
+
+ A is a pxn dense or sparse 'd' matrix.
+
+ b is a px1 dense 'd' matrix or None.
+
+ solver is None or 'mosek'.
+
+ The default values for G, h, A and b are empty matrices with
+ zero rows.
+
+
+ Returns a dictionary with keys 'status', 'x', 's', 'y', 'z'.
+
+ The default solver returns with status 'optimal' or 'unknown'.
+ The MOSEK solver can also return with status 'primal infeasible'
+ or 'dual infeasible'.
+
+ If status is 'optimal', x, s, y, z are the primal and dual
+ optimal solutions.
+
+ If status is 'primal infeasible', x = s = None and z, y are
+ a proof of primal infeasibility:
+
+ G'*z + A'*y = 0, h'*z + b'*y = -1, z >= 0.
+
+ If status is 'dual infeasible', z = y = None, and x, s are
+ a proof of dual infeasibility:
+
+ P*x = 0, q'*x = -1, G*x + s = 0, A*x = 0, s >=0
+
+ If status is 'unknown', x, y, s, z are None.
+ """
+
+ if solver == 'mosek':
+ try: from cvxopt import mosek
+ except ImportError: raise ValueError, "invalid option "\
+ "(solver='mosek'): cvxopt.mosek is not installed"
+ mosek.options = options
+ prosta, solsta, x, z, y = mosek.solveqp(P, q, G, h, A, b)
+ m = G.size[0]
+ if solsta == 'OPTIMAL':
+ s = matrix(0.0, (m,1))
+ blas.copy(h, s)
+ base.gemv(G, x, s, alpha=-1.0, beta=1.0)
+ status = 'optimal'
+ elif solsta == 'PRIMAL_INFEASIBLE_CER':
+ status = 'primal infeasible'
+ ducost = -blas.dot(h,z) - blas.dot(b,y)
+ blas.scal(1.0/ducost, y);
+ blas.scal(1.0/ducost, z);
+ x, s = None, None
+ elif solsta == 'DUAL_INFEASIBLE_CER':
+ status = 'dual infeasible'
+ qx = blas.dot(q,x)
+ if qx: x /= (-qx)
+ s = matrix(0.0, (m,1))
+ base.gemv(G, x, s, alpha=-1.0)
+ z, y = None, None
+ else:
+ status = 'unknown'
+ x, s, y, z = None, None, None, None
+ return {'status': status, 'x': x, 's': s, 'y': y, 'z': z}
+
+ if type(P) not in (matrix, spmatrix) or P.typecode != 'd' or \
+ P.size[0] != P.size[1]:
+ raise TypeError, "'P' must be a square dense or sparse 'd' "\
+ "matrix"
+ n = P.size[0]
+ if type(q) is not matrix or q.typecode != 'd' or q.size != (n,1):
+ raise TypeError, "'q' must be a dense 'd' matrix of "\
+ "size (%d,1)" %n
+
+ def F(x=None, z=None):
+ if x is None: return 0, matrix(0.0, (n,1))
+ grad = matrix(0.0, (1,n))
+ base.symv(P, x, grad)
+ f = .5 * blas.dot(grad, x) + blas.dot(q, x)
+ blas.axpy(q, grad)
+ if z is None: return f, grad
+ else: return f, grad, z[0]*P
+
+ sol = cp(F, G, h, A, b)
+ return {'status': sol['status'], 'x': sol['x'], 's': sol['sl'],
+ 'y': sol['y'], 'z': sol['zl']}
+
+
+
+def gp(K, F, g, G=None, h=None, A=None, b=None):
+
+ """
+ Solves a geometric program
+
+ minimize log sum exp (F0*x+g0)
+ subject to log sum exp (Fi*x+gi) <= 0, i=1,...,m
+ G*x <= h
+ A*x = b
+
+ Input arguments
+
+ K is a list of positive integers [K0, K1, K2, ..., Km].
+
+ F is a sum(K)xn dense or sparse 'd' matrix with block rows F0,
+ F1, ..., Fm. Each Fi is Kixn.
+
+ g is a sum(K)x1 dense or sparse 'd' matrix with blocks g0, g1,
+ g2, ..., gm. Each gi is Kix1.
+
+ G is an mxn dense or sparse 'd' matrix.
+
+ h is an mx1 dense 'd' matrix.
+
+ A is a pxn dense or sparse 'd' matrix.
+
+ b is a px1 dense 'd' matrix.
+
+ The default values for G, h, A and b are empty matrices with
+ zero rows.
+
+
+ Returns a dictionary with keys 'status', 'x', 'snl', 'sl, 'y',
+ 'znl', 'zl'.
+
+ If status is 'optimal', x is the optimal solution, snl and sl
+ are the optimal slacks for the nonlinear and linear
+ inequalities, znl and zl are the optimal dual veriables
+ associated with the nonlinear and linear inequalities, and
+ y are the optimal variables associated with the equality
+ constraints.
+
+ If status is 'unknown', x, snl, sl, y, znl and zl are None.
+ """
+
+ if type(K) is not list or [ k for k in K if type(k) is not int
+ or k <= 0 ]:
+ raise TypeError, "'K' must be a list of positive integers"
+ mnl = len(K)-1
+ l = sum(K)
+
+ if type(F) not in (matrix, spmatrix) or F.typecode != 'd' or \
+ F.size[0] != l:
+ raise TypeError, "'F' must be a dense or sparse 'd' matrix "\
+ "with %d rows" %l
+ if type(g) is not matrix or g.typecode != 'd' or g.size != (l,1):
+ raise TypeError, "'g' must be a dene 'd' matrix of "\
+ "size (%d,1)" %l
+ n = F.size[1]
+
+ if G is None: G = spmatrix([], [], [], (0,n))
+ if h is None: h = matrix(0.0, (0,1))
+ if type(G) not in (matrix, spmatrix) or G.typecode != 'd' or \
+ G.size[1] != n:
+ raise TypeError, "'G' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ ml = G.size[0]
+ if type(h) is not matrix or h.typecode != 'd' or h.size != (ml,1):
+ raise TypeError, "'h' must be a dense 'd' matrix of "\
+ "size (%d,1)" %ml
+
+ if A is None: A = spmatrix([], [], [], (0,n))
+ if b is None: b = matrix(0.0, (0,1))
+ if type(A) not in (matrix, spmatrix) or A.typecode != 'd' or \
+ A.size[1] != n:
+ raise TypeError, "'A' must be a dense or sparse 'd' matrix "\
+ "with %d columns" %n
+ p = A.size[0]
+ if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
+ raise TypeError, "'b' must be a dense 'd' matrix of "\
+ "size (%d,1)" %p
+
+ y = matrix(0.0, (l,1))
+ u = matrix(0.0, (max(K),1))
+ Fsc = matrix(0.0, (max(K),n))
+
+ cs1 = [ sum(K[:i]) for i in xrange(mnl+1) ]
+ cs2 = [ cs1[i] + K[i] for i in xrange(mnl+1) ]
+ ind = zip(range(mnl+1), cs1, cs2)
+
+ def Fgp(x=None, z=None):
+
+ if x is None: return mnl, matrix(0.0, (n,1))
+
+ f = matrix(0.0, (mnl+1,1))
+ Df = matrix(0.0, (mnl+1,n))
+
+ # y = F*x+g
+ blas.copy(g, y)
+ base.gemv(F, x, y, beta=1.0)
+
+ if z is not None: H = matrix(0.0, (n,n))
+
+ for i, start, stop in ind:
+
+ # yi := exp(yi) = exp(Fi*x+gi)
+ ymax = max(y[start:stop])
+ y[start:stop] = exp(y[start:stop] - ymax)
+
+ # fi = log sum yi = log sum exp(Fi*x+gi)
+ ysum = blas.asum(y, n=stop-start, offset=start)
+ f[i] = ymax + math.log(ysum)
+
+ # yi := yi / sum(yi) = exp(Fi*x+gi) / sum(exp(Fi*x+gi))
+ blas.scal(1.0/ysum, y, n=stop-start, offset=start)
+
+ # gradfi := Fi' * yi
+ # = Fi' * exp(Fi*x+gi) / sum(exp(Fi*x+gi))
+ base.gemv(F, y, Df, trans='T', m=stop-start, incy=mnl+1,
+ offsetA=start, offsetx=start, offsety=i)
+
+ if z is not None:
+
+ # Hi = Fi' * (diag(yi) - yi*yi') * Fi
+ # = Fisc' * Fisc
+ # where
+ # Fisc = diag(yi)^1/2 * (I - 1*yi') * Fi
+ # = diag(yi)^1/2 * (Fi - 1*gradfi')
+
+ Fsc[:K[i], :] = F[start:stop, :]
+ for k in xrange(start,stop):
+ blas.axpy(Df, Fsc, n=n, alpha=-1.0, incx=mnl+1,
+ incy=Fsc.size[0], offsetx=i, offsety=k-start)
+ blas.scal(math.sqrt(y[k]), Fsc, inc=Fsc.size[0],
+ offset=k-start)
+
+ # H += z[i]*Hi = z[i] * Fisc' * Fisc
+ blas.syrk(Fsc, H, trans='T', k=stop-start, alpha=z[i],
+ beta=1.0)
+
+ if z is None: return f, Df
+ else: return f, Df, H
+
+ return cp(Fgp, G, h, A, b)
diff --git a/src/python/info.py b/src/python/info.py
new file mode 100644
index 0000000..43dd9db
--- /dev/null
+++ b/src/python/info.py
@@ -0,0 +1,41 @@
+version = '0.8.2'
+
+def license(): print(
+"""CVXOPT version 0.8.2. Copyright (c) 2004-2007 J. Dahl and L. Vandenberghe.
+
+This program is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free Software
+Foundation; either version 2 of the License, or (at your option) any later
+version.
+
+This program is distributed in the hope that it will be useful, but WITHOUT
+ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+The full text of the GNU General Public License can be found at
+www.gnu.org/copyleft/gpl.html or in the LICENSE file distributed with CVXOPT.
+
+The CVXOPT distribution includes source code for the following software
+libraries. The copyright of these libraries is owned by their authors.
+
+1. Part of the SuiteSparse suite of sparse matrix algorithms, including:
+ - AMD Version 2.0. Copyright (c) 2006 by Timothy A. Davis,
+ Patrick R. Amestoy, and Iain S. Duff.
+ - CHOLMOD Version 1.4. Copyright (c) 2005-2006 by University of Florida,
+ Timothy A. Davis and W. Hager.
+ - COLAMD version 2.6. Copyright (c) 1998-2006 by Timothy A. Davis.
+ - UMFPACK Version 5.0.2. Copyright (c) 1995-2006 by Timothy A. Davis.
+
+ These packages are licensed under the terms of the GNU Lesser General Public
+ License (UMFPACK, parts of CHOLMOD, AMD, COLAMD) and the GNU General Public
+ License (parts of CHOLMOD). For details, consult the README files in the
+ source directories or the website listed below.
+
+ Availability: www.cise.ufl.edu/research/sparse.
+
+2. RNGS Random Number Generation -- Multiple Streams (Sep. 22, 1998) by Steve
+ Park and Dave Geyer.
+
+ Availability: www.cs.wm.edu/~va/software/park/park.html.
+"""
+)
diff --git a/src/python/misc.py b/src/python/misc.py
new file mode 100644
index 0000000..df2f8f2
--- /dev/null
+++ b/src/python/misc.py
@@ -0,0 +1,515 @@
+"""
+Miscellaneous functions used by the CVXOPT solvers.
+"""
+
+# This file is part of CVXOPT version 0.8.2.
+# Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+
+import math
+from cvxopt import base, blas, lapack, cholmod
+from cvxopt.base import matrix, spmatrix
+cholmod.options['supernodal'] = 2
+
+__all__ = []
+
+def had(x,y):
+ """
+ Returns Hadamard product x.*y of dense 'd' matrices x and y.
+
+ x and y are 'd' matrices of equal size.
+
+ Returns x .* y as a new matrix.
+ """
+
+ if x.size != y.size:
+ raise ValueError, "x and y must have the same size"
+ z = +x
+ blas.tbmv(y, z, n=len(y), k=0, ldA=1)
+ return z
+
+
+def had2(x, y, n=None):
+ """
+ In-place Hadamard product x.*y of dense 'd' matrices x and y.
+
+ x and y are 'd' matrices of equal size.
+
+ n is a nonnegative integer, with default value len(x). If the
+ default value is used, len(x) must be equal to len(y).
+
+ On exit x[:n] is replaced with x[:n].*y[:n].
+ """
+
+ if n is None:
+ if x.size != y.size:
+ raise ValueError, "x and y must have the same size"
+ else:
+ n = len(x)
+ if len(x) < n or len(y) < n:
+ raise ValueError, "x and y must have length at least n"
+ blas.tbmv(y, x, n=n, k=0, ldA=1)
+
+
+def ihad(x,y):
+ """
+ Returns componentwise division x./y of dense 'd' matrices x and y.
+
+ y is a 'd' matrix. x is a scalar or a 'd' matrix of the same
+ size as y.
+
+ Returns x ./ y as a new matrix.
+ """
+
+ if type(x) is float or type(x) is int:
+ z = matrix(x, y.size, tc='d')
+ else:
+ z = +x
+ if z.size != y.size:
+ raise ValueError, "x and y must have the same size"
+ blas.tbsv(y, z, n=len(y), k=0, ldA=1)
+ return z
+
+
+def ihad2(x, y, n=None):
+ """
+ In-place Hadamard division x./y of dense matrices x and y.
+
+ x and y are dense 'd' matrices of equal size.
+
+ n is a nonnegative integer, with default value len(x). If the
+ default value is used, len(x) must be equal to len(y).
+
+ On exit x[:n] is replaced with x[:n]./y[:n].
+ """
+
+ if n is None:
+ if x.size != y.size:
+ raise ValueError, "x and y must have the same size"
+ else:
+ n = len(x)
+ if len(x) < n or len(y) < n:
+ raise ValueError, "x and y must have length at least n"
+ blas.tbsv(y, x, n=n, k=0, ldA=1)
+
+
+def scopy(x, y):
+ """
+ y := x for symmetric or block-diagonal symmetric dense matrices.
+ """
+
+ if type(x) is matrix:
+ blas.copy(x, y)
+ else:
+ for k in xrange(len(x)): blas.copy(x[k], y[k])
+
+
+def sdot(x, y):
+ """
+ Inner product of two block-diagonal symmetric dense 'd' matrices.
+
+ x and y are square dense 'd' matrices, or lists of N square dense
+ 'd' matrices.
+ """
+
+ a = 0.0
+ if type(x) is matrix:
+ n = x.size[0]
+ a += blas.dot(x, y, incx=n+1, incy=n+1, n=n)
+ for j in xrange(1,n):
+ a += 2.0 * blas.dot(x, y, incx=n+1, incy=n+1, offsetx=j,
+ offsety=j, n=n-j)
+
+ else:
+ for k in xrange(len(x)):
+ n = x[k].size[0]
+ a += blas.dot(x[k], y[k], incx=n+1, incy=n+1, n=n)
+ for j in xrange(1,n):
+ a += 2.0 * blas.dot(x[k], y[k], incx=n+1, incy=n+1,
+ offsetx=j, offsety=j, n=n-j)
+ return a
+
+
+def sscal(alpha, x):
+ """
+ x := alpha*x for symmetric or block-diagonal symmetric dense 'd'
+ matrices.
+ """
+
+ if type(x) is matrix:
+ blas.scal(alpha, x)
+ else:
+ for xk in x: blas.scal(alpha, xk)
+
+
+def saxpy(x, y, alpha=1.0):
+ """
+ y := alpha*x + y for symmetric or block-diagonal symmetric dense
+ 'd' matrices.
+ """
+
+ if type(x) is matrix:
+ blas.axpy(x, y, alpha=alpha)
+ else:
+ for k in xrange(len(x)): blas.axpy(x[k], y[k], alpha=alpha)
+
+
+def snrm2(x):
+ """
+ Frobenius norm of symmetric matrix or block-diagonal symmetric
+ dense 'd' matrix.
+ """
+
+ return math.sqrt(sdot(x,x))
+
+
+def cngrnc(R, X, Y, trans='N', alpha=1.0, beta=0.0):
+ """
+ Congruence transformation
+
+ Y := alpha * R*X*R^T + beta*Y if trans is 'N'
+ Y := alpha * R^T*X*R + beta*Y if trans is 'T'
+
+ R, X and Y are lists of square dense 'd' matrices.
+ X may be equal to Y.
+ Note that trans='T' is slightly faster than trans='N'.
