[Pkg-octave-commit] [octave-lssa.git] 01/03: Imported Upstream version 0.1.2
Rafael Laboissière
rlaboiss-guest at moszumanska.debian.org
Mon Aug 29 21:41:51 UTC 2016
This is an automated email from the git hooks/post-receive script.
rlaboiss-guest pushed a commit to branch master
in repository octave-lssa.git.
commit 937783f4b8c43eaca92ef30cd9af170248c2636f
Author: Rafael Laboissiere <rafael at debian.org>
Date: Sat Aug 20 16:19:23 2016 -0300
Imported Upstream version 0.1.2
---
COPYING | 674 ++++++++++++++++++++++++++++++++++++++++++++++++++
DESCRIPTION | 15 ++
INDEX | 17 ++
NEWS | 33 +++
inst/cubicwgt.m | 54 ++++
inst/lombcoeff.m | 64 +++++
inst/lombnormcoeff.m | 67 +++++
inst/lscomplex.m | 95 +++++++
inst/lscorrcoeff.m | 136 ++++++++++
inst/lsreal.m | 111 +++++++++
inst/lswaveletcoeff.m | 106 ++++++++
src/Makefile | 15 ++
src/fastlscomplex.cc | 529 +++++++++++++++++++++++++++++++++++++++
src/fastlsreal.cc | 392 +++++++++++++++++++++++++++++
14 files changed, 2308 insertions(+)
diff --git a/COPYING b/COPYING
new file mode 100644
index 0000000..94a9ed0
--- /dev/null
+++ b/COPYING
@@ -0,0 +1,674 @@
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+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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+IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+ 16. Limitation of Liability.
+
+ IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM 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 PROGRAM (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 PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+ 17. Interpretation of Sections 15 and 16.
+
+ If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+state 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 program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ 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 3 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.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+ If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+ <program> Copyright (C) <year> <name of author>
+ This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+ You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+ The GNU General Public License does not permit incorporating your program
+into proprietary programs. If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library. If this is what you want to do, use the GNU Lesser General
+Public License instead of this License. But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
diff --git a/DESCRIPTION b/DESCRIPTION
new file mode 100644
index 0000000..3291e1e
--- /dev/null
+++ b/DESCRIPTION
@@ -0,0 +1,15 @@
+Name: lssa
+Version: 0.1.2
+Date: 2012-08-17
+Author: Ben Lewis <benjf5 at gmail.com>
+Maintainer: Ben Lewis <benjf5 at gmail.com>
+Title: Least squares spectral analysis
+Description: A package implementing tools to compute spectral decompositions of
+ irregularly-spaced time series. Currently includes functions based off the
+ Lomb-Scargle periodogram and Adolf Mathias' implementation for R and C (see
+ URLs).
+Url: http://www.jstatsoft.org/v11/i02
+Problems: fast implementations, wavelet functions are currently not functional.
+Depends: octave (>= 3.6.0)
+Autoload: no
+License: GPLv3+
diff --git a/INDEX b/INDEX
new file mode 100644
index 0000000..0e69892
--- /dev/null
+++ b/INDEX
@@ -0,0 +1,17 @@
+lssa >> Least Squares Spectral Analysis
+Windowing
+ cubicwgt
+Periodogram
+ lombcoeff lombnormcoeff
+Accelerated time-series functions
+ fastlscomplex
+Complex time-series functions
+ lscomplex
+Real time-series functions
+ lsreal
+Correlation
+ lscorrcoeff
+Wavelet Transform
+ lswaveletcoeff
+# lscomplexwavelet lsrealwavelet
+## The wavelet functions are unavailable until I can get them working.
diff --git a/NEWS b/NEWS
new file mode 100644
index 0000000..39cbf8a
--- /dev/null
+++ b/NEWS
@@ -0,0 +1,33 @@
+Summary of changes in lssa 0.1.2:
+
+ ** All functions now have input checks in place to return useful errors as
+ opposed to division by zero, etc. Documentation has also been improved.
+
+Summary of status of the intial lssa release, 0.1.1:
+
+Current status:
+
+ ** lscomplex and lsreal both produce accurate results; they can be slow for
+ very large datasets.
+
+ ** fastlscomplex is accurate for the first octave of results; there is still an
+ error I need to pin down in the merging for additional octaves. fastlsreal
+ is disabled at the moment as I move to an implementation based on the new
+ fastlscomplex.
+
+ ** lscorrcoeff works, although I'm still attempting to understand the initial
+ author's reasoning. Its generated results are relevant to any given data
+ set, but it does not appear to be normalized to any great extent.
+
+ ** There are two wavelet functions under development, but they are not included
+ in this release as they are currently not functional. For all your wavelet
+ needs, the specific transformation used is available in the lswaveletcoeff
+ function, and will generate a single cosine/sine magnitude pair (as a
+ complex number) for a complex-valued series (this function may be joined by
+ a companion for real-valued series) and can be looped to simulate a full
+ wavelet transform.
+
+ ** For all the working functions, tests have been written and formatted to
+ Octave coding standards. These tests should pass on any given architecture
+ (there was some question about that previously) and often provide examples
+ of how the function operates. For a few functions, there are demo scripts.
diff --git a/inst/cubicwgt.m b/inst/cubicwgt.m
new file mode 100644
index 0000000..147cd46
--- /dev/null
+++ b/inst/cubicwgt.m
@@ -0,0 +1,54 @@
+## Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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 3 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{a} =} cubicwgt (@var{series})
+##
+## Returns the input series, windowed by a polynomial similar to a Hanning
+## window. To window an arbitrary section of the series, subtract or add an
+## offset to it to adjust the centre of the window; for an offset of k, the call
+## would be cubicwgt (@var{s} - k). Similarly, the radius of the window is 1;
+## if an arbitrary radius r is desired, dividing the series by the radius after
+## centering is the best way to adjust to fit the window: cubicwgt ((@var{s} -
+## k) / r).
+##
+## The windowing function itself is:
+## w = 1 + ( x ^ 2 * ( 2 x - 3 ) ), x in [-1,1], else w = 0.
+##
+## @end deftypefn
+
+function a = cubicwgt (s)
+
+ if (nargin != 1)
+ print_usage ();
+ endif
+
+ ## s is the value/vector/matrix to be windowed
+ a = abs (s);
+ a = ifelse ((a < 1), 1 + ((a .^ 2) .* (2 .* a - 3)), 0);
+
+endfunction
+
+
+%!shared h, m, k
+%! h = 2;
+%! m = 0.01;
+%! k = [0, 3, 1.5, -1, -0.5, -0.25, 0.75];
+%!assert (cubicwgt (h), 0 );
+%!assert (cubicwgt (m), 1 + m ^ 2 * (2 * m - 3));
+%!assert (cubicwgt (k), [1.00000, 0.00000, 0.00000, 0.00000, ...
+%! 0.50000, 0.84375, 0.15625], 1e-6);
+%! ## Tests cubicwgt on two scalars and two vectors; cubicwgt will work
+%! ## on any array input.
diff --git a/inst/lombcoeff.m b/inst/lombcoeff.m
new file mode 100644
index 0000000..6c4d5f7
--- /dev/null
+++ b/inst/lombcoeff.m
@@ -0,0 +1,64 @@
+## Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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 3 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{c} =} lombcoeff (@var{time}, @var{mag}, @var{freq})
+##
+## Return the Lomb Periodogram value at one frequency for a time series.
