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annotate scripts/sparse/svds.m @ 20164:df437a52bcaf stable

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doc: Update more docstrings to have one sentence summary as first line. Reviewed miscellaneous, sparse, strings in scripts directory. * scripts/miscellaneous/bzip2.m, scripts/miscellaneous/citation.m, scripts/miscellaneous/compare_versions.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dir.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/error_ids.m, scripts/miscellaneous/fileattrib.m, scripts/miscellaneous/fullfile.m, scripts/miscellaneous/genvarname.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/news.m, scripts/miscellaneous/open.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/recycle.m, scripts/miscellaneous/run.m, scripts/miscellaneous/swapbytes.m, scripts/miscellaneous/tar.m, scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m, scripts/miscellaneous/what.m, scripts/sparse/bicg.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/gplot.m, scripts/sparse/ichol.m, scripts/sparse/ilu.m, scripts/sparse/pcg.m, scripts/sparse/pcr.m, scripts/sparse/qmr.m, scripts/sparse/spaugment.m, scripts/sparse/spconvert.m, scripts/sparse/spdiags.m, scripts/sparse/spfun.m, scripts/sparse/spones.m, scripts/sparse/sprandsym.m, scripts/sparse/spstats.m, scripts/sparse/spy.m, scripts/sparse/svds.m, scripts/sparse/treelayout.m, scripts/sparse/treeplot.m, scripts/strings/base2dec.m, scripts/strings/bin2dec.m, scripts/strings/blanks.m, scripts/strings/cstrcat.m, scripts/strings/deblank.m, scripts/strings/dec2base.m, scripts/strings/dec2bin.m, scripts/strings/dec2hex.m, scripts/strings/findstr.m, scripts/strings/hex2dec.m, scripts/strings/index.m, scripts/strings/isletter.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strchr.m, scripts/strings/strjoin.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/strsplit.m, scripts/strings/strtok.m, scripts/strings/strtrim.m, scripts/strings/strtrunc.m, scripts/strings/substr.m, scripts/strings/untabify.m, scripts/time/datenum.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Mon, 04 May 2015 14:22:02 -0700
parents 9fc020886ae9
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ## Copyright (C) 2006-2015 David Bateman
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{s} =} svds (@var{A})
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21 ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k})
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22 ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}, @var{sigma})
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23 ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}, @var{sigma}, @var{opts})
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24 ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}] =} svds (@dots{})
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25 ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}, @var{flag}] =} svds (@dots{})
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26 ##
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27 ## Find a few singular values of the matrix @var{A}.
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28 ##
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29 ## The singular values are calculated using
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30 ##
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31 ## @example
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32 ## @group
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33 ## [@var{m}, @var{n}] = size (@var{A});
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34 ## @var{s} = eigs ([sparse(@var{m}, @var{m}), @var{A};
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35 ## @var{A}', sparse(@var{n}, @var{n})])
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36 ## @end group
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37 ## @end example
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38 ##
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39 ## The eigenvalues returned by @code{eigs} correspond to the singular values
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40 ## of @var{A}. The number of singular values to calculate is given by @var{k}
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41 ## and defaults to 6.
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42 ##
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43 ## The argument @var{sigma} specifies which singular values to find. When
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44 ## @var{sigma} is the string @qcode{'L'}, the default, the largest singular
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45 ## values of @var{A} are found. Otherwise, @var{sigma} must be a real scalar
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46 ## and the singular values closest to @var{sigma} are found. As a corollary,
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47 ## @code{@var{sigma} = 0} finds the smallest singular values. Note that for
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48 ## relatively small values of @var{sigma}, there is a chance that the
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49 ## requested number of singular values will not be found. In that case
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50 ## @var{sigma} should be increased.
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51 ##
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52 ## @var{opts} is a structure defining options that @code{svds} will pass
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53 ## to @code{eigs}. The possible fields of this structure are documented in
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54 ## @code{eigs}. By default, @code{svds} sets the following three fields:
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55 ##
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56 ## @table @code
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57 ## @item tol
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58 ## The required convergence tolerance for the singular values. The default
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59 ## value is 1e-10. @code{eigs} is passed @code{@var{tol} / sqrt(2)}.
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60 ##
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61 ## @item maxit
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62 ## The maximum number of iterations. The default is 300.
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63 ##
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64 ## @item disp
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65 ## The level of diagnostic printout (0|1|2). If @code{disp} is 0 then
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66 ## diagnostics are disabled. The default value is 0.
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67 ## @end table
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68 ##
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69 ## If more than one output is requested then @code{svds} will return an
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70 ## approximation of the singular value decomposition of @var{A}
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71 ##
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72 ## @example
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73 ## @var{A}_approx = @var{u}*@var{s}*@var{v}'
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74 ## @end example
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75 ##
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76 ## @noindent
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77 ## where @var{A}_approx is a matrix of size @var{A} but only rank @var{k}.