+ """
+
+ maxn = max([0] + [R_k.size[0] for R_k in R])
+ W = matrix(0.0, (maxn,maxn))
+ for k in xrange(len(R)):
+ n = R[k].size[0]
+
+ # scale diagonal of X by 1/2
+ blas.scal(0.5, X[k], inc=n+1)
+
+ # W := R*tril(X) (trans is 'N') or W := tril(X)*R (trans is 'T')
+ blas.copy(R[k], W)
+ if trans == 'N':
+ blas.trmm(X[k], W, side='R', m=n, n=n, ldB=n)
+ else:
+ blas.trmm(X[k], W, side='L', m=n, n=n, ldB=n)
+
+ # scale diagonal of X by 2
+ blas.scal(2.0, X[k], inc=n+1)
+
+ # Y := alpha*(W*R' + R*W') + beta*Y
+ blas.syr2k(R[k], W, Y[k], trans=trans, n=n, k=n, ldB=n,
+ alpha=alpha, beta=beta)
+
+
+def kkt(H, A, Df, G, method=3):
+ """
+ Generates a solver for the KKT system
+
+ [ H * * * ] [ x ] [ bx ]
+ [ A 0 * * ] [ y ] = [ by ].
+ [ Df 0 -Dnl * ] [ znl ] [ bznl ]
+ [ G 0 0 -Dl ] [ zl ] [ bzl ]
+
+ kkt() does a symbolic factorization and returns a function for the
+ numeric factorization.
+
+ If f = kkt(H, A, Df, G, method) then f(H, Df, dnl, dl) does the
+ numeric factorization of the KKT matrix, with
+
+ Dnl = diag(dnl)^-2, Dl = diag(dl)^-2,
+
+ and returns a function for solving the system. The arguments H
+ and Df in f() can be different from the arguments in the call to
+ kkt() but they must have the same sparsity pattern.
+
+ If g = f(H, Df, dnl, dl) then g(x, y, znl, zl) solves the system.
+ On entry x, y, znl, zl are the righthand side. On exit they are
+ overwritten with the solution.
+ """
+
+ n, p, mnl, ml = H.size[0], A.size[0], Df.size[0], G.size[0]
+
+ if method == 1:
+
+ # Factor entire matrix via dense LDL.
+
+ ldK = n + p + mnl + ml
+ K = matrix(0.0, (ldK,ldK))
+ ipiv = matrix(0, (ldK,1))
+ u = matrix(0.0, (ldK,1))
+ def f(H, Df, dnl, dl):
+ blas.scal(0.0, K)
+ K[:n, :n] = H
+ K[n:n+p, :n] = A
+ K[n+p:n+p+mnl, :n] = Df
+ K[n+p+mnl:, :n] = G
+ K[(ldK+1)*(n+p) : (ldK+1)*(n+p+mnl) : ldK+1] = -dnl**-2
+ K[(ldK+1)*(n+p+mnl) :: ldK+1] = -dl**-2
+ lapack.sytrf(K, ipiv)
+ def g(x, y, znl, zl):
+ u[:n] = x
+ u[n:n+p] = y
+ u[n+p:n+p+mnl] = znl
+ u[n+p+mnl:] = zl
+ lapack.sytrs(K, ipiv, u)
+ x[:] = u[:n]
+ y[:] = u[n:n+p]
+ znl[:] = u[n+p:n+p+mnl]
+ zl[:] = u[n+p+mnl:]
+ return g
+ return f
+
+ elif method == 2:
+
+ # Factor
+ #
+ # [ H + Df'*Dnl^-2*Df + G'*Dl^-2*G * ]
+ # S = [ ]
+ # [ A 0 ]
+ #
+ # via dense LDL (if p > 0) or Cholesky (if p = 0).
+ # To solve the KKT system, first solve
+ #
+ # [ x ] [ bx + Df'*Dnl^-2*bznl + G'*Dl^-2*bzl ]
+ # S * [ ] = [ ]
+ # [ y ] [ by ]
+ #
+ # Dnl^2 * znl = Df*x - bznl
+ # Dl^2 * zl = Dl.^-2 * (G*x - bzl).
+
+ ldK = n + p
+ K = matrix(0.0, (ldK,ldK))
+ if p:
+ ipiv = matrix(0, (ldK,1))
+ if type(G) is matrix:
+ Gsc = matrix(0.0, G.size)
+ else:
+ Gsc = spmatrix(0.0, G.I, G.J, G.size)
+ if type(Df) is matrix:
+ Dfsc = matrix(0.0, Df.size)
+ else:
+ Dfsc = spmatrix(0.0, Df.I, Df.J, Df.size)
+ u = matrix(0.0, (ldK,1))
+ def f(H, Df, dnl, dl):
+ blas.scal(0.0, K)
+ K[:n, :n] = H
+ base.gemm(spmatrix(dnl, range(mnl), range(mnl), tc='d'),
+ Df, Dfsc, partial=True)
+ base.syrk(Dfsc, K, trans='T', beta=1.0)
+ base.gemm(spmatrix(dl, range(ml), range(ml), tc='d'), G,
+ Gsc, partial=True)
+ base.syrk(Gsc, K, trans='T', beta=1.0)
+ K[n:,:n] = A
+ if p:
+ lapack.sytrf(K, ipiv)
+ else:
+ lapack.potrf(K)
+ def g(x, y, znl, zl):
+ u[:n] = x
+ had2(znl, dnl)
+ base.gemv(Dfsc, znl, u, trans='T', beta=1.0)
+ had2(zl, dl)
+ base.gemv(Gsc, zl, u, trans='T', beta=1.0)
+ u[n:n+p] = y
+ if p:
+ lapack.sytrs(K, ipiv, u)
+ else:
+ lapack.potrs(K, u)
+ x[:] = u[:n]
+ y[:] = u[n:n+p]
+ base.gemv(Dfsc, x, znl, beta=-1.0)
+ had2(znl, dnl)
+ base.gemv(Gsc, x, zl, beta=-1.0)
+ had2(zl, dl)
+ return g
+ return f
+
+ else:
+
+ # Factor
+ #
+ # S = H + Df'*Dnl^-2*Df + G'*Dl^-2*G
+ # K = A*S^-1*A'
+ #
+ # using dense (L*L') or sparse (P'*L*L'*P) Cholesky
+ # factorizations. To solve the system, solve
+ #
+ # K*y = A * S^{-1} * (bx + Df'*Dnl^-2*bznl + G'*Dl^-2*bzl)
+ # - by
+ # S*x = bx + Df'*Dnl.^-2* bznl + G'*Dl^-2*bzl - A'*y
+ # Dnl^2 * znl = Df*x - bznl
+ # Dl^2 * zl = G*x - bzl
+ #
+ # If S turns out to be singular in the first factorization,
+ # then switch to the following method.
+ #
+ # Factor
+ #
+ # S = H + Df'*Dnl^-2*Df + G'*Dl^-2*G + A'*A
+ # K = A*S^-1*A'
+ #
+ # using dense (L*L') or sparse (P'*L*L'*P) Cholesky
+ # factorizations. To solve the system, solve
+ #
+ # K*y = A*S^{-1} * (bx + Df'*Dnl^-2*bznl + G'*Dl^-2*bzl +
+ # A'*by) - by
+ # S*x = bx + Df'*Dnl.^-2*bznl + G'*Dl^-2*bzl + A'*by - A'*y
+ # Dnl^2*znl = Df*x - bznl
+ # Dl^2*zl = G*x - bzl.
+
+ if type(G) is matrix:
+ Gsc = matrix(0.0, G.size)
+ else:
+ Gsc = spmatrix(0.0, G.I, G.J, G.size)
+ if type(Df) is matrix:
+ Dfsc = matrix(0.0, Df.size)
+ else:
+ Dfsc = spmatrix(0.0, Df.I, Df.J, Df.size)
+ F = {'firstcall': True, 'singular': False}
+ if matrix in (type(H), type(G), type(Df)):
+ F['S'] = matrix(0.0, (n,n))
+ F['K'] = matrix(0.0, (p,p))
+ else:
+ F['S'] = spmatrix([], [], [], (n,n), 'd')
+ F['Sf'] = None
+ if type(A) is matrix:
+ F['K'] = matrix(0.0, (p,p))
+ else:
+ F['K'] = spmatrix([], [], [], (p,p), 'd')
+
+ def f(H, Df, dnl, dl):
+ base.gemm(spmatrix(dnl, range(mnl), range(mnl), tc='d'), Df,
+ Dfsc, partial=True)
+ base.gemm(spmatrix(dl, range(ml), range(ml), tc='d'), G,
+ Gsc, partial=True)
+ if F['firstcall']:
+ F['firstcall'] = False
+ F['S'][:,:] = H
+ base.syrk(Dfsc, F['S'], trans='T', beta=1.0)
+ base.syrk(Gsc, F['S'], trans='T', beta=1.0)
+ try:
+ if type(F['S']) is matrix:
+ lapack.potrf(F['S'])
+ else:
+ F['Sf'] = cholmod.symbolic(F['S'])
+ cholmod.numeric(F['S'], F['Sf'])
+ except ArithmeticError:
+ F['singular'] = True
+ if type(A) is matrix and type(F['S']) is spmatrix:
+ F['S'] = matrix(0.0, (n,n))
+ F['S'][:,:] = H
+ base.syrk(Dfsc, F['S'], trans='T', beta=1.0)
+ base.syrk(Gsc, F['S'], trans='T', beta=1.0)
+ base.syrk(A, F['S'], trans='T', beta=1.0)
+ if type(F['S']) is matrix:
+ lapack.potrf(F['S'])
+ else:
+ F['Sf'] = cholmod.symbolic(F['S'])
+ cholmod.numeric(F['S'], F['Sf'])
+
+ else:
+ # S := H, but do not remove nonzeros from the zero
+ # pattern of S if S is sparse.
+ if type(F['S']) is spmatrix and type(H) is spmatrix:
+ F['S'] *= 0.0
+ F['S'] += H
+ else:
+ F['S'][:,:] = H
+
+ base.syrk(Dfsc, F['S'], trans='T', beta=1.0,
+ partial=True)
+ base.syrk(Gsc, F['S'], trans='T', beta=1.0,
+ partial=True)
+ if F['singular']:
+ base.syrk(A, F['S'], trans='T', beta=1.0,
+ partial=True)
+ if type(F['S']) is matrix:
+ lapack.potrf(F['S'])
+ else:
+ cholmod.numeric(F['S'], F['Sf'])
+
+ if type(F['S']) is matrix:
+ # Asct := L^-1*A', factor K = Asct'*Asct.
+ if type(A) is matrix:
+ Asct = A.T
+ else:
+ Asct = matrix(A.T)
+ blas.trsm(F['S'], Asct)
+ blas.syrk(Asct, F['K'], trans='T')
+ lapack.potrf(F['K'])
+
+ else:
+ # Asct := L^{-1}*P*A' and factor K = Asct'*Asct.
+ if type(A) is matrix:
+ Asct = A.T
+ cholmod.solve(F['Sf'], Asct, sys=7)
+ cholmod.solve(F['Sf'], Asct, sys=4)
+ blas.syrk(Asct, F['K'], trans='T')
+ lapack.potrf(F['K'])
+ else:
+ Asct = cholmod.spsolve(F['Sf'], A.T, sys=7)
+ Asct = cholmod.spsolve(F['Sf'], Asct, sys=4)
+ base.syrk(Asct, F['K'], trans='T')
+ Kf = cholmod.symbolic(F['K'])
+ cholmod.numeric(F['K'], Kf)
+
+ def g(x, y, znl, zl):
+
+ # If not F['singular']:
+ # x := L^{-1} * P * (x + Df'*(dnl.^2.*znl) +
+ # G'*dl.^2.*zl)
+ # = L^{-1} * P * (bx + Df'*Dnl^-2*bznl +
+ # G'*Dl^-2*bzl)
+ #
+ # If F['singular']:
+ # x := L^{-1} * P * (x + Df'*(dnl.^2.*znl) +
+ # G'*(dl.^2.*zl) + A'*y)
+ # = L^{-1} * P * (bx + Df'*Dnl^-2*bznl +
+ # G'*Dl^-2*bzl + A'*by)
+
+ had2(znl, dnl)
+ base.gemv(Dfsc, znl, x, trans='T', beta=1.0)
+ had2(zl, dl)
+ base.gemv(Gsc, zl, x, trans='T', beta=1.0)
+ if F['singular']:
+ base.gemv(A, y, x, trans='T', beta=1.0)
+ if type(F['S']) is matrix:
+ blas.trsv(F['S'], x)
+ else:
+ cholmod.solve(F['Sf'], x, sys=7)
+ cholmod.solve(F['Sf'], x, sys=4)
+
+ # y := K^{-1} * (Asc*x - y)
+ # = K^{-1} * (A * S^{-1} * (bx + Df'*Dnl^-2*bznl +
+ # G'*Dl^-2*bzl) - by) (if not F['singular'])
+ # = K^{-1} * (A * S^{-1} * (bx + Df'*Dnl^-2*bznl +
+ # G'*Dl^-2*bzl + A'*by) - by) (if F['singular'])
+
+ base.gemv(Asct, x, y, trans='T', beta=-1.0)
+ if type(F['K']) is matrix:
+ lapack.potrs(F['K'], y)
+ else:
+ cholmod.solve(Kf, y)
+
+ # x := P' * L^{-T} * (x - Asc'*y)
+ # = S^{-1} * (bx + Df'*Dnl^-2*bznl + G'*Dl^-2*bzl
+ # - A'*y) (if not F['singular'])
+ # = S^{-1} * (bx + Df'*Dnl^-2*bznl + G'*Dl^-2*bzl
+ # + A'*by - A'*y) (if F['singular'])
+
+ base.gemv(Asct, y, x, alpha=-1.0, beta=1.0)
+ if type(F['S']) is matrix:
+ blas.trsv(F['S'], x, trans='T')
+ else:
+ cholmod.solve(F['Sf'], x, sys=5)
+ cholmod.solve(F['Sf'], x, sys=8)
+
+ # znl := dnl .* (Dfsc*x - znl)
+ # = Dnl^-2 * (Df*x - bznl)
+ base.gemv(Dfsc, x, znl, beta=-1.0)
+ had2(znl, dnl)
+
+ # zl := dl .* (Gsc*x - zl)
+ # = Dl^-2 * (G*x - bzl)
+ base.gemv(Gsc, x, zl, beta=-1.0)
+ had2(zl, dl)
+
+ return g
+
+ return f
diff --git a/src/python/modeling.py b/src/python/modeling.py
new file mode 100644
index 0000000..8b8cb70
--- /dev/null
+++ b/src/python/modeling.py
@@ -0,0 +1,3214 @@
+"""
+Modeling tools for PWL convex optimization.
+
+Routines for specifying and solving convex optimization problems with
+piecewise-linear objective and constraint functions.
+"""
+
+# This file is part of CVXOPT version 0.8.2.
+# Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+
+from string import strip
+from cvxopt.base import matrix, spmatrix
+from cvxopt import blas, solvers
+import __builtin__
+
+__all__ = ["variable", "constraint", "op", "min", "max", "sum", "dot"]
+
+class variable(object):
+
+ """
+ Vector valued optimization variable.
+
+ variable(size=1, name='') creates a variable of length size.
