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annotate src/DLD-FUNCTIONS/svd.cc @ 8920:eb63fbe60fab

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update copyright notices
author John W. Eaton <jwe@octave.org>
date Sat, 07 Mar 2009 10:41:27 -0500
parents 81d6ab3ac93c
children 7c02ec148a3c
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1 /*
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2
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3 Copyright (C) 1996, 1997, 1999, 2000, 2003, 2005, 2006, 2007, 2008, 2009
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4 John W. Eaton
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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21
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22 */
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23
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24 #ifdef HAVE_CONFIG_H
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25 #include <config.h>
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26 #endif
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27
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28 #include "CmplxSVD.h"
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29 #include "dbleSVD.h"
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30 #include "fCmplxSVD.h"
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31 #include "floatSVD.h"
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32
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33 #include "defun-dld.h"
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34 #include "error.h"
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35 #include "gripes.h"
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36 #include "oct-obj.h"
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37 #include "pr-output.h"
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38 #include "utils.h"
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39
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40 DEFUN_DLD (svd, args, nargout,
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41 "-*- texinfo -*-\n\
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42 @deftypefn {Loadable Function} {@var{s} =} svd (@var{a})\n\
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43 @deftypefnx {Loadable Function} {[@var{u}, @var{s}, @var{v}] =} svd (@var{a})\n\
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44 @cindex singular value decomposition\n\
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45 Compute the singular value decomposition of @var{a}\n\
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46 @iftex\n\
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47 @tex\n\
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48 $$\n\
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49 A = U S V^H\n\
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50 $$\n\
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51 @end tex\n\
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52 @end iftex\n\
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53 @ifnottex\n\
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54 \n\
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55 @example\n\
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56 A = U*S*V'\n\
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57 @end example\n\
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58 @end ifnottex\n\
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59 \n\
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60 The function @code{svd} normally returns the vector of singular values.\n\
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61 If asked for three return values, it computes\n\
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62 @iftex\n\
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63 @tex\n\
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64 $U$, $S$, and $V$.\n\
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65 @end tex\n\
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66 @end iftex\n\
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67 @ifnottex\n\
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68 U, S, and V.\n\
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69 @end ifnottex\n\
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70 For example,\n\
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71 \n\
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72 @example\n\
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73 svd (hilb (3))\n\
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74 @end example\n\
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75 \n\
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76 @noindent\n\
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77 returns\n\
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78 \n\
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79 @example\n\
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80 ans =\n\
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81 \n\
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82 1.4083189\n\
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83 0.1223271\n\
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84 0.0026873\n\
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85 @end example\n\
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86 \n\
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87 @noindent\n\
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88 and\n\
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89 \n\
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90 @example\n\
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91 [u, s, v] = svd (hilb (3))\n\
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92 @end example\n\
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93 \n\
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94 @noindent\n\
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95 returns\n\
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96 \n\
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97 @example\n\
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98 u =\n\
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99 \n\
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100 -0.82704 0.54745 0.12766\n\
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101 -0.45986 -0.52829 -0.71375\n\
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102 -0.32330 -0.64901 0.68867\n\
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103 \n\
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104 s =\n\
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105 \n\
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106 1.40832 0.00000 0.00000\n\
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107 0.00000 0.12233 0.00000\n\
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108 0.00000 0.00000 0.00269\n\
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109 \n\
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110 v =\n\
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111 \n\
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112 -0.82704 0.54745 0.12766\n\
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113 -0.45986 -0.52829 -0.71375\n\
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114 -0.32330 -0.64901 0.68867\n\
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115 @end example\n\
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116 \n\
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117 If given a second argument, @code{svd} returns an economy-sized\n\
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118 decomposition, eliminating the unnecessary rows or columns of @var{u} or\n\
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119 @var{v}.\n\
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120 @end deftypefn")
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121 {
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122 octave_value_list retval;
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123
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124 int nargin = args.length ();
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125
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126 if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3)
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127 {
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128 print_usage ();
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129 return retval;
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130 }
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131
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132 octave_value arg = args(0);
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133
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134 octave_idx_type nr = arg.rows ();
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135 octave_idx_type nc = arg.columns ();
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136
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137 bool isfloat = arg.is_single_type ();
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138
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139 if (nr == 0 || nc == 0)
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140 {
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141 if (isfloat)
