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annotate libinterp/corefcn/svd.cc @ 26614:725f3f01f487 stable

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doc: Fix typo in svd_driver docstring. * svd.cc (Fsvd_driver): Change "use" to "used".
author Rik <rik@octave.org>
date Thu, 24 Jan 2019 10:52:07 -0800
parents 00f796120a6d
children 1212568010a8
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1 /*
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2
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3 Copyright (C) 1996-2019 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
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9 the Free Software Foundation, either version 3 of the License, or
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10 (at your 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
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13 WITHOUT ANY WARRANTY; without even the implied warranty of
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 GNU General Public License 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 <https://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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28
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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 = "gesdd";
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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, const octave_value_list & args, const T & A)
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42 {
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43 if (nargout == 0 || nargout == 1)
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44 return octave::math::svd<T>::Type::sigma_only;
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45 else if (nargin == 1)
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46 return octave::math::svd<T>::Type::std;
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47 else if (! args(1).is_real_scalar ())
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48 return octave::math::svd<T>::Type::economy;
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49 else
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50 {
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51 if (A.rows () > A.columns ())
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52 return octave::math::svd<T>::Type::economy;
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53 else
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54 return octave::math::svd<T>::Type::std;
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55 }
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56 }
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57
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58 template <typename T>
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59 static typename octave::math::svd<T>::Driver
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60 svd_driver (void)
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61 {
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62 return (Vsvd_driver == "gesvd"
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63 ? octave::math::svd<T>::Driver::GESVD
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64 : octave::math::svd<T>::Driver::GESDD);
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65 }
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66
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67 DEFUN (svd, args, nargout,
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68 classes: double single
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69 doc: /* -*- texinfo -*-
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70 @deftypefn {} {@var{s} =} svd (@var{A})
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71 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A})
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72 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, "econ")
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73 @deftypefnx {} {[@var{U}, @var{S}, @var{V}] =} svd (@var{A}, 0)
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74 @cindex singular value decomposition
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75 Compute the singular value decomposition of @var{A}.
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76
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77 The singular value decomposition is defined by the relation
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78
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79 @tex
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80 $$
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81 A = U S V^{\dagger}
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82 $$
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83 @end tex
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84 @ifnottex
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85
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86 @example
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87 A = U*S*V'
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88 @end example
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89
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90 @end ifnottex
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91
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92 The function @code{svd} normally returns only the vector of singular values.
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93 When called with three return values, it computes
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94 @tex
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95 $U$, $S$, and $V$.
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96 @end tex
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97 @ifnottex
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98 @var{U}, @var{S}, and @var{V}.
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99 @end ifnottex
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100 For example,
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101
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102 @example
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103 svd (hilb (3))
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104 @end example
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105
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106 @noindent
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107 returns
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108
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109 @example
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110 @group
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111 ans =
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112
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113 1.4083189
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114 0.1223271
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115 0.0026873
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116 @end group
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117 @end example
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118
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119 @noindent
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120 and
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121
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122 @example
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123 [u, s, v] = svd (hilb (3))
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124 @end example
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125
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126 @noindent
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127 returns
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128
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129 @example
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130 @group
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131 u =
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132
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133 -0.82704 0.54745 0.12766
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134 -0.45986 -0.52829 -0.71375
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135 -0.32330 -0.64901 0.68867
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136
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137 s =
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138
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139 1.40832 0.00000 0.00000
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140 0.00000 0.12233 0.00000
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141 0.00000 0.00000 0.00269
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142
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143 v =
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144
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145 -0.82704 0.54745 0.12766
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146 -0.45986 -0.52829 -0.71375
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147 -0.32330 -0.64901 0.68867
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148 @end group
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149 @end example
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150
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151 When given a second argument that is not 0, @code{svd} returns an economy-sized
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152 decomposition, eliminating the unnecessary rows or columns of @var{U} or
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153 @var{V}.
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154
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155 If the second argument is exactly 0, then the choice of decomposition is based
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156 on the matrix @var{A}. If @var{A} has more rows than columns then an
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157 economy-sized decomposition is returned, otherwise a regular decomposition
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158 is calculated.
