Mercurial > octave
annotate libinterp/corefcn/svd.cc @ 31191:bb9d776eafac stable
Fix wrong color in PDF printout of some latex strings (bug #62884)
* octave-svgconvert (draw): For "rect" elements only set brush color if
necessary and eventually restore to previous color.
author | Pantxo Diribarne <pantxo.diribarne@gmail.com> |
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date | Sun, 14 Aug 2022 18:24:07 +0200 |
parents | 796f54d4ddbf |
children | ed17822e7662 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
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30 #include "svd.h" |
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32 #include "defun.h" |
2928 | 33 #include "error.h" |
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34 #include "errwarn.h" |
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35 #include "ovl.h" |
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37 #include "utils.h" | |
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38 #include "variables.h" |
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40 OCTAVE_NAMESPACE_BEGIN |
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41 |
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42 static std::string Vsvd_driver = "gesvd"; |
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43 |
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44 template <typename T> |
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45 static typename math::svd<T>::Type |
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46 svd_type (int nargin, int nargout, const octave_value_list& args, const T& A) |
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47 { |
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48 if (nargout == 0 || nargout == 1) |
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49 return math::svd<T>::Type::sigma_only; |
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50 else if (nargin == 1) |
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51 return math::svd<T>::Type::std; |
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52 else if (! args(1).is_real_scalar ()) |
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53 return math::svd<T>::Type::economy; |
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54 else |
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55 { |
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56 if (A.rows () > A.columns ()) |
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57 return math::svd<T>::Type::economy; |
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58 else |
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59 return math::svd<T>::Type::std; |
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60 } |
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61 } |
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62 |
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63 template <typename T> |
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64 static typename math::svd<T>::Driver |
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65 svd_driver (void) |
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66 { |
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67 if (Vsvd_driver == "gejsv") |
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68 return math::svd<T>::Driver::GEJSV; |
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69 else if (Vsvd_driver == "gesdd") |
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70 return math::svd<T>::Driver::GESDD; |
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71 else |
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72 return math::svd<T>::Driver::GESVD; // default |
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73 } |
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75 DEFUN (svd, args, nargout, |
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76 classes: double single |
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77 doc: /* -*- texinfo -*- |
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78 @deftypefn {} {@var{s} =} svd (@var{A}) |
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79 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}) |
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80 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, "econ") |
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81 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, 0) |
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82 @cindex singular value decomposition |
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83 Compute the singular value decomposition of @var{A}. |
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84 |
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85 The singular value decomposition is defined by the relation |
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86 |
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87 @tex |
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88 $$ |
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89 A = U S V^{\dagger} |
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90 $$ |
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91 @end tex |
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92 @ifnottex |
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93 |
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94 @example |
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95 A = U*S*V' |
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96 @end example |
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97 |
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98 @end ifnottex |
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99 |
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100 The function @code{svd} normally returns only the vector of singular values. |
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101 When called with three return values, it computes |
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102 @tex |
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103 $U$, $S$, and $V$. |
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104 @end tex |
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105 @ifnottex |
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106 @var{U}, @var{S}, and @var{V}. |
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107 @end ifnottex |
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108 For example, |
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109 |
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110 @example |
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111 svd (hilb (3)) |
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112 @end example |
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113 |
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114 @noindent |
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115 returns |
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116 |
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117 @example |
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118 @group |
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119 ans = |
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120 |
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121 1.4083189 |
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122 0.1223271 |
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123 0.0026873 |
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124 @end group |
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125 @end example |
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126 |
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127 @noindent |
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128 and |
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129 |
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130 @example |
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131 [u, s, v] = svd (hilb (3)) |
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132 @end example |
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133 |
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134 @noindent |
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135 returns |
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136 |
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137 @example |
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138 @group |
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139 u = |
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140 |
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141 -0.82704 0.54745 0.12766 |
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142 -0.45986 -0.52829 -0.71375 |
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143 -0.32330 -0.64901 0.68867 |