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142 {
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143 if (nargout == 3)
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144 {
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145 retval(3) = float_identity_matrix (nr, nr);
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146 retval(2) = FloatMatrix (nr, nc);
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147 retval(1) = float_identity_matrix (nc, nc);
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148 }
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149 else
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150 retval(0) = FloatMatrix (0, 1);
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151 }
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152 else
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153 {
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154 if (nargout == 3)
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parents: 7017
diff changeset
155 {
82be108cc558 First attempt at single precision tyeps
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diff changeset
156 retval(3) = identity_matrix (nr, nr);
82be108cc558 First attempt at single precision tyeps
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diff changeset
157 retval(2) = Matrix (nr, nc);
82be108cc558 First attempt at single precision tyeps
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diff changeset
158 retval(1) = identity_matrix (nc, nc);
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parents: 7017
diff changeset
159 }
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
160 else
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parents: 7017
diff changeset
161 retval(0) = Matrix (0, 1);
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parents: 7017
diff changeset
162 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
163 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
164 else
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
165 {
4478
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166 SVD::type type = ((nargout == 0 || nargout == 1)
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
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diff changeset
167 ? SVD::sigma_only
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
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diff changeset
168 : (nargin == 2) ? SVD::economy : SVD::std);
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
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169
7789
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diff changeset
170 if (isfloat)
4478
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jwe
parents: 3548
diff changeset
171 {
7789
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parents: 7017
diff changeset
172 if (arg.is_real_type ())
4478
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jwe
parents: 3548
diff changeset
173 {
7789
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diff changeset
174 FloatMatrix tmp = arg.float_matrix_value ();
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parents: 7017
diff changeset
175
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
176 if (! error_state)
4478
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jwe
parents: 3548
diff changeset
177 {
7789
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parents: 7017
diff changeset
178 if (tmp.any_element_is_inf_or_nan ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
179 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
180 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
181 return retval;
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parents: 7017
diff changeset
182 }
4478
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jwe
parents: 3548
diff changeset
183
7789
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diff changeset
184 FloatSVD result (tmp, type);
4478
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185
7789
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diff changeset
186 FloatDiagMatrix sigma = result.singular_values ();
4478
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jwe
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187
7789
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diff changeset
188 if (nargout == 0 || nargout == 1)
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parents: 7017
diff changeset
189 {
82be108cc558 First attempt at single precision tyeps
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diff changeset
190 retval(0) = sigma.diag ();
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parents: 7017
diff changeset
191 }
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
192 else
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
193 {
82be108cc558 First attempt at single precision tyeps
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diff changeset
194 retval(2) = result.right_singular_matrix ();
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diff changeset
195 retval(1) = sigma;
82be108cc558 First attempt at single precision tyeps
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diff changeset
196 retval(0) = result.left_singular_matrix ();
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diff changeset
197 }
4478
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jwe
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diff changeset
198 }
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
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199 }
7789
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parents: 7017
diff changeset
200 else if (arg.is_complex_type ())
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
201 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
202 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
4478
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jwe
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diff changeset
203
7789
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parents: 7017
diff changeset
204 if (! error_state)
4478
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
205 {
7789
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
206 if (ctmp.any_element_is_inf_or_nan ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
207 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
208 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
209 return retval;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
210 }
4478
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
211
7789
82be108cc558 First attempt at single precision tyeps
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diff changeset
212 FloatComplexSVD result (ctmp, type);
4478
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jwe
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diff changeset
213
7789
82be108cc558 First attempt at single precision tyeps
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diff changeset
214 FloatDiagMatrix sigma = result.singular_values ();
4478
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jwe
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diff changeset
215
7789
82be108cc558 First attempt at single precision tyeps
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diff changeset
216 if (nargout == 0 || nargout == 1)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
217 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
218 retval(0) = sigma.diag ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
219 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
220 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
221 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
222 retval(2) = result.right_singular_matrix ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
223 retval(1) = sigma;
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
224 retval(0) = result.left_singular_matrix ();
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
225 }
4478
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
226 }
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
227 }
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
228 }
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
229 else
7afd4bf05aa8 [project @ 2003-07-30 19:15:31 by jwe]
jwe
parents: 3548
diff changeset
230 {
7789
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
231 if (arg.is_real_type ())
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
232 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
233 Matrix tmp = arg.matrix_value ();
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
234
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
235 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
236 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
237 if (tmp.any_element_is_inf_or_nan ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
238 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
239 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
240 return retval;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
241 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
242
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
243 SVD result (tmp, type);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
244
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
245 DiagMatrix sigma = result.singular_values ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
246