+
+
+ Arguments:
+
+ size length of the variable (positive integer)
+ name name of the variable (string)
+
+
+ Attributes:
+
+ name the name of the variable
+ value None or a 'd' matrix of size (len(self),1)
+ _size the length of the variable
+ """
+
+ def __init__(self, size=1, name=''):
+
+ self.name = name
+ self.value = None
+ if type(size) is int and size > 0:
+ self._size = size
+ else:
+ raise TypeError, "size must be a positive integer"
+
+
+ def __len__(self):
+
+ return self._size
+
+
+ def __repr__(self):
+
+ return "variable(%d,'%s')" %(len(self),self.name)
+
+
+ def __str__(self):
+
+ s = self.name
+ if self.name: s += ': '
+ s += 'variable of length %d\nvalue: ' %len(self)
+ if self.value is None:
+ s += 'None'
+ else:
+ s += '\n' + str(self.value)
+ return s
+
+
+ def __setattr__(self,name,value):
+
+ if name == 'value':
+ if value is None or (_isdmatrix(value) and
+ value.size == (len(self),1)):
+ object.__setattr__(self, name, value)
+
+ elif type(value) is int or type(value) is float:
+ object.__setattr__(self, name,
+ matrix(value, (len(self),1), tc='d'))
+
+ else:
+ raise AttributeError, "invalid type or size for "\
+ "attribute 'value'"
+
+ elif name == 'name':
+ if type(value) is str:
+ object.__setattr__(self,name,value)
+
+ else:
+ raise AttributeError, "invalid type for attribute "\
+ "'name'"
+
+ elif name == '_size':
+ object.__setattr__(self,name,value)
+
+ else:
+ raise AttributeError, "'variable' object has no attribute "\
+ "'%s'" %name
+
+
+ def __pos__(self):
+
+ f = _function()
+ f._linear._coeff[self] = matrix(1.0)
+ return f
+
+
+ def __neg__(self):
+
+ f = _function()
+ f._linear._coeff[self] = matrix(-1.0)
+ return f
+
+
+ def __abs__(self):
+
+ return max(self,-self)
+
+
+ def __add__(self,other):
+
+ return (+self).__add__(other)
+
+
+ def __radd__(self,other):
+
+ return (+self).__radd__(other)
+
+
+ def __iadd__(self,other):
+
+ raise NotImplementedError, "in-place addition not implemented"\
+ " for 'variable' objects"
+
+
+ def __sub__(self,other):
+
+ return (+self).__sub__(other)
+
+
+ def __rsub__(self,other):
+
+ return (+self).__rsub__(other)
+
+
+ def __isub__(self,other):
+
+ raise NotImplementedError, "in-place subtraction not "\
+ "implemented for 'variable' objects"
+
+
+ def __mul__(self,other):
+
+ return (+self).__mul__(other)
+
+
+ def __rmul__(self,other):
+
+ return (+self).__rmul__(other)
+
+
+ def __imul__(self,other):
+
+ raise NotImplementedError, "in-place multiplication not "\
+ "implemented for 'variable' objects"
+
+
+ def __div__(self,other):
+
+ return (+self).__div__(other)
+
+
+ def __idiv__(self,other):
+
+ raise NotImplementedError, "in-place division not implemented "\
+ "for 'variable' objects"
+
+
+ def __eq__(self,other):
+
+ return constraint(self-other, '=')
+
+
+ def __le__(self,other):
+
+ return constraint(self-other, '<')
+
+
+ def __ge__(self,other):
+
+ return constraint(other-self, '<')
+
+
+ def __lt__(self,other):
+
+ raise NotImplementedError
+
+
+ def __gt__(self,other):
+
+ raise NotImplementedError
+
+
+ def __getitem__(self,key):
+
+ return (+self).__getitem__(key)
+
+
+
+class _function(object):
+
+ """
+ Vector valued function.
+
+ General form:
+
+ f = constant + linear + sum of nonlinear convex terms +
+ sum of nonlinear concave terms
+
+ The length of f is the maximum of the lengths of the terms in the
+ sum. Each term must have length 1 or length equal to len(f).
+
+ _function() creates the constant function f=0 with length 1.
+
+
+ Attributes:
+
+ _constant constant term as a 1-column dense 'd' matrix of
+ length 1 or length len(self)
+ _linear linear term as a _lin object of length 1 or length
+ len(self)
+ _cvxterms nonlinear convex terms as a list [f1,f2,...] with
+ each fi of type _minmax or _sum_minmax. Each fi has
+ length 1 or length equal to len(self).
+ _ccvterms nonlinear concave terms as a list [f1,f2,...] with
+ each fi of type _minmax or _sum_minmax. Each fi has
+ length 1 or length equal to len(self).
+
+
+ Methods:
+
+ value() returns the value of the function: None if one of the
+ variables has value None; a dense 'd' matrix of size
+ (len(self),1) if all the variables have values
+ variables() returns a (copy of) the list of variables
+ _iszero() True if self is identically zero
+ _isconstant() True if there are no linear/convex/concave terms
+ _islinear() True if there are no constant/convex/concave terms
+ _isaffine() True if there are no nonlinear convex/concave terms
+ _isconvex() True if there are no nonlinear concave terms
+ _isconcave() True if there are no nonlinear convex terms
+ """
+
+ def __init__(self):
+
+ self._constant = matrix(0.0)
+ self._linear = _lin()
+ self._cvxterms = []
+ self._ccvterms = []
+
+
+ def __len__(self):
+
+ if len(self._constant) > 1: return len(self._constant)
+
+ lg = len(self._linear)
+ if lg > 1: return lg
+
+ for f in self._cvxterms:
+ lg = len(f)
+ if lg > 1: return lg
+
+ for f in self._ccvterms:
+ lg = len(f)
+ if lg > 1: return lg
+
+ return 1
+
+
+ def __repr__(self):
+
+ if self._iszero():
+ return '<zero function of length %d>' %len(self)
+
+ elif self._isconstant():
+ return '<constant function of length %d>' %len(self)
+
+ elif self._islinear():
+ return '<linear function of length %d>' %len(self)
+
+ elif self._isaffine():
+ return '<affine function of length %d>' %len(self)
+
+ elif self._isconvex():
+ return '<convex function of length %d>' %len(self)
+
+ elif self._isconcave():
+ return '<concave function of length %d>' %len(self)
+
+ else:
+ return '<function of length %d>' %len(self)
+
+
+ def __str__(self):
+
+ s = repr(self)[1:-1]
+
+ # print constant term if nonzero
+ if not self._iszero() and (len(self._constant) != 1 or
+ self._constant[0]):
+ s += '\nconstant term:\n' + str(self._constant)
+
+ else:
+ s += '\n'
+
+ # print linear term if nonzero
+ if self._linear._coeff:
+ s += 'linear term: ' + str(self._linear)
+
+ # print nonlinear convex term if nonzero
+ if self._cvxterms:
+ s += '%d nonlinear convex term(s):' %len(self._cvxterms)
+ for f in self._cvxterms: s += '\n' + str(f)
+
+ # print nonlinear concave term if nonzero
+ if self._ccvterms:
+ s += '%d nonlinear concave term(s):' %len(self._ccvterms)
+ for f in self._ccvterms: s += '\n' + str(f)
+
+ return s
+
+
+ def value(self):
+
+ val = self._constant
+
+ if self._linear._coeff:
+ nval = self._linear.value()
+ if nval is None: return None
+ else: val = val + nval
+
+ for f in self._cvxterms:
+ nval = f.value()
+ if nval is None: return None
+ else: val = val + nval
+
+ for f in self._ccvterms:
+ nval = f.value()
+ if nval is None: return None
+ else: val = val + nval
+
+ return val
+
+
+ def variables(self):
+
+ l = self._linear.variables()
+ for f in self._cvxterms:
+ l += [v for v in f.variables() if v not in l]
+ for f in self._ccvterms:
+ l += [v for v in f.variables() if v not in l]
+ return l
+
+
+ def _iszero(self):
+
+ if not self._linear._coeff and not self._cvxterms and \
+ not self._ccvterms and not blas.nrm2(self._constant):
+ return True
+ else: return False
+
+
+ def _isconstant(self):
+
+ if not self._linear._coeff and not self._cvxterms and \
+ not self._ccvterms: return True
+ else: return False
+
+
+ def _islinear(self):
+
+ if len(self._constant) == 1 and not self._constant[0] and \
+ not self._cvxterms and not self._ccvterms: return True
+ else: return False
+
+
+ def _isaffine(self):
+
+ if not self._cvxterms and not self._ccvterms: return True
+ else: return False
+
+
+ def _isconvex(self):
+
+ if not self._ccvterms: return True
+ else: return False
+
+
+ def _isconcave(self):
+
+ if not self._cvxterms: return True
+ else: return False
+
+
+ def __pos__(self):
+
+ f = _function()
+ f._constant = +self._constant
+ f._linear = +self._linear
+ f._cvxterms = [+g for g in self._cvxterms]
+ f._ccvterms = [+g for g in self._ccvterms]
+ return f
+
+
+ def __neg__(self):
+
+ f = _function()
+ f._constant = -self._constant
+ f._linear = -self._linear
+ f._ccvterms = [-g for g in self._cvxterms]
+ f._cvxterms = [-g for g in self._ccvterms]
+ return f
+
+
+ def __add__(self,other):
+
+ # convert other to matrix (dense 'd' or sparse) or _function
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+ elif _ismatrix(other): # ie, dense 'd' or sparse
+ if other.size[1] != 1:
+ raise ValueError, 'incompatible dimensions'
+ elif type(other) is variable:
+ other = +other
+ elif type(other) is not _function:
+ return NotImplemented
+
+ if 1 != len(self) != len(other) != 1:
+ raise ValueError, 'incompatible lengths'
+
+ f = _function()
+
+ if _ismatrix(other):
+ # this converts sparse other to dense 'd'
+ f._constant = self._constant + other
+ f._linear = +self._linear
+ f._cvxterms = [+fk for fk in self._cvxterms]
+ f._ccvterms = [+fk for fk in self._ccvterms]
+
+ else: #type(other) is _function:
+ if not (self._isconvex() and other._isconvex()) and \
+ not (self._isconcave() and other._isconcave()):
+ raise ValueError, 'operands must be both convex or '\
+ 'both concave'
+
+ f._constant = self._constant + other._constant
+ f._linear = self._linear + other._linear
+ f._cvxterms = [+fk for fk in self._cvxterms] + \
+ [+fk for fk in other._cvxterms]
+ f._ccvterms = [+fk for fk in self._ccvterms] + \
+ [+fk for fk in other._ccvterms]
+
+ return f
+
+
+ def __radd__(self,other):
+
+ return self.__add__(other)
+
+
+ def __iadd__(self,other):
+
+ # convert other to matrix (dense 'd' or sparse) or _function
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+ elif _ismatrix(other):
+ if other.size[1] != 1:
+ raise ValueError, 'incompatible dimensions'
+ elif type(other) is variable:
+ other = +other
+ elif type(other) is not _function:
+ return NotImplemented
+
+ if len(self) != len(other) != 1:
+ raise ValueError, 'incompatible lengths'
+
+ if _ismatrix(other):
+ if 1 == len(self._constant) != len(other):
+ self._constant = self._constant + other
+ else:
+ self._constant += other
+
+ else: #type(other) is _function:
+ if not (self._isconvex() and other._isconvex()) and \
+ not (self._isconcave() and other._isconcave()):
+ raise ValueError, 'operands must be both convex or '\
+ 'both concave'
+
+ if 1 == len(self._constant) != len(other._constant):
+ self._constant = self._constant + other._constant
+ else:
+ self._constant += other._constant
+
+ if 1 == len(self._linear) != len(other._linear):
+ self._linear = self._linear + other._linear
+ else:
+ self._linear += other._linear
+
+ self._cvxterms += [+fk for fk in other._cvxterms]
+ self._ccvterms += [+fk for fk in other._ccvterms]
+
+ return self
+
+
+ def __sub__(self,other):
+
+ # convert other to matrix (dense 'd' or sparse) or _function
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+ elif _ismatrix(other):
+ if other.size[1] != 1:
+ raise ValueError, 'incompatible dimensions'
+ elif type(other) is variable:
+ other = +other
+ elif type(other) is not _function:
+ return NotImplemented
+
+ if 1 != len(self) != len(other) != 1:
+ raise ValueError, 'incompatible lengths'
+
+ f = _function()
+
+ if _ismatrix(other):
+ f._constant = self._constant - other
+ f._linear = +self._linear
+ f._cvxterms = [+fk for fk in self._cvxterms]
+ f._ccvterms = [+fk for fk in self._ccvterms]
+
+ else: #type(other) is _function:
+ if not (self._isconvex() and other._isconcave()) and \
+ not (self._isconcave() and other._isconvex()):
+ raise ValueError, 'operands must be convex and '\
+ 'concave or concave and convex'
+
+ f._constant = self._constant - other._constant
+ f._linear = self._linear - other._linear
+ f._cvxterms = [+fk for fk in self._cvxterms] + \
+ [-fk for fk in other._ccvterms]
+ f._ccvterms = [+fk for fk in self._ccvterms] + \
+ [-fk for fk in other._cvxterms]
+
+ return f
+
+
+ def __rsub__(self,other):
+
+ # convert other to matrix (dense 'd' or sparse) or _function
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+ elif _isdmatrix(other):
+ if other.size[1] != 1:
+ raise ValueError, 'incompatible dimensions'
+ elif type(other) is variable:
+ other = +other
+ elif type(other) is not _function:
+ return NotImplemented
+
+ if 1 != len(self) != len(other) != 1:
+ raise ValueError, 'incompatible lengths'
+
+ f = _function()
+
+ if _ismatrix(other):
+ f._constant = other - self._constant
+ f._linear = -self._linear
+ f._cvxterms = [-fk for fk in self._ccvterms]
+ f._ccvterms = [-fk for fk in self._cvxterms]
+
+ else: # type(other) is _function:
+ if not (self._isconvex() and other._isconcave()) and \
+ not (self._isconcave() and other._isconvex()):
+ raise ValueError, 'operands must be convex and '\
+ 'concave or concave and convex'
+
+ f._constant = other._constant - self._constant
+ f._linear = other._linear - self._linear
+ f._cvxterms = [-fk for fk in self._ccvterms] + \
+ [fk for fk in other._cvxterms]
+ f._ccvterms = [-fk for fk in self._cvxterms] + \
+ [fk for fk in other._ccvterms]
+
+ return f
+
+
+ def __isub__(self,other):
+
+ # convert other to matrix (dense or sparse 'd') or _function
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+ elif _ismatrix(other):
+ if other.size[1] != 1:
+ raise ValueError, 'incompatible dimensions'
+ elif type(other) is variable:
+ other = +other
+ elif type(other) is not _function:
+ return NotImplemented
+
+ if len(self) != len(other) != 1:
+ raise ValueError, 'incompatible lengths'
+
+ if _ismatrix(other):
+ if 1 == len(self._constant) != len(other):
+ self._constant = self._constant - other
+ else:
+ self._constant -= other
+
+ else: #type(other) is _function:
+ if not (self._isconvex() and other._isconcave()) and \
+ not (self._isconcave() and other._isconvex()):
+ raise ValueError, 'operands must be convex and '\
+ 'concave or concave and convex'
+
+ if 1 == len(self._constant) != len(other._constant):
+ self._constant = self._constant - other._constant
+ else:
+ self._constant -= other._constant
+
+ if 1 == len(self._linear) != len(other._linear):
+ self._linear = self._linear - other._linear
+ else:
+ self._linear -= other._linear
+
+ self._cvxterms += [-fk for fk in other._ccvterms]
+ self._ccvterms += [-fk for fk in other._cvxterms]
+
+ return self
+
+
+ def __mul__(self,other):
+
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+
+ if (_ismatrix(other) and other.size == (1,1)) or \
+ (_isdmatrix(other) and other.size[1] == 1 == len(self)):
+
+ f = _function()
+
+ if other.size == (1,1) and other[0] == 0.0:
+ # if other is zero, return constant zero function
+ # of length len(self)
+ f._constant = matrix(0.0, (len(self),1))
+ return f
+
+ if len(self._constant) != 1 or self._constant[0]:
+ # skip if self._constant is zero
+ f._constant = self._constant*other
+
+ if self._linear._coeff:
+ # skip if self._linear is zero
+ f._linear = self._linear*other
+
+ if not self._isaffine():
+ # allow only multiplication with scalar
+ if other.size == (1,1):
+ if other[0] > 0.0:
+ f._cvxterms = \
+ [fk*other[0] for fk in self._cvxterms]
+ f._ccvterms = \
+ [fk*other[0] for fk in self._ccvterms]
+
+ elif other[0] < 0.0:
+ f._cvxterms = \
+ [fk*other[0] for fk in self._ccvterms]
+ f._ccvterms = \
+ [fk*other[0] for fk in self._cvxterms]
+
+ else: # already dealt with above
+ pass
+
+ else:
+ raise ValueError, 'can only multiply with scalar'
+
+ else:
+ raise TypeError, 'incompatible dimensions or types'
+
+ return f
+
+
+ def __rmul__(self,other):
+
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+
+ lg = len(self)
+
+ if (_ismatrix(other) and other.size[1] == lg) or \
+ (_isdmatrix(other) and other.size == (1,1)):
+
+ f = _function()
+
+ if other.size == (1,1) and other[0] == 0.0:
+ # if other is zero, return constant zero function
+ # of length len(self)
+ f._constant = matrix(0.0, (len(self),1))
+ return f
+
+ if len(self._constant) != 1 or self._constant[0]:
+ if 1 == len(self._constant) != lg and \
+ not _isscalar(other):
+ f._constant = other * self._constant[lg*[0]]
+ else:
+ f._constant = other * self._constant
+
+ if self._linear._coeff:
+ if 1 == len(self._linear) != lg and \
+ not _isscalar(other):
+ f._linear = other * self._linear[lg*[0]]
+ else:
+ f._linear = other * self._linear
+
+ if not self._isaffine():
+ # allow only scalar multiplication
+ if other.size == (1,1):
+ if other[0] > 0.0:
+ f._cvxterms = [other[0] * fk for
+ fk in self._cvxterms]
+ f._ccvterms = [other[0] * fk for
+ fk in self._ccvterms]
+
+ elif other[0] < 0.0:
+ f._cvxterms = [other[0] * fk for
+ fk in self._ccvterms]
+ f._ccvterms = [other[0] * fk for
+ fk in self._cvxterms]
+
+ else: pass
+
+ else:
+ raise ValueError, 'can only multiply with scalar'
+
+ else:
+ raise TypeError, 'incompatible dimensions or types'
+
+ return f
+
+
+ def __imul__(self,other):
+
+ if type(other) is int or type(other) is float:
+ other = matrix(other, tc='d')
+
+ if _isdmatrix(other) and other.size == (1,1):
+
+ if other[0] == 0.0:
+ self._constant = matrix(0.0, (len(self),1))
+ return self
+
+ if len(self._constant) != 1 or self._constant[0]:
+ self._constant *= other[0]
+
+ if self._linear._coeff: self._linear *= other[0]
+
+ if not self._isaffine():
+ if other[0] > 0.0:
+ for f in self._cvxterms: f *= other[0]
+ for f in self._ccvterms: f *= other[0]
+
+ elif other[0] < 0.0:
+ cvxterms = [f*other[0] for f in self._ccvterms]
+ self._ccvterms = [f*other[0] for f in
+ self._cvxterms]
+ self._cvxterms = cvxterms
+
+ else:
+ pass
+
+ return self
+
+ else:
+ raise TypeError, 'incompatible dimensions or types'
+
+
+ def __div__(self,other):
+
+ if type(other) is int or type(other) is float:
+ return self.__mul__(1.0/other)
+
+ elif _isdmatrix(other) and other.size == (1,1):
+ return self.__mul__(1.0/other[0])
+
+ else:
+ return NotImplemented
+
+
+ def __rdiv__(self,other):
+
+ return NotImplemented
+
+
+ def __idiv__(self,other):
+
+ if type(other) is int or type(other) is float:
+ return self.__imul__(1.0/other)
+
+ elif _isdmatrix(other) and other.size == (1,1):
+ return self.__imul__(1.0/other[0])
+
+ else:
+ return NotImplemented
+
+
+ def __abs__(self):
+
+ return max(self,-self)
+
+
+ def __eq__(self,other):
+
+ return constraint(self-other, '=')
+
+
+ def __le__(self,other):
+
+ return constraint(self-other, '<')
+
+
+ def __ge__(self,other):
+
+ return constraint(other-self, '<')
+
+
+ def __lt__(self,other):
+
+ raise NotImplementedError
+
+
+ def __gt__(self,other):
+
+ raise NotImplementedError
+
+
+ def __getitem__(self,key):
+
+ lg = len(self)
+ l = _keytolist(key,lg)
+ if not l: raise ValueError, 'empty index set'
+
+ f = _function()
+
+ if len(self._constant) != 1 or self._constant[0]:
+ if 1 == len(self._constant) != lg:
+ f._constant = +self._constant
+ else:
+ f._constant = self._constant[l]
+
+ if self._linear:
+ if 1 == len(self._linear) != lg:
+ f._linear = +self._linear
+ else:
+ f._linear = self._linear[l]
+
+ for fk in self._cvxterms:
+ if 1 == len(fk) != lg:
+ f._cvxterms += [+fk]
+
+ elif type(fk) is _minmax:
+ f._cvxterms += [fk[l]]
+
+ else: # type(fk) is _sum_minmax
+ # fk is defined as fk = sum(fmax)
+ fmax = _minmax('max', *fk._flist)
+ # take f += sum_j fk[j][l] = sum_{gk in fmax} gk[l]
+ f._cvxterms += [gk[l] for gk in fmax]
+
+ for fk in self._ccvterms:
+ if 1 == len(fk) != lg:
+ f._ccvterms += [+fk]
+
+ elif type(fk) is _minmax:
+ f._ccvterms += [fk[l]]
+
+ else: # type(fk) is _sum_minmax
+ # fk is defined as fk = sum(fmin)
+ fmin = _minmax('min',*fk._flist)
+ # take f += sum_j fk[j][l] = sum_{gk in fmin} gk[l]
+ f._ccvterms += [gk[l] for gk in fmin]
+
+ return f
+
+
+
+def sum(s):
+
+ """
+ Built-in sum redefined to improve efficiency when s is a vector
+ function.