+##
+## @seealso{lombnormcoeff}
+## @end deftypefn
+
+
+function coeff = lombcoeff (T, X, o)
+
+ if (nargin != 3)
+ print_usage ();
+ endif
+ if (! all (size (T) == size (X)))
+ error ("lombcoeff: Time series vectors of uneven size.\n");
+ endif
+ if (! isscalar (o))
+ error ("lombcoeff: Supplied frequency is not a scalar.\n");
+ endif
+ if (o == 0)
+ error ("lombcoeff: Supplied frequency is not a frequency.\n");
+ endif
+
+ oT = o .* T;
+
+ theta = atan2 (sum (sin (2 * oT)),
+ sum (cos (2 * oT))) ./ (2 * o);
+
+ coeff = (sum (X .* cos (oT - theta)) ^2 /
+ sum (cos (oT - theta) .^2) +
+ sum (X .* sin (oT - theta)) ^2 /
+ sum (sin (oT - theta) .^2));
+
+endfunction
+
+
+%!shared t, x, o, maxfreq
+%! maxfreq = 4 / (2 * pi);
+%! t = linspace (0, 8);
+%! x = (2 .* sin (maxfreq .* t) +
+%! 3 .* sin ((3/4) * maxfreq .* t) -
+%! 0.5 .* sin ((1/4) * maxfreq .* t) -
+%! 0.2 .* cos (maxfreq .* t) +
+%! cos ((1/4) * maxfreq .* t));
+%! o = [maxfreq , (3/4 * maxfreq) , (1/4 * maxfreq)];
+%!assert (lombcoeff (t, x, maxfreq), 1076.77574184435, 5e-10);
+%!assert (lombcoeff (t, x, 3/4*maxfreq), 1226.53572492183, 5e-10);
+%!assert (lombcoeff (t, x, 1/4*maxfreq), 1341.63962181896, 5e-10);
diff --git a/inst/lombnormcoeff.m b/inst/lombnormcoeff.m
new file mode 100644
index 0000000..481f722
--- /dev/null
+++ b/inst/lombnormcoeff.m
@@ -0,0 +1,67 @@
+## Copyright (c) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{c} =} lombnormcoeff (@var{time}, @var{mag}, @var{freq})
+##
+## Return the normalized Lomb Periodogram value at one frequency for a time
+## series.
+##
+## @seealso{lombcoeff}
+##
+## @end deftypefn
+
+
+function coeff = lombnormcoeff (T, X, omega)
+
+ if (nargin != 3)
+ print_usage ();
+ endif
+ if (! all (size (T) == size (X)))
+ error ("lombnormcoeff: Time series vectors of uneven size.\n");
+ endif
+ if (! isscalar (omega))
+ error ("lombnormcoeff: Supplied frequency is not a scalar.\n");
+ endif
+ if (omega == 0)
+ error ("lombnormcoeff: Supplied frequency is not a frequency.\n");
+ endif
+
+
+ xmean = mean (X);
+
+ theta = atan2 (sum (sin (2 .* omega .*T)),
+ sum (cos (2 .* omega .* T))) / (2*omega);
+
+ coeff = ((sum ((X-xmean) .* cos (omega .* T - theta)) .^ 2 /
+ sum (cos (omega .* T - theta) .^ 2) +
+ sum ((X-xmean) .* sin (omega .* T - theta)) .^ 2 /
+ sum (sin (omega .* T - theta) .^ 2 )) /
+ (2 * var(X)));
+
+endfunction
+
+%!shared t, x, o, maxfreq
+%! maxfreq = 4 / (2 * pi);
+%! t = linspace (0, 8);
+%! x = (2 .* sin (maxfreq .* t) +
+%! 3 .* sin ((3/4) * maxfreq .* t) -
+%! 0.5 .* sin((1/4) * maxfreq .* t) -
+%! 0.2 .* cos (maxfreq .* t) +
+%! cos ((1/4) * maxfreq .*t));
+%! o = [maxfreq , (3/4 * maxfreq) , (1/4 * maxfreq)];
+%!assert (lombnormcoeff (t,x,o(1)), 44.7068607258824, 5e-10);
+%!assert (lombnormcoeff (t,x,o(2)), 35.7769955188467, 5e-10);
+%!assert (lombnormcoeff (t,x,o(3)), 20.7577786183241, 5e-10);
diff --git a/inst/lscomplex.m b/inst/lscomplex.m
new file mode 100644
index 0000000..db212df
--- /dev/null
+++ b/inst/lscomplex.m
@@ -0,0 +1,95 @@
+## Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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 3 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{t} =} lscomplex (@var{time}, @var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctaves})
+##
+## Return a series of least-squares transforms of a complex-valued time series.
+## Each transform is minimized independently at each frequency. @var{numcoeff}
+## frequencies are tested for each of @var{numoctaves} octaves, starting from
+## @var{maxfreq}.
+##
+## Each result (a + bi) at a given frequency, o, defines the real and imaginary
+## coefficients for a sum of cosine and sine functions: a cos(ot) + b i
+## sin(ot). The specific frequency can be determined by its index in @var{t},
+## @var{ind}, as @var{maxfreq} * 2 ^ (- (@var{ind} - 1) / @var{numcoeff}).
+##
+## @seealso{lsreal}
+## @end deftypefn
+
+
+function transform = lscomplex (t, x, omegamax, ncoeff, noctave)
+
+ if (nargin != 5)
+ print_usage ();
+ endif
+ if (! isvector (t))
+ error ("lscomplex: Time values are not a vector.\n");
+ endif
+ if (! isvector (x))
+ error ("lscomplex: Magnitude values are not a vector.\n");
+ endif
+ if (! all (size (t) == size (x)))
+ error ("lscomplex: Size of time vector, magnitude vector unequal.\n");
+ endif
+ if (! isscalar (omegamax))
+ error ("lscomplex: More than one value for maximum frequency specified.\n");
+ endif
+ if (! isscalar (ncoeff))
+ error ("lscomplex: More than one number of frequencies per octave specified.\n");
+ endif
+ if (! isscalar (noctave))
+ error ("lscomplex: More than one number of octaves to traverse specified.\n");
+ endif
+ if (omegamax == 0)
+ error ("lscomplex: Specified maximum frequency is not a frequency.\n");
+ endif
+ if (noctave == 0)
+ error ("lscomplex: No octaves of results requested.\n");
+ endif
+ if (ncoeff == 0)
+ error ("lscomplex: No frequencies per octave requested.\n");
+ endif
+ if (ncoeff != floor (ncoeff))
+ error ("lscomplex: Specified number of frequencies per octave is not integral.\n");
+ endif
+ if (noctave != floor (noctave))
+ error ("lscomplex: Specified number of octaves of results is not integral.\n");
+ endif
+
+ n = numel (t);
+
+ iter = 0 : (ncoeff * noctave - 1);
+ omul = (2 .^ (- iter / ncoeff));
+
+ ot = t(:) * (omul * omegamax);
+
+ transform = sum ((cos (ot) - (sin (ot) .* i)) .* x(:), 1) / n;
+
+endfunction
+
+%!test
+%! maxfreq = 4 / ( 2 * pi );
+%! t = [0:0.008:8];
+%! x = ( 2 .* sin (maxfreq .* t) +
+%! 3 .* sin ( (3 / 4) * maxfreq .* t)-
+%! 0.5 .* sin ((1/4) * maxfreq .* t) -
+%! 0.2 .* cos (maxfreq .* t) +
+%! cos ((1/4) * maxfreq .* t));
+%! assert (lscomplex (t, x, maxfreq, 2, 2),
+%! [(-0.400924546169395 - 2.371555305867469i), ...
+%! (1.218065147708429 - 2.256125004156890i), ...
+%! (1.935428592212907 - 1.539488163739336i), ...
+%! (2.136692292751917 - 0.980532175174563i)], 5e-10);
diff --git a/inst/lscorrcoeff.m b/inst/lscorrcoeff.m
new file mode 100644
index 0000000..60bd6a2
--- /dev/null
+++ b/inst/lscorrcoeff.m
@@ -0,0 +1,136 @@
+## Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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 3 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{c} =} lscorrcoeff (@var{time1}, @var{mag1}, @var{time2}, @var{mag2}, @var{time}, @var{freq})
+## @deftypefnx {Function File} {@var{c} =} lscorrcoeff (@var{time1}, @var{mag1}, @var{time2}, @var{mag2}, @var{time}, @var{freq}, @var{window} = @var{cubicwgt})
+## @deftypefnx {Function File} {@var{c} =} lscorrcoeff (@var{time1}, @var{mag1}, @var{time2}, @var{mag2}, @var{time}, @var{freq}, @var{window} = @var{cubicwgt}, @var{winradius} = 1)
+##
+## Return the coefficient of the wavelet correlation of two complex time
+## series. The correlation is only effective at a given time and frequency.