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
247 if (nargout == 0 || nargout == 1)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
248 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
249 retval(0) = sigma.diag ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
250 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
251 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
252 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
253 retval(2) = result.right_singular_matrix ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
254 retval(1) = sigma;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
255 retval(0) = result.left_singular_matrix ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
256 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
257 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
258 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
259 else if (arg.is_complex_type ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
260 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
261 ComplexMatrix ctmp = arg.complex_matrix_value ();
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
262
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
263 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
264 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
265 if (ctmp.any_element_is_inf_or_nan ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
266 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
267 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
268 return retval;
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
269 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
270
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
271 ComplexSVD result (ctmp, type);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
272
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
273 DiagMatrix sigma = result.singular_values ();
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
274
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
275 if (nargout == 0 || nargout == 1)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
276 {
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
277 retval(0) = sigma.diag ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
278 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
279 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
280 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
281 retval(2) = result.right_singular_matrix ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
282 retval(1) = sigma;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
283 retval(0) = result.left_singular_matrix ();
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
284 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
285 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
286 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
287 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
288 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
289 gripe_wrong_type_arg ("svd", arg);
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
290 return retval;
82be108cc558 First attempt at single precision tyeps
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parents: 7017
diff changeset
291 }
4478
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jwe
parents: 3548
diff changeset
292 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
293 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
294
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
295 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
296 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
297
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
298 /*
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
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299
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
300 %!assert(svd ([1, 2; 2, 1]), [3; 1], sqrt (eps));
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
301
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
302 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
303 %! [u, s, v] = svd ([1, 2; 2, 1]);
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
304 %! x = 1 / sqrt (2);
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
305 %! assert (u, [-x, -x; -x, x], sqrt (eps));
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
306 %! assert (s, [3, 0; 0, 1], sqrt (eps));
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
307 %! assert (v, [-x, x; -x, -x], sqrt (eps));
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
308
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
309 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
310 %! a = [1, 2, 3; 4, 5, 6];
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
311 %! [u, s, v] = svd (a);
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
312 %! assert (u * s * v', a, sqrt (eps));
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
313
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
314 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
315 %! a = [1, 2; 3, 4; 5, 6];
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
316 %! [u, s, v] = svd (a);
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
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317 %! assert (u * s * v', a, sqrt (eps));
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318
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319 %!test
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320 %! a = [1, 2, 3; 4, 5, 6];
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321 %! [u, s, v] = svd (a, 1);
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322 %! assert (u * s * v', a, sqrt (eps));
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323
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324 %!test
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325 %! a = [1, 2; 3, 4; 5, 6];
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326 %! [u, s, v] = svd (a, 1);
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327 %! assert (u * s * v', a, sqrt (eps));
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328
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329 %!assert(svd (single([1, 2; 2, 1])), single([3; 1]), sqrt (eps('single')));
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330
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331 %!test
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332 %! [u, s, v] = svd (single([1, 2; 2, 1]));
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333 %! x = single (1 / sqrt (2));
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334 %! assert (u, [-x, -x; -x, x], sqrt (eps('single')));
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335 %! assert (s, single([3, 0; 0, 1]), sqrt (eps('single')));
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336 %! assert (v, [-x, x; -x, -x], sqrt (eps('single')));
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337
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338 %!test
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339 %! a = single([1, 2, 3; 4, 5, 6]);
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340 %! [u, s, v] = svd (a);
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341 %! assert (u * s * v', a, sqrt (eps('single')));
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342
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343 %!test
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344 %! a = single([1, 2; 3, 4; 5, 6]);
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345 %! [u, s, v] = svd (a);
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346 %! assert (u * s * v', a, sqrt (eps('single')));
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347
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348 %!test
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349 %! a = single([1, 2, 3; 4, 5, 6]);
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350 %! [u, s, v] = svd (a, 1);
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351 %! assert (u * s * v', a, sqrt (eps('single')));
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352
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353 %!test
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354 %! a = single([1, 2; 3, 4; 5, 6]);
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355 %! [u, s, v] = svd (a, 1);
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356 %! assert (u * s * v', a, sqrt (eps('single')));
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357
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358 %!error <Invalid call to svd.*> svd ();
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359 %!error <Invalid call to svd.*> svd ([1, 2; 4, 5], 2, 3);
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360 %!error <Invalid call to svd.*> [u, v] = svd ([1, 2; 3, 4]);
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361
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362 */
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363
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364 /*
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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365 ;;; Local Variables: ***
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366 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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367 ;;; End: ***
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368 */