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Add generalized eigenvalue functions
author Jarkko Kaleva <d3roga@gmail.com>
date Mon, 24 Nov 2008 10:55:50 +0100
parents 87865ed7405f
children eb63fbe60fab
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1 /*
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2
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3 Copyright (C) 1996, 1997, 1999, 2000, 2003, 2004, 2005, 2006, 2007
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe]
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4 John W. Eaton
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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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 "EIG.h"
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29 #include "fEIG.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 "utils.h"
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36
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37 DEFUN_DLD (eig, args, nargout,
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38 "-*- texinfo -*-\n\
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39 @deftypefn {Loadable Function} {@var{lambda} =} eig (@var{a})\n\
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40 @deftypefnx {Loadable Function} {@var{lambda} =} eig (@var{a}, @var{b})\n\
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41 @deftypefnx {Loadable Function} {[@var{v}, @var{lambda}] =} eig (@var{a})\n\
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42 @deftypefnx {Loadable Function} {[@var{v}, @var{lambda}] =} eig (@var{a}, @var{b})\n\
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43 The eigenvalues (and eigenvectors) of a matrix are computed in a several\n\
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44 step process which begins with a Hessenberg decomposition, followed by a\n\
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45 Schur decomposition, from which the eigenvalues are apparent. The\n\
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46 eigenvectors, when desired, are computed by further manipulations of the\n\
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47 Schur decomposition.\n\
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48 \n\
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49 The eigenvalues returned by @code{eig} are not ordered.\n\
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50 @end deftypefn")
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51 {
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52 octave_value_list retval;
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53
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54 int nargin = args.length ();
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55
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56 if (nargin > 2 || nargin == 0 || nargout > 2)
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57 {
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58 print_usage ();
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59 return retval;
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60 }
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61
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62 octave_value arg_a, arg_b;
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63
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64 octave_idx_type nr_a = 0, nr_b = 0;
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65 octave_idx_type nc_a = 0, nc_b = 0;
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66
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67 arg_a = args(0);
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68 nr_a = arg_a.rows ();
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69 nc_a = arg_a.columns ();
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70
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71 int arg_is_empty = empty_arg ("eig", nr_a, nc_a);
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72 if (arg_is_empty < 0)
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73 return retval;
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74 else if (arg_is_empty > 0)
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75 return octave_value_list (2, Matrix ());
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76
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77 if (!(arg_a.is_single_type () || arg_a.is_double_type ()))
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78 {
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79 gripe_wrong_type_arg ("eig", arg_a);
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80 return retval;
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81 }
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82
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83 if (nargin == 2)
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84 {
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85 arg_b = args(1);
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86 nr_b = arg_b.rows ();
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87 nc_b = arg_b.columns ();
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88
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89 arg_is_empty = empty_arg ("eig", nr_b, nc_b);
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90 if (arg_is_empty < 0)
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91 return retval;
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92 else if (arg_is_empty > 0)
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93 return octave_value_list (2, Matrix ());
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94
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95 if (!(arg_b.is_single_type() || arg_b.is_double_type ()))
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96 {
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97 gripe_wrong_type_arg ("eig", arg_b);
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98 return retval;
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99 }
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100 }
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101
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102 if (nr_a != nc_a)
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103 {
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104 gripe_square_matrix_required ("eig");
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105 return retval;
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106 }
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107
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108 if (nargin == 2 && nr_b != nc_b)
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109 {
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110 gripe_square_matrix_required ("eig");
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111 return retval;
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112 }
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113
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114 Matrix tmp_a, tmp_b;
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115 ComplexMatrix ctmp_a, ctmp_b;
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116 FloatMatrix ftmp_a, ftmp_b;
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117 FloatComplexMatrix fctmp_a, fctmp_b;
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118
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119 if (arg_a.is_single_type ())
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120 {
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121 FloatEIG result;
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123 if (nargin == 1)
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124 {
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125 if (arg_a.is_real_type ())
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126 {
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127 ftmp_a = arg_a.float_matrix_value ();
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128
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129 if (error_state)
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130 return retval;
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131 else
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132 result = FloatEIG (ftmp_a, nargout > 1);
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133 }
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134 else
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135 {
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136 fctmp_a = arg_a.float_complex_matrix_value ();
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137
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138 if (error_state)
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139 return retval;
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140 else
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141 result = FloatEIG (fctmp_a, nargout > 1);
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142 }
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143 }
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144 else if (nargin == 2)
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145 {
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146 if (arg_a.is_real_type () && arg_b.is_real_type ())
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147 {
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148 ftmp_a = arg_a.float_matrix_value ();
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149 ftmp_b = arg_b.float_matrix_value ();
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150
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151 if (error_state)
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152 return retval;
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153 else
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154 result = FloatEIG (ftmp_a, ftmp_b, nargout > 1);
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155 }
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156 else
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157 {
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158 fctmp_a = arg_a.float_complex_matrix_value ();
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159 fctmp_b = arg_b.float_complex_matrix_value ();
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160
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161 if (error_state)
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162 return retval;
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163 else
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164 result = FloatEIG (fctmp_a, fctmp_b, nargout > 1);
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165 }
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166 }
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167
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168 if (! error_state)
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169 {
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170 if (nargout == 0 || nargout == 1)
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171 {
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172 retval(0) = result.eigenvalues ();
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173 }
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174 else
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175 {
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176 // Blame it on Matlab.
