annotate libinterp/corefcn/svd.cc @ 22592:ee0df00e12d6 stable

fix complex svd (bug #49232) * liboctave/numeric/svd.cc (svd<T>::svd): Use hermitian, not transpose. * libinterp/corefcn/svd.cc: New test for complex svd.
author John W. Eaton <jwe@octave.org>
date Wed, 05 Oct 2016 23:09:31 -0400
parents 34ce5be04942
children 68e9bdb7cde3 e9a0469dedd9
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1 /*
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2
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3 Copyright (C) 1996-2016 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #if defined (HAVE_CONFIG_H)
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24 # include "config.h"
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25 #endif
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26
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27 #include "svd.h"
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29 #include "defun.h"
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30 #include "error.h"
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31 #include "errwarn.h"
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32 #include "ovl.h"
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33 #include "pr-output.h"
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34 #include "utils.h"
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35 #include "variables.h"
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36
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37 static std::string Vsvd_driver = "gesvd";
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38
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39 template <typename T>
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40 static typename octave::math::svd<T>::Type
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41 svd_type (int nargin, int nargout)
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42 {
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43 return ((nargout == 0 || nargout == 1)
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44 ? octave::math::svd<T>::Type::sigma_only
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45 : ((nargin == 2)
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46 ? octave::math::svd<T>::Type::economy
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47 : octave::math::svd<T>::Type::std));
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48 }
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49
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50 template <typename T>
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51 static typename octave::math::svd<T>::Driver
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52 svd_driver (void)
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53 {
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54 return (Vsvd_driver == "gesvd"
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55 ? octave::math::svd<T>::Driver::GESVD
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56 : octave::math::svd<T>::Driver::GESDD);
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57 }
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58
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59 DEFUN (svd, args, nargout,
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60 doc: /* -*- texinfo -*-
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61 @deftypefn {} {@var{s} =} svd (@var{A})
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62 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A})
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63 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, @var{econ})
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64 @cindex singular value decomposition
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65 Compute the singular value decomposition of @var{A}
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66 @tex
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67 $$
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68 A = U S V^{\dagger}
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69 $$
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70 @end tex
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71 @ifnottex
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72
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73 @example
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74 A = U*S*V'
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75 @end example
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77 @end ifnottex
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78
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79 The function @code{svd} normally returns only the vector of singular values.
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80 When called with three return values, it computes
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81 @tex
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82 $U$, $S$, and $V$.
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83 @end tex
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84 @ifnottex
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85 @var{U}, @var{S}, and @var{V}.
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86 @end ifnottex
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87 For example,
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88
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89 @example
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90 svd (hilb (3))
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91 @end example
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92
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93 @noindent
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94 returns
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95
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96 @example
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97 @group
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98 ans =
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99
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100 1.4083189
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101 0.1223271
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102 0.0026873
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103 @end group
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104 @end example
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105
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106 @noindent
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107 and
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108
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109 @example
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110 [u, s, v] = svd (hilb (3))
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111 @end example
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112
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113 @noindent
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114 returns
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115
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116 @example
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117 @group
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118 u =
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119
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120 -0.82704 0.54745 0.12766
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121 -0.45986 -0.52829 -0.71375
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122 -0.32330 -0.64901 0.68867
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123
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124 s =
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125
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126 1.40832 0.00000 0.00000
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127 0.00000 0.12233 0.00000
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128 0.00000 0.00000 0.00269
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129
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130 v =
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131
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132 -0.82704 0.54745 0.12766
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133 -0.45986 -0.52829 -0.71375
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134 -0.32330 -0.64901 0.68867
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135 @end group
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136 @end example
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137
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138 If given a second argument, @code{svd} returns an economy-sized
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139 decomposition, eliminating the unnecessary rows or columns of @var{U} or
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140 @var{V}.
