octave-nkf: scripts/sparse/svds.m annotate

annotate scripts/sparse/svds.m @ 17281:bc924baa2c4e

doc: Add new @qcode macro for code samples which are quoted. Macro handles options ("on") or properties ("position") more elegantly than @code{"text"}. * doc/interpreter/macros.texi: Add new @qcode macro. * doc/interpreter/tips.txi: Add documentation about @qcode macro. * doc/interpreter/basics.txi, doc/interpreter/container.txi, doc/interpreter/emacs.txi, doc/interpreter/errors.txi, doc/interpreter/eval.txi, doc/interpreter/expr.txi, doc/interpreter/external.txi, doc/interpreter/func.txi, doc/interpreter/grammar.txi, doc/interpreter/image.txi, doc/interpreter/install.txi, doc/interpreter/interp.txi, doc/interpreter/io.txi, doc/interpreter/matrix.txi, doc/interpreter/numbers.txi, doc/interpreter/oop.txi, doc/interpreter/package.txi, doc/interpreter/plot.txi, doc/interpreter/quad.txi, doc/interpreter/sparse.txi, doc/interpreter/strings.txi, doc/interpreter/system.txi, doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc, libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc, libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc, libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc, libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc, libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc, libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc, libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc, libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc, libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc, libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc, libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc, libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc, libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc, libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc, libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc, libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc, libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc, libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc, libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc, libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc, libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc, libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc, libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc, libinterp/octave-value/ov-fcn-handle.cc, libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc, libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc, libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy, libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc, libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m, scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m, scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m, scripts/general/dblquad.m, scripts/general/display.m, scripts/general/genvarname.m, scripts/general/idivide.m, scripts/general/interp1.m, scripts/general/interp2.m, scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m, scripts/general/profexplore.m, scripts/general/profile.m, scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m, scripts/general/subsindex.m, scripts/general/triplequad.m, scripts/geometry/griddata.m, scripts/geometry/griddata3.m, scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m, scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m, scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m, scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m, scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m, scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m, scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m, scripts/java/javaclasspath.m, scripts/java/usejava.m, scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m, scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m, scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m, scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m, scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m, scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m, scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m, scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m, scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m, scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m, scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m, scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m, scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m, scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m, scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m, scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m, scripts/plot/plot.m, scripts/plot/print.m, scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m, scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m, scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m, scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m, scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m, scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m, scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m, scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m, scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m, scripts/polynomial/conv.m, scripts/polynomial/polyout.m, scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m, scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m, scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/periodogram.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m, scripts/specfun/legendre.m, scripts/special-matrix/gallery.m, scripts/statistics/base/mean.m, scripts/statistics/base/moment.m, scripts/statistics/tests/cor_test.m, scripts/statistics/tests/kolmogorov_smirnov_test.m, scripts/statistics/tests/kolmogorov_smirnov_test_2.m, scripts/statistics/tests/kruskal_wallis_test.m, scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m, scripts/statistics/tests/t_test_regression.m, scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m, scripts/statistics/tests/welch_test.m, scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m, scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m, scripts/strings/index.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/validatestring.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m, scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m, scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m, scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m, scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.

author	Rik <rik@octave.org>
date	Mon, 19 Aug 2013 20:46:38 -0700
parents	9deb214ae9d5
children	b81b9d079515

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 14041 diff changeset	1 ## Copyright (C) 2006-2012 David Bateman
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	2 ##
11104 2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	3 ## This file is part of Octave.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	4 ##
11104 2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	6 ## under the terms of the GNU General Public License as published by
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	8 ## your option) any later version.