+## The windowing function applied by default is cubicwgt, this can be changed by
+## passing a different function handle to @var{window}, while the radius applied
+## is set by @var{winradius}. Note that this will be most effective when both
+## series have had their mean value (if it is not zero) subtracted (and stored
+## separately); this reduces the constant-offset error further, and allows the
+## functions to be compared on their periodic features rather than their
+## constant features.
+##
+## @seealso{lswaveletcoeff, lscomplexwavelet, lsrealwavelet}
+##
+## @end deftypefn
+
+function coeff = lscorrcoeff (x1, y1, x2, y2, t, o, wgt = @cubicwgt, wgtrad = 1)
+
+ ## Input checking is absolutely necessary.
+
+ if (!((nargin >= 6) && (nargin <= 8)))
+ print_usage ();
+ endif
+
+ ## Test to be sure x1, y1, x2, y2 are all vectors, and that t and o are
+ ## scalars.
+ if (! isvector (x1))
+ error ("lscorrcoeff: First time series time values are not a vector.\n");
+ endif
+ if (! isvector (y1))
+ error ("lscorrcoeff: First time series magnitude values are not a vector.\n");
+ endif
+ if (! isvector (x2))
+ error ("lscorrcoeff: Second time series time values are not a vector.\n");
+ endif
+ if (! isvector (y2))
+ error ("lscorrcoeff: Second time series magnitude values are not a vector.\n");
+ endif
+ if (! isscalar (t))
+ error ("lscorrcoeff: Window centre is not a scalar.\n");
+ endif
+ if (! isscalar (o))
+ error ("lscorrcoeff: Specified frequency is not a scalar.\n");
+ endif
+ if (! isscalar (wgtrad))
+ error ("lscorrcoeff: Window radius is not a scalar.\n");
+ endif
+ if (! all (size (x1) == size (y1)))
+ error ("lscorrcoeff: First time series vectors not of matching size.\n");
+ endif
+ if (! all (size (x2) == size (y2)))
+ error ("lscorrcoeff: Second time series vectors not of matching size.\n");
+ endif
+
+ ## How to determine if a weight function has been assigned or not? (Possible
+ ## to get name of function?)
+
+ so = 0.05 * o;
+
+ ## The first solution that comes to mind is admittedly slightly
+ ## ugly and has a data footprint of O(2n) but it is vectorised.
+ mask = (abs (x1 - t) * so) < wgtrad;
+
+ rx1 = x1(mask);
+ ## FIXME : Needs to have a noisy error if length(y1) != length(x1) -- add this!
+ ry1 = y1(mask);
+
+ mask = (abs (x2 - t) * so ) < wgtrad;
+ rx2 = x2(mask);
+ ry2 = y2(mask);
+
+ windowed_element_count = length (rx1);
+ if (windowed_element_count == 0)
+ error("lscorrcoeff: No time-series elements contained in window.\n");
+ endif
+
+ s = sum (wgt ((rx1 - t) .* so)) * sum (wgt ((rx2 - t ) .* so ));
+ if (s != 0)
+ coeff = sum (wgt ((rx1 - t) .* so) .* exp (i * o .* rx1) .* ry1) * ...
+ sum (wgt ((rx2 - t) .* so) .* exp (i * o .* rx2) .* conj (ry2)) / s;
+ else
+ coeff = 0;
+ endif
+
+endfunction
+
+
+%!shared t, p, x, y, z, o, maxfreq
+%! maxfreq = 4 / (2 * pi);
+%! t = linspace (0, 8);
+%! x = (2 .* sin (maxfreq .* t) +
+%! 3 .* sin ((3/4) * maxfreq .* t) -
+%! 0.5 .* sin ((1/4) * maxfreq .* t) -
+%! 0.2 .* cos (maxfreq .* t) +
+%! cos ((1/4) * maxfreq .* t));
+%! y = - x;
+%! p = linspace (0, 8, 500);
+%! z = (2 .* sin (maxfreq .* p) +
+%! 3 .* sin ((3/4) * maxfreq .* p) -
+%! 0.5 .* sin ((1/4) * maxfreq .* p) -
+%! 0.2 .* cos (maxfreq .* p) +
+%! cos ((1/4) * maxfreq .* p));
+%! o = [maxfreq , (3/4 * maxfreq) , (1/4 * maxfreq)];
+%!assert (lscorrcoeff (t, x, t, x, 0.5, maxfreq),
+%! -5.54390340863576 - 1.82439880893383i, 5e-10);
+%!assert (lscorrcoeff (t, x, t, y, 0.5, maxfreq),
+%! 5.54390340863576 + 1.82439880893383i, 5e-10);
+%!assert (lscorrcoeff (t, x, p, z, 0.5, maxfreq),
+%! -5.55636741054624 - 1.82803733863170i, 5e-10);
+
+## Demo with sin, cos as Nir suggested.
+%!demo
+%! ## This generates the correlation coefficient at time 0.5 and circular freq. 0.9
+%! x = 1:10;
+%! y = sin (x);
+%! z = cos (x);
+%! a = lscorrcoeff (x, y, x, z, 0.5, 0.9)
+
diff --git a/inst/lsreal.m b/inst/lsreal.m
new file mode 100644
index 0000000..48f4c0c
--- /dev/null
+++ b/inst/lsreal.m
@@ -0,0 +1,111 @@
+## Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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 3 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{t} =} lsreal (@var{time}, @var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctaves})
+##
+## Return a series of least-squares transforms of a real-valued time series.
+## Each transform is minimized independently for each frequency. The method
+## used is a Lomb-Scargle transform of the real-valued (@var{time}, @var{mag})
+## series, starting from frequency @var{maxfreq} and descending @var{numoctaves}
+## octaves with @var{numcoeff} coefficients per octave.
+##
+## The result of the transform for each frequency is the coefficient of a sum of
+## sine and cosine functions modified by that frequency, in the form of a
+## complex number—where the cosine coefficient is encoded in the real term, and
+## the sine coefficient is encoded in the imaginary term. Each frequency is fit
+## independently from the others, and to minimize very low frequency error,
+## consider storing the mean of a dataset with a constant or near-constant
+## offset separately, and subtracting it from the dataset.
+##
+## @seealso{lscomplex}
+## @end deftypefn
+
+
+
+function transform = lsreal (t, x, omegamax, ncoeff, noctave)
+
+ ## Sanity checks to make sure that the user can get meaningful errors.
+ if (nargin != 5)
+ print_usage ();
+ endif
+ if (! isvector (t))
+ error ("lsreal: Time values are not a vector.\n");
+ endif
+ if (! isvector (x))
+ error ("lsreal: Magnitude values are not a vector.\n");
+ endif
+ if (! all (size (t) == size (x)))
+ error ("lsreal: Size of time vector, magnitude vector unequal.\n");
+ endif
+ if (! isscalar (omegamax))
+ error ("lsreal: More than one value for maximum frequency specified.\n");
+ endif
+ if (! isscalar (ncoeff))
+ error ("lsreal: More than one number of frequencies per octave specified.\n");
+ endif
+ if (! isscalar (noctave))
+ error ("lsreal: More than one number of octaves to traverse specified.\n");
+ endif
+ if (omegamax == 0)
+ error ("lsreal: Specified maximum frequency is not a frequency.\n");
+ endif
+ if (noctave == 0)
+ error ("lsreal: No octaves of results requested.\n");
+ endif
+ if (ncoeff == 0)
+ error ("lsreal: No frequencies per octave requested.\n");
+ endif
+ if (ncoeff != floor (ncoeff))
+ error ("lsreal: Specified number of frequencies per octave is not integral.\n");
+ endif
+ if (noctave != floor (noctave))
+ error ("lsreal: Specified number of octaves of results is not integral.\n");
+ endif
+
+ n = numel (t);
+
+ iter = 0 : (ncoeff * noctave - 1);
+ omul = (2 .^ (- iter / ncoeff));
+
+ ## For a given frequency, the iota term is taken at twice the frequency of the
+ ## zeta term.