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144 |
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145 s = |
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146 |
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147 1.40832 0.00000 0.00000 |
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148 0.00000 0.12233 0.00000 |
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149 0.00000 0.00000 0.00269 |
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150 |
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151 v = |
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152 |
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153 -0.82704 0.54745 0.12766 |
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154 -0.45986 -0.52829 -0.71375 |
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155 -0.32330 -0.64901 0.68867 |
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156 @end group |
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157 @end example |
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158 |
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159 When given a second argument that is not 0, @code{svd} returns an economy-sized |
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160 decomposition, eliminating the unnecessary rows or columns of @var{U} or |
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161 @var{V}. |
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162 |
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163 If the second argument is exactly 0, then the choice of decomposition is based |
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164 on the matrix @var{A}. If @var{A} has more rows than columns then an |
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165 economy-sized decomposition is returned, otherwise a regular decomposition |
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166 is calculated. |
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167 |
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168 Algorithm Notes: When calculating the full decomposition (left and right |
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169 singular matrices in addition to singular values) there is a choice of two |
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170 routines in @sc{lapack}. The default routine used by Octave is @code{gesvd}. |
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171 The alternative is @code{gesdd} which is 5X faster, but may use more memory |
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172 and may be inaccurate for some input matrices. There is a third routine |
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173 @code{gejsv}, suitable for better accuracy at extreme scale. See the |
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174 documentation for @code{svd_driver} for more information on choosing a driver. |
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175 @seealso{svd_driver, svds, eig, lu, chol, hess, qr, qz} |
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176 @end deftypefn */) |
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178 int nargin = args.length (); | |
179 | |
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180 if (nargin < 1 || nargin > 2 || nargout > 3) |
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181 print_usage (); |
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183 octave_value arg = args(0); | |
184 | |
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185 if (arg.ndims () != 2) |
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186 error ("svd: A must be a 2-D matrix"); |
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187 |
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188 octave_value_list retval; |
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189 |
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190 bool isfloat = arg.is_single_type (); |
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191 |
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192 if (isfloat) |
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193 { |
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194 if (arg.isreal ()) |
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195 { |
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196 FloatMatrix tmp = arg.float_matrix_value (); |
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197 |
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198 if (tmp.any_element_is_inf_or_nan ()) |
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199 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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200 |
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201 math::svd<FloatMatrix> result |
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202 (tmp, |
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203 svd_type<FloatMatrix> (nargin, nargout, args, tmp), |
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204 svd_driver<FloatMatrix> ()); |
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205 |
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206 FloatDiagMatrix sigma = result.singular_values (); |
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207 |
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208 if (nargout == 0 || nargout == 1) |
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209 retval(0) = sigma.extract_diag (); |
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210 else if (nargout == 2) |
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211 retval = ovl (result.left_singular_matrix (), |
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212 sigma); |
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213 else |
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214 retval = ovl (result.left_singular_matrix (), |
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215 sigma, |
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216 result.right_singular_matrix ()); |
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217 } |
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218 else if (arg.iscomplex ()) |
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219 { |
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220 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
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221 |
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222 if (ctmp.any_element_is_inf_or_nan ()) |
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223 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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224 |
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225 math::svd<FloatComplexMatrix> result |
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226 (ctmp, |
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227 svd_type<FloatComplexMatrix> (nargin, nargout, args, ctmp), |
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228 svd_driver<FloatComplexMatrix> ()); |
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229 |
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230 FloatDiagMatrix sigma = result.singular_values (); |
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231 |
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232 if (nargout == 0 || nargout == 1) |
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233 retval(0) = sigma.extract_diag (); |
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234 else if (nargout == 2) |
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235 retval = ovl (result.left_singular_matrix (), |
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236 sigma); |
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237 else |
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238 retval = ovl (result.left_singular_matrix (), |
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239 sigma, |
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240 result.right_singular_matrix ()); |
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241 } |
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243 else | |
244 { | |
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245 if (arg.isreal ()) |
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246 { |
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247 Matrix tmp = arg.matrix_value (); |
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248 |
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249 if (tmp.any_element_is_inf_or_nan ()) |
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250 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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252 math::svd<Matrix> result |
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253 (tmp, |