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	9 ##
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	13 ## General Public License for more details.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	14 ##
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
11104 2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
2c356a35d7f5 fix copyright notices John W. Eaton <jwe@octave.org> parents: 10846 diff changeset	17 ## <http://www.gnu.org/licenses/>.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	18
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	19 ## -- texinfo --
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	20 ## @deftypefn {Function File} {@var{s} =} svds (@var{A})
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	21 ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k})
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	22 ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}, @var{sigma})
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	23 ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}, @var{sigma}, @var{opts})
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	24 ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}] =} svds (@dots{})
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	25 ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}, @var{flag}] =} svds (@dots{})
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	26 ##
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	27 ## Find a few singular values of the matrix @var{A}. The singular values
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	28 ## are calculated using
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	29 ##
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	30 ## @example
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	31 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14182 diff changeset	32 ## [@var{m}, @var{n}] = size (@var{A});
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14182 diff changeset	33 ## @var{s} = eigs ([sparse(@var{m}, @var{m}), @var{A};
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14182 diff changeset	34 ## @var{A}', sparse(@var{n}, @var{n})])
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	35 ## @end group
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	36 ## @end example
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	37 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	38 ## The eigenvalues returned by @code{eigs} correspond to the singular values
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	39 ## of @var{A}. The number of singular values to calculate is given by @var{k}
10663 b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	40 ## and defaults to 6.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	41 ##
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	42 ## The argument @var{sigma} specifies which singular values to find. When
17281 bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17199 diff changeset	43 ## @var{sigma} is the string @qcode{'L'}, the default, the largest singular
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17199 diff changeset	44 ## values of @var{A} are found. Otherwise, @var{sigma} must be a real scalar
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17199 diff changeset	45 ## and the singular values closest to @var{sigma} are found. As a corollary,
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	46 ## @code{@var{sigma} = 0} finds the smallest singular values. Note that for
17281 bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17199 diff changeset	47 ## relatively small values of @var{sigma}, there is a chance that the
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17199 diff changeset	48 ## requested number of singular values will not be found. In that case
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17199 diff changeset	49 ## @var{sigma} should be increased.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	50 ##
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	51 ## @var{opts} is a structure defining options that @code{svds} will pass
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	52 ## to @code{eigs}. The possible fields of this structure are documented in
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	53 ## @code{eigs}. By default, @code{svds} sets the following three fields:
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	54 ##
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	55 ## @table @code
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	56 ## @item tol
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	57 ## The required convergence tolerance for the singular values. The default
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	58 ## value is 1e-10. @code{eigs} is passed @code{@var{tol} / sqrt(2)}.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	59 ##
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	60 ## @item maxit
9066 be150a172010 Cleanup documentation for diagperm.texi, sparse.texi Rik <rdrider0-list@yahoo.com> parents: 9051 diff changeset	61 ## The maximum number of iterations. The default is 300.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	62 ##
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	63 ## @item disp
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	64 ## The level of diagnostic printout (0\|1\|2). If @code{disp} is 0 then
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	65 ## diagnostics are disabled. The default value is 0.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	66 ## @end table
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	67 ##
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	68 ## If more than one output is requested then @code{svds} will return an
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	69 ## approximation of the singular value decomposition of @var{A}
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	70 ##
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	71 ## @example
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	72 ## @var{A}_approx = @var{u}@var{s}@var{v}'
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	73 ## @end example
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	74 ##
10846 a4f482e66b65 Grammarcheck more of the documentation. Rik <octave@nomad.inbox5.com> parents: 10671 diff changeset	75 ## @noindent
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	76 ## where @var{A}_approx is a matrix of size @var{A} but only rank @var{k}.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	77 ##
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	78 ## @var{flag} returns 0 if the algorithm has succesfully converged, and 1
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	79 ## otherwise. The test for convergence is
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	80 ##
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	81 ## @example
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	82 ## @group