+ ot = t(:) * (omul * omegamax);
+ oit = t(:) * (omul * omegamax * 2);
+
+ zeta = sum ((cos (ot) - (sin (ot) .* i)) .* x(:), 1) / n;
+ iota = sum ((cos (oit) - (sin (oit) .* i)), 1) / n;
+
+ transform = 2 .* (conj (zeta) - conj (iota) .* zeta) ./ (1 - abs (iota) .^ 2);
+
+endfunction
+
+%!test
+%! maxfreq = 4 / ( 2 * pi );
+%! t = linspace(0,8);
+%! x = ( 2 .* sin ( maxfreq .* t ) +
+%! 3 .* sin ( (3/4) * maxfreq .* t ) -
+%! 0.5 .* sin ( (1/4) * maxfreq .* t ) -
+%! 0.2 .* cos ( maxfreq .* t ) +
+%! cos ( (1/4) * maxfreq .* t ) );
+%! # In the assert here, I've got an error bound large enough to catch
+%! # individual system errors which would present no real issue.
+%! assert (lsreal (t,x,maxfreq,2,2),
+%! [(-1.68275915310663 + 4.70126183846743i), ...
+%! (1.93821553170889 + 4.95660209883437i), ...
+%! (4.38145452686697 + 2.14403733658600i), ...
+%! (5.27425332281147 - 0.73933440226597i)],
+%! 5e-10)
+
diff --git a/inst/lswaveletcoeff.m b/inst/lswaveletcoeff.m
new file mode 100644
index 0000000..f830a5b
--- /dev/null
+++ b/inst/lswaveletcoeff.m
@@ -0,0 +1,106 @@
+## Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+##
+## 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 3 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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{c} =} lswaveletcoeff (@var{t}, @var{x}, @var{time}, @var{freq})
+## @deftypefnx {Function File} {@var{c} =} lswaveletcoeff (@var{t}, @var{x}, @var{time}, @var{freq}, @var{window}=cubicwgt)
+## @deftypefnx {Function File} {@var{c} =} lswaveletcoeff (@var{t}, @var{x}, @var{time}, @var{freq}, @var{window}=cubicwgt, @var{winradius}=1)
+##
+## Return the wavelet transform of a complex time series in a given window. The
+## transform takes a complex time series (@var{t}, @var{x}) at time @var{time}
+## and frequency @var{freq}, then applies a windowing function to it; the
+## default is cubicwgt, however by providing a function handle for the optional
+## variable @var{window}, the user may select their own function; to determine
+## the radius of the interval around the @var{time} selected, set
+## @var{winradius} to some value other than 1.
+##
+## This transform operates identically to the transform at the heart of
+## lscomplexwavelet, however for one window only.
+##
+## @seealso{lscorrcoeff, lscomplexwavelet, lsrealwavelet}
+##
+## @end deftypefn
+
+
+function coeff = lswaveletcoeff (x, y, t, o, wgt = @cubicwgt, wgtrad = 1)
+
+ if (! (nargin >= 4) && (nargin <= 6))
+ print_usage ();
+ endif
+ if (! isvector (x))
+ error ("lswaveletcoeff: Time values are not a vector.\n");
+ endif
+ if (! isvector (y))
+ error ("lswaveletcoeff: Magnitude values are not a vector.\n");
+ endif
+ if (! all (size (x) == size (y)))
+ error ("lswaveletcoeff: Time series vectors of uneven size.\n");
+ endif
+ if (! isscalar (t))
+ error ("lswaveletcoeff: Window centre specified is not scalar.\n");
+ endif
+ if (! isscalar (o))
+ error ("lswaveletcoeff: Frequency specified is not scalar.\n");
+ endif
+ if (! isscalar (wgtrad))
+ error ("lswaveletcoeff: Window radius specified is not scalar.\n");
+ endif
+
+ so = 0.05 .* o;
+
+ if ((ndims (x) == 2) && ! (rows (x) == 1))
+ x = reshape (x, 1, length (x));
+ y = reshape (y, 1, length (y));
+ endif
+
+ mask = (abs (x - t) * so < wgtrad);
+ rx = x(mask);
+ ry = y(mask);
+
+ ## Going by the R code, this can use the same mask.
+ s = sum (wgt ((x - t) .* so));
+ coeff = ifelse (s != 0,
+ sum (wgt ((rx - t) .* so) .*
+ exp (i .* o .* (rx - t)) .* ry) ./ s,
+ 0);
+
+endfunction
+
+
+%!shared t, p, x, y, maxfreq
+%! maxfreq = 4 / (2 * pi);
+%! t = linspace (0, 8);
+%! x = (2 .* sin (maxfreq .* t) +
+%! 3 .* sin ((3/4) * maxfreq .* t) -
+%! 0.5 .* sin ((1/4) * maxfreq .* t) -
+%! 0.2 .* cos (maxfreq .* t) +
+%! cos ((1/4) * maxfreq .* t));
+%! y = - x;
+%! p = linspace (0, 8, 500);
+%!assert (lswaveletcoeff (t, x, 0.5, maxfreq),
+%! 0.383340407638780 + 2.385251997545446i, 5e-10);
+%!assert (lswaveletcoeff (t, y, 3.3, 3/4 * maxfreq),
+%! -2.35465091096084 + 1.01892561714824i, 5e-10);
+
+
+%!demo
+%! ## Generates the wavelet transform coefficient for time 0.5 and circ. freq. 0.9, for row & column vectors.
+%! x = 1:10;
+%! y = sin (x);
+%! xt = x';
+%! yt = y';
+%! a = lswaveletcoeff (x, y, 0.5, 0.9)
+%! b = lswaveletcoeff (xt, yt, 0.5, 0.9)
+
diff --git a/src/Makefile b/src/Makefile
new file mode 100644
index 0000000..d3b48ca
--- /dev/null
+++ b/src/Makefile
@@ -0,0 +1,15 @@
+MKOCTFILE ?= mkoctfile
+
+all: fastlscomplex.oct #\
+# fastlsreal.oct
+
+fastlscomplex.oct: fastlscomplex.cc
+ $(MKOCTFILE) fastlscomplex.cc
+
+# fastlsreal compilation is disabled for the time being
+#fastlsreal.oct: fastlsreal.cc
+# $(MKOCTFILE) fastlsreal.cc
+
+# helper function just in case
+clean:
+ rm *.o *.oct *~ octave-core
diff --git a/src/fastlscomplex.cc b/src/fastlscomplex.cc
new file mode 100644
index 0000000..99c52d3
--- /dev/null
+++ b/src/fastlscomplex.cc
@@ -0,0 +1,529 @@
+/* Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+ *
+ * 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 3 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.