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78 ##
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79 ## @var{flag} returns 0 if the algorithm has succesfully converged, and 1
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80 ## otherwise. The test for convergence is
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81 ##
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82 ## @example
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83 ## @group
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84 ## norm (@var{A}*@var{v} - @var{u}*@var{s}, 1) <= @var{tol} * norm (@var{A}, 1)
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85 ## @end group
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86 ## @end example
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87 ##
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88 ## @code{svds} is best for finding only a few singular values from a large
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89 ## sparse matrix. Otherwise, @code{svd (full (@var{A}))} will likely be more
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90 ## efficient.
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91 ## @end deftypefn
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92 ## @seealso{svd, eigs}
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93
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94 function [u, s, v, flag] = svds (A, k, sigma, opts)
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95
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96 persistent root2 = sqrt (2);
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97
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98 if (nargin < 1 || nargin > 4)
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99 print_usage ();
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100 endif
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101
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102 if (ndims (A) > 2)
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103 error ("svds: A must be a 2-D matrix");
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104 endif
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105
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106 if (nargin < 4)
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107 opts.tol = 0; # use ARPACK default
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108 opts.disp = 0;
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109 opts.maxit = 300;
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110 else
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111 if (! isstruct (opts))
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112 error ("svds: OPTS must be a structure");
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113 endif
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114 if (! isfield (opts, "tol"))
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115 opts.tol = 0; # use ARPACK default
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116 else
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117 opts.tol = opts.tol / root2;
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118 endif
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119 if (isfield (opts, "v0"))
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9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
120 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
121 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
122 endif
8417
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 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
125
8507
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John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
126 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
127 if (isreal (A))
8417
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David Bateman <dbateman@free.fr>
parents:
diff changeset
128 sigma = "LA";
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
129 else
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
130 sigma = "LR";
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
131 endif
10671
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Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
132 elseif (isscalar (sigma) && isnumeric (sigma) && isreal (sigma))
8507
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John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
133 if (sigma < 0)
10671
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Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
134 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
135 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
136 else
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
137 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
138 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
139
11471
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Rik <octave@nomad.inbox5.com>
parents: 11104
diff changeset
140 [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
141 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
142 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
143 max_a = 0;
c8bbab6b9e7a Avoid converting sparse matrix to full format in svds.
Carlo de Falco <cdf@users.sourceforge.net>
parents: 16414
diff changeset
144 endif
17185
6992c1bb4773 svds.m: Initialize flag variable so interpreter doesn't use flag() colormap instead.
Rik <rik@octave.org>
parents: 16722
diff changeset
145 ## 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
146 ## that code is trying to call flag() colormap function.
19593
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 17744
diff changeset
147 flag = 0;
16722
c8bbab6b9e7a Avoid converting sparse matrix to full format in svds.
Carlo de Falco <cdf@users.sourceforge.net>
parents: 16414
diff changeset
148
8507
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John W. Eaton <jwe@octave.org>
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diff changeset
149 if (max_a == 0)
10671
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Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
150 s = zeros (k, 1); # special case of zero matrix
8417
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David Bateman <dbateman@free.fr>
parents:
diff changeset
151 else
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
152 if (nargin < 2)
8507
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John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
153 k = min ([6, m, n]);
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
154 else
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
155 k = min ([k, m, n]);
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
156 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
157
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
158 ## 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
159 b = A / max_a;
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
160 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
161 ## 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
162 b_opts.issym = true;
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
163 b_sigma = sigma;
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
164 if (! ischar (b_sigma))
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
165 b_sigma = b_sigma / max_a;
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
166 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
167
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
168 if (b_sigma == 0)
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
169 ## Find the smallest eigenvalues
11587
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John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
170 ## 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
171 ## As we are only interested in the positive eigenvalues, we have to
11587
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John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
172 ## double k and then throw out the k negative eigenvalues.
18812
9ac2357f19bc doc: Replace "non-zero" with "nonzero" to match existing usage.
Rik <rik@octave.org>
parents: 17744
diff changeset
173 ## Separately, if sigma is nonzero, but smaller than the smallest
11587
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John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
174 ## 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
175 ## 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
176 ## scalar values of sigma.
11587
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John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
177 b_k = 2 * k;
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
178 else
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
179 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
180 endif
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
181
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
182 if (nargout > 1)
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
183 [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
184 b_k, b_sigma, b_opts);
12517
c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds.
Rik <octave@nomad.inbox5.com>
parents: 12329
diff changeset
185 s = diag (s);
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
186 else
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
187 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
188 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
189
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
190 if (ischar (sigma))
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
191 norma = max (s);
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
192 else
11471
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents: 11104
diff changeset
193 norma = normest (A);
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
194 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
195 ## We wish to exclude all eigenvalues that are less than zero as these
11587
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John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
196 ## 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
197 ## 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
198 ## 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
199 ## 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
200 ## 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
201 ## 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
202 ## values.
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
203 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
204 ind = find (s > tol);
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
205 if (length (ind) < k)
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
206 ## 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
207 ## including the nominally negative ones.