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	83 ## norm (@var{A}@var{v} - @var{u}@var{s}, 1) <= @var{tol} * norm (@var{A}, 1)
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	84 ## @end group
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	85 ## @end example
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	86 ##
10846 a4f482e66b65 Grammarcheck more of the documentation. Rik <octave@nomad.inbox5.com> parents: 10671 diff changeset	87 ## @code{svds} is best for finding only a few singular values from a large
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	88 ## sparse matrix. Otherwise, @code{svd (full (@var{A}))} will likely be more
10846 a4f482e66b65 Grammarcheck more of the documentation. Rik <octave@nomad.inbox5.com> parents: 10671 diff changeset	89 ## efficient.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	90 ## @end deftypefn
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	91 ## @seealso{svd, eigs}
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	92
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	93 function [u, s, v, flag] = svds (A, k, sigma, opts)
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	94
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	95 persistent root2 = sqrt (2);
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	96
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	97 if (nargin < 1 \|\| nargin > 4)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	98 print_usage ();
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	99 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	100
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	101 if (ndims (A) > 2)
17199 9deb214ae9d5 Use 2-D, not 2D, in error messages. Rik <rik@octave.org> parents: 17185 diff changeset	102 error ("svds: A must be a 2-D matrix");
10663 b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	103 endif
b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	104
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	105 if (nargin < 4)
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	106 opts.tol = 0; ## use ARPACK default
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	107 opts.disp = 0;
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	108 opts.maxit = 300;
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	109 else
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	110 if (!isstruct (opts))
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	111 error ("svds: OPTS must be a structure");
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	112 endif
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	113 if (!isfield (opts, "tol"))
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	114 opts.tol = 0; ## use ARPACK default
10663 b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	115 else
b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	116 opts.tol = opts.tol / root2;
b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	117 endif
b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	118 if (isfield (opts, "v0"))
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	119 if (!isvector (opts.v0) \|\| (length (opts.v0) != sum (size (A))))
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	120 error ("svds: OPTS.v0 must be a vector with rows(A)+columns(A) entries");
10663 b90328525985 svds.m: Validate struct input argument. Rik <octave@nomad.inbox5.com> parents: 10660 diff changeset	121 endif
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	122 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	123 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	124
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	125 if (nargin < 3 \|\| strcmp (sigma, "L"))
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	126 if (isreal (A))
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	127 sigma = "LA";
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	128 else
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	129 sigma = "LR";
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	130 endif
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	131 elseif (isscalar (sigma) && isnumeric (sigma) && isreal (sigma))
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	132 if (sigma < 0)
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	133 error ("svds: SIGMA must be a positive real value");
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	134 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	135 else
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	136 error ("svds: SIGMA must be a positive real value or the string 'L'");
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	137 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	138
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	139 [m, n] = size (A);
16722 c8bbab6b9e7a Avoid converting sparse matrix to full format in svds. Carlo de Falco <cdf@users.sourceforge.net> parents: 16414 diff changeset	140 max_a = max (abs (nonzeros (A)));
c8bbab6b9e7a Avoid converting sparse matrix to full format in svds. Carlo de Falco <cdf@users.sourceforge.net> parents: 16414 diff changeset	141 if (isempty (max_a))
c8bbab6b9e7a Avoid converting sparse matrix to full format in svds. Carlo de Falco <cdf@users.sourceforge.net> parents: 16414 diff changeset	142 max_a = 0;
c8bbab6b9e7a Avoid converting sparse matrix to full format in svds. Carlo de Falco <cdf@users.sourceforge.net> parents: 16414 diff changeset	143 endif
17185 6992c1bb4773 svds.m: Initialize flag variable so interpreter doesn't use flag() colormap instead. Rik <rik@octave.org> parents: 16722 diff changeset	144 ## Must initialize variable value, otherwise it may appear to interpreter
6992c1bb4773 svds.m: Initialize flag variable so interpreter doesn't use flag() colormap instead. Rik <rik@octave.org> parents: 16722 diff changeset	145 ## that code is trying to call flag() colormap function.
6992c1bb4773 svds.m: Initialize flag variable so interpreter doesn't use flag() colormap instead. Rik <rik@octave.org> parents: 16722 diff changeset	146 flag = 0;
16722 c8bbab6b9e7a Avoid converting sparse matrix to full format in svds. Carlo de Falco <cdf@users.sourceforge.net> parents: 16414 diff changeset	147
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	148 if (max_a == 0)
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	149 s = zeros (k, 1); # special case of zero matrix
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	150 else
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	151 if (nargin < 2)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	152 k = min ([6, m, n]);
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	153 else
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	154 k = min ([k, m, n]);
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	155 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	156
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	157 ## Scale everything by the 1-norm to make things more stable.
