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annotate libinterp/corefcn/pinv.cc @ 18794:03c2671493f9

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maint: Periodic merge of gui-release to default.
author Rik <rik@octave.org>
date Mon, 02 Jun 2014 11:17:59 -0700
parents 1fa5bba16218
children 4197fc428c7d
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1 /*
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2
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3 Copyright (C) 1996-2013 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef 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 "defun.h"
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28 #include "error.h"
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29 #include "gripes.h"
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30 #include "oct-obj.h"
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31 #include "utils.h"
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32 #include "ops.h"
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33 #include "ov-re-diag.h"
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34 #include "ov-cx-diag.h"
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35 #include "ov-flt-re-diag.h"
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36 #include "ov-flt-cx-diag.h"
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37 #include "ov-perm.h"
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38
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39 DEFUN (pinv, args, ,
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40 "-*- texinfo -*-\n\
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41 @deftypefn {Built-in Function} {} pinv (@var{x})\n\
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42 @deftypefnx {Built-in Function} {} pinv (@var{x}, @var{tol})\n\
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43 Return the pseudoinverse of @var{x}. Singular values less than\n\
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44 @var{tol} are ignored.\n\
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45 \n\
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46 If the second argument is omitted, it is taken to be\n\
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47 \n\
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48 @example\n\
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49 tol = max (size (@var{x})) * sigma_max (@var{x}) * eps,\n\
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50 @end example\n\
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51 \n\
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52 @noindent\n\
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53 where @code{sigma_max (@var{x})} is the maximal singular value of @var{x}.\n\
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54 @end deftypefn")
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55 {
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56 octave_value retval;
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57
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58 int nargin = args.length ();
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59
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60 if (nargin < 1 || nargin > 2)
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61 {
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62 print_usage ();
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63 return retval;
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64 }
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65
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66 octave_value arg = args(0);
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67
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68 int arg_is_empty = empty_arg ("pinv", arg.rows (), arg.columns ());
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69
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70 if (arg_is_empty < 0)
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71 return retval;
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72 else if (arg_is_empty > 0)
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73 return octave_value (Matrix ());
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74
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75 bool isfloat = arg.is_single_type ();
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76
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77 if (arg.is_diag_matrix ())
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78 {
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79 if (isfloat)
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80 {
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81 float tol = 0.0;
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82 if (nargin == 2)
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83 tol = args(1).float_value ();
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84
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85 if (error_state)
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86 return retval;
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87
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88 if (tol < 0.0)
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89 {
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90 error ("pinv: TOL must be greater than zero");
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91 return retval;
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92 }
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93
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94 if (arg.is_real_type ())
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95 retval = arg.float_diag_matrix_value ().pseudo_inverse (tol);
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96 else
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97 retval = arg.float_complex_diag_matrix_value ().pseudo_inverse (tol);
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98 }
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99 else
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100 {
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101 double tol = 0.0;
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102 if (nargin == 2)
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103 tol = args(1).double_value ();
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104
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105 if (error_state)
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106 return retval;
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107
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108 if (tol < 0.0)
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109 {
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110 error ("pinv: TOL must be greater than zero");
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111 return retval;
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112 }
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113
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114 if (arg.is_real_type ())
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115 retval = arg.diag_matrix_value ().pseudo_inverse (tol);
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116 else
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117 retval = arg.complex_diag_matrix_value ().pseudo_inverse (tol);
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118 }
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119 }
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120 else if (arg.is_perm_matrix ())
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121 {
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122 retval = arg.perm_matrix_value ().inverse ();
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123 }
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124 else if (isfloat)
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125 {
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126 float tol = 0.0;
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127 if (nargin == 2)
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128 tol = args(1).float_value ();
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129
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130 if (error_state)
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131 return retval;
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132
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133 if (tol < 0.0)
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134 {
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135 error ("pinv: TOL must be greater than zero");
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136 return retval;
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137 }
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138
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139 if (arg.is_real_type ())
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140 {
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141 FloatMatrix m = arg.float_matrix_value ();
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142
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143 if (! error_state)
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144 retval = m.pseudo_inverse (tol);
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145 }
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146 else if (arg.is_complex_type ())
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147 {
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148 FloatComplexMatrix m = arg.float_complex_matrix_value ();
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149
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150 if (! error_state)
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151 retval = m.pseudo_inverse (tol);
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152 }
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153 else
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154 {
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155 gripe_wrong_type_arg ("pinv", arg);
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156 }
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157 }
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158 else
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159 {
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160 double tol = 0.0;
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161 if (nargin == 2)
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162 tol = args(1).double_value ();
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163
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164 if (error_state)
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165 return retval;
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166
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167 if (tol < 0.0)
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168 {
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169 error ("pinv: TOL must be greater than zero");
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170 return retval;
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171 }
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172
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173 if (arg.is_real_type ())
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174 {
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175 Matrix m = arg.matrix_value ();
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176
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177 if (! error_state)
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178 retval = m.pseudo_inverse (tol);
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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 ComplexMatrix m = arg.complex_matrix_value ();
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183
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184 if (! error_state)
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185 retval = m.pseudo_inverse (tol);
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186 }
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187 else
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188 {
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189 gripe_wrong_type_arg ("pinv", arg);
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190 }
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191 }
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192
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193 return retval;
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194 }
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195
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196 /*
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197 %!shared a, b, tol, hitol, d, u, x, y
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198 %! a = reshape (rand*[1:16], 4, 4); # Rank 2 matrix
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199 %! b = pinv (a);
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200 %! tol = 4e-14;
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201 %! hitol = 40*sqrt (eps);
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202 %! d = diag ([rand, rand, hitol, hitol]);
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203 %! u = rand (4); # Could be singular by freak accident
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204 %! x = inv (u)*d*u;
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205 %! y = pinv (x, sqrt (eps));
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206 %!
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207 %!assert (a*b*a, a, tol)
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208 %!assert (b*a*b, b, tol)
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209 %!assert ((b*a)', b*a, tol)
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210 %!assert ((a*b)', a*b, tol)
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211 %!assert (x*y*x, x, -hitol)
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212 %!assert (y*x*y, y, -hitol)
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213 %!assert ((x*y)', x*y, hitol)
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214 %!assert ((y*x)', y*x, hitol)
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215
1fa5bba16218 [mq]: pinv
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216 ## Clear shared variables
1fa5bba16218 [mq]: pinv
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217 %!shared
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218
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219 ## Test pinv for Diagonal matrices
1fa5bba16218 [mq]: pinv
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220 %!test
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221 %! x = diag ([3 2 1 0 -0.5]);
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222 %! y = pinv (x);
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223 %! assert (typeinfo (y)(1:8), "diagonal");
1fa5bba16218 [mq]: pinv
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224 %! assert (isa (y, "double"));
1fa5bba16218 [mq]: pinv
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225 %! assert (diag (y), [1/3, 1/2, 1, 0 1/-0.5]');
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226 %! y = pinv (x, 1);
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227 %! assert (diag (y), [1/3 1/2 1 0 0]');
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228 %! y = pinv (x, 2);
1fa5bba16218 [mq]: pinv
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229 %! assert (diag (y), [1/3 1/2 0 0 0]');
1fa5bba16218 [mq]: pinv
Rik <rik@octave.org>
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diff changeset
230
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diff changeset
231 */