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254 svd_type<Matrix> (nargin, nargout, args, tmp), |
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255 svd_driver<Matrix> ()); |
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256 |
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257 DiagMatrix sigma = result.singular_values (); |
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259 if (nargout == 0 || nargout == 1) |
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260 retval(0) = sigma.extract_diag (); |
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261 else if (nargout == 2) |
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262 retval = ovl (result.left_singular_matrix (), |
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263 sigma); |
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264 else |
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265 retval = ovl (result.left_singular_matrix (), |
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266 sigma, |
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267 result.right_singular_matrix ()); |
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268 } |
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269 else if (arg.iscomplex ()) |
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270 { |
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271 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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273 if (ctmp.any_element_is_inf_or_nan ()) |
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274 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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276 math::svd<ComplexMatrix> result |
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277 (ctmp, |
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278 svd_type<ComplexMatrix> (nargin, nargout, args, ctmp), |
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279 svd_driver<ComplexMatrix> ()); |
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281 DiagMatrix sigma = result.singular_values (); |
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282 |
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283 if (nargout == 0 || nargout == 1) |
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284 retval(0) = sigma.extract_diag (); |
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285 else if (nargout == 2) |
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286 retval = ovl (result.left_singular_matrix (), |
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287 sigma); |
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288 else |
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289 retval = ovl (result.left_singular_matrix (), |
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290 sigma, |
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291 result.right_singular_matrix ()); |
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292 } |
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294 err_wrong_type_arg ("svd", arg); |
2928 | 295 } |
296 | |
297 return retval; | |
298 } | |
299 | |
300 /* | |
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301 %!assert (svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)) |
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302 |
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303 %!test |
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304 %! a = [1, 2; 3, 4] + [5, 6; 7, 8]*i; |
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305 %! [u,s,v] = svd (a); |
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306 %! assert (a, u * s * v', 128 * eps); |
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307 |
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308 %!test |
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309 %! [u, s, v] = svd ([1, 2; 2, 1]); |
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310 %! x = 1 / sqrt (2); |
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311 %! assert (u, [-x, -x; -x, x], sqrt (eps)); |
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312 %! assert (s, [3, 0; 0, 1], sqrt (eps)); |
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313 %! assert (v, [-x, x; -x, -x], sqrt (eps)); |
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314 |
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315 %!test |
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316 %! a = [1, 2, 3; 4, 5, 6]; |
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317 %! [u, s, v] = svd (a); |
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318 %! assert (u * s * v', a, sqrt (eps)); |
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319 |
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320 %!test |
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321 %! a = [1, 2; 3, 4; 5, 6]; |
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322 %! [u, s, v] = svd (a); |
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323 %! assert (u * s * v', a, sqrt (eps)); |
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324 |
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325 %!test |
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326 %! a = [1, 2, 3; 4, 5, 6]; |
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327 %! [u, s, v] = svd (a, 1); |
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328 %! assert (u * s * v', a, sqrt (eps)); |
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329 |
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330 %!test |
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331 %! a = [1, 2; 3, 4; 5, 6]; |
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332 %! [u, s, v] = svd (a, 1); |
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333 %! assert (u * s * v', a, sqrt (eps)); |
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334 |
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335 %!assert (svd (single ([1, 2; 2, 1])), single ([3; 1]), sqrt (eps ("single"))) |
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336 |
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337 %!test |
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338 %! [u, s, v] = svd (single ([1, 2; 2, 1])); |
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339 %! x = single (1 / sqrt (2)); |
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340 %! assert (u, [-x, -x; -x, x], sqrt (eps ("single"))); |
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341 %! assert (s, single ([3, 0; 0, 1]), sqrt (eps ("single"))); |
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342 %! assert (v, [-x, x; -x, -x], sqrt (eps ("single"))); |
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343 |
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344 %!test |
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345 %! a = single ([1, 2, 3; 4, 5, 6]); |
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346 %! [u, s, v] = svd (a); |
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347 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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348 |
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349 %!test |
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350 %! a = single ([1, 2; 3, 4; 5, 6]); |
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351 %! [u, s, v] = svd (a); |
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352 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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353 |
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354 %!test |
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355 %! a = single ([1, 2, 3; 4, 5, 6]); |
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356 %! [u, s, v] = svd (a, 1); |
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357 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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358 |
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359 %!test |
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360 %! a = single ([1, 2; 3, 4; 5, 6]); |
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361 %! [u, s, v] = svd (a, 1); |
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362 %! assert (u * s * v', a, sqrt (eps ("single"))); |
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363 |
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364 %!test |
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365 %! a = zeros (0, 5); |
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366 %! [u, s, v] = svd (a); |
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367 %! assert (size (u), [0, 0]); |
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368 %! assert (size (s), [0, 5]); |