+
+ If type(s) is not _function object, this is the built-in sum
+ without start argument.
+ """
+
+ if type(s) is _function:
+ lg = len(s)
+ f = _function()
+
+ if 1 == len(s._constant) != lg:
+ f._constant = lg * s._constant
+ else:
+ f._constant = matrix(sum(s._constant), tc='d')
+
+ if 1 == len(s._linear) != lg:
+ f._linear = lg * s._linear
+ else:
+ f._linear = sum(s._linear)
+
+ for c in s._cvxterms:
+ if len(c) == 1:
+ f._cvxterms += [lg*c]
+ else: #type(c) must be _minmax if len(c) > 1
+ f._cvxterms += [_sum_minmax('max', *c._flist)]
+
+ for c in s._ccvterms:
+ if len(c) == 1:
+ f._ccvterms += [lg*c]
+ else: #type(c) must be _minmax if len(c) > 1
+ f._ccvterms += [_sum_minmax('min', *c._flist)]
+
+ return f
+
+ else:
+ return __builtin__.sum(s)
+
+
+
+class _lin(object):
+
+ """
+ Vector valued linear function.
+
+
+ Attributes:
+
+ _coeff dictionary {variable: coefficient}. The coefficients
+ are dense or sparse matrices. Scalar coefficients are
+ stored as 1x1 'd' matrices.
+
+
+ Methods:
+
+ value() returns the value of the function: None if one of the
+ variables has value None; a dense 'd' matrix of size
+ (len(self),1) if all the variables have values
+ variables() returns a (copy of) the list of variables
+ _addterm() adds a linear term a*v
+ _mul() in-place multiplication
+ _rmul() in-place right multiplication
+ """
+
+
+ def __init__(self):
+
+ self._coeff = {}
+
+
+ def __len__(self):
+
+ for v,c in self._coeff.iteritems():
+ if c.size[0] > 1:
+ return c.size[0]
+ elif _isscalar(c) and len(v) > 1:
+ return len(v)
+ return 1
+
+
+ def __repr__(self):
+
+ return '<linear function of length %d>' %len(self)
+
+
+ def __str__(self):
+
+ s = repr(self)[1:-1] + '\n'
+ for v,c in self._coeff.iteritems():
+ s += 'coefficient of ' + repr(v) + ':\n' + str(c)
+ return s
+
+
+ def value(self):
+
+ value = matrix(0.0, (len(self),1))
+ for v,c in self._coeff.iteritems():
+ if v.value is None:
+ return None
+ else:
+ value += c*v.value
+ return value
+
+
+ def variables(self):
+
+ return varlist(self._coeff.keys())
+
+
+ def _addterm(self,a,v):
+
+ """
+ self += a*v with v variable and a int, float, 1x1 dense 'd'
+ matrix, or sparse or dense 'd' matrix with len(v) columns.
+ """
+
+ lg = len(self)
+
+ if self._coeff.has_key(v):
+
+ # self := self + a*v with v a variable of self
+ #
+ # Valid types/sizes:
+ #
+ # 1. a is a matrix (sparse or dense) with a.size[0]>1,
+ # a.size[1]=len(v), and either lg=1 or lg=a.size[0].
+ #
+ # 2. a is a matrix (sparse or dense), a.size = (1,len(v)),
+ # lg arbitrary.
+ #
+ # 3. a is int or float or 1x1 dense matrix, and len(v)>1
+ # and either lg=1 or lg=len(v)
+ #
+ # 4. a is int or float or 1x1 dense matrix, and len(v)=1
+
+ c = self._coeff[v]
+ if _ismatrix(a) and a.size[0] > 1 and a.size[1] == len(v)\
+ and (lg == 1 or lg == a.size[0]):
+ newlg = a.size[0]
+ if c.size == a.size:
+ self._coeff[v] = c + a
+ elif c.size == (1,len(v)):
+ self._coeff[v] = c[newlg*[0],:] + a
+ elif _isdmatrix(c) and c.size == (1,1):
+ m = +a
+ m[::newlg+1] += c[0]
+ self._coeff[v] = m
+ else:
+ raise TypeError, 'incompatible dimensions'
+
+ elif _ismatrix(a) and a.size == (1,len(v)):
+ if c.size == (lg,len(v)):
+ self._coeff[v] = c + a[lg*[0],:]
+ elif c.size == (1,len(v)):
+ self._coeff[v] = c + a
+ elif _isdmatrix(c) and c.size == (1,1):
+ m = a[lg*[0],:]
+ m[::lg+1] += c[0]
+ self._coeff[v] = m
+ else:
+ raise TypeError, 'incompatible dimensions'
+
+ elif _isscalar(a) and len(v) > 1 and (lg == 1 or
+ lg == len(v)):
+ newlg = len(v)
+ if c.size == (newlg,len(v)):
+ self._coeff[v][::newlg+1] = c[::newlg+1] + a
+ elif c.size == (1,len(v)):
+ self._coeff[v] = c[newlg*[0],:]
+ self._coeff[v][::newlg+1] = c[::newlg+1] + a
+ elif _isscalar(c):
+ self._coeff[v] = c + a
+ else:
+ raise TypeError, 'incompatible dimensions'
+
+ elif _isscalar(a) and len(v) == 1:
+ self._coeff[v] = c + a # add a to every elt of c
+
+ else:
+ raise TypeError, 'coefficient has invalid type or '\
+ 'incompatible dimensions '
+
+ elif type(v) is variable:
+
+ # self := self + a*v with v not a variable of self
+ #
+ # 1. if a is a scalar and len(v)=lg or lg=1 or len(v)=1:
+ # convert a to dense 1x1 matrix and add v:a pair to
+ # dictionary
+ #
+ # 2. If a is a matrix (dense or sparse) and a.size[1]=len(v)
+ # and a.size[0]=lg or lg=1 or a.size[0]=1:
+ # make a copy of a and add v:a pair to dictionary
+
+ if _isscalar(a) and (lg == 1 or len(v) == 1 or
+ len(v) == lg):
+ self._coeff[v] = matrix(a, tc='d')
+
+ elif _ismatrix(a) and a.size[1] == len(v) and \
+ (lg == 1 or a.size[0] == 1 or a.size[0] == lg):
+ self._coeff[v] = +a
+
+ else:
+ raise TypeError, 'coefficient has invalid type or '\
+ 'incompatible dimensions '
+
+ else:
+ raise TypeError, 'second argument must be a variable'
+
+
+ def _mul(self,a):
+
+ '''
+ self := self*a where a is scalar or matrix
+ '''
+
+ if type(a) is int or type(a) is float:
+ for v in self._coeff.iterkeys(): self._coeff[v] *= a
+
+ elif _ismatrix(a) and a.size == (1,1):
+ for v in self._coeff.iterkeys(): self._coeff[v] *= a[0]
+
+ elif len(self) == 1 and _isdmatrix(a) and a.size[1] == 1:
+ for v,c in self._coeff.iteritems(): self._coeff[v] = a*c
+
+ else:
+ raise TypeError, 'incompatible dimensions'
+
+
+ def _rmul(self,a):
+
+ '''
+ self := a*self where a is scalar or matrix
+ '''
+
+ lg = len(self)
+ if _isscalar(a):
+ for v in self._coeff.iterkeys(): self._coeff[v] *= a
+
+ elif lg == 1 and _ismatrix(a) and a.size[1] == 1:
+ for v,c in self._coeff.iteritems(): self._coeff[v] = a*c
+
+ elif _ismatrix(a) and a.size[1] == lg:
+ for v,c in self._coeff.iteritems():
+ if c.size == (1,len(v)):
+ self._coeff[v] = a*c[lg*[0],:]
+ else:
+ self._coeff[v] = a*c
+
+ else:
+ raise TypeError, 'incompatible dimensions'
+
+
+ def __pos__(self):
+
+ f = _lin()
+ for v,c in self._coeff.iteritems(): f._coeff[v] = +c
+ return f
+
+
+ def __neg__(self):
+
+ f = _lin()
+ for v,c in self._coeff.iteritems(): f._coeff[v] = -c
+ return f
+
+
+ def __add__(self,other):
+
+ # self + other with other variable or _lin
+
+ f = +self
+
+ if type(other) is int or type(other) is float and not other:
+ # Needed to make sum(f) work, because it defaults to
+ # 0 + f[0] + ... + f[len(f)-1].
+ return f
+
+ if type(other) is variable:
+ f._addterm(1.0, other)
+
+ elif type(other) is _lin:
+ for v,c in other._coeff.iteritems(): f._addterm(c,v)
+
+ else: return NotImplemented
+
+ return f
+
+
+ def __radd__(self,other):
+
+ return self.__add__(other)
+
+
+ def __iadd__(self,other):
+
+ '''
+ self += other
+
+ Only allowed if it does not change the length of self.
+ '''
+
+ lg = len(self)
+
+ if type(other) is variable and (len(other) == 1 or
+ len(other) == lg):
+ self._addterm(1.0,other)
+
+ elif type(other) is _lin and (len(other) == 1 or
+ len(other) == lg):
+ for v,c in other._coeff.iteritems(): self._addterm(c,v)
+
+ else:
+ raise NotImplementedError, 'in-place addition must result '\
+ 'in a function of the same length'
+
+ return self
+
+
+ def __sub__(self,other):
+
+ f = +self
+
+ if type(other) is variable:
+ f._addterm(-1.0, other)
+ elif type(other) is _lin:
+ for v,c in other._coeff.iteritems(): f._addterm(-c,v)
+ else:
+ return NotImplemented
+
+ return f
+
+
+ def __rsub__(self,other):
+
+ f = -self
+
+ if type(other) is variable:
+ f._addterm(1.0, other)
+ elif type(other) is _lin:
+ for v,c in other._coeff.iteritems(): f._addterm(c,v)
+ else:
+ return NotImplemented
+
+ return f
+
+
+ def __isub__(self,other):
+
+ '''
+ self -= other
+
+ Only allowed if it does not change the length of self.
+ '''
+
+ lg = len(self)
+
+ if type(other) is variable and (len(other) == 1 or
+ len(other) == lg):
+ self._addterm(-1.0, other)
+
+ elif type(other) is _lin and (len(other) == 1 or
+ len(other) == lg):
+ for v,c in other._coeff.iteritems(): self._addterm(-c,v)
+
+ else:
+ raise NotImplementedError, 'in-place subtraction must '\
+ 'result in a function of the same length'
+
+ return self
+
+
+ def __mul__(self,other):
+
+ if _isscalar(other) or _ismatrix(other):
+ f = +self
+ f._mul(other)
+
+ else:
+ return NotImplemented
+
+ return f
+
+
+ def __rmul__(self,other):
+
+ if _isscalar(other) or _ismatrix(other):
+ f = +self
+ f._rmul(other)
+
+ else:
+ return NotImplemented
+
+ return f
+
+
+ def __imul__(self,other):
+
+ '''
+ self *= other
+
+ Only allowed for scalar multiplication with a constant (int,
+ float, 1x1 'd' matrix).
+ '''
+
+ if _isscalar(other):
+ self._mul(other)
+ else:
+ raise NotImplementedError, 'in-place multiplication ' \
+ 'only defined for scalar multiplication'
+ return self
+
+
+ def __getitem__(self,key):
+
+ l = _keytolist(key,len(self))
+ if not l: raise ValueError, 'empty index set'
+
+ f = _lin()
+ for v,c in self._coeff.iteritems():
+ if c.size == (len(self), len(v)):
+ f._coeff[v] = c[l,:]
+
+ elif _isscalar(c) and len(v) == 1:
+ f._coeff[v] = matrix(c, tc='d')
+
+ elif c.size == (1,1) and len(v) > 1:
+ # create a sparse matrix with 1.0 element in
+ # position (k,l[k]) for k in xrange(len(l))
+ f._coeff[v] = spmatrix([], [], [], (len(l),len(v)), 'd')
+ f._coeff[v][[l[k]*len(l)+k for k in xrange(len(l))]] \
+ = c[0]
+
+ else: # c is 1 by len(v)
+ f._coeff[v] = c[len(l)*[0],:]
+
+ return f
+
+
+
+class _minmax(object):
+
+ """
+ Componentwise maximum or minimum of functions.