+ *
+ * You should have received a copy of the GNU General Public License along
+ * with this program; if not, write to the Free Software Foundation, Inc.,
+ * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+
+
+#include <octave/oct.h>
+#include <octave/unwind-prot.h>
+#include <complex>
+#include <string>
+#include <math.h>
+#include <iostream>
+#include <exception>
+
+bool flscomplex (const RowVector & tvec, const ComplexRowVector & xvec,
+ double maxfreq, int coefficients, int octaves, ComplexRowVector & result);
+
+DEFUN_DLD(fastlscomplex,args,nargout,
+"-*- texinfo -*-\n\
+ at deftypefn {Function File} { C = } fastlscomplex \
+(@var{time}, at var{magnitude}, at var{maxfreq}, at var{ncoeff}, at var{noctave})\n \
+\n\
+Return a series of least-squares transforms of a complex time series via a divide and\n\
+conquer algorithm. Each transform is minimized independently at each frequency,\n\
+starting from @var{maxfreq} and descending over @var{ncoeff} frequencies for\n\
+each of @var{noctave} octaves.\n\
+\n\
+For each result, the complex result for a given frequency o defines the real and\n\
+imaginary sinusoids which have the least distance to the data set: for a + bi,\n\
+the matching sinusoids are a cos (ot) + b i sin (ot).\n\
+\n\
+ at seealso{lscomplex, fastlsreal}\n\
+\n\
+ at end deftypefn")
+{
+
+ octave_value_list retval;
+
+ if (args.length() != 5)
+ print_usage();
+ else
+ {
+
+ RowVector tvals = args(0).row_vector_value ();
+ ComplexRowVector xvals = args(1).complex_row_vector_value ();
+ double omegamax = args(2).double_value ();
+ int noctaves = args(3).int_value ();
+ int ncoeff = args(4).int_value ();
+
+ if (tvals.numel () != xvals.numel ())
+ if (tvals.numel () > xvals.numel ())
+ error ("fastlscomplex: More time values than magnitude values");
+ else
+ error ("fastlscomplex: More magnitude values than time values");
+ if (ncoeff == 0)
+ error ("fastlscomplex: No coefficients to compute");
+ if (noctaves == 0)
+ error ("fastlscomplex: No octaves to compute over");
+ if (omegamax == 0)
+ error ("fastlscomplex: No difference between minimal and maximal frequency");
+
+ if (! error_state)
+ {
+ ComplexRowVector results;
+ if (flscomplex (tvals, xvals, omegamax, noctaves, ncoeff, results))
+ retval(0) = octave_value (results);
+ else
+ error ("fastlscomplex: error in the underlying flscomplex function");
+ }
+
+ }
+
+ return retval;
+}
+
+bool flscomplex (const RowVector & tvec, const ComplexRowVector & xvec,
+ double maxfreq, int octaves, int coefficients,
+ ComplexRowVector & results)
+{
+
+ struct Precomputation_Record
+ {
+ Precomputation_Record *next;
+ std::complex<double> power_series[12]; // I'm using 12 as a matter of compatibility, only.
+ bool stored_data;
+ };
+
+ const std::complex<double> *xvec_ptr = xvec.data ();
+ const double *tvec_ptr = tvec.data ();
+
+ results.resize (coefficients * octaves);
+ const std::complex<double> *results_ptr = results.fortran_vec ();
+
+ double tau, delta_tau, tau_0, tau_h, n_inv, mu, te,
+ omega_oct, omega_multiplier, octavemax, omega_working,
+ loop_tau_0, loop_delta_tau, on_1, n_1, o;
+
+ double length = tvec_ptr[tvec.numel () - 1] - tvec_ptr[0];
+
+ int octave_iter, coeff_iter;
+
+ std::complex<double> zeta, zz, z_accumulator, exp_term, exp_multiplier,
+ alpha, h, *tpra, *temp_ptr_alpha, temp_alpha[12], *tprb, *temp_ptr_beta,
+ temp_beta[12], temp_array[12], *p, x;
+
+ octave_idx_type n = tvec.numel ();
+
+ for (int array_iter = 0; array_iter < 12; array_iter++)
+ temp_array[array_iter] = std::complex<double> (0 , 0);
+
+ int factorial_array[12];
+ factorial_array[0] = 1;
+
+ for (int i = 1; i < 12; i++)
+ factorial_array[i] = factorial_array[i-1] * i;
+
+ n_1 = n_inv = 1.0 / n;
+ mu = (0.5 * M_PI) / length; // Per the article; this is in place to improve numerical accuracy if desired.
+ /* Viz. the paper, in which Dtau = c / omega_max, and c is stated as pi/2 for floating point processors,
+ * In the case of this computation, I'll go by the recommendation.
+ */
+
+ delta_tau = (0.5 * M_PI) / maxfreq;
+ tau_0 = tvec_ptr[0] + delta_tau;
+ tau_h = tau_0;
+ te = tau_h + delta_tau;
+
+ octave_idx_type k = 0; // Iterator for accessing xvec, tvec.
+
+ Precomputation_Record * precomp_records_head, *record_current, *record_tail, *record_ref, *record_next;
+ record_current = precomp_records_head = new Precomputation_Record;
+
+ for (te = tvec_ptr[k] + (2 * delta_tau) ; ;)
+ {
+ x = xvec_ptr[k];
+ {
+ double t = mu *(tvec_ptr[k] - tau_h), tt;
+ p = record_current->power_series;
+ // p = 0
+ *p++ = x;
+ // p = 1
+ tt = -t;
+ h = x * tt;
+ *p++ = std::complex<double> (-h.imag (), h.real ());
+ // p = 2
+ tt *= t*(1.0/2.0);
+ *p++ = x*tt;
+ // p = 3
+ tt *= t*(-1.0/3.0);
+ h = x * tt;
+ *p++ = std::complex<double> (-h.imag (), h.real ());
+ // p = 4
+ tt *= t*(1.0/4.0);
+ *p++ = x*tt;
+ // p = 5
+ tt *= t*(-1.0/5.0);
+ h = x * tt;
+ *p++ = std::complex<double>(-h.imag () ,h.real ());
+ // p = 6
+ tt *= t*(1.0/6.0);
+ *p++ = x*tt;
+ // p = 7
+ tt *= t*(-1.0/7.0);
+ h = x * tt;
+ *p++ = std::complex<double>(-h.imag(),h.real());
+ // p = 8
+ tt *= t*(1.0/8.0);
+ *p++ = x*tt;
+ // p = 9
+ tt *= t*(-1.0/9.0);
+ h = x * tt;
+ *p++ = std::complex<double>(-h.imag(),h.real());
+ // p = 10
+ tt *= t*(1.0/10.0);
+ *p++ = x*tt;
+ // p = 11
+ tt *= t*(-1.0/11.0);
+ h = x * tt;
+ *p++ = std::complex<double>(-h.imag(),h.real());
+ }
+
+ record_current->stored_data = true;
+ for(k++; k < n && tvec_ptr[k] < te; k++)
+ {
+ x = std::complex<double> (xvec_ptr[k]);
+ {
+ double t = mu * (tvec_ptr[k] - tau_h), tt;
+ p = record_current->power_series;
+ // p = 0
+ *p++ += std::complex<double>(x);
+ // p = 1
+ tt = -t;
+ h = x * tt;
+ *p++ += std::complex<double>(- h.imag(), h.real());
+ // p = 2
+ tt *= t*(1.0/2.0);
+ *p++ += x*tt;
+ // p = 3
+ tt *= t*(-1.0/3.0);
+ h = x * tt;
+ *p++ += std::complex<double>(-h.imag(),h.real());
+ // p = 4
+ tt *= t*(1.0/4.0);
+ *p++ += x*tt;
+ // p = 5
+ tt *= t*(-1.0/5.0);
+ h = x * tt;
+ *p++ += std::complex<double>(-h.imag(),h.real());
+ // p = 6
+ tt *= t*(1.0/6.0);
+ *p++ += x*tt;
+ // p = 7
+ tt *= t*(-1.0/7.0);
+ h = x * tt;
+ *p++ += std::complex<double>(-h.imag(),h.real());
+ // p = 8
+ tt *= t*(1.0/8.0);
+ *p++ += x*tt;
+ // p = 9
+ tt *= t*(-1.0/9.0);
+ h = x * tt;
+ *p++ += std::complex<double>(-h.imag(),h.real());
+ // p = 10
+ tt *= t*(1.0/10.0);
+ *p++ += x*tt;
+ // p = 11
+ tt *= t*(-1.0/11.0);
+ h = x * tt;
+ *p++ += std::complex<double>(-h.imag(),h.real());
+ }
+ record_current->stored_data = true;
+ }
+
+ if (k >= n)
+ break;
+
+ tau_h = te + delta_tau;
+ te = tau_h + delta_tau;
+
+ record_current->next = new Precomputation_Record;
+ record_current = record_current->next;
+ }
+
+ record_tail = record_current;
+ record_current = precomp_records_head;
+ record_tail->next = 0;
+
+ /* Summation of coefficients for each frequency. As we have ncoeffs * noctaves elements,
+ * it makes sense to work from the top down, as we have omega_max by default (maxfreq)
+ */
+
+ omega_oct = maxfreq / mu;
+ omega_multiplier = exp (-log(2) / coefficients);
+ octavemax = maxfreq;
+ loop_tau_0 = tau_0;
+ loop_delta_tau = delta_tau;
+
+ octave_idx_type iter = 0;
+
+ // Loops need to first travel over octaves, then coefficients;
+ for (octave_iter = octaves; ;
+ omega_oct *= 0.5, octavemax *= 0.5, loop_tau_0 += loop_delta_tau, loop_delta_tau *= 2)
+ {
+ o = omega_oct;
+ omega_working = octavemax;
+ for (coeff_iter = 0;
+ coeff_iter < coefficients;
+ coeff_iter++, o *= omega_multiplier,
+ omega_working *= omega_multiplier)
+ {
+ exp_term = std::complex<double> (cos (- omega_working * loop_tau_0),
+ sin (- omega_working * loop_tau_0));
+
+ exp_multiplier = std::complex<double> (cos (- 2 * omega_working * loop_delta_tau) ,
+ sin (- 2 * omega_working * loop_delta_tau));
+
+ for (zeta = 0, record_current = precomp_records_head;
+ record_current;
+ record_current = record_current->next, exp_term *= exp_multiplier )
+ {
+ if (record_current->stored_data)
+ {
+ int p;
+ for (zz = 0, p = 0, on_1 = n_1; p < 12; p++)
+ {
+ zz += record_current->power_series[p] * on_1;
+ on_1 *= o;
+ }
+ zeta += exp_term * zz;
+ }
+ }
+ results(iter) = std::complex<double> (zeta);
+ iter++;
+ }
+ if (! (--octave_iter))
+ break;
+
+ /* If we've already reached the lowest value, stop.