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141 @seealso{svd_driver, svds, eig, lu, chol, hess, qr, qz}
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142 @end deftypefn */)
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143 {
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144 int nargin = args.length ();
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145
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146 if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3)
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147 print_usage ();
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148
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149 octave_value arg = args(0);
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150
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151 if (arg.ndims () != 2)
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152 error ("svd: A must be a 2-D matrix");
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153
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154 octave_value_list retval;
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155
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156 bool isfloat = arg.is_single_type ();
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157
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158 if (isfloat)
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159 {
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160 if (arg.is_real_type ())
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161 {
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162 FloatMatrix tmp = arg.float_matrix_value ();
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163
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164 if (tmp.any_element_is_inf_or_nan ())
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165 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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166
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167 octave::math::svd<FloatMatrix> result
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168 (tmp, svd_type<FloatMatrix> (nargin, nargout),
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169 svd_driver<FloatMatrix> ());
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170
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171 FloatDiagMatrix sigma = result.singular_values ();
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172
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173 if (nargout == 0 || nargout == 1)
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174 retval(0) = sigma.extract_diag ();
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175 else
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176 retval = ovl (result.left_singular_matrix (),
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177 sigma,
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178 result.right_singular_matrix ());
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179 }
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180 else if (arg.is_complex_type ())
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181 {
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182 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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183
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184 if (ctmp.any_element_is_inf_or_nan ())
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185 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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186
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187 octave::math::svd<FloatComplexMatrix> result
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188 (ctmp, svd_type<FloatComplexMatrix> (nargin, nargout),
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189 svd_driver<FloatComplexMatrix> ());
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190
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191 FloatDiagMatrix sigma = result.singular_values ();
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192
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193 if (nargout == 0 || nargout == 1)
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194 retval(0) = sigma.extract_diag ();
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195 else
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196 retval = ovl (result.left_singular_matrix (),
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197 sigma,
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198 result.right_singular_matrix ());
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199 }
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200 }
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201 else
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202 {
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203 if (arg.is_real_type ())
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204 {
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205 Matrix tmp = arg.matrix_value ();
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206
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207 if (tmp.any_element_is_inf_or_nan ())
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208 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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209
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210 octave::math::svd<Matrix> result
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211 (tmp, svd_type<Matrix> (nargin, nargout),
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212 svd_driver<Matrix> ());
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213
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214 DiagMatrix sigma = result.singular_values ();
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215
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216 if (nargout == 0 || nargout == 1)
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217 retval(0) = sigma.extract_diag ();
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218 else
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219 retval = ovl (result.left_singular_matrix (),
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diff changeset
220 sigma,
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221 result.right_singular_matrix ());
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222 }
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223 else if (arg.is_complex_type ())
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224 {
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225 ComplexMatrix ctmp = arg.complex_matrix_value ();
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226
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227 if (ctmp.any_element_is_inf_or_nan ())
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diff changeset
228 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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229
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diff changeset
230 octave::math::svd<ComplexMatrix> result
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diff changeset
231 (ctmp, svd_type<ComplexMatrix> (nargin, nargout),
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232 svd_driver<ComplexMatrix> ());
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233
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234 DiagMatrix sigma = result.singular_values ();
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235
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236 if (nargout == 0 || nargout == 1)
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237 retval(0) = sigma.extract_diag ();
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238 else
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239 retval = ovl (result.left_singular_matrix (),
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diff changeset
240 sigma,
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diff changeset
241 result.right_singular_matrix ());
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242 }
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243 else
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244 err_wrong_type_arg ("svd", arg);
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245 }
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246
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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247 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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248 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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249
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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250 /*
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251 %!assert (svd ([1, 2; 2, 1]), [3; 1], sqrt (eps))
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252
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253 %!test
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254 a = [1, 2; 3, 4] + [5, 6; 7, 8]*i;