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177
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178 FloatComplexDiagMatrix d (result.eigenvalues ());
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179
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180 retval(1) = d;
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181 retval(0) = result.eigenvectors ();
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182 }
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183 }
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184 }
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185 else
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186 {
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187 EIG result;
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188
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189 if (nargin == 1)
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190 {
8339
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191 if (arg_a.is_real_type ())
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192 {
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193 tmp_a = arg_a.matrix_value ();
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194
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195 if (error_state)
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196 return retval;
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197 else
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198 result = EIG (tmp_a, nargout > 1);
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199 }
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200 else
8339
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201 {
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202 ctmp_a = arg_a.complex_matrix_value ();
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203
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204 if (error_state)
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205 return retval;
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206 else
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207 result = EIG (ctmp_a, nargout > 1);
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208 }
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209 }
8339
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210 else if (nargin == 2)
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211 {
8339
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212 if (arg_a.is_real_type () && arg_b.is_real_type ())
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213 {
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214 tmp_a = arg_a.matrix_value ();
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215 tmp_b = arg_b.matrix_value ();
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216
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217 if (error_state)
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218 return retval;
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219 else
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220 result = EIG (tmp_a, tmp_b, nargout > 1);
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221 }
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222 else
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223 {
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224 ctmp_a = arg_a.complex_matrix_value ();
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225 ctmp_b = arg_b.complex_matrix_value ();
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226
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227 if (error_state)
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228 return retval;
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229 else
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230 result = EIG (ctmp_a, ctmp_b, nargout > 1);
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231 }
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232 }
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233
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234 if (! error_state)
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235 {
82be108cc558 First attempt at single precision tyeps
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236 if (nargout == 0 || nargout == 1)
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237 {
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238 retval(0) = result.eigenvalues ();
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239 }
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240 else
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241 {
82be108cc558 First attempt at single precision tyeps
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242 // Blame it on Matlab.
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243
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244 ComplexDiagMatrix d (result.eigenvalues ());
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245
82be108cc558 First attempt at single precision tyeps
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246 retval(1) = d;
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247 retval(0) = result.eigenvectors ();
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248 }
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91f8446ce4ae handle possible error from EIG
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249 }
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250 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
diff changeset
251
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
diff changeset
252 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
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253 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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diff changeset
254
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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diff changeset
255 /*
7814
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256
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257 %!assert(eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps));
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258
87865ed7405f Second set of single precision test code and fix of resulting bugs
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259 %!test
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260 %! [v, d] = eig ([1, 2; 2, 1]);
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261 %! x = 1 / sqrt (2);
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262 %! assert(d, [-1, 0; 0, 3], sqrt (eps));
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263 %! assert(v, [-x, x; x, x], sqrt (eps));
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264
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David Bateman <dbateman@free.fr>
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265 %!assert(eig (single ([1, 2; 2, 1])), single([-1; 3]), sqrt (eps('single')));
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266
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267 %!test
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268 %! [v, d] = eig (single([1, 2; 2, 1]));
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269 %! x = single(1 / sqrt (2));
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270 %! assert(d, single([-1, 0; 0, 3]), sqrt (eps('single')));
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271 %! assert(v, [-x, x; x, x], sqrt (eps('single')));
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272
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273 %!test
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274 %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2];
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275 %! [v, d] = eig (A, B);
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276 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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277 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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278
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279 %!test
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280 %! A = single([1, 2; -1, 1]); B = single([3, 3; 1, 2]);
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281 %! [v, d] = eig (A, B);
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282 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
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283 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));
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284
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285 %!test
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286 %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3];
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287 %! [v, d] = eig (A, B);
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288 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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289 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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290
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291 %!test
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292 %! A = single([1, 2; 2, 1]); B = single([3, -2; -2, 3]);
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293 %! [v, d] = eig (A, B);
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diff changeset
294 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
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295 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));
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diff changeset
296
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297 %!test
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diff changeset
298 %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i];
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299 %! [v, d] = eig (A, B);
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300 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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301 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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302
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303 %!test
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304 %! A = single([1+3i, 2+i; 2-i, 1+3i]); B = single([5+9i, 2+i; 2-i, 5+9i]);
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305 %! [v, d] = eig (A, B);
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306 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
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307 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));
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308
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309 %!test
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310 %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i];
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311 %! [v, d] = eig (A, B);
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312 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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313 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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314
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315 %!test
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316 %! A = single([1+3i, 2+3i; 3-8i, 8+3i]); B = single([8+i, 3+i; 4-9i, 3+i]);
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317 %! [v, d] = eig (A, B);
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318 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
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319 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));
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320
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321 %!test
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322 %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3];
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323 %! [v, d] = eig (A, B);
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324 %! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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325 %! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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326
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327 %!error <Invalid call to eig.*> eig ();
8339
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328 %!error <Invalid call to eig.*> eig ([1, 2; 3, 4], [4, 3; 2, 1], 1);
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329 %!error eig ([1, 2; 3, 4], 2);
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330 %!error eig ([1, 2; 3, 4; 5, 6]);
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331 %!error eig ("abcd");
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332 %!error eig ([1 2 ; 2 3], "abcd");
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333 %!error eig (false, [1 2 ; 2 3]);
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334
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335 */
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336
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337 /*
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
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338 ;;; Local Variables: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
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339 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
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340 ;;; End: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
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341 */