+
+ A function of the form f = max(f1,f2,...,fm) or f = max(f1) or
+ f = min(f1,f2,...,fm) or f = min(f1) with each fi an object of
+ type _function.
+
+ If m>1, then len(f) = max(len(fi)) and f is the componentwise
+ maximum/minimum of f1,f2,...,fm. Each fi has length 1 or length
+ equal to len(f).
+
+ If m=1, then len(f) = 1 and f is the maximum/minimum of the
+ components of f1: f = max(f1[0],f1[1],...) or
+ f = min(f1[0],f1[1],...).
+
+
+ Attributes:
+
+ _flist [f1,f2,...,fm]
+ _ismax True for 'max', False for 'min'
+
+
+ Methods:
+
+ value() returns the value of the function
+ variables() returns a copy of the list of variables
+ """
+
+ def __init__(self,op,*s):
+
+ self._flist = []
+
+ if op == 'max':
+ self._ismax = True
+ else:
+ self._ismax = False
+
+ if len(s) == 1:
+
+ if type(s[0]) is variable or (type(s[0]) is _function and
+ (s[0]._isconvex() and self._ismax) or
+ (s[0]._isconcave() and not self._ismax)):
+ self._flist += [+s[0]]
+ else:
+ raise TypeError, 'unsupported argument type'
+
+ else:
+ # cnst will be max/min of the constant arguments
+ cnst = None
+
+ lg = 1
+ for f in s:
+ if type(f) is int or type(f) is float:
+ f = matrix(f, tc='d')
+
+ if _isdmatrix(f) and f.size[1] == 1:
+ if cnst is None:
+ cnst = +f
+ elif self._ismax:
+ cnst = _vecmax(cnst,f)
+ else:
+ cnst = _vecmin(cnst,f)
+
+ elif type(f) is variable or type(f) is _function:
+ self._flist += [+f]
+
+ else:
+ raise TypeError, 'unsupported argument type'
+
+ lgf = len(f)
+ if 1 != lg != lgf != 1:
+ raise ValueError, 'incompatible dimensions'
+ elif 1 == lg != lgf:
+ lg = lgf
+
+ if cnst: self._flist += [_function()+cnst]
+
+
+ def __len__(self):
+
+ if len(self._flist) == 1: return 1
+ for f in self._flist:
+ lg = len(f)
+ if len(f) > 1: return lg
+ return 1
+
+
+ def __repr__(self):
+
+ if self._ismax: s = 'maximum'
+ else: s = 'minimum'
+
+ if len(self._flist) == 1:
+ return '<' + s + ' component of a function of length %d>'\
+ %len(self._flist[0])
+ else:
+ return "<componentwise " + s + " of %d functions of "\
+ "length %d>" %(len(self._flist),len(self))
+
+
+ def __str__(self):
+
+ s = repr(self)[1:-1] + ':'
+ if len(self._flist) == 1:
+ s += '\n' + repr(self._flist[0])[1:-1]
+ else:
+ for k in xrange(len(self._flist)):
+ s += "\nfunction %d: " %k + repr(self._flist[k])[1:-1]
+ return s
+
+
+ def value(self):
+
+ if self._ismax:
+ return _vecmax(*[f.value() for f in self._flist])
+ else:
+ return _vecmin(*[f.value() for f in self._flist])
+
+
+ def variables(self):
+
+ l = varlist()
+ for f in self._flist:
+ l += [v for v in f.variables() if v not in l]
+ return l
+
+
+ def __pos__(self):
+
+ if self._ismax:
+ f = _minmax('max', *[+fk for fk in self._flist])
+ else:
+ f = _minmax('min', *[+fk for fk in self._flist])
+
+ return f
+
+
+ def __neg__(self):
+
+ if self._ismax:
+ f = _minmax('min', *[-fk for fk in self._flist])
+ else:
+ f = _minmax('max', *[-fk for fk in self._flist])
+ return f
+
+
+ def __mul__(self,other):
+
+ if type(other) is int or type(other) is float or \
+ (_ismatrix(other) and other.size == (1,1)):
+ if _ismatrix(other): other = other[0]
+
+ if other >= 0.0:
+ if self._ismax:
+ f = _minmax('max', *[other*fk for fk in
+ self._flist])
+ else:
+ f = _minmax('min', *[other*fk for fk in
+ self._flist])
+
+ else:
+ if self._ismax:
+ f = _minmax('min', *[other*fk for fk in
+ self._flist])
+ else:
+ f = _minmax('max', *[other*fk for fk in
+ self._flist])
+
+ return f
+
+ else:
+ return NotImplemented
+
+
+ def __rmul__(self,other):
+
+ return self.__mul__(other)
+
+
+ def __imul__(self,other):
+
+ if _isscalar(other):
+ if type(other) is matrix: other = other[0]
+ for f in self._flist: f *= other
+ if other < 0.0: self._ismax = not self._ismax
+ return self
+
+ raise NotImplementedError, 'in-place multiplication is only '\
+ 'defined for scalars'
+
+
+ def __getitem__(self,key):
+
+ lg = len(self)
+ l = _keytolist(key,lg)
+ if not l: raise ValueError, 'empty index set'
+
+ if len(self._flist) == 1: fl = list(self._flist[0])
+ else: fl = self._flist
+
+ if self._ismax: f = _minmax('max')
+ else: f = _minmax('min')
+
+ for fk in fl:
+ if 1 == len(fk) != lg: f._flist += [+fk]
+ else: f._flist += [fk[l]]
+
+ return f
+
+
+
+def max(*s):
+
+ """
+ Identical to the built-in max except when some of the arguments are
+ variables or functions.
+
+ f = max(s1,s2,...) returns the componentwise maximum of s1,s2,..,
+ as a convex function with len(f) = max(len(si)).
+ The arguments si can be scalars, 1-column dense 'd' matrices,
+ variables, or functions. At least one argument must be a function
+ or a variable. The arguments can be scalars or vectors with length
+ equal to len(f).
+
+ f = max(s) with len(s) > 1 returns the maximum component of s as
+ a function with len(f) = 1. The argument can be a variable or a
+ function.
+
+ f = max(s) with len(s) = 1 and s[0] a function returns s[0].
+
+ f = max(s) with s a list or tuple of variables, functions,
+ constants, returns f = max(*s).
+
+ Does not work with generators (Python 2.4).
+ """
+
+ try: return __builtin__.max(*s)
+ except NotImplementedError:
+ f = _function()
+ try:
+ f._cvxterms = [_minmax('max',*s)]
+ return f
+ except:
+ # maybe s[0] is a list or tuple of variables, functions
+ # and constants
+ try: return max(*s[0])
+ except: raise NotImplementedError
+
+
+
+def min(*s):
+
+ """
+ Identical to the built-in min except when some of the arguments are
+ variables or functions.
+
+ f = min(s1,s2,...) returns the componentwise minimum of s1,s2,..,
+ as function with len(f) = max(len(si)).
+ The arguments si can be scalars, 1-column dense 'd' matrices,
+ variables, or functions. At least one argument must be a function
+ or a variable. The arguments can be scalars or vectors with length
+ equal to len(f).
+
+ f = min(s) with len(s) > 1 returns the minimum component of s as
+ a function with len(f) = 1. The argument can be a variable or a
+ function.
+
+ f = min(s) with len(s) = 1 returns s[0].
+
+ f = min(s) with s a list or tuple of variables, functions,
+ constants, returns f = min(*s).
+
+ Does not work with generators (Python 2.4).
+ """
+
+ try: return __builtin__.min(*s)
+ except NotImplementedError:
+ f = _function()
+ try:
+ f._ccvterms = [_minmax('min',*s)]
+ return f
+ except:
+ # maybe s[0] is a list or tuple of variables, functions
+ # and constants
+ try: return min(*s[0])
+ except: raise NotImplementedError
+
+
+
+class _sum_minmax(_minmax):
+
+ """
+ Sum of componentwise maximum or minimum of functions.
+
+ A function of the form f = sum(max(f1,f2,...,fm)) or
+ f = sum(min(f1,f2,...,fm)) with each fi an object of
+ type _function.
+
+ m must be greater than 1. len(f) = 1.
+ Each fi has length 1 or length equal to max_i len(fi)).
+
+
+ Attributes:
+
+ _flist [f1,f2,...,fm]
+ _ismax True for 'max', False for 'min'
+
+
+ Methods:
+
+ value() returns the value of the function
+ variables() returns a copy of the list of variables
+ _length() number of terms in the sum
+ """
+
+ def __init__(self,op,*s):
+
+ _minmax.__init__(self,op,*s)
+ if len(self._flist) == 1:
+ raise TypeError, 'expected more than 1 argument'
+
+
+ def __len__(self):
+
+ return 1
+
+
+ def _length(self):
+
+ for f in self._flist:
+ lg = len(f)
+ if len(f) > 1: return lg
+ return 1
+
+
+ def __repr__(self):
+
+ if self._ismax: s = 'maximum'
+ else: s = 'minimum'
+ return "<sum of componentwise " + s + " of %d functions of "\
+ "length %d>" %(len(self._flist),len(self))
+
+
+ def __str__(self):
+
+ s = repr(self)[1:-1]
+ for k in xrange(len(self._flist)):
+ s += "\nfunction %d: " %k + repr(self._flist[k])[1:-1]
+ return s
+
+
+ def value(self):
+
+ if self._ismax:
+ return matrix(sum(_vecmax(*[f.value() for f in
+ self._flist])), tc='d')
+ else:
+ return matrix(sum(_vecmin(*[f.value() for f in
+ self._flist])), tc='d')
+
+
+ def __pos__(self):
+
+ if self._ismax:
+ f = _sum_minmax('max', *[+fk for fk in self._flist])
+ else:
+ f = _sum_minmax('min', *[+fk for fk in self._flist])
+
+ return f
+
+
+ def __neg__(self):
+
+ if self._ismax:
+ f = _sum_minmax('min', *[-fk for fk in self._flist])
+ else:
+ f = _sum_minmax('max', *[-fk for fk in self._flist])
+ return f
+
+
+ def __mul__(self,other):
+
+ if type(other) is int or type(other) is float or \
+ (_ismatrix(other) and other.size == (1,1)):
+
+ if _ismatrix(other): other = other[0]
+
+ if other >= 0.0:
+ if self._ismax:
+ f = _sum_minmax('max', *[other*fk for fk in
+ self._flist])
+ else:
+ f = _sum_minmax('min', *[other*fk for fk in
+ self._flist])
+
+ else:
+ if self._ismax:
+ f = _sum_minmax('min', *[other*fk for fk in
+ self._flist])
+ else:
+ f = _sum_minmax('max', *[other*fk for fk in
+ self._flist])
+
+ return f
+
+ else:
+ return NotImplemented
+
+
+ def __rmul__(self,other):
+
+ return self.__mul__(other)
+
+
+ def __getitem__(self,key):
+
+ l = _keytolist(key,1)
+ if not l: raise ValueError, 'empty index set'
+
+ # expand sum and convert to a _function
+ if self._ismax: f = sum(_minmax('max',*self._flist))
+ else: f = sum(_minmax('min',*self._flist))
+
+ return f[l]
+
+
+
+class constraint(object):
+
+ """
+ Equality or inequality constraint.
+
+ constraint(f, ctype='=', name='') constructs a constraint
+ f=0 (if ctype is '=') or f<=0 (if ctype is '<').
+
+
+ Arguments:
+
+ f convex function if '<', affine function if '='
+ ctype '=' or '<'
+ name string with the constraint name
+
+
+ Attributes:
+
+ multiplier a variable of length len(f). multiplier.name is
+ the constraint name with '_mul' appended.
+ name constraint name. Writing to .name also modifies
+ the name of .multiplier.
+ _f the constraint function (borrowed reference)
+ _type '=' or '<'
+
+
+ Methods:
+
+ value() returns the value of the constraint function
+ variables() returns the variables of the constraint function
+ type() returns ._type
+ _aslinearineq() converts convex piecewise-linear inequality into
+ an equivalent set of linear inequalities
+ """
+
+ def __init__(self, f, ctype='=', name=''):
+
+ if ctype == '=' or ctype == '<':
+ self._type = ctype
+ else:
+ raise TypeError, "'ctype' argument must be '<' or '='"
+
+ if type(f) is not _function:
+ raise TypeError, "'f' argument must be a function"
+
+ if ctype == '=':
+ if f._isaffine(): self._f = f
+ else:
+ raise TypeError, "constraint function must be affine"
+
+ else:
+ if f._isconvex(): self._f = f
+ else:
+ raise TypeError, "constraint function must be convex"
+
+ self.name = name
+ self.multiplier = variable(len(self), name + '_mul')
+
+
+ def __len__(self):
+
+ return len(self._f)
+
+
+ def __repr__(self):
+
+ lg = len(self)
+
+ if self._type == '=': s = 'equality'
+ else: s = 'inequality'
+
+ if lg == 1: t = "<scalar %s" %s
+ else: t = "<%s in R^%d" %(s,lg)
+
+ if self.name != '': return t + ", '" + self.name + "'>"
+ else: return t + ">"
+
+
+ def __str__(self):
+
+ return repr(self)[1:-1] + '\nconstraint function:\n' + \
+ str(self._f)
+
+
+ def __setattr__(self,name,value):
+
+ if name == 'name':
+ if type(value) is str:
+ object.__setattr__(self,name,value)
+ if hasattr(self,'multiplier'):
+ self.multiplier.name = value + '_mul'
+ else:
+ raise TypeError, "invalid type for attribute 'name'"
+
+ elif name == 'multiplier' or name == '_type' or name == '_f':
+ object.__setattr__(self,name,value)
+
+ else:
+ raise AttributeError, "'constraint' object has no "\
+ "attribute '%s'" %name
+
+
+ def type(self):
+
+ """ Returns '=' for equality constraints, '<' for inequality."""
+
+ return self._type
+
+
+ def value(self):
+
+ """ Returns value of the constraint function."""
+
+ return self._f.value()
+
+
+ def variables(self):
+
+ """ Returns a list of variables of the constraint function."""
+
+ return self._f.variables()
+
+
+ def _aslinearineq(self):
+
+ """
+ Converts a convex PWL inequality into an equivalent set of
+ linear inequalities.
+
+ Returns a tuple (ineqs, aux_ineqs, aux_vars).
+
+ If self is a linear inequailty, then ineqs = [self],
+ aux_ineqs = [], aux_vars = [].
+
+ If self is PWL then ineqs and aux_ineqs are two lists of
+ linear inequalities that together are equivalent to self.
+ They are separated in two sets so that the multiplier for self
+ depends only on the multipliers of the constraints in ineqs:
+ - if len(self) == max(len(ineqs[k])), then the multiplier of
+ self is sum_k ineqs[k].multiplier
+ - if len(self) == max(len(ineqs[k])), then the multiplier of
+ self is sum(sum_k ineqs[k].multiplier)
+
+ aux_vars is a varlist with new auxiliary variables.
+ """
+
+ if self.type() != '<':
+ raise TypeError, 'constraint must be an inequality'
+
+ ineqs, aux_ineqs, aux_vars = [], [], varlist()
+
+ # faff._constant and faff._linear are references to the
+ # affine part of the constraint function
+ faff = _function()
+ faff._constant = self._f._constant
+ faff._linear = self._f._linear
+
+ cvxterms = self._f._cvxterms
+ if not cvxterms: # inequality is linear
+ ineqs += [self]
+
+ elif len(cvxterms) == 1 and type(cvxterms[0]) is _minmax:
+ # constraint is of the form f = faff + max() <= 0
+
+ if len(cvxterms[0]._flist) == 1:
+ # constraint of the form f = faff + max(f0) <= 0
+ f0 = cvxterms[0]._flist[0]
+
+ if len(faff) == 1:
+ # write as scalar + f0 <= 0 with f0 possibly a
+ # vector
+ c = faff + f0 <= 0
+ c.name = self.name
+ c, caux, newvars = c._aslinearineq()
+ ineqs += c
+ aux_ineqs += caux
+ aux_vars += newvars
+
+ else:
+ # write as vector + f0[k] <= 0 for all k
+ for k in xrange(len(f0)):
+ c = faff + f0[k] <= 0
+ c.name = self.name + '(%d)' %k
+ c, caux, newvars = c._aslinearineq()
+ ineqs += c
+ aux_ineqs += caux
+ aux_vars += newvars
+
+ else:
+ # constraint of the form f = faff + max(f0,f1,...) <= 0
+ for k in xrange(len(cvxterms[0]._flist)):
+ c = faff + cvxterms[0]._flist[k] <= 0
+ c.name = self.name + '(%d)' %k
+ c, caux, newvars = c._aslinearineq()
+ ineqs += c
+ aux_ineqs += caux
+ aux_vars += newvars
+
+ else:
+ # constraint is of the form f = faff + g1 + g2 .... <= 0
+ # with gi = max() or sum max() and the number of gi's can
+ # be one.