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159
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160 Algorithm Notes: When calculating the full decomposition (left and right
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161 singular matrices in addition to singular values) there is a choice of two
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162 routines in @sc{lapack}. The default routine used by Octave is @code{gesdd}
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163 which is 5X faster than the alternative @code{gesvd}, but may use more memory
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164 and may be less accurate for some matrices. See the documentation for
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165 @code{svd_driver} for more information.
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166 @seealso{svd_driver, svds, eig, lu, chol, hess, qr, qz}
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167 @end deftypefn */)
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168 {
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169 int nargin = args.length ();
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170
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171 if (nargin < 1 || nargin > 2 || nargout > 3)
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172 print_usage ();
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173
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174 octave_value arg = args(0);
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175
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176 if (arg.ndims () != 2)
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177 error ("svd: A must be a 2-D matrix");
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178
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179 octave_value_list retval;
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180
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181 bool isfloat = arg.is_single_type ();
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182
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183 if (isfloat)
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184 {
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185 if (arg.isreal ())
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186 {
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187 FloatMatrix tmp = arg.float_matrix_value ();
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188
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189 if (tmp.any_element_is_inf_or_nan ())
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190 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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191
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192 octave::math::svd<FloatMatrix> result
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193 (tmp,
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194 svd_type<FloatMatrix> (nargin, nargout, args, tmp),
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195 svd_driver<FloatMatrix> ());
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196
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197 FloatDiagMatrix sigma = result.singular_values ();
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198
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199 if (nargout == 0 || nargout == 1)
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200 retval(0) = sigma.extract_diag ();
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201 else if (nargout == 2)
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202 retval = ovl (result.left_singular_matrix (),
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203 sigma);
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204 else
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205 retval = ovl (result.left_singular_matrix (),
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206 sigma,
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207 result.right_singular_matrix ());
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208 }
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209 else if (arg.iscomplex ())
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210 {
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211 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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212
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213 if (ctmp.any_element_is_inf_or_nan ())
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214 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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215
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216 octave::math::svd<FloatComplexMatrix> result
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217 (ctmp,
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218 svd_type<FloatComplexMatrix> (nargin, nargout, args, ctmp),
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219 svd_driver<FloatComplexMatrix> ());
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220
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221 FloatDiagMatrix sigma = result.singular_values ();
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222
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223 if (nargout == 0 || nargout == 1)
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224 retval(0) = sigma.extract_diag ();
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225 else if (nargout == 2)
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226 retval = ovl (result.left_singular_matrix (),
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227 sigma);
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228 else
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229 retval = ovl (result.left_singular_matrix (),
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230 sigma,
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231 result.right_singular_matrix ());
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232 }
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233 }
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234 else
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235 {
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236 if (arg.isreal ())
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237 {
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238 Matrix tmp = arg.matrix_value ();
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239
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240 if (tmp.any_element_is_inf_or_nan ())
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241 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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242
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243 octave::math::svd<Matrix> result
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244 (tmp,
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245 svd_type<Matrix> (nargin, nargout, args, tmp),
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246 svd_driver<Matrix> ());
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247
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248 DiagMatrix sigma = result.singular_values ();
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249
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250 if (nargout == 0 || nargout == 1)
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251 retval(0) = sigma.extract_diag ();
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252 else if (nargout == 2)
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253 retval = ovl (result.left_singular_matrix (),
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254 sigma);
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255 else
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256 retval = ovl (result.left_singular_matrix (),
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257 sigma,
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258 result.right_singular_matrix ());
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259 }
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260 else if (arg.iscomplex ())
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261 {
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262 ComplexMatrix ctmp = arg.complex_matrix_value ();
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263
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264 if (ctmp.any_element_is_inf_or_nan ())
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265 error ("svd: cannot take SVD of matrix containing Inf or NaN values");
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266
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267 octave::math::svd<ComplexMatrix> result
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268 (ctmp,
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269 svd_type<ComplexMatrix> (nargin, nargout, args, ctmp),
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270 svd_driver<ComplexMatrix> ());
