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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 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 2, or (at your option) any |
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10 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, write to the Free |
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19 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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20 02110-1301, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include "CmplxSVD.h" |
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29 #include "dbleSVD.h" |
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30 |
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31 #include "defun-dld.h" |
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32 #include "error.h" |
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33 #include "gripes.h" |
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34 #include "oct-obj.h" |
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35 #include "pr-output.h" |
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36 #include "utils.h" |
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37 |
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38 DEFUN_DLD (svd, args, nargout, |
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39 "-*- texinfo -*-\n\ |
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40 @deftypefn {Loadable Function} {@var{s} =} svd (@var{a})\n\ |
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41 @deftypefnx {Loadable Function} {[@var{u}, @var{s}, @var{v}] =} svd (@var{a})\n\ |
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42 @cindex singular value decomposition\n\ |
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43 Compute the singular value decomposition of @var{a}\n\ |
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44 @iftex\n\ |
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45 @tex\n\ |
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46 $$\n\ |
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47 A = U\\Sigma V^H\n\ |
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48 $$\n\ |
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49 @end tex\n\ |
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50 @end iftex\n\ |
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51 @ifinfo\n\ |
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52 \n\ |
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53 @example\n\ |
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54 a = u * sigma * v'\n\ |
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55 @end example\n\ |
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56 @end ifinfo\n\ |
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57 \n\ |
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58 The function @code{svd} normally returns the vector of singular values.\n\ |
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59 If asked for three return values, it computes\n\ |
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60 @iftex\n\ |
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61 @tex\n\ |
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62 $U$, $S$, and $V$.\n\ |
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63 @end tex\n\ |
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64 @end iftex\n\ |
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65 @ifinfo\n\ |
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66 U, S, and V.\n\ |
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67 @end ifinfo\n\ |
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68 For example,\n\ |
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69 \n\ |
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70 @example\n\ |
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71 svd (hilb (3))\n\ |
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72 @end example\n\ |
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73 \n\ |
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74 @noindent\n\ |
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75 returns\n\ |
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76 \n\ |
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77 @example\n\ |
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78 ans =\n\ |
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79 \n\ |
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80 1.4083189\n\ |
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81 0.1223271\n\ |
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82 0.0026873\n\ |
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83 @end example\n\ |
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84 \n\ |
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85 @noindent\n\ |
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86 and\n\ |
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87 \n\ |
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88 @example\n\ |
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89 [u, s, v] = svd (hilb (3))\n\ |
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90 @end example\n\ |
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91 \n\ |
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92 @noindent\n\ |
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93 returns\n\ |
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94 \n\ |
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95 @example\n\ |
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96 u =\n\ |
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97 \n\ |
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98 -0.82704 0.54745 0.12766\n\ |
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99 -0.45986 -0.52829 -0.71375\n\ |
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100 -0.32330 -0.64901 0.68867\n\ |
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101 \n\ |
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102 s =\n\ |
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103 \n\ |
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104 1.40832 0.00000 0.00000\n\ |
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105 0.00000 0.12233 0.00000\n\ |
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106 0.00000 0.00000 0.00269\n\ |
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107 \n\ |
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108 v =\n\ |
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109 \n\ |
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110 -0.82704 0.54745 0.12766\n\ |
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111 -0.45986 -0.52829 -0.71375\n\ |
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112 -0.32330 -0.64901 0.68867\n\ |
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113 @end example\n\ |
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114 \n\ |
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115 If given a second argument, @code{svd} returns an economy-sized\n\ |
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116 decomposition, eliminating the unnecessary rows or columns of @var{u} or\n\ |
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117 @var{v}.\n\ |
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118 @end deftypefn") |
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119 { |
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120 octave_value_list retval; |
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121 |
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122 int nargin = args.length (); |
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123 |
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124 if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3) |
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125 { |
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126 print_usage ("svd"); |
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127 return retval; |
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128 } |
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129 |
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130 octave_value arg = args(0); |
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131 |
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132 octave_idx_type nr = arg.rows (); |
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133 octave_idx_type nc = arg.columns (); |
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134 |
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135 if (nr == 0 || nc == 0) |
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136 { |
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137 if (nargout == 3) |
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138 { |
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139 retval(3) = identity_matrix (nr, nr); |
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140 retval(2) = Matrix (nr, nc); |
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141 retval(1) = identity_matrix (nc, nc); |
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142 } |
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143 else |
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144 retval(0) = Matrix (0, 1); |
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145 } |
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146 else |
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147 { |
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148 SVD::type type = ((nargout == 0 || nargout == 1) |
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149 ? SVD::sigma_only |
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150 : (nargin == 2) ? SVD::economy : SVD::std); |
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151 |
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152 if (arg.is_real_type ()) |
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153 { |
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154 Matrix tmp = arg.matrix_value (); |
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155 |
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156 if (! error_state) |
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157 { |
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158 if (tmp.any_element_is_inf_or_nan ()) |
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159 { |
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160 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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161 return retval; |
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162 } |
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163 |
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164 SVD result (tmp, type); |
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165 |
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166 DiagMatrix sigma = result.singular_values (); |
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167 |
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168 if (nargout == 0 || nargout == 1) |
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169 { |
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170 retval(0) = sigma.diag (); |
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171 } |
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172 else |
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173 { |
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174 retval(2) = result.right_singular_matrix (); |
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175 retval(1) = sigma; |
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176 retval(0) = result.left_singular_matrix (); |
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177 } |
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178 } |
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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 ctmp = arg.complex_matrix_value (); |
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183 |
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184 if (! error_state) |
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185 { |
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186 if (ctmp.any_element_is_inf_or_nan ()) |
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187 { |
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188 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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189 return retval; |
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190 } |
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191 |
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192 ComplexSVD result (ctmp, type); |
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193 |
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194 DiagMatrix sigma = result.singular_values (); |
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195 |
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196 if (nargout == 0 || nargout == 1) |
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197 { |
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198 retval(0) = sigma.diag (); |
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199 } |
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200 else |
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201 { |
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202 retval(2) = result.right_singular_matrix (); |
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203 retval(1) = sigma; |
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204 retval(0) = result.left_singular_matrix (); |
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205 } |
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206 } |
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207 } |
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208 else |
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209 { |
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210 gripe_wrong_type_arg ("svd", arg); |
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211 return retval; |
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212 } |
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213 } |
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214 |
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215 return retval; |
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216 } |
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217 |
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218 /* |
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219 ;;; Local Variables: *** |
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220 ;;; mode: C++ *** |
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221 ;;; End: *** |
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222 */ |
