Mercurial > octave
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> |
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date | Wed, 05 Oct 2016 23:09:31 -0400 |
parents | 34ce5be04942 |
children | 68e9bdb7cde3 e9a0469dedd9 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2016 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
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23 #if defined (HAVE_CONFIG_H) |
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24 # include "config.h" |
2928 | 25 #endif |
26 | |
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27 #include "svd.h" |
2928 | 28 |
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29 #include "defun.h" |
2928 | 30 #include "error.h" |
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31 #include "errwarn.h" |
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32 #include "ovl.h" |
2928 | 33 #include "pr-output.h" |
34 #include "utils.h" | |
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35 #include "variables.h" |
2928 | 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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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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76 |
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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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144 int nargin = args.length (); | |
145 | |
146 if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3) | |
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147 print_usage (); |
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149 octave_value arg = args(0); | |
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 } |
2928 | 200 } |
201 else | |
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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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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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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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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227 if (ctmp.any_element_is_inf_or_nan ()) |
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228 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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230 octave::math::svd<ComplexMatrix> result |
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231 (ctmp, svd_type<ComplexMatrix> (nargin, nargout), |
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232 svd_driver<ComplexMatrix> ()); |
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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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240 sigma, |
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241 result.right_singular_matrix ()); |
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242 } |
4478 | 243 else |
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244 err_wrong_type_arg ("svd", arg); |
2928 | 245 } |
246 | |
247 return retval; | |
248 } | |
249 | |
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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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]) |
2928 | 332 */ |
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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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350 static const char *driver_names[] = { "gesvd", "gesdd", 0 }; |
10601 | 351 |
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352 return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names); |
10601 | 353 } |
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354 |
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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 |