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271
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272 DiagMatrix sigma = result.singular_values ();
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273
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274 if (nargout == 0 || nargout == 1)
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275 retval(0) = sigma.extract_diag ();
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276 else if (nargout == 2)
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277 retval = ovl (result.left_singular_matrix (),
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278 sigma);
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279 else
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280 retval = ovl (result.left_singular_matrix (),
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281 sigma,
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282 result.right_singular_matrix ());
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283 }
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284 else
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285 err_wrong_type_arg ("svd", arg);
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286 }
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287
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288 return retval;
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289 }
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290
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291 /*
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292 %!assert (svd ([1, 2; 2, 1]), [3; 1], sqrt (eps))
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293
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294 %!test
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295 %! a = [1, 2; 3, 4] + [5, 6; 7, 8]*i;
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296 %! [u,s,v] = svd (a);
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297 %! assert (a, u * s * v', 128 * eps);
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298
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299 %!test
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300 %! [u, s, v] = svd ([1, 2; 2, 1]);
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301 %! x = 1 / sqrt (2);
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302 %! assert (u, [-x, -x; -x, x], sqrt (eps));
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303 %! assert (s, [3, 0; 0, 1], sqrt (eps));
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304 %! assert (v, [-x, x; -x, -x], sqrt (eps));
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305
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306 %!test
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307 %! a = [1, 2, 3; 4, 5, 6];
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308 %! [u, s, v] = svd (a);
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309 %! assert (u * s * v', a, sqrt (eps));
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310
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311 %!test
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312 %! a = [1, 2; 3, 4; 5, 6];
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313 %! [u, s, v] = svd (a);
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314 %! assert (u * s * v', a, sqrt (eps));
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315
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316 %!test
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317 %! a = [1, 2, 3; 4, 5, 6];
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318 %! [u, s, v] = svd (a, 1);
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319 %! assert (u * s * v', a, sqrt (eps));
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320
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321 %!test
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322 %! a = [1, 2; 3, 4; 5, 6];
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323 %! [u, s, v] = svd (a, 1);
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324 %! assert (u * s * v', a, sqrt (eps));
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325
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326 %!assert (svd (single ([1, 2; 2, 1])), single ([3; 1]), sqrt (eps ("single")))
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327
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328 %!test
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329 %! [u, s, v] = svd (single ([1, 2; 2, 1]));
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330 %! x = single (1 / sqrt (2));
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331 %! assert (u, [-x, -x; -x, x], sqrt (eps ("single")));
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332 %! assert (s, single ([3, 0; 0, 1]), sqrt (eps ("single")));
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333 %! assert (v, [-x, x; -x, -x], sqrt (eps ("single")));
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334
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335 %!test
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336 %! a = single ([1, 2, 3; 4, 5, 6]);
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337 %! [u, s, v] = svd (a);
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338 %! assert (u * s * v', a, sqrt (eps ("single")));
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339
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340 %!test
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341 %! a = single ([1, 2; 3, 4; 5, 6]);
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342 %! [u, s, v] = svd (a);
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343 %! assert (u * s * v', a, sqrt (eps ("single")));
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344
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345 %!test
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346 %! a = single ([1, 2, 3; 4, 5, 6]);
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347 %! [u, s, v] = svd (a, 1);
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348 %! assert (u * s * v', a, sqrt (eps ("single")));
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349
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350 %!test
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351 %! a = single ([1, 2; 3, 4; 5, 6]);
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352 %! [u, s, v] = svd (a, 1);
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353 %! assert (u * s * v', a, sqrt (eps ("single")));
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354
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355 %!test
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356 %! a = zeros (0, 5);
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357 %! [u, s, v] = svd (a);
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358 %! assert (size (u), [0, 0]);
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359 %! assert (size (s), [0, 5]);
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360 %! assert (size (v), [5, 5]);
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361
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362 %!test
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363 %! a = zeros (5, 0);
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364 %! [u, s, v] = svd (a, 1);
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365 %! assert (size (u), [5, 0]);
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366 %! assert (size (s), [0, 0]);
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367 %! assert (size (v), [0, 0]);
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368
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369 %!test <*49309>
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370 %! [~,~,v] = svd ([1, 1, 1], 0);
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371 %! assert (size (v), [3 3]);
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372 %! [~,~,v] = svd ([1, 1, 1], "econ");
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373 %! assert (size (v), [3 1]);
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374
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375 %!error svd ()
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376 %!error svd ([1, 2; 4, 5], 2, 3)
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377 */
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378
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379 DEFUN (svd_driver, args, nargout,
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380 doc: /* -*- texinfo -*-
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381 @deftypefn {} {@var{val} =} svd_driver ()
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382 @deftypefnx {} {@var{old_val} =} svd_driver (@var{new_val})
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383 @deftypefnx {} {} svd_driver (@var{new_val}, "local")
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384 Query or set the underlying @sc{lapack} driver used by @code{svd}.