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369 %! assert (size (v), [5, 5]); |
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370 |
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371 %!test |
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372 %! a = zeros (5, 0); |
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373 %! [u, s, v] = svd (a, 1); |
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374 %! assert (size (u), [5, 0]); |
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375 %! assert (size (s), [0, 0]); |
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376 %! assert (size (v), [0, 0]); |
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377 |
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378 %!test <*49309> |
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379 %! [~,~,v] = svd ([1, 1, 1], 0); |
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380 %! assert (size (v), [3 3]); |
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381 %! [~,~,v] = svd ([1, 1, 1], "econ"); |
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382 %! assert (size (v), [3 1]); |
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383 |
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384 %!assert <*55710> (1 / svd (-0), Inf) |
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385 |
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386 %!test |
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387 %! old_driver = svd_driver ("gejsv"); |
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388 %! s0 = [1e-20; 1e-10; 1]; # only gejsv can pass |
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389 %! q = sqrt (0.5); |
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390 %! a = s0 .* [q, 0, -q; -0.5, q, -0.5; 0.5, q, 0.5]; |
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391 %! s1 = svd (a); |
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392 %! svd_driver (old_driver); |
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393 %! assert (sort (s1), s0, -10 * eps); |
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394 |
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395 %!error svd () |
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396 %!error svd ([1, 2; 4, 5], 2, 3) |
2928 | 397 */ |
10601 | 398 |
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399 DEFUN (svd_driver, args, nargout, |
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400 doc: /* -*- texinfo -*- |
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401 @deftypefn {} {@var{val} =} svd_driver () |
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402 @deftypefnx {} {@var{old_val} =} svd_driver (@var{new_val}) |
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403 @deftypefnx {} {} svd_driver (@var{new_val}, "local") |
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404 Query or set the underlying @sc{lapack} driver used by @code{svd}. |
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405 |
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406 Currently recognized values are @qcode{"gesdd"}, @qcode{"gesvd"}, and |
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407 @qcode{"gejsv"}. The default is @qcode{"gesvd"}. |
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408 |
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409 When called from inside a function with the @qcode{"local"} option, the |
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410 variable is changed locally for the function and any subroutines it calls. |
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411 The original variable value is restored when exiting the function. |
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412 |
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413 Algorithm Notes: The @sc{lapack} library routines @code{gesvd} and @code{gesdd} |
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414 are different only when calculating the full singular value decomposition (left |
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415 and right singular matrices as well as singular values). When calculating just |
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416 the singular values the following discussion is not relevant. |
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417 |
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418 The newer @code{gesdd} routine is based on a Divide-and-Conquer algorithm that |
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419 is 5X faster than the alternative @code{gesvd}, which is based on QR |
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420 factorization. However, the new algorithm can use significantly more memory. |
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421 For an @nospell{MxN} input matrix the memory usage is of order O(min(M,N) ^ 2), |
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422 whereas the alternative is of order O(max(M,N)). |
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423 |
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424 The routine @code{gejsv} uses a preconditioned Jacobi SVD algorithm. Unlike |
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425 @code{gesvd} and @code{gesdd}, in @code{gejsv}, there is no bidiagonalization |
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426 step that could contaminate accuracy in some extreme cases. Also, @code{gejsv} |
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427 is known to be optimally accurate in some sense. However, the speed is slower |
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428 (single threaded at its core) and uses more memory (O(min(M,N) ^ 2 + M + N)). |
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429 |
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430 Beyond speed and memory issues, there have been instances where some input |
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431 matrices were not accurately decomposed by @code{gesdd}. See currently active |
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432 bug @url{https://savannah.gnu.org/bugs/?55564}. Until these accuracy issues |
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433 are resolved in a new version of the @sc{lapack} library, the default driver |
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434 in Octave has been set to @qcode{"gesvd"}. |
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435 |
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436 @seealso{svd} |
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437 @end deftypefn */) |
10601 | 438 { |
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439 static const char *driver_names[] = { "gesvd", "gesdd", "gejsv", nullptr }; |
10601 | 440 |
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441 return set_internal_variable (Vsvd_driver, args, nargout, |
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442 "svd_driver", driver_names); |
10601 | 443 } |
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444 |
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445 /* |
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446 %!test |
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447 %! A = [1+1i, 1-1i, 0; 0, 2, 0; 1i, 1i, 1+2i]; |
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448 %! old_driver = svd_driver ("gesvd"); |
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449 %! [U1, S1, V1] = svd (A); |
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450 %! svd_driver ("gesdd"); |
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451 %! [U2, S2, V2] = svd (A); |
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452 %! svd_driver ("gejsv"); |
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453 %! [U3, S3, V3] = svd (A); |
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454 %! assert (svd_driver (), "gejsv"); |
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455 %! svd_driver (old_driver); |
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456 %! assert (U1, U2, 6*eps); |
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457 %! assert (S1, S2, 6*eps); |
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458 %! assert (V1, V2, 6*eps); |
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459 %! z = U1(1,:) ./ U3(1,:); |
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460 %! assert (U1, U3 .* z, 100*eps); |
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461 %! assert (S1, S3, 6*eps); |
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462 %! assert (V1, V3 .* z, 100*eps); |
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463 */ |
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464 |
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465 OCTAVE_NAMESPACE_END |