+ * Otherwise, merge with the next computation range.
+ */
+ double *exp_pse_ptr, *exp_ptr, exp_power_series_elements[12];
+ {
+ double t = mu * loop_delta_tau, tt;
+ exp_ptr = exp_power_series_elements;
+ *exp_ptr++ = 1;
+ *exp_ptr++ = t;
+ tt = t * t * ( 1.0 / 2.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 3.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 4.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 5.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 6.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 7.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 8.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 9.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 10.0 );
+ *exp_ptr++ = tt;
+ tt *= t * ( 1.0 / 11.0 );
+ *exp_ptr++ = tt;
+ }
+ exp_pse_ptr = exp_ptr = exp_power_series_elements;
+
+ try
+ {
+ for (record_current = precomp_records_head;
+ record_current;
+ record_current = record_current->next)
+ {
+ if (! (record_ref = record_current->next )
+ || ! record_ref->stored_data )
+ {
+ // In this case, there is no next record, but this record has data.
+ if (record_current->stored_data)
+ {
+ int p = 0;
+ for (exp_pse_ptr = exp_power_series_elements + 1, temp_ptr_alpha = temp_alpha;
+ p < 12;
+ p++ , exp_pse_ptr++)
+ {
+ tpra = temp_ptr_alpha;
+ *(temp_ptr_alpha++) = std::complex<double>(record_current->power_series[p]);
+ for( exp_ptr = exp_power_series_elements, record_current->power_series[p] = *temp_ptr_alpha * *exp_ptr; ; ) {
+ /* This next block is from Mathias' code, and it does a few
+ * ... unsavoury things. First off, it uses conditionals with
+ * break in order to avoid potentially accessing null regions
+ * of memory, and then it does ... painful things with a few
+ * numbers. However, remembering that most of these will not
+ * actually be accessed for the first iterations, it's easier.
+ */
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ --tpra;
+ h = *tpra * *exp_ptr;
+ record_current->power_series[p].real() -= h.imag();
+ record_current->power_series[p].imag() += h.real();
+
+ if (++exp_ptr >= exp_pse_ptr )
+ break;
+
+ --tpra;
+ record_current->power_series[p] -= *tpra * *exp_ptr;
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ --tpra;
+ h = -*tpra * *exp_ptr;
+ record_current->power_series[p].real() -= h.imag();
+ record_current->power_series[p].imag() += h.real();
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ --tpra;
+ record_current->power_series[p] += *tpra * *exp_ptr;
+ }
+ }
+
+ if ( ! record_ref )
+ break; // Last record was reached
+
+ }
+ else
+ {
+ record_next = record_ref;
+ if ( record_current->stored_data )
+ {
+ int p = 0, q = 0;
+ for (exp_pse_ptr = exp_power_series_elements + 1, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta;
+ p < 12; p++, q++, exp_pse_ptr++)
+ {
+ tpra = temp_ptr_alpha;
+ *temp_ptr_alpha++ = record_current->power_series[p] + record_next->power_series[q];
+ *temp_ptr_beta++ = record_current->power_series[p] - record_next->power_series[q];
+ tprb = temp_ptr_beta;
+
+ for (exp_ptr = exp_power_series_elements, record_current->power_series[p] = *tpra * *exp_ptr; ;)
+ {
+ if (++exp_ptr >= exp_pse_ptr )
+ break;
+
+ tprb -= 2;
+ h = *tprb * *exp_ptr;
+ record_current->power_series[p].real() -= h.imag();
+ record_current->power_series[p].imag() += h.real();
+
+ if ( ++exp_ptr >= exp_pse_ptr )
+ break;
+
+ tpra -= 2;
+ record_current->power_series[p] -= *tpra * *exp_ptr;
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ tprb -= 2;
+ h = - *tprb * *exp_ptr;
+ record_current->power_series[p].real() -= h.imag();
+ record_current->power_series[p].imag() += h.real();
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ tpra -= 2;
+ record_current->power_series[p] += *tpra * *exp_ptr;
+ }
+ }
+ }
+ else
+ {
+ int q = 0;
+ for (exp_pse_ptr = exp_power_series_elements + 1,
+ temp_ptr_alpha = temp_alpha,
+ temp_ptr_beta = temp_beta;
+ q < 12;
+ q++, exp_pse_ptr++)
+ {
+ tpra = temp_ptr_alpha;
+ *temp_ptr_alpha++ = std::complex<double>(record_next->power_series[q]);
+
+ for (exp_ptr = exp_power_series_elements,
+ record_next->power_series[q] = *tpra * *exp_ptr; ;)
+ {
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ --tpra;
+ h = *tpra * *exp_ptr;
+ record_next->power_series[q].real() -= h.imag();
+ record_next->power_series[q].imag() += h.real();
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ --tpra;
+ record_next->power_series[q] -= *tpra * *exp_ptr;
+
+ if ( ++exp_ptr >= exp_pse_ptr )
+ break;
+
+ --tpra;
+ h = -*tpra * *exp_ptr;
+ record_next->power_series[q].real() -= h.imag();
+ record_next->power_series[q].imag() += h.real();
+
+ if (++exp_ptr >= exp_pse_ptr)
+ break;
+
+ --tpra;
+ record_next->power_series[q] += *tpra * *exp_ptr;
+ }
+ }
+ }
+
+ record_current->stored_data = true;
+ record_ref = record_next;
+ record_current->next = record_ref->next;
+ delete record_ref;
+
+ }
+ }
+ }
+ }
+ catch (std::exception & e)
+ {//This section was part of my debugging, and may be removed.
+ std::cout << "Exception thrown: " << e.what() << std::endl;
+ return (false);
+ }
+ }
+
+ return true;
+}
+
+/*
+%!test
+%! maxfreq = 4 / ( 2 * pi );
+%! t = [0:0.008:8];
+%! x = ( 2 .* sin (maxfreq .* t) +
+%! 3 .* sin ( (3 / 4) * maxfreq .* t)-
+%! 0.5 .* sin ((1/4) * maxfreq .* t) -
+%! 0.2 .* cos (maxfreq .* t) +
+%! cos ((1/4) * maxfreq .* t));
+%! assert (fastlscomplex (t, x, maxfreq, 2, 2),
+%! [(-0.400924546169395 - 2.371555305867469i), ...
+%! (1.218065147708429 - 2.256125004156890i), ...
+%! (1.935428592212907 - 1.539488163739336i), ...
+%! (2.136692292751917 - 0.980532175174563i)], 5e-10);
+*/
diff --git a/src/fastlsreal.cc b/src/fastlsreal.cc
new file mode 100644
index 0000000..b7d49f0
--- /dev/null
+++ b/src/fastlsreal.cc
@@ -0,0 +1,392 @@
+/* Copyright (C) 2012 Benjamin Lewis <benjf5 at gmail.com>
+ *
+ * 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 3 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.