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385
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386 Currently recognized values are @qcode{"gesdd"} and @qcode{"gesvd"}.
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387 The default is @qcode{"gesdd"}.
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388
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389 When called from inside a function with the @qcode{"local"} option, the
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390 variable is changed locally for the function and any subroutines it calls.
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391 The original variable value is restored when exiting the function.
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392
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393 Algorithm Notes: The @sc{lapack} library provides two routines for calculating
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394 the full singular value decomposition (left and right singular matrices as
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395 well as singular values). When calculating just the singular values the
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396 following discussion is not relevant.
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397
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398 The default routine used by Octave is the newer @code{gesdd} which is based on
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399 a Divide-and-Conquer algorithm that is 5X faster than the alternative
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400 @code{gesvd}, which is based on QR factorization. However, the new algorithm
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401 can use significantly more memory. For an @nospell{MxN} input matrix the
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402 memory usage is of order O(min(M,N) ^ 2), whereas the alternative is of order
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403 O(max(M,N)). In general, modern computers have abundant memory so Octave has
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404 chosen to prioritize speed.
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405
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406 In addition, there have been instances in the past where some input matrices
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407 were not accurately decomposed by @code{gesdd}. This appears to have been
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408 resolved with modern versions of @sc{lapack}. However, if certainty is
750c8b4b7164 Switch svd_driver to gesdd for performance (bug #49940).
Rik <rik@octave.org>
parents: 22893
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409 required the accuracy of the decomposition can always be tested after the fact
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Rik <rik@octave.org>
parents: 22893
diff changeset
410 with
750c8b4b7164 Switch svd_driver to gesdd for performance (bug #49940).
Rik <rik@octave.org>
parents: 22893
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411
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Rik <rik@octave.org>
parents: 22893
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412 @example
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Rik <rik@octave.org>
parents: 22893
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413 @group
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parents: 22893
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414 [@var{u}, @var{s}, @var{v}] = svd (@var{x});
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Rik <rik@octave.org>
parents: 22893
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415 norm (@var{x} - @var{u}*@var{s}*@var{v'}, "fro")
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parents: 22893
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416 @end group
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Rik <rik@octave.org>
parents: 22893
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417 @end example
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Rik <rik@octave.org>
parents: 22893
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418
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21724
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419 @seealso{svd}
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21724
diff changeset
420 @end deftypefn */)
10601
3ce0c530a9c9 implement svd_driver
Jaroslav Hajek <highegg@gmail.com>
parents: 10185
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421 {
23795
980f39c3ab90 Use C++11 nullptr rather than 0 in code (bug #51565).
Rik <rik@octave.org>
parents: 23582
diff changeset
422 static const char *driver_names[] = { "gesvd", "gesdd", nullptr };
10601
3ce0c530a9c9 implement svd_driver
Jaroslav Hajek <highegg@gmail.com>
parents: 10185
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423
10638
e1559a8a60b4 general mechanism for string enum variables
Jaroslav Hajek <highegg@gmail.com>
parents: 10601
diff changeset
424 return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names);
10601
3ce0c530a9c9 implement svd_driver
Jaroslav Hajek <highegg@gmail.com>
parents: 10185
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425 }
15887
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
426
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
427 /*
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
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428 %!test
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Rik <rik@octave.org>
parents: 14138
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429 %! A = [1+1i, 1-1i, 0; 0, 2, 0; 1i, 1i, 1+2i];
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
430 %! old_driver = svd_driver ("gesvd");
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
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431 %! [U1, S1, V1] = svd (A);
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Rik <rik@octave.org>
parents: 14138
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432 %! svd_driver ("gesdd");
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
433 %! [U2, S2, V2] = svd (A);
22977
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Rik <rik@octave.org>
parents: 22893
diff changeset
434 %! svd_driver (old_driver);
15887
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
435 %! assert (U1, U2, 5*eps);
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
436 %! assert (S1, S2, 5*eps);
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
437 %! assert (V1, V2, 5*eps);
8ced82e96b48 Fix segfaults with gesdd driver for svd (bug #37998).
Rik <rik@octave.org>
parents: 14138
diff changeset
438 */