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255 [u,s,v] = svd (a);
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diff changeset
256 assert (a, u * s * v', 128 * eps);
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257
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258
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259 %!test
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260 %! [u, s, v] = svd ([1, 2; 2, 1]);
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261 %! x = 1 / sqrt (2);
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262 %! assert (u, [-x, -x; -x, x], sqrt (eps));
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263 %! assert (s, [3, 0; 0, 1], sqrt (eps));
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264 %! assert (v, [-x, x; -x, -x], sqrt (eps));
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265
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266 %!test
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267 %! a = [1, 2, 3; 4, 5, 6];
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268 %! [u, s, v] = svd (a);
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269 %! assert (u * s * v', a, sqrt (eps));
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270
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271 %!test
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272 %! a = [1, 2; 3, 4; 5, 6];
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273 %! [u, s, v] = svd (a);
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274 %! assert (u * s * v', a, sqrt (eps));
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275
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276 %!test
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277 %! a = [1, 2, 3; 4, 5, 6];
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278 %! [u, s, v] = svd (a, 1);
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279 %! assert (u * s * v', a, sqrt (eps));
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280
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281 %!test
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282 %! a = [1, 2; 3, 4; 5, 6];
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283 %! [u, s, v] = svd (a, 1);
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284 %! assert (u * s * v', a, sqrt (eps));
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285
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286 %!assert (svd (single ([1, 2; 2, 1])), single ([3; 1]), sqrt (eps ("single")))
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287
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288 %!test
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289 %! [u, s, v] = svd (single ([1, 2; 2, 1]));
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290 %! x = single (1 / sqrt (2));
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291 %! assert (u, [-x, -x; -x, x], sqrt (eps ("single")));
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292 %! assert (s, single ([3, 0; 0, 1]), sqrt (eps ("single")));
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293 %! assert (v, [-x, x; -x, -x], sqrt (eps ("single")));
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294
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295 %!test
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296 %! a = single ([1, 2, 3; 4, 5, 6]);
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297 %! [u, s, v] = svd (a);
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298 %! assert (u * s * v', a, sqrt (eps ("single")));
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299
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300 %!test
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301 %! a = single ([1, 2; 3, 4; 5, 6]);
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302 %! [u, s, v] = svd (a);
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303 %! assert (u * s * v', a, sqrt (eps ("single")));
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304
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305 %!test
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306 %! a = single ([1, 2, 3; 4, 5, 6]);
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307 %! [u, s, v] = svd (a, 1);
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308 %! assert (u * s * v', a, sqrt (eps ("single")));
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309
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310 %!test
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311 %! a = single ([1, 2; 3, 4; 5, 6]);
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312 %! [u, s, v] = svd (a, 1);
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313 %! assert (u * s * v', a, sqrt (eps ("single")));
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314
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315 %!test
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316 %! a = zeros (0, 5);
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317 %! [u, s, v] = svd (a);
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318 %! assert (size (u), [0, 0]);
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319 %! assert (size (s), [0, 5]);
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320 %! assert (size (v), [5, 5]);
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321
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322 %!test
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323 %! a = zeros (5, 0);
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324 %! [u, s, v] = svd (a, 1);
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325 %! assert (size (u), [5, 0]);
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326 %! assert (size (s), [0, 0]);
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327 %! assert (size (v), [0, 0]);
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328
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329 %!error svd ()
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330 %!error svd ([1, 2; 4, 5], 2, 3)
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331 %!error [u, v] = svd ([1, 2; 3, 4])
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332 */
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333
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334 DEFUN (svd_driver, args, nargout,
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335 doc: /* -*- texinfo -*-
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336 @deftypefn {} {@var{val} =} svd_driver ()
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337 @deftypefnx {} {@var{old_val} =} svd_driver (@var{new_val})
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338 @deftypefnx {} {} svd_driver (@var{new_val}, "local")
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339 Query or set the underlying @sc{lapack} driver used by @code{svd}.
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340
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341 Currently recognized values are @qcode{"gesvd"} and @qcode{"gesdd"}.
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342 The default is @qcode{"gesvd"}.
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343
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344 When called from inside a function with the @qcode{"local"} option, the
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345 variable is changed locally for the function and any subroutines it calls.
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346 The original variable value is restored when exiting the function.
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347 @seealso{svd}
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348 @end deftypefn */)
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349 {
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350 static const char *driver_names[] = { "gesvd", "gesdd", 0 };
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351
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352 return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names);
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353 }
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355 /*
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356 %!test
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357 %! A = [1+1i, 1-1i, 0; 0, 2, 0; 1i, 1i, 1+2i];
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358 %! old_driver = svd_driver ("gesvd");
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359 %! [U1, S1, V1] = svd (A);
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360 %! svd_driver ("gesdd");
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361 %! [U2, S2, V2] = svd (A);
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362 %! assert (U1, U2, 5*eps);
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363 %! assert (S1, S2, 5*eps);
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364 %! assert (V1, V2, 5*eps);
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365 %! svd_driver (old_driver);
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366 */
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367