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
208 zind = find (abs (s) <= tol);
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
209 p = min (length (zind), k - length (ind));
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
210 ind = [ind; zind(1:p)];
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
211 elseif (length (ind) > k)
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
212 ## 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
213 if (b_sigma == 0)
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
214 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
215 else
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
216 ind = ind(1:k); # largest eigenvalues
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
217 endif
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
218 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
219 s = s(ind);
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
220
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
221 if (length (s) < k)
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
222 warning ("returning fewer singular values than requested");
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
223 if (! ischar (sigma))
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9209
diff changeset
224 warning ("try increasing the value of sigma");
8417
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 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
227
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8417
diff changeset
228 s = s * max_a;
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
229 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
230
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
231 if (nargout < 2)
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
232 u = s;
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
233 else
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
234 if (max_a == 0)
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
235 u = eye (m, k);
12517
c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds.
Rik <octave@nomad.inbox5.com>
parents: 12329
diff changeset
236 s = diag (s);
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
237 v = eye (n, k);
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
238 else
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
239 u = root2 * V(1:m,ind);
12517
c2e8c9d9e284 Fix bug #32818, nonconformant arguments in svds.
Rik <octave@nomad.inbox5.com>
parents: 12329
diff changeset
240 s = diag (s);
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
241 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
242 endif
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
243
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
244 if (nargout > 3)
16414
610e02bf9579 use the default ARPACK convergence tolerance (bug #34461)
Ed Meyer <eem2314@gmail.com>
parents: 15538
diff changeset
245 flag = (flag != 0);
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
246 endif
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
247 endif
10671
f5f9bc8e83fc svds.m: Overhaul code while fixing bug #29721.
Rik <octave@nomad.inbox5.com>
parents: 10663
diff changeset
248
8417
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
249 endfunction
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
250
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
251
16414
610e02bf9579 use the default ARPACK convergence tolerance (bug #34461)
Ed Meyer <eem2314@gmail.com>
parents: 15538
diff changeset
252 %!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
253 %! n = 100;
654bcfb937bf Add the eigs and svds functions
David Bateman <dbateman@free.fr>
parents:
diff changeset
254 %! k = 7;
14041
6cb6e390e58c svds.m: Correctly restore random seed state after %!tests
Rik <octave@nomad.inbox5.com>
parents: 13747
diff changeset
255 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),0.4*n*ones(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
256 %! [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
257 %! s = diag (s);
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258 %! [~, idx] = sort (abs (s));
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259 %! s = s(idx);
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260 %! u = u(:, idx);
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261 %! v = v(:, idx);
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262 %! randn_state = randn ("state");
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263 %! rand_state = rand ("state");
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264 %! randn ("state", 42); % Initialize to make normest function reproducible
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265 %! rand ("state", 42);
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266 %! opts.v0 = rand (2*n,1); % Initialize eigs ARPACK starting vector
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267 %! % to guarantee reproducible results
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268 %!
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269 %!testif HAVE_ARPACK
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270 %! [u2,s2,v2,flag] = svds (A,k);
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271 %! s2 = diag (s2);
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272 %! assert (flag, !1);
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273 %! tol = 10 * eps() * norm(s2, 1);
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274 %! assert (s2, s(end:-1:end-k+1), tol);
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275 %!
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276 %!testif HAVE_ARPACK, HAVE_UMFPACK
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277 %! [u2,s2,v2,flag] = svds (A,k,0,opts);
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278 %! s2 = diag (s2);
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279 %! assert (flag, !1);
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280 %! tol = 10 * eps() * norm(s2, 1);
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281 %! assert (s2, s(k:-1:1), tol);
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282 %!
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283 %!testif HAVE_ARPACK, HAVE_UMFPACK
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284 %! idx = floor (n/2);
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285 %! % Don't put sigma right on a singular value or there are convergence issues
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286 %! sigma = 0.99*s(idx) + 0.01*s(idx+1);
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287 %! [u2,s2,v2,flag] = svds (A,k,sigma,opts);
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288 %! s2 = diag (s2);
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289 %! assert (flag, !1);
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290 %! tol = 10 * eps() * norm(s2, 1);
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291 %! assert (s2, s((idx+floor(k/2)):-1:(idx-floor(k/2))), tol);
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292 %!
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293 %!testif HAVE_ARPACK
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294 %! [u2,s2,v2,flag] = svds (zeros (10), k);
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295 %! assert (u2, eye (10, k));
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296 %! assert (s2, zeros (k));
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297 %! assert (v2, eye (10, 7));
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298 %!
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299 %!testif HAVE_ARPACK
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300 %! s = svds (speye (10));
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301 %! assert (s, ones (6, 1), 8*eps);
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302
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303 %!test
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304 %! ## Restore random number generator seeds at end of tests
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305 %! rand ("state", rand_state);
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306 %! randn ("state", randn_state);
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307