+
+ sumt = _function()
+
+ for k in xrange(len(cvxterms)):
+ if type(cvxterms[k]) is _minmax:
+ # gk is max(f0,f1,...)
+
+ tk = variable(len(cvxterms[k]),
+ self.name + '_x' + str(k))
+ aux_vars += [tk]
+ sumt = sumt + tk
+
+ if len(cvxterms[k]._flist) == 1:
+ # add constraint gk = max(f0) <= tk
+
+ f0 = cvxterms[k]._flist[0]
+ c = f0 <= tk
+ c.name = self.name + '[%d]' %k
+ c, caux, newvars = c._aslinearineq()
+ aux_ineqs += c + caux
+ aux_vars += newvars
+
+ else:
+ # add constraint gk = max(f0,f1, ... ) <= tk
+
+ for j in xrange(len(cvxterms[k]._flist)):
+ fj = cvxterms[k]._flist[j]
+ c = fj <= tk
+ c.name = self.name + '[%d](%d)' %(k,j)
+ c, caux, newvars = c._aslinearineq()
+ aux_ineqs += c + caux
+ aux_vars += newvars
+
+ else:
+ # gk is sum(max(f0,f1,...)
+
+ tk = variable(cvxterms[k]._length(), self.name +
+ '_x' + str(k))
+ aux_vars += [tk]
+ sumt = sumt + sum(tk)
+
+ # add contraint max(f0,f1, ... ) <= tk
+ for j in xrange(len(cvxterms[k]._flist)):
+ fj = cvxterms[k]._flist[j]
+ c = fj <= tk
+ c.name = self.name + '[%d](%d)' %(k,j)
+ c, caux, newvars = c._aslinearineq()
+ aux_ineqs += c + caux
+ aux_vars += newvars
+
+ c = faff + sumt <= 0
+ c.name = self.name
+ ineqs += [c]
+
+ return (ineqs, aux_ineqs, aux_vars)
+
+
+
+class op(object):
+
+ """
+ An optimization problem.
+
+ op(objective=0.0, constraints=None, name '') constructs an
+ optimization problem.
+
+
+ Arguments:
+
+ objective scalar (int, float, 1x1 dense 'd' matrix), scalar
+ variable, scalar affine function or scalar convex
+ piecewise-linear function. Scalars and variables
+ are converted to affine functions.
+ constraints None, a single constraint, or a list of constraints
+ None means the same as an empty list. A single
+ constraint means the same as a singleton list.
+ name string with the name of the LP
+
+
+ Attributes:
+
+ objective the objective function (borrowed reference to the
+ function passed as argument).
+ name the name of the optimization problem
+ status initially None. After solving the problem,
+ summarizes the outcome.
+ _inequalities list of inequality constraints
+ _equalities list of equality constraints
+ _variables a dictionary {v: dictionary with keys 'o','i','e'}
+ The keys v are the variables in the problem.
+ 'o': True/False depending on whether v appears in
+ the objective or not;
+ 'i': list of inequality constraints v appears in;
+ 'e': list of equality constraints v appears in.
+
+
+ Methods:
+
+ variables() returns a list of variables. The list is a varlist
+ (defined below), ie, a subclass of 'list'.
+ constraints() returns a list of constraints
+ inequalities() returns a list of inequality constraints
+ equalities() returns a list of equality constraints
+ delconstraint() deletes a constraint
+ addconstraint() adds a constraint
+ _inmatrixform() returns an equivalent LP in matrix form
+ solve() solves the problem
+ tofile() if the problem is an LP, writes it to an MPS file
+ fromfile() reads an LP from an MPS file
+ """
+
+ def __init__(self, objective=0.0, constraints=None, name=''):
+
+ self._variables = dict()
+
+ self.objective = objective
+ for v in self.objective.variables():
+ self._variables[v] = {'o': True, 'i': [], 'e': []}
+
+ self._inequalities, self._equalities = [], []
+ if constraints is None:
+ pass
+ elif type(constraints) is constraint:
+ if constraints.type() == '<':
+ self._inequalities += [constraints]
+ else:
+ self._equalities += [constraints]
+ elif type(constraints) == list and not [c for c in constraints
+ if type(c) is not constraint]:
+ for c in constraints:
+ if c.type() == '<':
+ self._inequalities += [c]
+ else:
+ self._equalities += [c]
+ else:
+ raise TypeError, 'invalid argument for constraints'
+
+ for c in self._inequalities:
+ for v in c.variables():
+ if self._variables.has_key(v):
+ self._variables[v]['i'] += [c]
+ else:
+ self._variables[v] = {'o': False, 'i': [c], 'e': []}
+
+ for c in self._equalities:
+ for v in c.variables():
+ if self._variables.has_key(v):
+ self._variables[v]['e'] += [c]
+ else:
+ self._variables[v] = {'o': False, 'i': [], 'e': [c]}
+
+ self.name = name
+ self.status = None
+
+
+ def __repr__(self):
+
+ n = sum(map(len,self._variables))
+ m = sum(map(len,self._inequalities))
+ p = sum(map(len,self._equalities))
+ return "<optimization problem with %d variables, %d inequality"\
+ " and %d equality constraint(s)>" %(n,m,p)
+
+
+ def __setattr__(self,name,value):
+
+ if name == 'objective':
+
+ if _isscalar(value):
+ value = _function() + value
+ elif type(value) is variable and len(value) == 1:
+ value = +value
+ elif type(value) is _function and value._isconvex() and \
+ len(value) == 1:
+ pass
+ else:
+ raise TypeError, "attribute 'objective' must be a "\
+ "scalar affine or convex PWL function"
+
+ # remove variables in _variables that only appear in current
+ # objective
+ for v in self.variables():
+ if not self._variables[v]['i'] and not \
+ self._variables[v]['e']: del self._variables[v]
+
+ object.__setattr__(self,'objective',value)
+
+ # update _variables
+ for v in self.objective.variables():
+ if not self._variables.has_key(v):
+ self._variables[v] = {'o': True, 'i': [], 'e': []}
+ else:
+ self._variables[v]['o'] = True
+
+ elif name == 'name':
+ if type(value) is str:
+ object.__setattr__(self,name,value)
+ else:
+ raise TypeError, "attribute 'name' must be string"
+
+ elif name == '_inequalities' or name == '_equalities' or \
+ name == '_variables' or name == 'status':
+ object.__setattr__(self,name,value)
+
+ else:
+ raise AttributeError, "'op' object has no attribute "\
+ "'%s'" %name
+
+
+ def variables(self):
+
+ """ Returns a list of variables of the LP. """
+
+ return varlist(self._variables.keys())
+
+
+ def constraints(self):
+
+ """ Returns a list of constraints of the LP."""
+
+ return self._inequalities + self._equalities
+
+
+ def equalities(self):
+
+ """ Returns a list of equality constraints of the LP."""
+
+ return list(self._equalities)
+
+
+ def inequalities(self):
+
+ """ Returns a list of inequality constraints of the LP."""
+
+ return list(self._inequalities)
+
+
+ def delconstraint(self,c):
+
+ """
+ Deletes constraint c from the list of constrains
+ """
+
+ if type(c) is not constraint:
+ raise TypeError, "argument must be of type 'constraint'"
+
+ try:
+ if c.type() == '<':
+ self._inequalities.remove(c)
+ for v in c.variables():
+ self._variables[v]['i'].remove(c)
+ else:
+ self._equalities.remove(c)
+ for v in c.variables():
+ self._variables[v]['e'].remove(c)
+ if not self._variables[v]['o'] and \
+ not self._variables[v]['i'] and \
+ not self._variables[v]['e']:
+ del self._variables[v]
+
+ except ValueError: # c is not a constraint
+ pass
+
+
+ def addconstraint(self,c):
+
+ """
+ Adds constraint c to the list of constraints.
+ """
+
+ if type(c) is not constraint:
+ raise TypeError, 'argument must be of type constraint'
+
+ if c.type() == '<': self._inequalities += [c]
+ if c.type() == '=': self._equalities += [c]
+ for v in c.variables():
+ if c.type() == '<':
+ if self._variables.has_key(v):
+ self._variables[v]['i'] += [c]
+ else:
+ self._variables[v] = {'o': False, 'i': [c], 'e': []}
+ else:
+ if self._variables.has_key(v):
+ self._variables[v]['e'] += [c]
+ else:
+ self._variables[v] = {'o': False, 'i': [], 'e': [c]}
+
+
+ def _islp(self):
+
+ """
+ Returns True if self is an LP; False otherwise.
+ """
+
+ if not self.objective._isaffine(): return False
+ for c in self._inequalities:
+ if not c._f._isaffine(): return False
+ for c in self._equalities:
+ if not c._f._isaffine(): return False
+ return True
+
+
+ def _inmatrixform(self, format='dense'):
+
+ """
+ Converts self to an LP in matrix form
+
+ minimize c'*x+d
+ subject to G*x <= h
+ A*x = b.
+
+ c, h, b are dense column matrices; G and A sparse or dense
+ matrices depending on format ('sparse' or 'dense').
+
+ If self is already an LP in matrix form with the correct matrix
+ types, then _inmatrixform() returns None. Otherwise it returns
+ a tuple (newlp, vmap, mmap).
+
+ newlp is an LP in matrix form with the correct format and
+ matrix types.
+
+ vmap is a dictionary with the variables of self as keys and
+ affine functions as values. For each variable v of self,
+ vmap[v] is a function of the new variable x that can be
+ evaluated to obtain the solution v from the solution x.
+
+ mmap is a dictionary with the constraints of self as keys and
+ affine functions as values. For each constraint c of self,
+ mmap[c] is a function of the multipliers of the new lp that can
+ be evaluated to obtain the optimal multiplier for c.
+ """
+
+ variables, aux_variables = self.variables(), varlist()
+
+ # lin_ineqs is a list of linear inequalities in the original
+ # problem. pwl_ineqs is a dictionary {i: [c1,c2,...], ...}
+ # where i is a PWL inequality in the original problem.
+ # aux_ineqs are new auxiliary inequalities that together
+ # with the ck constraints in pwl_ineqs are equivalent to the
+ # original ones. The sum of the multipliers of the constraints
+ # in pwl_ineqs[i] forms the multiplier of i.
+
+ lin_ineqs, pwl_ineqs, aux_ineqs = [], dict(), []
+ for i in self._inequalities:
+ if i._f._isaffine(): lin_ineqs += [i]
+ else: pwl_ineqs[i] = []
+
+ equalities = self._equalities
+ objective = +self.objective
+
+ # return None if self is already an LP in the requested form
+ if objective._isaffine() and len(variables) == 1 and \
+ not pwl_ineqs and len(lin_ineqs) <= 1 and \
+ len(equalities) <= 1:
+ v = variables[0]
+
+ if lin_ineqs: G = lin_ineqs[0]._f._linear._coeff[v]
+ else: G = None
+
+ if equalities: A = equalities[0]._f._linear._coeff[v]
+ else: A = None
+
+ if (format == 'dense' and (G is None or _isdmatrix(G)) and
+ (A is None or _isdmatrix(A))) or \
+ (format == 'sparse' and (G is None or _isspmatrix(G))
+ and (A is None or _isspmatrix(A))):
+ return None
+
+
+ # convert PWL objective to linear
+ if not objective._isaffine():
+
+ # f = affine + sum_k fk with each fk a maximum of convex
+ # functions or a sum of a maximum of convex functions.
+ # If fk is a maximum of convex functions we introduce a
+ # new variable tk and replace fk in the objective with tk,
+ # with a new constraint fk <= tk.
+ # If fk is sum(gk) where gk is a maximum of convex
+ # functions we introduce a new variable tk and replace fk
+ # in the objective with sum(tk) with a new constraint
+ # gk <= tk.
+
+ newobj = _function()
+ newobj._constant = +objective._constant
+ newobj._linear = +objective._linear
+
+ for k in xrange(len(objective._cvxterms)):
+ fk = objective._cvxterms[k]
+
+ if type(fk) is _minmax:
+ tk = variable(1, self.name + '_x' + str(k))
+ newobj += tk
+ else:
+ tk = variable(fk._length(), self.name +
+ '_x' + str(k))
+ newobj += sum(tk)
+
+ aux_variables += [tk]
+
+ for j in xrange(len(fk._flist)):
+ c = fk._flist[j] <= tk
+ if xrange(len(fk._flist)) > 1:
+ c.name = self.name + '[%d](%d)' %(k,j)
+ else:
+ c.name = self.name + '[%d]' %k
+ c, caux, newvars = c._aslinearineq()
+ aux_ineqs += c + caux
+ aux_variables += newvars
+ objective = newobj
+
+
+ # convert PWL inequalities to linear
+ for i in pwl_ineqs:
+ pwl_ineqs[i], caux, newvars = i._aslinearineq()
+ aux_ineqs += caux
+ aux_variables += newvars
+
+
+ # n is the length of x, c
+ # The variables are available in variables and aux_variables.
+ # variable v is stored in x[vslc[v]]
+ vslc = dict()
+ n = 0
+ for v in variables + aux_variables:
+ vslc[v] = slice(n, n+len(v))
+ n += len(v)
+ c = matrix(0.0, (1,n))
+ for v,cf in objective._linear._coeff.iteritems():
+ if _isscalar(cf):
+ c[vslc[v]] = cf[0]
+ elif _isdmatrix(cf):
+ c[vslc[v]] = cf[:]
+ else:
+ c[vslc[v]] = matrix(cf[:], tc='d')
+ if n > 0:
+ x = variable(n)
+ cost = c*x + objective._constant
+ else:
+ cost = _function() + objective._constant[0]
+ vmap = dict()
+ for v in variables: vmap[v] = x[vslc[v]]
+
+
+ # m is the number of rows of G, h
+ # The inequalities are available in lin_lineqs, pwl_ineqs,
+ # aux_ineqs.
+ # inequality i is stored in G[islc[i],:]*x <= h[islc[i]]
+ islc = dict()
+ for i in lin_ineqs + aux_ineqs: islc[i] = None
+ for c in pwl_ineqs:
+ for i in pwl_ineqs[c]: islc[i] = None
+ m = 0
+ for i in islc:
+ islc[i] = slice(m, m+len(i))
+ m += len(i)
+ if format == 'sparse':
+ G = spmatrix(0.0, [], [], (m,n))
+ else:
+ G = matrix(0.0, (m,n))
+ h = matrix(0.0, (m,1))
+
+ for i in islc:
+ lg = len(i)
+ for v,cf in i._f._linear._coeff.iteritems():
+ if cf.size == (lg, len(v)):
+ if _isspmatrix(cf) and _isdmatrix(G):
+ G[islc[i], vslc[v]] = matrix(cf, tc='d')
+ else:
+ G[islc[i], vslc[v]] = cf
+ elif cf.size == (1, len(v)):
+ if _isspmatrix(cf) and _isdmatrix(G):
+ G[islc[i], vslc[v]] = \
+ matrix(cf[lg*[0],:], tc='d')
+ else:
+ G[islc[i], vslc[v]] = cf[lg*[0],:]
+ else: #cf.size[0] == (1,1):
+ G[islc[i].start+m*vslc[v].start:
+ islc[i].stop+m*vslc[v].stop:m+1] = cf[0]
+ if _isscalar(i._f._constant):
+ h[islc[i]] = -i._f._constant[0]
+ else:
+ h[islc[i]] = -i._f._constant[:]
+
+
+ # p is the number of rows in A, b
+ # equality e is stored A[eslc[e],:]*x == b[eslc[e]]
+ eslc = dict()
+ p = 0
+ for e in equalities:
+ eslc[e] = slice(p, p+len(e))
+ p += len(e)
+ if format == 'sparse':
+ A = spmatrix(0.0, [], [], (p,n))
+ else:
+ A = matrix(0.0, (p,n))
+ b = matrix(0.0, (p,1))
+
+ for e in equalities:
+ lg = len(e)
+ for v,cf in e._f._linear._coeff.iteritems():
+ if cf.size == (lg,len(v)):
+ if _isspmatrix(cf) and _isdmatrix(A):
+ A[eslc[e], vslc[v]] = matrix(cf, tc='d')
+ else:
+ A[eslc[e], vslc[v]] = cf
+ elif cf.size == (1, len(v)):
+ if _isspmatrix(cf) and _isdmatrix(A):
+ A[eslc[e], vslc[v]] = \
+ matrix(cf[lg*[0],:], tc='d')
+ else:
+ A[eslc[e], vslc[v]] = cf[lg*[0],:]
+ else: #cf.size[0] == (1,1):
+ A[eslc[e].start+p*vslc[v].start:
+ eslc[e].stop+p*vslc[v].stop:p+1] = cf[0]
+ if _isscalar(e._f._constant):
+ b[eslc[e]] = -e._f._constant[0]
+ else:
+ b[eslc[e]] = -e._f._constant[:]
+
+ constraints = []
+ if n:
+ if m: constraints += [G*x<=h]
+ if p: constraints += [A*x==b]
+ else:
+ if m: constraints += [_function()-h <= 0]
+ if p: constraints += [_function()-b == 0]
+
+ mmap = dict()
+
+ for i in lin_ineqs:
+ mmap[i] = constraints[0].multiplier[islc[i]]
+
+ for i in pwl_ineqs:
+ mmap[i] = _function()
+ for c in pwl_ineqs[i]:
+ mmap[i] = mmap[i] + constraints[0].multiplier[islc[c]]
+ if len(i) == 1 != len(mmap[i]):
+ mmap[i] = sum(mmap[i])
+
+ for e in equalities:
+ mmap[e] = constraints[1].multiplier[eslc[e]]
+ return (op(cost, constraints), vmap, mmap)
+
+
+ def solve(self, format='dense', solver = 'default'):
+
+ """
+ Solves LP using dense or sparse solver.