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	158 b = A / max_a;
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	159 b_opts = opts;
12649 8579e7a6e6e0 Improve performance (2X) of svds by avoiding issymmetric calculation (bug #33073) Rik <octave@nomad.inbox5.com> parents: 12517 diff changeset	160 ## Call to eigs is always a symmetric matrix by construction
8579e7a6e6e0 Improve performance (2X) of svds by avoiding issymmetric calculation (bug #33073) Rik <octave@nomad.inbox5.com> parents: 12517 diff changeset	161 b_opts.issym = true;
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	162 b_sigma = sigma;
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	163 if (!ischar (b_sigma))
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	164 b_sigma = b_sigma / max_a;
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	165 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	166
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	167 if (b_sigma == 0)
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	168 ## Find the smallest eigenvalues
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	169 ## The eigenvalues returns by eigs for sigma=0 are symmetric about 0.
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	170 ## As we are only interested in the positive eigenvalues, we have to
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	171 ## double k and then throw out the k negative eigenvalues.
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	172 ## Separately, if sigma is non-zero, but smaller than the smallest
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	173 ## singular value, ARPACK may not return k eigenvalues. However, as
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	174 ## computation scales with k we'd like to avoid doubling k for all
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	175 ## scalar values of sigma.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	176 b_k = 2 * k;
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	177 else
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	178 b_k = k; # Normal case, find just the k largest eigenvalues
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	179 endif
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	180
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	181 if (nargout > 1)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	182 [V, s, flag] = eigs ([sparse(m,m), b; b', sparse(n,n)],
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	183 b_k, b_sigma, b_opts);
12517 c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds. Rik <octave@nomad.inbox5.com> parents: 12329 diff changeset	184 s = diag (s);
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	185 else
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	186 s = eigs ([sparse(m,m), b; b', sparse(n,n)], b_k, b_sigma, b_opts);
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	187 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	188
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	189 if (ischar (sigma))
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	190 norma = max (s);
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	191 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 11104 diff changeset	192 norma = normest (A);
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	193 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	194 ## We wish to exclude all eigenvalues that are less than zero as these
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	195 ## are artifacts of the way the matrix passed to eigs is formed. There
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	196 ## is also the possibility that the value of sigma chosen is exactly
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	197 ## a singular value, and in that case we're dead!! So have to rely on
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	198 ## the warning from eigs. We exclude the singular values which are
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	199 ## less than or equal to zero to within some tolerance scaled by the
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	200 ## norm since if we don't we might end up with too many singular
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	201 ## values.
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	202 tol = norma * opts.tol;
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	203 ind = find (s > tol);
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	204 if (length (ind) < k)
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	205 ## Too few eigenvalues returned. Add in any zero eigenvalues of B,
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	206 ## including the nominally negative ones.
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	207 zind = find (abs (s) <= tol);
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	208 p = min (length (zind), k - length (ind));
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	209 ind = [ind; zind(1:p)];
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	210 elseif (length (ind) > k)
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	211 ## Too many eigenvalues returned. Select according to criterium.
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	212 if (b_sigma == 0)
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	213 ind = ind(end+1-k:end); # smallest eigenvalues
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	214 else
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	215 ind = ind(1:k); # largest eigenvalues
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	216 endif
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	217 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	218 s = s(ind);
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	219
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	220 if (length (s) < k)
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	221 warning ("returning fewer singular values than requested");
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	222 if (!ischar (sigma))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9209 diff changeset	223 warning ("try increasing the value of sigma");
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	224 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	225 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	226
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8417 diff changeset	227 s = s * max_a;
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	228 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	229
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	230 if (nargout < 2)
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	231 u = s;
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	232 else
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	233 if (max_a == 0)
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	234 u = eye (m, k);
12517 c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds. Rik <octave@nomad.inbox5.com> parents: 12329 diff changeset	235 s = diag (s);
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	236 v = eye (n, k);
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	237 else
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	238 u = root2 * V(1:m,ind);
12517 c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds. Rik <octave@nomad.inbox5.com> parents: 12329 diff changeset	239 s = diag (s);
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	240 v = root2 * V(m+1:end,ind);
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	241 endif
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	242
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	243 if (nargout > 3)
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	244 flag = (flag != 0);
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	245 endif
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	246 endif
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	247
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	248 endfunction
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	249
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	250
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	251 %!shared n, k, A, u, s, v, opts, rand_state, randn_state, tol
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	252 %! n = 100;
654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	253 %! k = 7;
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	254 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),0.4nones(1,n),ones(1,n-2)]);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	255 %! [u,s,v] = svd (full (A));
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	256 %! s = diag (s);
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	257 %! [~, idx] = sort (abs (s));
8417 654bcfb937bf Add the eigs and svds functions David Bateman <dbateman@free.fr> parents: diff changeset	258 %! s = s(idx);
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	259 %! u = u(:, idx);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	260 %! v = v(:, idx);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	261 %! randn_state = randn ("state");
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	262 %! rand_state = rand ("state");
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	263 %! randn ("state", 42); % Initialize to make normest function reproducible
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	264 %! rand ("state", 42);
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	265 %! opts.v0 = rand (2*n,1); % Initialize eigs ARPACK starting vector
10671 f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721. Rik <octave@nomad.inbox5.com> parents: 10663 diff changeset	266 %! % to guarantee reproducible results
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	267 %!