+ *
+ * You should have received a copy of the GNU General Public License along
+ * with this program; if not, write to the Free Software Foundation, Inc.,
+ * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+
+
+#include <octave/oct.h>
+#include <octave/unwind-prot.h>
+#include <complex>
+#include <string>
+#include <math.h>
+#include <iostream>
+#include <exception>
+
+ComplexRowVector flsreal( RowVector tvec , ComplexRowVector xvec ,
+ double maxfreq , int octaves , int coefficients);
+
+
+DEFUN_DLD(fastlsreal,args,nargout,
+ "-*- texinfo -*-\n\
+ at deftypefn {Function File} { C = } fastlsreal(@var{time}, at var{magnitude}, at var{maximum_frequency}, at var{octaves}, at var{coefficients})\n\
+\n\
+Return the real least-sqaures spectral fit to the (@var{time}, at var{magnitude})\n\
+data supplied, using the fast algorithm.\n\
+\n\
+ at seealso{lsreal, fastlscomplex}\n\
+ at end deftypefn") {
+ if ( args.length() != 5 ) {
+ print_usage();
+ return octave_value_list ();
+ }
+ RowVector tvals = args(0).row_vector_value();
+ ComplexRowVector xvals = args(1).complex_row_vector_value();
+ double omegamax = args(2).double_value();
+ int noctaves = args(3).int_value();
+ int ncoeff = args(4).int_value();
+ if ( tvals.numel() != xvals.numel() ){
+ if ( tvals.numel() > xvals.numel() ) {
+ error("More time values than magnitude values.");
+ } else {
+ error("More magnitude values than time values.");
+ }
+ }
+ if ( ncoeff == 0 ) error("No coefficients to compute.");
+ if ( noctaves == 0 ) error("No octaves to compute over.");
+ if ( omegamax == 0 ) error("No difference between minimal and maximal frequency.");
+ octave_value_list retval;
+ if ( !error_state) {
+ ComplexRowVector results = flsreal(tvals,xvals,omegamax,noctaves,ncoeff);
+ retval(0) = octave_value(results);
+ } else {
+ return octave_value_list ();
+ }
+ return retval;
+
+}
+
+ComplexRowVector flsreal( RowVector tvec , RowVector xvec ,
+ double maxfreq, int octaves, int coefficients ) {
+ struct XTElem {
+ double x, t;
+ };
+ struct Precomputation_Record {
+ Precomputation_Record *next;
+ XTElem power_series[12]; // I'm using 12 as a matter of compatibility, only.
+ bool stored_data;
+ };
+
+ ComplexRowVector results = ComplexRowVector (coefficients * octaves );
+
+ double tau, delta_tau, tau_0, tau_h, n_inv, mu,
+ omega_oct, omega_multiplier, octavemax, omega_working,
+ loop_tau_0, loop_delta_tau, x;
+ double length = ( tvec((tvec.numel()-1)) - tvec( octave_idx_type (0)));
+ int octave_iter, coeff_iter;
+ std::complex<double> zeta, z_accumulator, zeta_exp_term, zeta_exp_multiplier, alpha,
+ iota, i_accumulator, iota_exp_term, iota_exp_multiplier, exp_squared, exp_squared_multiplier;
+ octave_idx_type n = tvec.numel();
+ XTElem *tpra, *temp_ptr_alpha, temp_alpha[12], *tprb, *temp_ptr_beta, temp_beta[12], temp_array[12];
+
+
+ int factorial_array[12];
+ factorial_array[0] = 1;
+ for ( int i = 1 ; i < 12 ; i++ ) {
+ factorial_array[i] = factorial_array[i-1] * i;
+ }
+ n_inv = 1.0 / n;
+ mu = (0.5 * M_PI)/length; // Per the article; this is in place to improve numerical accuracy if desired.
+ /* Viz. the paper, in which Dtau = c / omega_max, and c is stated as pi/2 for floating point processors,
+ * In the case of this computation, I'll go by the recommendation.
+ */
+ delta_tau = M_PI / ( 2 * maxfreq );
+ tau_0 = tvec(0) + delta_tau;
+ tau_h = tau_0;
+ size_t precomp_subset_count = (size_t) ceil( ( tvec(tvec.numel()-1) - tvec(0) ) / ( 2 * delta_tau ) );
+ // I've used size_t because it will work for my purposes without threatening undefined behaviour.
+ const std::complex<double> im = std::complex<double> ( 0 , 1 ); //I seriously prefer C99's complex numbers.
+
+ octave_idx_type k ( 0 ); // Iterator for accessing xvec, tvec.
+
+ Precomputation_Record * precomp_records_head, *record_current, *record_tail, *record_ref, *record_next;
+ record_current = precomp_records_head = new Precomputation_Record;
+ for ( te = tvec(k) + (2 * delta_tau) ; ; ) {
+ x = xvec(k);
+ {
+ double t = mu*(tvec(k)-tau_h), tt;
+ p = record_current->power_series;
+ // p = 0
+ p->x = x;
+ (p++)->t = 1;
+ // p = 1
+ tt = -t;
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 2
+ tt *= t*(1.0/2.0);
+ p->x = x*tt;
+ (p++)->t = tt;
+ // p = 3
+ tt *= t*(-1.0/3.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 4
+ tt *= t*(1.0/4.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 5
+ tt *= t*(-1.0/5.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 6
+ tt *= t*(1.0/6.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 7
+ tt *= t*(-1.0/7.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 8
+ tt *= t*(1.0/8.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 9
+ tt *= t*(-1.0/9.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 10
+ tt *= t*(1.0/10.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ // p = 11
+ tt *= t*(-1.0/11.0);
+ p->x = x * tt;
+ (p++)->t = tt;
+ }
+ record_current->stored_data = true;
+ for(k++; ( k < n ) && tvec(k) < te ; k++ ) {
+ x = xvec(k);
+ {
+ double t = mu*(tvec(k)-tau_h), tt;
+ p = record_current->power_series;
+ // p = 0
+ p->x += x;
+ (p++)->t += 1;
+ // p = 1
+ tt = -t;
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 2
+ tt *= t*(1.0/2.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 3
+ tt *= t*(-1.0/3.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 4
+ tt *= t*(1.0/4.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 5
+ tt *= t*(-1.0/5.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 6
+ tt *= t*(1.0/6.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 7
+ tt *= t*(-1.0/7.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 8
+ tt *= t*(1.0/8.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 9
+ tt *= t*(-1.0/9.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 10
+ tt *= t*(1.0/10.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ // p = 11
+ tt *= t*(-1.0/11.0);
+ p->x += x * tt;
+ (p++)->t += tt;
+ }
+ record_current->stored_data = true;
+ }
+ if( k >= n ) break;
+ tau_h = te + delta_tau;
+ te = tau_h + delta_tau;
+ record_current->next = new Precomputation_Record;
+ record_current = record_current->next;
+ }
+ record_tail = record_current;
+ record_current = precomp_records_head;
+ record_tail->next = 0;
+
+ /* Summation of coefficients for each frequency. As we have ncoeffs * noctaves elements,
+ * it makes sense to work from the top down, as we have omega_max by default (maxfreq)
+ */
+
+ omega_oct = maxfreq / mu;
+ omega_multiplier = exp(-log(2)/coefficients);
+ octavemax = maxfreq;
+ loop_tau_0 = tau_0;
+ loop_delta_tau = delta_tau;
+
+ octave_idx_type iter ( 0 );
+
+ // Loops need to first travel over octaves, then coefficients;
+
+ for ( octave_iter = octaves ; ; omega_oct *= 0.5 , octavemax *= 0.5 , loop_tau_0 += loop_delta_tau , loop_delta_tau *= 2 ) {
+ o = omega_oct;
+ omega_working = octavemax;
+ for ( coeff_iter = 0 ; coeff_iter < coefficients ; coeff_iter++, o *= omega_multiplier, omega_working *= omega_multiplier){
+ exp_term = std::complex<double> ( cos( - omega_working * loop_tau_0 ) ,
+ sin ( - omega_working * loop_tau_0 ) );
+ exp_squared = exp_term * exp_term;
+ exp_multiplier = std::complex<double> ( cos ( - 2 * omega_working * loop_delta_tau ) ,
+ sin ( - 2 * omega_working * loop_delta_tau ) );
+ exp_squared_multiplier = exp_multiplier * exp_multiplier;
+ for ( zeta = iota = 0, record_current = precomp_records_head ; record_current ;
+ record_current = record_current->next, exp_term *= exp_multiplier,
+ exp_squared *= exp_squared_multiplier ) {
+ if ( record_current->stored_data ) {
+ int p;
+ for ( zz = ii = 0 , p = 0, on_1 = n_1 ; p < 12 ; ) {
+ zz.real() += record_current->power_series[p]->x * on_1;
+ ii.real() += record_current->power_series[p++]-> t * o2n_1;
+ on_1 *= o;
+ o2n_1 *= o2;
+ zz.imag() += record_current->power_series[p]->x * on_1;
+ ii.imag() += record_current->power_series[p++]-> t * o2n_1;
+ on_1 *= o;
+ o2n_1 *= o2;
+ }
+ zeta += exp_term * zz;
+ iota += exp_squared * ii;
+ }
+ }
+ results(iter) = 2 / ( 1 - ( iota.real() * iota.real() ) - (iota.imag() *
+ iota.imag() )
+ * ( conj(zeta) - conj(iota) * zeta );
+ iter++;
+ }
+ if ( !(--octave_iter) ) break;
+ /* If we've already reached the lowest value, stop.