+
+ format is 'dense' or 'sparse'
+
+ solver is 'default', 'glpk' or 'mosek'
+
+ solve() sets self.status, and if status is 'optimal', also
+ the value attributes of the variables and the constraint
+ multipliers. If solver is 'python' then if status is
+ 'primal infeasible', the constraint multipliers are set to
+ a proof of infeasibility; if status is 'dual infeasible' the
+ variables are set to a proof of dual infeasibility.
+ """
+
+ t = self._inmatrixform(format)
+
+ if t is None:
+ lp1 = self
+ else:
+ lp1, vmap, mmap = t[0], t[1], t[2]
+
+ variables = lp1.variables()
+ if not variables:
+ raise TypeError, 'lp must have at least one variable'
+ x = variables[0]
+ c = lp1.objective._linear._coeff[x]
+ if _isspmatrix(c): c = matrix(c, tc='d')
+
+ inequalities = lp1._inequalities
+ if not inequalities:
+ raise TypeError, 'lp must have at least one inequality'
+ G = inequalities[0]._f._linear._coeff[x]
+ h = -inequalities[0]._f._constant
+
+ equalities = lp1._equalities
+ if equalities:
+ A = equalities[0]._f._linear._coeff[x]
+ b = -equalities[0]._f._constant
+ elif format == 'dense':
+ A = matrix(0.0, (0,len(x)))
+ b = matrix(0.0, (0,1))
+ else:
+ A = spmatrix(0.0, [], [], (0,len(x)))
+ b = matrix(0.0, (0,1))
+
+ sol = solvers.lp(c[:], G, h, A, b, solver=solver)
+
+ x.value = sol['x']
+ inequalities[0].multiplier.value = sol['z']
+ if equalities: equalities[0].multiplier.value = sol['y']
+
+ self.status = sol['status']
+ if type(t) is tuple:
+ for v,f in vmap.iteritems(): v.value = f.value()
+ for c,f in mmap.iteritems(): c.multiplier.value = f.value()
+
+
+
+ def tofile(self, filename):
+
+ '''
+ writes LP to file 'filename' in MPS format.
+ '''
+
+ if not self._islp(): raise TypeError, 'problem must be an LP'
+
+ constraints = self.constraints()
+ variables = self.variables()
+ inequalities = self.inequalities()
+ equalities = self.equalities()
+
+ f = open(filename,'w')
+ f.write('NAME')
+ if self.name: f.write(10*' ' + self.name[:8].rjust(8))
+ f.write('\n')
+
+ f.write('ROWS\n')
+ f.write(' N %8s\n' %'cost')
+ for k in xrange(len(constraints)):
+ c = constraints[k]
+ for i in xrange(len(c)):
+ if c._type == '<':
+ f.write(' L ')
+ else:
+ f.write(' E ')
+ if c.name:
+ name = c.name
+ else:
+ name = str(k)
+ name = name[:(7-len(str(i)))] + '_' + str(i)
+ f.write(name.rjust(8))
+ f.write('\n')
+
+ f.write('COLUMNS\n')
+ for k in xrange(len(variables)):
+ v = variables[k]
+ for i in xrange(len(v)):
+ if v.name:
+ varname = v.name
+ else:
+ varname = str(k)
+ varname = varname[:(7-len(str(i)))] + '_' + str(i)
+
+ if self.objective._linear._coeff.has_key(v):
+ cf = self.objective._linear._coeff[v]
+ if cf[i] != 0.0:
+ f.write(4*' ' + varname[:8].rjust(8))
+ f.write(2*' ' + '%8s' %'cost')
+ f.write(2*' ' + '% 7.5E\n' %cf[i])
+
+ for j in xrange(len(constraints)):
+ c = constraints[j]
+ if c.name:
+ cname = c.name
+ else:
+ cname = str(j)
+ if c._f._linear._coeff.has_key(v):
+ cf = c._f._linear._coeff[v]
+ if cf.size == (len(c),len(v)):
+ nz = [k for k in xrange(cf.size[0])
+ if cf[k,i] != 0.0]
+ for l in nz:
+ conname = cname[:(7-len(str(l)))] \
+ + '_' + str(l)
+ f.write(4*' ' + varname[:8].rjust(8))
+ f.write(2*' ' + conname[:8].rjust(8))
+ f.write(2*' ' + '% 7.5E\n' %cf[l,i])
+ elif cf.size == (1,len(v)):
+ if cf[0,i] != 0.0:
+ for l in xrange(len(c)):
+ conname = cname[:(7-len(str(l)))] \
+ + '_' + str(l)
+ f.write(4*' ' +
+ varname[:8].rjust(8))
+ f.write(2*' ' +
+ conname[:8].rjust(8))
+ f.write(2*' '+'% 7.5E\n' %cf[0,i])
+ elif _isscalar(cf):
+ if cf[0,0] != 0.0:
+ conname = cname[:(7-len(str(i)))] \
+ + '_' + str(i)
+ f.write(4*' ' + varname[:8].rjust(8))
+ f.write(2*' ' + conname[:8].rjust(8))
+ f.write(2*' ' + '% 7.5E\n' %cf[0,0])
+
+ f.write('RHS\n')
+ for j in xrange(len(constraints)):
+ c = constraints[j]
+ if c.name:
+ cname = c.name
+ else:
+ cname = str(j)
+ const = -c._f._constant
+ for l in xrange(len(c)):
+ conname = cname[:(7-len(str(l)))] + '_' + str(l)
+ f.write(14*' ' + conname[:8].rjust(8))
+ if const.size[0] == len(c):
+ f.write(2*' ' + '% 7.5E\n' %const[l])
+ else:
+ f.write(2*' ' + '% 7.5E\n' %const[0])
+
+ f.write('RANGES\n')
+
+ f.write('BOUNDS\n')
+ for k in xrange(len(variables)):
+ v = variables[k]
+ for i in xrange(len(v)):
+ if v.name:
+ varname = v.name
+ else:
+ varname = str(k)
+ varname = varname[:(7-len(str(i)))] + '_' + str(i)
+ f.write(' FR ' + 10*' ' + varname[:8].rjust(8) + '\n')
+
+ f.write('ENDATA\n')
+ f.close()
+
+
+ def fromfile(self, filename):
+
+ '''
+ Reads LP from file 'filename' assuming it is a fixed format
+ ascii MPS file.
+
+ Does not include serious error checking.
+
+ MPS features that are not allowed: comments preceded by
+ dollar signs, linear combinations of rows, multiple righthand
+ sides, ranges columns or bounds columns.
+ '''
+
+ self._inequalities = []
+ self._equalities = []
+ self.objective = _function()
+ self.name = ''
+
+ f = open(filename,'r')
+
+ s = f.readline()
+ while s[:4] != 'NAME':
+ s = f.readline()
+ if not s:
+ raise SyntaxError, "EOF reached before 'NAME' section "\
+ "was found"
+ self.name = strip(s[14:22])
+
+ s = f.readline()
+ while s[:4] != 'ROWS':
+ if not s:
+ raise SyntaxError, "EOF reached before 'ROWS' section "\
+ "was found"
+ s = f.readline()
+ s = f.readline()
+
+
+ # ROWS section
+ functions = dict() # {MPS row label: affine function}
+ rowtypes = dict() # {MPS row label: 'E', 'G' or 'L'}
+ foundobj = False # first occurrence of 'N' counts
+ while s[:7] != 'COLUMNS':
+ if not s: raise SyntaxError, "file has no 'COLUMNS' section"
+ if len(strip(s)) == 0 or s[0] == '*':
+ pass
+ elif strip(s[1:3]) in ['E','L','G']:
+ rowlabel = strip(s[4:12])
+ functions[rowlabel] = _function()
+ rowtypes[rowlabel] = strip(s[1:3])
+ elif strip(s[1:3]) == 'N':
+ rowlabel = strip(s[4:12])
+ if not foundobj:
+ functions[rowlabel] = self.objective
+ foundobj = True
+ else:
+ raise ValueError, "unknown row type '%s'" %strip(s[1:3])
+ s = f.readline()
+ s = f.readline()
+
+
+ # COLUMNS section
+ variables = dict() # {MPS column label: variable}
+ while s[:3] != 'RHS':
+ if not s:
+ raise SyntaxError, "EOF reached before 'RHS' section "\
+ "was found"
+ if len(strip(s)) == 0 or s[0] == '*':
+ pass
+ else:
+ if strip(s[4:12]): collabel = strip(s[4:12])
+ if not variables.has_key(collabel):
+ variables[collabel] = variable(1,collabel)
+ v = variables[collabel]
+ rowlabel = strip(s[14:22])
+ if not functions.has_key(rowlabel):
+ raise KeyError, "no row label '%s'" %rowlabel
+ functions[rowlabel]._linear._coeff[v] = \
+ matrix(float(s[24:36]), tc='d')
+ rowlabel = strip(s[39:47])
+ if rowlabel:
+ if not functions.has_key(rowlabel):
+ raise KeyError, "no row label '%s'" %rowlabel
+ functions[rowlabel]._linear._coeff[v] = \
+ matrix(float(s[49:61]), tc='d')
+ s = f.readline()
+ s = f.readline()
+
+
+ # RHS section
+ # The RHS section may contain multiple right hand sides,
+ # identified with different labels in s[4:12].
+ # We read in only one rhs, the one with the first rhs label
+ # encountered.
+ rhslabel = None
+ while s[:6] != 'RANGES' and s[:6] != 'BOUNDS' and \
+ s[:6] != 'ENDATA':
+ if not s: raise SyntaxError, \
+ "EOF reached before 'ENDATA' was found"
+ if len(strip(s)) == 0 or s[0] == '*':
+ pass
+ else:
+ if None != rhslabel != strip(s[4:12]):
+ # skip if rhslabel is different from 1st rhs label
+ # encountered
+ pass
+ else:
+ if rhslabel is None: rhslabel = strip(s[4:12])
+ rowlabel = strip(s[14:22])
+ if not functions.has_key(rowlabel):
+ raise KeyError, "no row label '%s'" %rowlabel
+ functions[rowlabel]._constant = \
+ matrix(-float(s[24:36]), tc='d')
+ rowlabel = strip(s[39:47])
+ if rowlabel:
+ if not functions.has_key(rowlabel):
+ raise KeyError, "no row label '%s'" \
+ %rowlabel
+ functions[rowlabel]._constant = \
+ matrix(-float(s[49:61]), tc='d')
+ s = f.readline()
+
+
+ # RANGES section
+ # The RANGES section may contain multiple range vectors,
+ # identified with different labels in s[4:12].
+ # We read in only one vector, the one with the first range label
+ # encountered.
+ ranges = dict()
+ for l in rowtypes.iterkeys():
+ ranges[l] = None # {rowlabel: range value}
+ rangeslabel = None
+ if s[:6] == 'RANGES':
+ s = f.readline()
+ while s[:6] != 'BOUNDS' and s[:6] != 'ENDATA':
+ if not s: raise SyntaxError, \
+ "EOF reached before 'ENDATA' was found"
+ if len(strip(s)) == 0 or s[0] == '*':
+ pass
+ else:
+ if None != rangeslabel != strip(s[4:12]):
+ pass
+ else:
+ if rangeslabel == None:
+ rangeslabel = strip(s[4:12])
+ rowlabel = strip(s[14:22])
+ if not rowtypes.has_key(rowlabel):
+ raise KeyError, "no row label '%s'"%rowlabel
+ ranges[rowlabel] = float(s[24:36])
+ rowlabel = strip(s[39:47])
+ if rowlabel != '':
+ if not functions.has_key(rowlabel):
+ raise KeyError, "no row label '%s'" \
+ %rowlabel
+ ranges[rowlabel] = float(s[49:61])
+ s = f.readline()
+
+
+ # BOUNDS section
+ # The BOUNDS section may contain bounds vectors, identified
+ # with different labels in s[4:12].
+ # We read in only one bounds vector, the one with the first
+ # label encountered.
+ boundslabel = None
+ bounds = dict()
+ for v in variables.iterkeys():
+ bounds[v] = [0.0, None] #{column label: [l.bound, u. bound]}
+ if s[:6] == 'BOUNDS':
+ s = f.readline()
+ while s[:6] != 'ENDATA':
+ if not s: raise SyntaxError, \
+ "EOF reached before 'ENDATA' was found"
+ if len(strip(s)) == 0 or s[0] == '*':
+ pass
+ else:
+ if None != boundslabel != strip(s[4:12]):
+ pass
+ else:
+ if boundslabel is None:
+ boundslabel = strip(s[4:12])
+ collabel = strip(s[14:22])
+ if not variables.has_key(collabel):
+ raise ValueError, 'unknown column label ' \
+ + "'%s'" %collabel
+ if strip(s[1:3]) == 'LO':
+ if bounds[collabel][0] != 0.0:
+ raise ValueError, "repeated lower "\
+ "bound for variable '%s'" %collabel
+ bounds[collabel][0] = float(s[24:36])
+ elif strip(s[1:3]) == 'UP':
+ if bounds[collabel][1] != None:
+ raise ValueError, "repeated upper "\
+ "bound for variable '%s'" %collabel
+ bounds[collabel][1] = float(s[24:36])
+ elif strip(s[1:3]) == 'FX':
+ if bounds[collabel] != [0, None]:
+ raise ValueError, "repeated bounds "\
+ "for variable '%s'" %collabel
+ bounds[collabel][0] = float(s[24:36])
+ bounds[collabel][1] = float(s[24:36])
+ elif strip(s[1:3]) == 'FR':
+ if bounds[collabel] != [0, None]:
+ raise ValueError, "repeated bounds "\
+ "for variable '%s'" %collabel
+ bounds[collabel][0] = None
+ bounds[collabel][1] = None
+ elif strip(s[1:3]) == 'MI':
+ if bounds[collabel][0] != 0.0:
+ raise ValueError, "repeated lower " \
+ "bound for variable '%s'" %collabel
+ bounds[collabel][0] = None
+ elif strip(s[1:3]) == 'PL':
+ if bounds[collabel][1] != None:
+ raise ValueError, "repeated upper " \
+ "bound for variable '%s'" %collabel
+ else:
+ raise ValueError, "unknown bound type '%s'"\
+ %strip(s[1:3])
+ s = f.readline()
+
+ for l, type in rowtypes.iteritems():
+
+ if type == 'L':
+ c = functions[l] <= 0.0
+ c.name = l
+ self._inequalities += [c]
+ if ranges[l] != None:
+ c = functions[l] >= -abs(ranges[l])
+ c.name = l + '_lb'
+ self._inequalities += [c]
+ if type == 'G':
+ c = functions[l] >= 0.0
+ c.name = l
+ self._inequalities += [c]
+ if ranges[l] != None:
+ c = functions[l] <= abs(ranges[l])
+ c.name = l + '_ub'
+ self._inequalities += [c]
+ if type == 'E':
+ if ranges[l] is None or ranges[l] == 0.0:
+ c = functions[l] == 0.0
+ c.name = l
+ self._equalities += [c]
+ elif ranges[l] > 0.0:
+ c = functions[l] >= 0.0
+ c.name = l + '_lb'
+ self._inequalities += [c]
+ c = functions[l] <= ranges[l]
+ c.name = l + '_ub'
+ self._inequalities += [c]
+ else:
+ c = functions[l] <= 0.0
+ c.name = l + '_ub'
+ self._inequalities += [c]
+ c = functions[l] >= ranges[l]
+ c.name = l + '_lb'
+ self._inequalities += [c]
+
+ for l,bnds in bounds.iteritems():
+ v = variables[l]
+ if None != bnds[0] != bnds[1]:
+ c = v >= bnds[0]
+ self._inequalities += [c]
+ if bnds[0] != bnds[1] != None:
+ c = v <= bnds[1]
+ self._inequalities += [c]
+ if None != bnds[0] == bnds[1]:
+ c = v == bnds[0]
+ self._equalities += [c]
+
+ # Eliminate constraints with no variables
+ for c in self._inequalities + self._equalities:
+ if len(c._f._linear._coeff) == 0:
+ if c.type() == '=' and c._f._constant[0] != 0.0:
+ raise ValueError, "equality constraint '%s' "\
+ "has no variables and a nonzero righthand side"\
+ %c.name
+ elif c.type() == '<' and c._f._constant[0] > 0.0:
+ raise ValueError, "inequality constraint '%s' "\
+ "has no variables and a negative righthand side"\
+ %c.name
+ else:
+ print "removing redundant constraint '%s'" %c.name
+ if c.type() == '<': self._inequalities.remove(c)
+ if c.type() == '=': self._equalities.remove(c)
+
+
+ self._variables = dict()
+ for v in self.objective._linear._coeff.keys():
+ self._variables[v] = {'o': True, 'i': [], 'e': []}
+ for c in self._inequalities:
+ for v in c._f._linear._coeff.keys():
+ if self._variables.has_key(v):
+ self._variables[v]['i'] += [c]
+ else:
+ self._variables[v] = {'o': False, 'i': [c], 'e': []}
+ for c in self._equalities:
+ for v in c._f._linear._coeff.keys():
+ if self._variables.has_key(v):
+ self._variables[v]['e'] += [c]
+ else:
+ self._variables[v] = {'o': False, 'i': [], 'e': [c]}
+
+ self.status = None
+
+ f.close()
+
+
+
+def dot(x,y):
+
+ """
+ Inner products of variable or affine function with constant vector.