14144 834df9f10963 remove ARPACK files from sources and restore configure checks for external ARPACK library John W. Eaton <jwe@octave.org> parents: 14138 diff changeset	268 %!testif HAVE_ARPACK
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	269 %! [u2,s2,v2,flag] = svds (A,k);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	270 %! s2 = diag (s2);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	271 %! assert (flag, !1);
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	272 %! tol = 10 * eps() * norm(s2, 1);
610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	273 %! assert (s2, s(end:-1:end-k+1), tol);
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	274 %!
14182 f8d99761244c test: Expand %!testif functionality to multiple conditions Rik <octave@nomad.inbox5.com> parents: 14144 diff changeset	275 %!testif HAVE_ARPACK, HAVE_UMFPACK
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	276 %! [u2,s2,v2,flag] = svds (A,k,0,opts);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	277 %! s2 = diag (s2);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	278 %! assert (flag, !1);
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	279 %! tol = 10 * eps() * norm(s2, 1);
610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	280 %! assert (s2, s(k:-1:1), tol);
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	281 %!
14182 f8d99761244c test: Expand %!testif functionality to multiple conditions Rik <octave@nomad.inbox5.com> parents: 14144 diff changeset	282 %!testif HAVE_ARPACK, HAVE_UMFPACK
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	283 %! idx = floor (n/2);
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	284 %! % Don't put sigma right on a singular value or there are convergence issues
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	285 %! sigma = 0.99s(idx) + 0.01s(idx+1);
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	286 %! [u2,s2,v2,flag] = svds (A,k,sigma,opts);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	287 %! s2 = diag (s2);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	288 %! assert (flag, !1);
16414 610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	289 %! tol = 10 * eps() * norm(s2, 1);
610e02bf9579 use the default ARPACK convergence tolerance (bug #34461) Ed Meyer <eem2314@gmail.com> parents: 15538 diff changeset	290 %! assert (s2, s((idx+floor(k/2)):-1:(idx-floor(k/2))), tol);
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	291 %!
14144 834df9f10963 remove ARPACK files from sources and restore configure checks for external ARPACK library John W. Eaton <jwe@octave.org> parents: 14138 diff changeset	292 %!testif HAVE_ARPACK
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	293 %! [u2,s2,v2,flag] = svds (zeros (10), k);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	294 %! assert (u2, eye (10, k));
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	295 %! assert (s2, zeros (k));
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	296 %! assert (v2, eye (10, 7));
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	297 %!
14144 834df9f10963 remove ARPACK files from sources and restore configure checks for external ARPACK library John W. Eaton <jwe@octave.org> parents: 14138 diff changeset	298 %!testif HAVE_ARPACK
12517 c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds. Rik <octave@nomad.inbox5.com> parents: 12329 diff changeset	299 %! s = svds (speye (10));
15535 fe159d11b864 increase tolerance for svds test John W. Eaton <jwe@octave.org> parents: 14327 diff changeset	300 %! assert (s, ones (6, 1), 4*eps);
13747 e8564e8b0043 Restore random number state after %!demos or %!tests Rik <octave@nomad.inbox5.com> parents: 12939 diff changeset	301
14041 6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	302 %!test
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	303 %! ## Restore random number generator seeds at end of tests
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	304 %! rand ("state", rand_state);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	305 %! randn ("state", randn_state);
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests Rik <octave@nomad.inbox5.com> parents: 13747 diff changeset	306

Mercurial > octave-nkf

annotate scripts/sparse/svds.m @ 17281:bc924baa2c4e