+ * Otherwise, merge with the next computation range.
+ */
+ double *exp_pse_ptr, *exp_ptr, exp_power_series_elements[12];
+ exp_power_series_elements[0] = 1;
+ exp_pse_ptr = exp_ptr = exp_power_series_elements;
+ for ( int r_iter = 1 ; r_iter < 12 ; r_iter++ ) {
+ exp_power_series_elements[r_iter] = exp_power_series_elements[r_iter-1]
+ * ( mu * loop_delta_tau) * ( 1.0 / ( (double) r_iter ) );
+ }
+ try{
+ for ( record_current = precomp_records_head ; record_current ;
+ record_current = record_current->next ) {
+ if ( ! ( record_ref = record_current->next ) || ! record_ref->stored_data ) {
+ // In this case, there is no next record, but this record has data.
+ if ( record_current->stored_data ) {
+ int p = 0;
+ for( exp_pse_ptr = exp_power_series_elements , temp_ptr_alpha = temp_alpha ; ; ) {
+ tpra = temp_ptr_alpha;
+ temp_ptr_alpha->x = record_current->power_series[p]->x;
+ (temp_ptr_alpha++)->t = record_current->power_series[p]->t;
+ temp_ptr_beta->x = -record_current->power_series[p]->x;
+ (temp_ptr_beta++)->t = -record_current->power_series[p]->t;
+ for( exp_ptr = exp_pse_ptr++, record_current->power_series[p]->x = tpra->x * *exp_ptr, record_current->power_series[p]->t = tpra->t * *exp_ptr ; ; ) {
+ /* This next block is from Mathias' code, and it does a few
+ * ... unsavoury things. First off, it uses conditionals with
+ * break in order to avoid potentially accessing null regions
+ * of memory, and then it does ... painful things with a few
+ * numbers. However, remembering that most of these will not
+ * actually be accessed for the first iterations, it's easier.
+ */
+ if ( --exp_ptr < exp_power_series_elements ) break;
+ ++tpra;
+ record_current->power_series[p]->x -= tpra->x * *exp_ptr;
+ record_current->power_series[p]->t -= tpra->t * *exp_ptr;
+ if ( --exp_ptr < exp_power_series_elements ) break;
+ ++tpra;
+ record_current->power_series[p]->x += tpra->x * *exp_ptr;
+ record_current->power_series[p]->t += tpra->x * *exp_ptr;
+ }
+ if ( ++p >= 12 ) break;
+ temp_ptr_alpha->x = -record_current->power_series[p]->x;
+ (temp_ptr_alpha++)->t = -record_current->power_series[p]->t;
+ temp_ptr_beta->x = record_current->power_series[p]->x;
+ (temp_ptr_beta++)->t = record_current->power_series[p]->t;
+ for( tprb = temp_beta, exp_ptr = exp_pse_ptr++, record_current->power_series[p]->t = tprb->t * *exp_ptr; exp_ptr > exp_power_series_elements ; ) {
+ ++tprb;
+ --exp_ptr;
+ record_current->power_series[p]->t += tprb->t * *exp_ptr;
+ }
+ if ( ++p >= 12 ) break;
+ }
+ }
+ if ( ! record_ref ) break; // Last record was reached
+ }
+ else {
+ record_next = record_ref;
+ if ( record_current->stored_data ) {
+ int p = 0;
+ for( exp_pse_ptr = exp_power_series_elements, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta; ; ) {
+ temp_ptr_alpha->x = record_current->power_series[p]->x + record_next->power_series[p]->x;
+ (temp_ptr_alpha++)->t = record_current->power_series[p]->t + record_next->power_series[p]->t;
+ temp_ptr_beta->x = record_ref->power_series[p]->x - record_current->power_series[p]->x;
+ (temp_ptr_beta++)->t = record_ref->power_series[p]->t - record_current->power_series[p]->t;
+ for( tpra = temp_alpha, exp_ptr = exp_pse_ptr++, record_current->power_series[p]->x = tpra->x * *exp_ptr, record_current->power_series[p]->t = tpra->x * *exp_ptr; ; ) {
+ if ( --exp_ptr < exp_pse_ptr ) break;
+ ++tpra;
+ record_current->power_series[p]->x -= tpra->x * *exp_ptr;
+ record_current->power_series[p]->t -= tpra->t * *exp_ptr;
+ if ( --exp_ptr < exp_pse_ptr ) break;
+ ++tpra;
+ record_current->power_series[p]->x += tpra->x * *exp_ptr;
+ record_current->power_series[p]->t += tpra->t * *exp_ptr;
+ }
+ if ( ++p >= 12 ) break;
+ temp_ptr_alpha->x = record_next->power_series[p]->x - record_current->power_series[p]->x;
+ (temp_ptr_alpha++)->t = record_next->power_series[p]->t - record_current->power_series[p]->t;
+ temp_ptr_beta->x = record_current->power_series[p]->x + record_next->power_series[p]->x;
+ (temp_ptr_beta++)->t = record_current->power_series[p]->t + record_next->power_series[p]->t;
+ for(tprb = temp_beta, exp_ptr = exp_pse_ptr++, record_current->power_series[p]->x = tprb->x * *exp_ptr, record_current->power_series[p]->t = tprb->x * *exp_ptr; exp_ptr > exp_power_series_elements; ) {
+ ++tprb;
+ --exp_ptr;
+ record_current->power_series[p]->x += tprb->x * *exp_ptr;
+ record_current->power_series[p]->t += tprb->t * *exp_ptr;
+ }
+ if ( ++p >= 12 ) break;
+ }
+ } else {
+ int q = 0;
+ for( exp_pse_ptr = exp_power_series_elements, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta; ; ) {
+ temp_ptr_alpha->x = record_next->power_series[q]->x;
+ temp_ptr_alpha->t = record_next->power_series[q]->t;
+ for(tpra = temp_alpha, exp_ptr = exp_pse_ptr++, record_next->power_series[q]->x = tpra->x * *exp_ptr, record_next->power_series[q]->t = tpra->t * *exp_ptr; exp_ptr > exp_power_series_elements; ) {
+ ++tpra;
+ --exp_ptr;
+ record_next->power_series[q]->x += tpra->x * *exp_ptr;
+ record_next->power_series[q]->t += tpra->t * *exp_ptr;
+ }
+ if ( ++q >= 12 ) break;
+ }
+ record_current->stored_data = true;
+ record_ref = record_next;
+ record_current->next = record_ref->next;
+ record_next = 0;
+ delete record_ref;
+ }
+ }
+ }
+ return results;
+}
--
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