+ """
+
+ if _isdmatrix(x) and _isdmatrix(y):
+ return blas.dot(x,y)
+
+ elif _isdmatrix(x) and (type(y) is variable or
+ (type(y) is _function and y._isaffine()) and
+ x.size == (len(y),1)):
+ return x.trans() * y
+
+ elif _isdmatrix(y) and (type(x) is variable or
+ (type(x) is _function and x._isaffine()) and
+ y.size == (len(x),1)):
+ return y.trans() * x
+
+ else:
+ raise TypeError, 'invalid argument types or incompatible '\
+ 'dimensions'
+
+
+
+def _isscalar(a):
+
+ """ True if a is an int or float or 1x1 dense 'd' matrix. """
+
+ if type(a) is int or type(a) is float or (_isdmatrix(a) and
+ a.size == (1,1)): return True
+ else: return False
+
+
+
+def _isdmatrix(a):
+
+ """ True if a is a nonempty dense 'd' matrix. """
+
+ if type(a) is matrix and a.typecode == 'd' and min(a.size) != 0:
+ return True
+ else:
+ return False
+
+
+
+def _isspmatrix(a):
+
+ """ True if a is a nonempty sparse 'd' matrix. """
+
+ if type(a) is spmatrix and a.typecode == 'd' and min(a.size) != 0:
+ return True
+ else:
+ return False
+
+
+
+def _ismatrix(a):
+
+ """ True if a is a nonempty 'd' matrix. """
+
+ if type(a) in (matrix, spmatrix) and a.typecode == 'd' and \
+ min(a.size) != 0:
+ return True
+ else:
+ return False
+
+
+
+def _keytolist(key,n):
+
+ """
+ Converts indices, index lists, index matrices, and slices of
+ a length n sequence into lists of integers.
+
+ key is the index passed to a call to __getitem__().
+ """
+
+ if type(key) is int:
+ if -n <= key < 0:
+ l = [key+n]
+ elif 0 <= key < n:
+ l = [key]
+ else:
+ raise IndexError, 'variable index out of range'
+
+ elif (type(key) is list and not [k for k in key if type(k) is not
+ int]) or (type(key) is matrix and key.typecode == 'i'):
+ l = [k for k in key if -n <= k < n]
+ if len(l) != len(key):
+ raise IndexError, 'variable index out of range'
+ for i in xrange(len(l)):
+ if l[i] < 0: l[i] += n
+
+ elif type(key) is slice:
+
+ ind = key.indices(n)
+ l = range(ind[0],ind[1],ind[2])
+
+ else:
+ raise TypeError, 'invalid key'
+
+ return l
+
+
+
+class varlist(list):
+
+ """
+ Standard list with __contains__() redefined to use 'is'
+ instead of '=='.
+ """
+
+ def __contains__(self,item):
+
+ for k in xrange(len(self)):
+ if self[k] is item: return True
+ return False
+
+
+
+def _vecmax(*s):
+
+ """
+ _vecmax(s1,s2,...) returns the componentwise maximum of s1, s2,...
+ _vecmax(s) returns the maximum component of s.
+
+ The arguments can be None, scalars or 1-column dense 'd' vectors
+ with lengths equal to 1 or equal to the maximum len(sk).
+
+ Returns None if one of the arguments is None.
+ """
+
+ if not s:
+ raise TypeError, "_vecmax expected at least 1 argument, got 0"
+
+ val = None
+ for c in s:
+
+ if c is None:
+ return None
+
+ elif type(c) is int or type(c) is float:
+ c = matrix(c, tc='d')
+
+ elif not _isdmatrix(c) or c.size[1] != 1:
+ raise TypeError, "incompatible type or size"
+
+ if val is None:
+ if len(s) == 1: return matrix(max(c), tc='d')
+ else: val = +c
+
+ elif len(val) == 1 != len(c):
+ val = matrix([max(val[0],x) for x in c], tc='d')
+
+ elif len(val) != 1 == len(c):
+ val = matrix([max(c[0],x) for x in val], tc='d')
+
+ elif len(val) == len(c):
+ val = matrix( [max(val[k],c[k]) for k in xrange(len(c))],
+ tc='d' )
+
+ else:
+ raise ValueError, 'incompatible dimensions'
+
+ return val
+
+
+
+def _vecmin(*s):
+
+ """
+ _vecmin(s1,s2,...) returns the componentwise minimum of s1, s2,...
+ _vecmin(s) returns the minimum component of s.
+
+ The arguments can be None, scalars or 1-column dense 'd' vectors
+ with lengths equal to 1 or equal to the maximum len(sk).
+
+ Returns None if one of the arguments is None.
+ """
+
+ if not s:
+ raise TypeError, "_vecmin expected at least 1 argument, got 0"
+
+ val = None
+ for c in s:
+
+ if c is None:
+ return None
+
+ elif type(c) is int or type(c) is float:
+ c = matrix(c, tc='d')
+
+ elif not _isdmatrix(c) or c.size[1] != 1:
+ raise TypeError, "incompatible type or size"
+
+ if val is None:
+ if len(s) == 1: return matrix(min(c), tc='d')
+ else: val = +c
+
+ elif len(val) == 1 != len(c):
+ val = matrix( [min(val[0],x) for x in c], tc='d' )
+
+ elif len(val) != 1 == len(c):
+ val = matrix( [min(c[0],x) for x in val], tc='d' )
+
+ elif len(val) == len(c):
+ val = matrix( [min(val[k],c[k]) for k in xrange(len(c))],
+ tc='d' )
+
+ else:
+ raise ValueError, 'incompatible dimensions'
+
+ return val
diff --git a/src/python/solvers.py b/src/python/solvers.py
new file mode 100644
index 0000000..5184dab
--- /dev/null
+++ b/src/python/solvers.py
@@ -0,0 +1,24 @@
+"""
+Convex optimization solvers.
+
+conelp: solves semidefinite programs specified via functions.
+cp: solves nonlinear convex problems.
+lp: solves linear programs.
+gp: solves geometric programs.
+nlcp: solves nonlinear convex problems specified via functions.
+qp: solves quadratic programs.
+sdp: solves semidefinite programs.
+options: dictionary with customizable algorithm parameters.
+"""
+
+# This file is part of CVXOPT version 0.8.2.
+# Copyright 2004-2007 J. Dahl and L. Vandenberghe.
+
+import cvxopt
+from cvxopt.cvxprog import cp, qp, gp, nlcp
+from cvxopt.coneprog import conelp, lp, sdp
+solvecp, solveqp, solvegp, solvelp, solvesdp = cp, qp, gp, lp, sdp
+options = {}
+cvxopt.cvxprog.options = options
+cvxopt.coneprog.options = options
+__all__ = ['conelp', 'cp', 'lp', 'gp', 'nlcp', 'qp', 'sdp']
diff --git a/src/setup.py b/src/setup.py
new file mode 100644
index 0000000..d3fb1dd
--- /dev/null
+++ b/src/setup.py
@@ -0,0 +1,165 @@
+from distutils.core import setup, Extension
+from os import listdir
+
+# directory containing libblas and liblapack
+ATLAS_LIB_DIR = '/usr/lib'
+
+# Set to 1 if you are installing the fftw module.
+BUILD_FFTW = 0
+
+# directory containing libfftw3 (used only when BUILD_FFTW = 1)
+FFTW_LIB_DIR = '/usr/lib'
+
+# directory containing fftw.h (used only when BUILD_FFTW = 1)
+FFTW_INC_DIR = '/usr/include'
+
+# Set to 1 if you are installing the glpk module.
+BUILD_GLPK = 0
+
+# directory containing libglpk (used only when BUILD_GLPK = 1)
+GLPK_LIB_DIR = '/usr/lib'
+
+# directory containing glpk.h (used only when BUILD_GLPK = 1)
+GLPK_INC_DIR = '/usr/include'
+
+# Set to 1 if you are installing the MOSEK 4.0 module.
+BUILD_MOSEK = 0
+
+# directory containing libmosek (used only when BUILD_MOSEK = 1)
+MOSEK_LIB_DIR = '/usr/local/mosek/4/tools/platform/linux32x86/bin'
+
+# directory containing mosek.h (used only when BUILD_MOSEK = 1)
+MOSEK_INC_DIR = '/usr/local/mosek/4/tools/platform/linux32x86/h'
+
+# Set to 1 if you are installing the DSDP module.
+BUILD_DSDP = 0
+
+# directory containing libdsdp.a (used only when BUILD_DSDP = 1)
+DSDP_LIB_DIR = '/usr/lib'
+
+# directory containing dsdp5.h (used only when BUILD_DSDP = 1)
+DSDP_INC_DIR = '/usr/include'
+
+extmods = []
+
+# optional modules
+
+if BUILD_FFTW:
+ fftw = Extension('fftw', libraries = ['fftw3', 'blas'],
+ include_dirs = [ FFTW_INC_DIR ],
+ library_dirs = [ FFTW_LIB_DIR, ATLAS_LIB_DIR ],
+ sources = ['C/fftw.c'] )
+ extmods += [fftw];
+
+if BUILD_GLPK:
+ glpk = Extension('glpk', libraries = ['glpk'],
+ include_dirs = [ GLPK_INC_DIR ],
+ library_dirs = [ GLPK_LIB_DIR ],
+ sources = ['C/glpk.c'] )
+ extmods += [glpk];
+
+# If the MOSEK module fails to build, modify the script according to
+# http://www.mosek.com/products/4_0/tools/doc/html/tools/node20.html,
+# section 18.13.
+if BUILD_MOSEK:
+ mosek = Extension('mosek',
+ include_dirs = [ MOSEK_INC_DIR ],
+ library_dirs = [ MOSEK_LIB_DIR ],
+ libraries = ['mosek', 'pthread', 'c', 'dl', 'm'],
+ sources = ['C/mosek.c'] )
+ extmods += [mosek];
+
+if BUILD_DSDP:
+ dsdp = Extension('dsdp', libraries = ['dsdp', 'blas', 'lapack'],
+ include_dirs = [ DSDP_INC_DIR ],
+ library_dirs = [ DSDP_LIB_DIR, ATLAS_LIB_DIR ],
+ sources = ['C/dsdp.c'] )
+ extmods += [dsdp];
+
+
+# required modules
+
+# Modify this for compilation on Windows.
+# Set to True if your BLAS/LAPACK do not use trailing underscores
+# (eg, on Windows).
+BLAS_NOUNDERSCORES = False
+if BLAS_NOUNDERSCORES:
+ MACROS = [('BLAS_NO_UNDERSCORE','')]
+else:
+ MACROS = []
+
+base = Extension('base', libraries = ['m','lapack','blas','g2c'],
+ library_dirs = [ ATLAS_LIB_DIR ],
+ define_macros = MACROS,
+ sources = ['C/base.c','C/dense.c','C/sparse.c'])
+
+random = Extension('random',
+ sources = ['C/random.c', 'C/rngs/rngs.c', 'C/rngs/rvgs.c'])
+
+blas = Extension('blas', libraries = ['blas','g2c'],
+ library_dirs = [ ATLAS_LIB_DIR ],
+ define_macros = MACROS,
+ sources = ['C/blas.c'] )
+
+lapack = Extension('lapack', libraries = ['lapack','blas','g2c'],
+ library_dirs = [ ATLAS_LIB_DIR ],
+ define_macros = MACROS,
+ sources = ['C/lapack.c'] )
+
+umfpack = Extension('umfpack',
+ include_dirs = [ 'C/SuiteSparse/UMFPACK/Include',
+ 'C/SuiteSparse/AMD/Include', 'C/SuiteSparse/AMD/Source',
+ 'C/SuiteSparse/UFconfig' ],
+ library_dirs = [ ATLAS_LIB_DIR ],
+ define_macros = MACROS,
+ libraries = [ 'blas', 'lapack', 'g2c'],
+ sources = [ 'C/umfpack.c',
+ 'C/SuiteSparse/UMFPACK/Source/umfpack_global.c',
+ 'C/SuiteSparse/UMFPACK/Source/umfpack_tictoc.c' ] +
+ ['C/SuiteSparse_cvxopt_extra/umfpack/' + s for s in
+ listdir('C/SuiteSparse_cvxopt_extra/umfpack')])
+
+
+# Build for int or long?
+import sys
+if sys.maxint > 2**31: MACROS += [('DLONG','')]
+
+cholmod = Extension('cholmod',
+ library_dirs = [ ATLAS_LIB_DIR ],
+ libraries = ['lapack', 'blas', 'g2c'],
+ include_dirs = [ 'C/SuiteSparse/CHOLMOD/Include',
+ 'C/SuiteSparse/COLAMD', 'C/SuiteSparse/AMD/Include',
+ 'C/SuiteSparse/UFconfig' ],
+ define_macros = MACROS + [('NPARTITION', '1')],
+ sources = [ 'C/cholmod.c' ] +
+ ['C/SuiteSparse/AMD/Source/' + s for s in ['amd_global.c',
+ 'amd_postorder.c', 'amd_post_tree.c', 'amd_2.c']] +
+ ['C/SuiteSparse/COLAMD/' + s for s in ['colamd.c',
+ 'colamd_global.c']] +
+ ['C/SuiteSparse/CHOLMOD/Core/' + s for s in
+ listdir('C/SuiteSparse/CHOLMOD/Core') if s[-2:] == '.c' and
+ s[0] == 'c'] +
+ ['C/SuiteSparse/CHOLMOD/Cholesky/' + s for s in
+ listdir('C/SuiteSparse/CHOLMOD/Cholesky') if s[-2:] == '.c'
+ and s[0] == 'c'] +
+ ['C/SuiteSparse/CHOLMOD/Check/cholmod_check.c'] +
+ ['C/SuiteSparse/CHOLMOD/Supernodal/' + s for s in
+ listdir('C/SuiteSparse/CHOLMOD/Supernodal') if
+ s[-2:] == '.c' and s[0] == 'c'] )
+
+amd = Extension('amd',
+ include_dirs = [ 'C/SuiteSparse/AMD/Include',
+ 'C/SuiteSparse/UFconfig' ],
+ define_macros = MACROS,
+ sources = [ 'C/amd.c' ] + [ 'C/SuiteSparse/AMD/Source/' + s for s in
+ listdir('C/SuiteSparse/AMD/Source') if s[-2:] == '.c' ])
+
+extmods += [base, blas, lapack, random, umfpack, cholmod, amd]
+
+setup (name = 'cvxopt',
+ description = 'Convex optimization package',
+ version = '0.8.2',
+ ext_package = "cvxopt",
+ ext_modules = extmods,
+ package_dir = {"cvxopt": "python"},
+ packages = ["cvxopt"])
--
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